THE
PRINCIPLES OF LOGIC
Oxford University Press, Amen House, London E.G. 4
GLASGOW NEW YORK TORONTO MELBOURNE WELLINGTON
BOMBAY CALCUTTA MADRAS CAPE TOWN
Geoffrey Cumberlege, Publisher to the University
THE
PRINCIPLES OF LOGIC
BY
F. H. BRADLEY
O.M., LL.D., LATE FELLOW OF MERTON COLLEGE, OXFORD
SECOND EDITION
REVISED, WITH COMMENTARY AND
TERMINAL ESSAYS
VOL. II
OXFORD UNIVERSITY PRESS
LONDON: GEOFFREY CUMBERLEGE
FIRST EDITION, 1883
SECOND EDITION, IQ22
CORRECTED IMPRESSION OF 1928
REPRINTED, IQ5O
PRINTED IN GREAT BRITAIN
BOOK III. PART I
INFERENCE CONTINUED
CHAPTER I
THE ENQUIRY REOPENED
I. In the Second Part of the foregoing Book we were
concerned with negations. We were employed in banishing
some views of inference which appeared erroneous. From
this negative process we turn with relief, and with the hope of
rest in a positive result. But we must not deceive ourselves.
The positive result we have already reached, offers a welcome
in part illusive, and a rest that is doomed to speedy dis
turbance. We saw in all inference an ideal synthesis, which
united round a centre or centres of identity, 1 not less than two
terms into one construction. The conclusion was then a new
relation of these terms, and it was by an intuition that we
perceived it to exist within the individual whole we had com
pacted. And this account that we gave was not a false ac
count, for it was true of those inferences to which we applied
ourselves. But there are other reasonings no less important,
which we then ignored, and which fall beyond it. It was
thus a theory provisional and limited in range.
2. And there came a point where we had to transcend
it. In negative inference we were forced to contemplate the
possibility of retaining the middle (Book II. Part I. V. 8).
If, our construction being reached, we choose to rest in it, if
we refuse to isolate a single relation within that whole, if we
prefer to treat the entire compound synthesis as the conclusion
we want, are we logically wrong? Is there any law which
orders us to eliminate, and, where we can not eliminate,
forbids us to argue ? The question once asked is its own reply,
and it rings the knell of a blind superstition which vanishes in
daylight.
If so, we have been forced beyond our formula. For the
389
3QO THE PRINCIPLES OF LOGIC BOOK II. PT. II
conclusion is not always a new relation of the extremes ; 2 it
may be merely that interrelation of the whole which does not
permit the ideal separation of a new relation. And, having
gone so far, we are led to go farther. If, the synthesis being
made, we do not always go on to get from that a fresh rela
tion, if we sometimes rest in the whole we have constructed,
why not sometimes again do something else? Why not try a
new exit? There are other things in the world besides rela
tions; we all know there are qualities, and a whole put to
gether may surely, if not always at least sometimes, develope
new qualities. If then by construction we can get to a quality,
and not to a relation, once more we shall have passed from
the limit of our formula.
3. The next Chapter will show that this kind of infer
ence really exists, but at present we must follow the lead of
those doubts which it tends to awaken. If our formula is
not wide enough, and if we framed it to suit the facts we had
before us, it is natural to suspect those facts we trusted in.
Are they complete? Are there not other inferences, which
we failed to consider, and which, if we considered them,
would affect the result? And this question once asked leads
to consequences we hid. Though we widened our facts be
yond the boundary of the traditional logic, we stopped short
of the truth. We desired to inveigle by doubtful promises,
and commit the reader to a voyage he could not easily be quit
of. We are now at sea where alarm brings no risk, and we
may avow the truth that, in our former account, we left out
a very great part of the subject. There are large branches
of reasoning which we deliberately ignored, and which explode
the formula we went on to set up. The following Chapter
will detail their nature, and we may content ourselves here with
a brief enumeration.
4. Our education in logical superstition leads us first to
think of Immediate Inferences. Are they provided for?
The syllogism itself perhaps failed to provide for them, but
the failure of the syllogism can not be our excuse. No doubt
we might appropriate the doctrines advanced by some enemies
of tradition, and reply that the so-called Immediate Inferences
are not inferences at all, and that we are not required to
provide specially for illusions. But I do not think that this
CHAP. I THE ENQUIRY REOPENED 39!
answer will hold. If some immediate inferences seem to be
tautologies, yet others are more stubborn. They appear to
get to a fresh result, and they certainly do not seem to move
in accord with our formula.
5. We have now begun the list of our difficulties, and it
does not much matter how we proceed with it. We may
take up next the operations of Arithmetic. Addition and sub
traction seem processes of reasoning, but they scarcely can be
said to present a new relation of extremes existing by virtue
of relation to a 3 middle. So too with Geometry : when I
prove equality by ideal superposition, is this no reasoning
and no kind of inference? On the other hand does it show
that terms are related because of a common relation to a
third term? However in the end we may answer this ques
tion, it certainly seems to suggest a problem which we took
no account of. Our formula once more perhaps is not ade
quate.
6. Then come other difficulties. When A is given us,
and we are able to find two further possibilities, Ab and Ac,
and when again some other knowledge assures us that Ac is
not real on this we assume that A& is fact. We seem here
to reason, and to reason with at least a show of correctness,
but the form of our inference is not provided for. Even if
we assume that it can be reduced to the type we have ac
knowledged, the reduction is at least a task we have not yet
taken in hand. And the reduction may possibly prove not
practicable.
7. We are not at an end. When an object AB is recog
nized as C, the C is added by ideal supplement, and we seem
to have a genuine inference. But this inference has not got
the premises we required. In the cases which we considered
the premises were data, but we see here no datum beyond the
perception. This is once more a ground for amending our
formula. And then again we seem to find yet another ground
in the hypothetic judgment. Imagine A, 4 and perhaps nothing
follows ; but suppose A real, and we may then seem compelled
to get A-B. This operation suggests enquiry, and it leads
us to think of yet another trouble. In the method of Dialectic
a result is got by an ideal operation, which hardly consists in
the act of putting terms together. Now it may be said that
392 THE PRINCIPLES OF LOGIC BOOK III. PT. I
the method is a pure illusion, but that short way would per
haps prove long in the end, and would lead to enquiries not
easy to dispose of. It is better in the interest of logic to ask
under what type of reasoning this method will fall ; a ques
tion which once more may cause a strain in the fabric of our
formula.
8. If ideal operations which lead to fresh judgments all
claim to be inferences and this claim, we may be sure, will
now be set up we shall have to consider some other questions
which we before ignored. Take first Abstraction; here an
operation of analysis is performed on some datum, and in
conclusion a judgment is got which is concerned with one ele
ment of the original whole. 5 Is this judgment which we thus
have reached a conclusion? And, if it is a conclusion, will the
reasoning fall under the type which we recognize? There is
matter here for doubt and discussion, and the discussion seems
likely to carry us further. For in Comparison and Distinction
we get to results, and we get to them by an ideal experiment.
Is that experiment inference? If so, we once more are asked
to what type the inference conforms. We may already and
by anticipation have provided a place for it, but appearances,
I confess, are much against us. We can not off hand dismiss
the claim set up by these processes, and we can not easily
bring them under our formula.
9. It is clear that our hope, if we had any hope, of a
speedy termination, must now be relinquished. We must
prepare ourselves to reopen our enquiry as to the general
nature of the reasoning process. The next Chapter must go
through the mental operations we have here enumerated. It
will ask first if they really are inferences, and will next dis
cuss the peculiar nature of each. From this basis we may
hope to arrive in the end at some positive result.
ADDITIONAL NOTES
1 " A centre or centres, etc." But always in the end " a centre."
Cf. Bk. III. I. V.
" Is not always a new relation of the extremes " should have
been " is not always to a relation of, etc."
CHAP. I THE ENQUIRY REOPENED 393
3 " By virtue of relation to a middle." It would be better to insert
"given" before "middle."
4 "Imagine A, etc." But see on Bk. I. II. 48, and III. I. II.
18, and the Index, s. v. Suggestion.
5 " Is concerned with one element of, etc." " Seems concerned with
but part of, etc.," would be better. Cf. Bk. III. I. V. 13. And see
T. E. I. and IX.
CHAPTER II
FRESH SPECIMENS OF INFERENCE
I. In the preceding Book we possessed an advantage we
no longer enjoy. Those examples of reasoning, upon which
we worked, were too clear to be doubted. No unprejudiced
mind could deny the fact of their being inferences, and the
issue was confined to the question of their principle and inner
nature. But at the point which we have reached, doubt is
possible on all sides. Not only will the character of the speci
mens we produce be matter of debate, but their claim to be
specimens will be disallowed. We must ask not merely, To
what kind of inferences do they belong, but, Are they really
inferences at all ?
With this prospect in sight a preliminary reflection, before
we argue, seems likely to be useful. What test shall we apply,
when any claim to inference is sent in? Where the facts are
not palpable it will clearly be a gain if we are able to agree to
an explicit Canon, for we then shall have something to which
we can appeal in the course of the discussion.
2. We may say that inference is the same as reasoning,
that to reason without inferring, or to infer without reasoning,
does not sound possible. But when do we reason? Do we
always reason when a judgment is given as a judgment for
which we have a reason? If that reason were taken as a fact
merely got by simple perception, then this question would
probably be answered in the negative. But suppose our reason
is no fact of sense, but is another judgment; not something
that exists but some knowledge that we have of it the answer
surely will in that case be different. We should be said to
reason where a truth is given as a reason for belief in another
truth. In other words where, instead of affirming that S is P,
we say S must be P, wherever we have a necessary truth, there
is reasoning and inference. We apply the same test in a dif
ferent form when we turn to the use of " why " and " be
cause." If these have a sense, if it is possible to ask Why,
394
CHAP. II FRESH SPECIMENS OF INFERENCE 395
and then to answer Because, in all such cases we seem to have
an actual inference. There is judgment as to which a doubt
can be raised, and that doubt is satisfied, not by pointing to a
fact, but by reference to a truth. There is a mental operation,
in which a result is seen to follow from an ideal datum. And
we may agree that, wherever this mark exists, an inference is
present.
3. And there is another mark which perhaps we may
use. Where illusion exists it seems to arise from mistaken in
ference; for the senses are infallible because they do not
reason, and fallacy can come from nothing but inferring. If
this is true, then possibility of error means presence of infer
ence, and we may employ the first as a test of the second. But
we are treading here upon dangerous ground. It may be
denied that, when water is hot to one hand and cold to the
other, the mistake that exists is a fallacy of inference ; l and
the denial could not well be discussed in these pages. We
can not assume that in every case where error is possible,
reasoning exists, and so we are disappointed in our canon ;
but for all that we have an admitted indication. It will be
agreed that, where we discover mistake, we shall not be
wrong in looking for inference, and that, to some extent at
least, we may expect to find it.
4. Armed with this understanding we may begin at once,
and may take up the claims which our first Chapter found
were demanding a scrutiny. They make no pretence to ex
haust the array of possible applicants, and they enter in no
systematic order. Still we hope, and believe, that the worst
has shown itself, and we at least do not know of more terrors
in the background.
(A) The first to come in are the three-term constructions;
(i) those where elision is simply not used, and (ii) those
operations where we also go to a quality. What reply shall we
make to each of these?
(i) I cannot think of any way by which to escape the claim
of the first. If A is given to the right of B, and B again to
the right of C, and I therefore judge that the terms are ar
ranged as C B A, this is clearly an inference. I did not
know it before, and I get it by putting two truths together.
And if this is not an inference, why is it an inference when I
396 THE PRINCIPLES OF LOGIC BOOK III. Px. I
go -to C A? No answer can be given; we are forced to
admit that C B A is inferred; and yet it is not an infer
ence according to our formula.
5. (ii) But there follows close a further consequence.
We have reasoned to a whole C -- B A, and this whole may
have a new quality x. But, if so, we have reasoned from terms
in relation, C B and B A, to no new relation but to the
presence of a fresh quality ; 2 and hence once more our formula
has broken down.
A friend of our youth may be called upon here to supply
us with an instance. I sail round land, and reconstruct my
course by a synthetic process, and the whole shore that I com
bine is then interpreted as belonging to an island. A B,
B C, C D, D F, F H, H A become, when united,
H A
; B; and from this circular frontage I go to the
name and to the other qualities possessed by islands. I may
be told in reply that the name and the qualities, if indeed there
are such, do not come directly from the construction itself,
but are got by a further and additional premise that does not
appear. And this, I admit, is true altogether of the name,
and true in part of the other qualities. But it still leaves
something which comes from the construction, and which
comes directly. The circular shape and self-contained single
ness are more than the mere interrelation of the premises,
and need not be got from previous knowledge of islands. You
do not go outside the construction to get them, the whole
would not be itself without them; and yet they are another
side of that whole, which is distinct from the putting together
of the parts. But, if so, surely you have reasoned to a quality.
At some time, I presume, we have all been visited with the
pleasing pain of hanging our pictures and arranging our fur
niture. How many combinations were we forced to reject,
until we came upon one which would do. But these attempts
were all inferences from hypothetical data, and we went from
the construction direct to a quality, and so to a judgment. If
the quality was aesthetic that made no difference; for we did
CHAP. II FRESH SPECIMENS OF INFERENCE 397
not say of the whole psychological image, That now hurts me,
or gives me a pleasant sensation. We said of the content,
which we had in the premises, That leads and must lead to a
certain result. And this was an inference, which certainly fell
outside our formula.
It is clear, I think, that when trying experiments in the
actual world by combining and dividing real things, or by
drawing upon paper, we may be surprised by qualities which
we did not anticipate. And the same must be true of ideal
experiment. 3 In both cases, the interrelation being given, we
perceive a quality which comes from that, and which is more
than and beyond the bare interrelation. But in the second
case the construction, being got by an ideal process, is itself
an inference, and its result is also nothing but a conclusion.
But it is not any fresh relation of the original data; it is an
issuing quality.
6. It seems clear that reasoning does not always give us
a new relation of the terms we began with. Our formula has
now too palpably lost its virtue ; and virtue being gone, we
may proceed less anxiously. The advances of those more
audacious claimants, who showed their heads in the foregoing
Chapter, may be calmly received. There is no longer any
absolute presumption against them, and the reception of each
is a matter not of principle, but of choice and convenience.
(B) In this spirit we may meet the approaches of Arith
metic, 4 the claim of which I will bring in indirectly. An in
troduction is certainly not required, but it may serve to make
the change less startling.
We saw long ago that, when spatial relations with points
of identity were forced on our attention, we could put them
together and find a new relation. We have lately seen that,
instead of a relation, these premises could supply us with an
unknown quality. Given lines A B, B C, C A, we can
A
construct -p/\r an< ^ f rom that construction get the quality
-D~ ^
possessed by a certain triangle. In this case the conclusion is
categorical and necessary.
But there was something else which we hardly glanced at.
We may have three lines such as A B, C D, E F.
398 THE PRINCIPLES OF LOGIC BOOK III. PT. I
In these, as they are given us, there are no points marked
identical, and we have no given reason for putting them to
gether. But we may do so if we choose ; if their lengths do
not forbid it, we may arrange them ideally, combining them
into the form of a triangle, and thus endowing them with a
certain quality. We have here an intuition which follows on a
synthesis, and the doubt which arises is, Have we an inference ?
If we have one what is it? It is not " AB, CD, EF have
x." That would be false, since they are not combined, and
since they have not together any quality at all. And again
the inference can not run thus, " AB, CD, EF, when their ter
minal points are identified, have x." That certainly is true,
but then it is not an inference. For, though the quality is
perceived in an ideal arrangement, it has not been got by it. 5
The combination in this case would not be such a construction
as was tnade to get the judgment, and therefore connects the
judgment with the original data. The judgment is passed on
a whole that is found, and it says nothing about the ideal com
position of that whole. And for this reason it can not be a
conclusion.
The real conclusion is " AB, CD, EF may be combined,
and when combined they have a quality x," or " If AB, CD,
EF are manipulated in a certain way, they give rise to x."
The lines plus my arranging activity are the premises, and the
construction with its quality follows.
This has all the marks of inference, but it obviously differs
from the inference we got from A B, B C, C A. In
this case the construction follows from the data themselves, 6
but in the other example it does not follow, unless an arbi
trary arrangement of my own is added. My free manipu
lation has taken the place of the compulsory synthesis through
identity of the terminal points B, C, A. The lines need not
have any point that is identical, and I am not obliged to put
them together. The premises are hypothetical, and the con
clusion is thus arbitrary. 7 But it still is an inference, for if
the lines are combined, then the quality must come because
they are combined.
7. This foregoing section has been no digression, for we
may consider both addition and subtraction as cases of the
process we have just sketched. Let us clear our ideas by
CHAP. II FRESH SPECIMENS OF INFERENCE 399
asking what we mean by the simple proposition " Twice one
is two." Do we mean to assert that one unit and another unit
are the integer two ? Such a statement would be false, for the
integer is more than one unit considered along with another
unit. There is a quality in the whole, which belongs to the
units first when combined and made into an integer. It is
false then that " one and one are two." They make two, but
do not make it unless I put them together; and I need not do
so unless I happen to choose. The result is thus hypothetical
and arbitrary.
8. There is a mistake we must correct before we proceed.
The reader may (or may not) be aware, that the logical and
temporal relation which exists between degree and quantity is
a difficult subject. 8 It is a question that could not be fully
discussed in a narrow compass, and on which we can offer but
a brief observation. You may use " degree " in more than
one sense. You may understand by the term a scale of quali
ties which are related explicitly to a scale of quantities, and
which depend on this scale. Or again you may mean a scale
of differences, which are simply felt as more or less of a cer
tain thing, but which are not referred to any scale of numbers
of units. If we adopt the former sense of degree, then both
in time and logically the knowledge of number, or the power
of counting, precedes the knowledge of that scale of intensi
ties which stands in explicit relation to the varying units.
Quantity here will precede degree. But, if we use the latter
meaning and understand by degree the mere vague sense of a
more and a less, of a rise and a fall, a swelling and a shrink
ing, then without any doubt degree comes first and quantity
follows.
The mistake we referred to springs partly from the neglect
of these metaphysical abstractions, and partly from blindness
to palpable facts. It is assumed, that the perception of dif
ferences in quantity implies the power of counting units.
There is a well-known tale, not worth repeating, of the experi
ment which proves that a magpie can count up to two or
three, but not any further. 9 Thus if three men go in and but
two come out, the bird knows that all have not been accounted
for, and therefore it counts. But if so, and if the power to
perceive the difference of more food and less food, a larger
4OO THE PRINCIPLES OF LOGIC BOOK III. PT. I
beast and a smaller beast, demonstrate counting, few animals
will not count. If again the ability to distinguish part from
the whole, and, when but part appears, to expect the rest,
shows the practice of arithmetic then the higher animals are
all arithmeticians, and all habitually add and subtract. This
perhaps may not seem a reductio ad absurdum, but then this
is not all. Though the higher (and even lower) animals can
all count, there are races of men who can hardly count at all,
and are only beginning in the rudest way. But these very
savages, who are staggered by the difference between three
and four, and are thus led into errors which would never occur
to an average dog on the other hand count much better than
we could. Take one from a flock of forty sheep, and in a
moment they perceive the difference. They have finished
counting before we could have begun. And on this view
of the subject I think it is clear that there is something
unexplained.
The mistake lies in the failure to see that number, in the
proper sense, is a late product of abstraction, and that, long
before this could come into the world, the perception of more
and less, of the whole and the parts, already existed. They
existed in an unanalyzed qualitative form.
9. Now this observation has important consequences, for
it points to the conclusion that, in considering number, we
have no right to strike out the qualitative side. If the con
fused feeling of difference in degree between wholes came first,
and these wholes were then afterwards analyzed into parts,
and these parts were then once again reduced to equivalent
units if this was the psychological process, as I think we
may agree it clearly must have been then I venture to argue
that this shows we are wrong, if we take quantities to consist
in nothing but units, somehow taken together and barely co
existing. Even when we get down to abstract number, each
integer must be more than units and units. As an integer it
will have an additional quality which results from addition
and disappears on subtraction. One and one are not the same
as two, two and two are not the same as four, nor are they
the same as three and one. For integers are individuals; each
has an unity which makes it a whole, and joins together its
units by a higher bond than mere co-existence before the atten-
CHAP. II FRESH SPECIMENS OF INFERENCE 4OI
tion. If that bond is a residuum of spatial perception or
comes from elsewhere, we need not here consider. Enough
that it exists, that each integer is one whole, with qualitative
relations of higher and lower persisting between it and other
integers. Hence we may say that mere counting is not the
integers ; it does but make them. It progressively produces
and destroys them as it goes up and down the scale.
The integer then is different from its units. To say of
the units that they are the integer, is not a tautology but a
downright false statement. That they become the integer, on
the other hand is true and is not a tautology.
10. Addition and subtraction produce new results ; they
are ideal operations which give conclusions, and justify what
they give ; they are palpable inferences. The reasoning which
they employ no doubt may be very simple in its nature and
very easy to disparage. " It is the work of a machine," we
may hear the reproach, " and not of a brain." But if, starting
from certain data, it is a brain that by means of ideal experi
ment procures a fresh judgment, we must call this reasoning ;
for we do not know what else we can call it. And the re
proach, we must add, betrays a prejudice that is not philo
sophical.
The operation is the analogue of that arbitrary arrange
ment in ideal space which we mentioned above (6). We
start with the units one and one, we freely rearrange them,
and we end with the result of integer two. But the result is
hypothetical, for we can not say, one and one must give two.
They may be arranged in such a way that two must appear,
or, if I choose to manipulate one and one, then two comes out.
Hence there is nothing categorical. One and one, if I leave
them alone, are one and one. I may handle them or not at
my private pleasure, and when I handle them, I need not add
them. They do not necessitate their own addition, it is only
when I add them that necessity appears. But then they must
become two, and I have made an inference.
This is still more patent if we consider subtraction. We
might say " Three is one," or " The integer three is one of its
units ; " and of course such a proposition would be false. But
the integer turns of necessity to one unit, when I first break
it up and then set aside two of its component parts. Three,
4O2 THE PRINCIPLES OF LOGIC BOOK III. PT. I
if two be subtracted, is obviously one ; but this result is hypo
thetical. We are not obliged to analyze the dattmi and to set
part on one side; and we are in no way compelled to get the
conclusion unless we have taken this arbitrary step. 10
ii. These inferences, it is clear, will not come under the
formula we set up. They suit it no better than did that ideal
arrangement of wholes in space, which gave a new quality.
But we need not dwell on this point, for there is something
which presses for more serious attention. " The above ac
count," it may fairly be said, " is not a right view of addition
and subtraction, for these give a conclusion which is true
categorically. Arithmetical judgments are in no sense arbi
trary, nor, given the data, is the inference conditional. Bricks
and mortar, if the builder choose, may make a house; but
one and one are equal to two, whether we choose or do not
choose to have it so." I admit the distinction and desire to
endorse it, but it is in no sense contrary to the statement we
have made; for, up to this time, we have never said a word
about equality. What we wanted was to emphasize a side
of arithmetical processes, which, if neglected, makes them ob
scure or tautologous ; and, whatever else is right, it still re
mains true that addition is an inference of the kind we de
scribed. It does prove hypothetically that, if units are added,
they become something different; and for the right under
standing of the subject this truth is all important.
Having made this clear, we may now proceed to regard the
process from a different side, and to consider it as a cate
gorical proof of equality in difference.
12. What is equality? It is certainly not the same as
mere identity, nor would it be safe for any one except a
" powerful thinker " to be guilty of such elementary confusion.
Because things are the same they need not be equal; and
when they are equal, they need not be the same in more than
one aspect. Equality is sameness in respect of quantity, it is
a relation between things that may otherwise be different, but
are identical in regard to their number of units. Or, more
accurately, we may call it the identity of the units, as units, in
two different things. This definition certainly gives rise to
problems which in another place I should be glad to discuss ;
but for present purposes it will be found sufficient. One and
CHAP. II FRESH SPECIMENS OF INFERENCE 403
one are equal to two because the mere units in both are the
same, and three minus two is equal to one because on both
sides the unit is identical.
This result is true, and it seems categorical, and we there
fore are led to ask once more how we reach the result. If
the conclusion is not hypothetical, were we right in taking the
operation to be arbitrary? Yet, on the other hand, how do I
know that one and one are equal to two? I know it because
when I add the units, they become two, and when I analyze
two it becomes the units. I thus see the identity of the units
throughout, but I see it in consequence of a free manipulation
which I might have omitted. So again in subtraction I infer
that 3 2= I. But how do I reach this? I break up the
three into three separate units ; I break up the two in the
self-same manner, and, removing it, I perceive that two units
of the three have been removed. One is left, and that as an
unit is precisely the same as any other one. The conclusion is
necessary, but the operation is optional, for there was nothing
which demanded my analysis and comparison. The result has
thus depended on my arbitrary choice.
13. We seem left with this difficulty the result is uncon
ditional, though the process on which it depends is arbitrary.
And this difficulty for the present must be simply accepted.
We are indeed only too ready to accept it or ignore it. The
operation in arithmetic, which gives the result, is supposed to
have no influence upon it ; there is a postulate that, so long as
you do not alter the number of the units, you may do what
you please with them, and whatever you bring out is uncon
ditionally true. The process is a mere preparation of the
data, and it demonstrates an element which already was there.
It is not an arbitrary alteration of my own, since it does not
alter the element at all ; it constructs no artificial and novel
spectacle, it does but remove an obstacle to my vision. 11
In other words the relation of equality between any quan
tities is supposed to exist, and the judgment which expresses
it is supposed to have independent validity. Whether I see
it or not, it is taken to be true, and the way in which I get
to it affects it in no way. Thus my inferring is optional and
entirely arbitrary but the inference itself is eternal truth.
It is my process from a datum which enables me to see what
404 THE PRINCIPLES OF LOGIC BOOK III. PT. I
is true of that datum, yet it is only my insight, and it is not
the truth, which depends on that process. One and one
two, not because I add them, but because they are equal.
14. The general relation of the ground of knowledge 12 to
the ground of reality will vex us hereafter, and we will not
anticipate; for our present task is simply to find the process
which is used. It consists, as we have seen, in a free re
arrangement, resulting in a perception of quantitative identity,
which is taken as true independent of the process. The new
result, which is got by experiment with the units, is held valid
of those units apart from the experiment. And we do not
propose in the present chapter to question this result ; but, the
process being such, our wish is to know if it really is an
inference, and again if it will come under the formula which
we first accepted but now hold suspect.
That it really is inference w r e can not long doubt. We
might indeed dispute for ever about " twice one is two " ; for,
when a product has been learnt before it was understood, and
now comes to the mind as so ready-made, self -apparent, and
obvious, it is hard to see that it ever has been a painful infer
ence, a slow result of time for which ages had to wait. But
more complex instances soon convict us of our error. The
moment we desert the table we have learnt, we find there is
a process which proves the result, and in which mistakes are
only too easy. And this process is the movement of an ideal
experiment which gives a judgment we had not got before.
But, unless we have somehow apart from the facts decided in
our minds what reasoning is to be, then this must be reason
ing and its result must be an inference.
But is it an inference according to our formula ? That at
least it can not be, for it establishes no relation between the
terms of the premises. On the contrary the relation, which
appears in the conclusion, has one terminal point which never
appeared in the data at all. Our poor formula at this rate
will hardly be able to claim respectful treatment in the future,
and what presumption there is seems against its virtue.
15. Spaces and times admit of treatment by a similar
process. If an optional arrangement of superposition, division
into parts, or construction into a whole by arbitrary additions,
results in relations of equality or inequality, this result is taken
CHAP. II FRESH SPECIMENS OF INFERENCE 405
as a categorical conclusion. The alterations which we intro
duce do not alter the fact as long as they do not alter the
magnitude ; and it is a postulate that no change of place or
context, no analysis or synthesis, can make any difference to
the relations of quantity. The operations (we assume) are
external to the data themselves ; the work done upon them is
really work that falls outside them, and that but renders them
apparent as they were before. The truth is shown to us by
a process which does not give the reason why the thing ac
tually is so. The demonstration removes a barrier from our
sight, or provides us with artificial vision, but it does not pro
duce the fact from its elements.
Yet we can not doubt that here once more we have an
inference ; an inference again which we have failed to provide
for, since it can not be reduced to interrelation. When I show,
for instance, by superposition that one triangle is equal to
another, what third term is it that connects the couple, or
what syllogism will express the actual process? I know that
an application of reckless torture will reduce anything you
please to any possible form; but the fact remains otherwise.
We have here an intuition of comparison, taking place by
means of free ideal rearrangement. This is an inference, and
it is a new kind of inference.
16. (C) And new itself it suggests fresh innovation, for
it leads us to ask if comparison 13 is reasoning, and if, when
ever we compare, we may be said to infer. The suggestion is
contrary to our established ideas, but how can we repulse it?
We start from data, we subject these data to an ideal process,
and we get a new truth about these data. The new truth, so
far as our knowing it is concerned, depends on the operation,
is because of it, and would not be unless for that reason;
but, if so, we surely must call it a conclusion.
Take an instance; we have ABC, DBF, and we may not
know that they are the same in any point. We then inspect
them with a desire to discover sameness, general or special;
that is we attend to them from a certain point of view. We
compare them in respect of identity, either in quality or quan
tity or again in some more special development. No doubt it
is not easy to lay down the precise character of the process
employed, but there certainly is some process. There is an
406 THE PRINCIPLES OF LOGIC BOOK III. PT. I
ideal operation on ABC, DBF, and that operation presents us
with a judgment. We did not know that ABC, DBF were
alike ; now we know that they possess the point B in common,
and this intuition depends on the operation. The conclusion
runs " If ABC, DBF are compared they are alike in B ; " and,
since the operation is assumed to make no difference to the
fact, we may say categorically, " The two are alike." No
doubt we may question the validity of this inference, but I
do not see how we can deny its existence. On the other hand
it is not a relation between two given terms that is seen in a
construction through identity.
We shall perhaps not be wrong to place under this head
the copulative process. 14 " A is C, B is C, and therefore both
are C." So far as this connects, and does not barely conjoin,
it concludes to an identity between A and B.
17. And what holds of the comparison which establishes
identity, must hold too of the process which brings out differ
ence. If distinction is an ideal operation which demonstrates
new truth, that is truth new to its, then so far it must be reason
ing. 15 We may illustrate simply; what is really B 1 B 2 B 3 has
been taken throughout as simply B. We subject this datum
B to an ideal process, the nature of which we do not at present
discuss, and the result is B 1 B 2 B 3 . Now since the operation
is arbitrary the product is hypothetical, but because once
again the operation is assumed not to alter the datum, as it
really is we take the product as categorical. The marks have
been found, and therefore they are. True there is no distinc
tion unless things are first different ; but for us there can be no
difference which does not follow on distinction. It becomes
apparent and is shown to exist by virtue of a process, which
must therefore be taken as a demonstration and a genuine
inference.
A difficulty, we admit, besets the operations of distinction
and identification ; for they do not, it may be said, give the
actual reason of the real truth in which we are finally landed.
Nay, they do not even profess to give it, and we may say that
they even protest above all things that they demonstrate noth
ing that was not there without them. This difficulty, which
has bearings we perhaps do not suspect, will engage us here
after. But for our present purpose we must insist on the
CHAP. II FRESH SPECIMENS OF INFERENCE 407
other side of the process. We have reached a result by ideal
experiment ; and of this we can say, Though it be not made
true by our operation, yet we know it for that reason, and it is
for us because of our activity. 16 But, if so, then once again
we have reasoned.
1 8. (D) It would seem that we may reason, though we
do not give the reason of the fact itself, and when our demon
stration less establishes than recognizes. Mere consistency
now prompts us to raise the doubt if recognition 1T is not
always reasoning. And perhaps to our surprise we discover
that this is really the case, for to find that AB is C, and to
recognize it as such, implies a process of ideal redintegration.
I start with AB, and the function of ideal synthesis BC sup
plies the construction from which I proceed. Even where I
merely recall the name, or where I can but say that somewhere
I must have seen that face before, there is still a conclusion.
The connection may be dim and the element that is added may
be trifling or obscure ; but whatever it is, we get it by a syn
thetic process of restoration, and this is reasoning.
" Yes, reasoning," I may be told, " but normal reasoning
and with the usual three terms. First AB and BC, then a
whole ABC, and an elision leaving the result A C." But, I
answer, in what sense is BC a premise? It is by no means
an original datum. Indeed it is not a datum at all; for it is
a function which does not come before the mind, but which
presents the result of its action on the only datum that we
possess. If BC is a premise, it is a premise in no usual
sense of the term. We have at any rate found a case that
has not been yet provided for, and a case where the inference
seems quite indisputable.
We may add to this section a remark on the hypothetical
judgment. 18 This is always an inference. I do not simply
mean that it is an inference, when we first say, " If anything
is B it is C, but here A is B, and therefore it is C." The
inference I mean is one which dispenses with the explicit
statement of the general principle. A is merely supposed ;
it is offered in experiment as an attribute of reality, and from
this we go on to arrive at C without any other premise which
comes before the mind. This process is, I think, an infer
ence of a kind we did not anticipate; but it hardly can claim
408 THE PRINCIPLES OF LOGIC BOOK III. Pi. I
an independent position. Where it does not fall under the
foregoing head of Recognition, it will find its place in the
ensuing section.
19. (E) The subject of this section is forced upon us.
I should be very glad in a work of this kind to say nothing
about the Dialectic Method, but I can find no excuse for
passing it over, for it is irresistibly suggested by the inference
which we had to notice last. I am far from implying that
the Method falls under the previous section, and that it is a
mere process of recognition. Such a view, if adopted, would
annihilate its claims, and my object is here not to criticize or
to advocate. I wish simply to consider what sort of operation
is performed by Dialectic, assuming that it has a real way of its
own.
If we make that assumption, we pass naturally from the
process of Recognition on to the Dialectic movement. Like
recognition this starts from a single datum, and without the
help of any other premise it brings out a fresh result. Yet
the result is not got by mere analysis of the starting-point,
but is got by the action of a mental function which extends
the datum through an ideal synthesis. So far the method of
Dialectic is precisely the same as the common recognition
which works by means of redintegration. But now comes a
difference ; the ideal synthesis, which in Dialectic meets and
supplements the starting-point, is not reproduction from past
perception; or rather, and to speak more correctly, it is not
merely such ideal reproduction. Even though the synthesis
which it brings into play does repeat a connection we have
got from presentation, there still is more than bare repetition.
The function is felt not as what the mind does because it has
thus been trained to perform it ; the naturalness seems more
than the ease of habit, and the necessity above any vis inertia.
And the cause of the difference we find is this ; the message
in the one case seems external tidings which are so believed,
since thus received ; but in the other it seems like a revelation
of ourselves, which is true because we have the witness in
our own experience. The content in one case, itself irrational,
seems to come to our reason from a world without, while in
the other it appears as that natural outcome of our inmost
constitution, which satisfies us because it is our own selves.
CHAP. II FRESH SPECIMENS OF INFERENCE 409
This internal necessity, of the function and of its product, is
the characteristic of the Dialectical Method and constitutes
its claim and title to existence.
20. I do not propose to criticize that title, and prefer to
attempt the removal of misunderstandings. One of these we
have already noticed ; you make no answer to the claim of
Dialectic, if you establish the fact that external experience has
already given it what it professes to evolve, and that no syn
thesis comes out but what before has gone in. All this may
be admitted, for the question at issue is not, What can appear
and How comes it to appear? The question is as to the
manner of its -appearing, when it is induced to appear, and
as to the special mode in which the mind recasts and regards
the matter it may have otherwise acquired. To use two tech
nical terms which I confess I regard with some aversion
the point in dispute is not whether the product is a posteriori,
but whether, being a posteriori, it is not a priori also and as
well. And misunderstanding on this head has caused some
waste of time.
The second misunderstanding is of a different nature. An
idea prevails that the Dialectic Method is a sort of experiment
with conceptions in vacua. We are supposed to have nothing
but one single isolated abstract idea, and this solitary monad
then proceeds to multiply by gemmation from or by fission of
its private substance, or by fetching matter from the impal
pable void. But this is a mere caricature, and it comes from
confusion between that which the mind has got before it and
that which it has within itself. Before the mind there is a
single conception, but the whole mind itself, which does not
appear, engages in the process, operates on the datum, and
produces the result. The opposition between the real, in that
fragmentary character in which the mind possesses it, and the
true reality felt within the mind, is the moving cause of that
unrest which sets up the dialectical process.
21. We may understand that process in two different
ways. On one view the method advances on the strength of
negation ; the synthesis, which unites and adds a fresh element,
comes always from denial, and from the contradiction of the
starting-point. Every truth is taken to have two sides, and to
consist in the assertion of a pair of correlatives, each of which
4IO THE PRINCIPLES OF LOGIC BOOK III. FT. I
is the logical negation of the other. Each of these by conse
quence, to assert itself, denies the other ; but at the same time
each depends on what it denies, and so reasserts it. Affirming
itself, it thus on the other hand is driven to affirm its own
negation, and so becomes its own opposite by a self-seeking
self-denial. Or, more correctly, the whole, which is both sides
of this process, rejects the claim of a one-sided datum, and
supplements it by that other and opposite side which really
is implied so begetting by negation a balanced unity. This
path once entered on, the process starts afresh with the whole
just reached. But this also is seen to be the one-sided expres
sion of a higher synthesis ; and it gives birth to an opposite
which co-unites with it into a second whole, a whole which in
its turn is degraded into a fragment of truth. So the process
goes on till the mind, therein implicit, finds a product which
answers its unconscious idea; and here, having become in its
own entirety a datum to itself, it rests in the activity which is
self-conscious in its object. This great ideal of self-develop
ment and natural evolution led in Hegel s hands to most
fruitful results, and in the main these will stand when the
principle of negativity is rejected as an error.
For the Dialectic Method does not necessarily involve the
identity of opposites, in the sense that one element in its own
assertion supplements itself by self-denial; and it is possible
to take a simpler view which keeps clear of this difficulty.
We may suppose, as before, that the reality has before it and
contemplates itself in an isolated datum. What comes next
is that the datum is felt insufficient, and as such is denied.
But in and through this denial the reality produces that sup
plement which was required to complete the datum, and which
very supplement, forefelt in the mind, was the active base of
the dissatisfaction and the consequent negation. The im
portant point is that, on this second view, both sides of the
correlation are positive, and one is not the mere denial of the
other. The presence of either is inconsistent with the absence
of the other, and it is inconsistent with the solitary presence of
the other. Thus either by itself is denied, not by, but from
the ground of its positive counterpart, which in that denial
makes itself conscious and so comes to light. I am perfectly
aware that this doctrine is a heresy ; 10 but it is a heresy which,
CHAP. II FRESH SPECIMENS OF INFERENCE 411
I think, will be found to save the real substance of the ortho
dox doctrine.
22. We are not concerned here with the truth of this
heresy, and we turn to the question which is really in hand ; In
what sense is Dialectic an inference ? 20 It certainly is reason
ing, which by an ideal operation gets a fresh result. Take a
datum a, and by your operation you get a- ft with a further
result y. The conclusion here is, that a must be /3 t and there
fore it is Y- And because the operation is not arbitrary, be
cause throughout it keeps to reality, you have no hypothesis.
For your middle is not something you have chosen to make;
it is wholly necessary, and hence you may end in the conclu
sion a is y. We need hardly ask if our original formula
provided for this inference.
23. (F) We next may take the process of abstraction. , 21
In recognition we used a function of synthesis which was
clearly universal, and it is natural to ask how this function is
acquired. If it comes from an operation of analysis and
abstraction, we are thence led to ask whether such an opera
tion must not be an inference. For it is an ideal experiment
which procures a new result. We start here with a given
whole abed; we operate on this by the neglect of or by the
removal of be, and ad is left ; and we then predicate this ad of
the reality. The real was abed, and in consequence of our
action we know now it is ad. The nature of the process by
which we remove what seems unessential, need not at present
be discussed, but it is certain that there is some process, and
that the result of this process is accepted as truth for no other
reason. And once again it is true that the experiment is
arbitrary, 22 for we need not perform it, and it is not supposed
to make a difference to the fact itself. Still it makes a differ
ence to our knowledge and judgment, it supplies the because
of a new perception, and it has therefore the mark of reason
ing and inference.
24. We have first analysis, then elimination or elision of
part of the content, followed in the end by a positive attri
bution of the remaining content to the original subject. The
operation is familiar and is largely employed, but its validity
is open to grave objection. We shall consider this hereafter,
but may remark at present that the doubt is whether by your
412 THE PRINCIPLES OF LOGIC BOOK III. Pi. I
elimination you have not fatally altered the subject. By
removing one element you may destroy the condition which
made the rest predicable. Our old friend, J. S. Mill s so-
called Method of Difference, fell into this blunder, and may
serve us as a warning (Book II. Part II. Chap. III.). Reality
was first ABC dcf, then BC ef, and we assumed that, if
we elided BC ef, we should leave A d standing good of
reality. But here (we may repeat) were two errors. Suppose
first that our data are pure universals, 23 still you have not ex
perimented with that very BC which goes with A. You have
worked with a second and an other BC, and you can not be sure
that there is not a difference in the way in which they operate.
The first BC may give something to A, and get something in
exchange, so that A may be concerned in the first ef, and BC
be partly concerned in d. This unconsidered possibility
wrecks your proof ; and your Method of Difference is self-
condemned, since it is not a method of the only difference.
And your error is not single ; for you have withal ignored
the fundamental difficulty. How can you procure your pure
universal ABC def without using to get it a process of eli
sion, a " method of difference," which is still more precarious?
Your premises, " Reality is ABC def and BC ef," are the
products of an abstraction which has separated these ele
ments from a mass of detail in which they appeared. This
original process, what justifies that? What tells you that the
detail, which you cut away, is wholly irrelevant, and that, with
out it, the reality is still just as much ABC def and BC ef
as it was before? This objection is as fatal to the founda
tion of the Method as the former was to its superstructure.
It points to the result that a product of elision is always to be
received with the gravest suspicion ; and with this result we
must at present be satisfied.
But, valid or invalid, abstraction is reasoning; and it does
not appear to come under the head of any foregoing process.
25. (G) We have not yet reached the end. In the
account, which in our First Book we gave of the Disjunctive
judgment, we observed that it contained a latent inference;
and the time has now come to draw this to the light. 24 We
might indeed be tempted to dispose of the enquiry by reducing
the process to a three-term inference. " A is b or c f A is not
CHAP. II FRESH SPECIMENS OF INFERENCE 413
c, and therefore it is b " the reasoning here, we might say, is
syllogistic, and falls under the type, " A not-c is b, A is A
not-c, and therefore A is b." But this attempt would be
futile, 25 since the reduction presupposes that the alternatives
are stated explicitly, in the character of exclusive alternatives.
But the question as to how we become possessed of this
explicit statement, remains thus unanswered, and we shall find
that it comes to us by way of an inference that is not syllo
gistic. The syllogism is not the soul and principle of dis
junctive reasoning; it is an artificial way of expressing the
product and result of that reasoning (Chap. IV. 6, 7).
26. Before it in time and before it in idea comes the
actual process, and we must see what this is. We know that
A may be b, and again may be c, and once more may be d;
we know that it is nothing which excludes all three; and we
may call this our starting-point. We then go on to learn that
A is not b, and we conclude that therefore it falls within cd.
Once more we find that A is not c, and on this we conclude,
therefore A is d. We have here an obvious and palpable
inference, but in what does it consist? It consists in removing
the possible predicates of a given subject until the residue is
self-consistent, 26 and in then passing at once from this residual
possibility to an assertion of its reality. One possibility is
left, and therefore that is fact.
Our inference is not got by arguing from the major " What
is not b or c must be d" and that major does not give the proof
of our conclusion. On the contrary our process is the ideal
experiment which proves this major. We know that A, which
is not b and not c, must be d, only because we have tried and
have seen that d comes out as the result. Thus our major, if
we had one, would be the principle that a sole possibility must
be actual fact. But then this again is not given as a premise,
and we do not argue because we know that this is true. We
know it is true because we have argued, and itself is the result
of ideal experiment.
27. And even this principle is not quite fundamental.
For it presupposes a judgment that we have before us an
explicit exhaustion of the possibilities of A. One step of our
reasoning consisted in the statement, that b, c, and d are the
whole sphere of A, and that A must fall (if anywhere) within
414 THE PRINCIPLES OF LOGIC BOOK III. PT. I
this sphere. But the earliest form of disjunctive reasoning
dispenses with such a preliminary statement. 27 Incompatible
suggestions with respect to A come before the mind, and the
suggestion which survives in that ideal struggle is accepted
as fact. Thus we go direct to the assertion without any
declaration that our previous denial has exhausted the subject.
We shall return to this process when we begin to sketch the
beginnings of inference in the lower stages of mind, and at
present we must content ourselves with saying a few words on
the principle which underlies this early operation.
There is an axiom 28 which we can not fail to use, how
ever little we may be aware of its nature or existence. All
suggested ideas, we assume, are real, unless they are excluded.
If an ideal content is discrepant with reality, then it is not
fact. If again it is discrepant with another content, then
both are, at present, not yet real. The suggested idea is
so far possible ; but if nothing is found incompatible with it,
the idea is held actual. Thus all suggestions are true unless
they are opposed, and the suggestion, which maintains itself
in ideal experiment, and abolishes incompatible ideas, has
demonstrated its own validity. The survivor from the struggle
of competing ideas has shown itself fittest, and it therefore is
the truth. This ominous dictum, which contains the soul of
disjunctive reasoning, awakens our scruples, and when we
discuss the validity of the process it gives rise to, we shall
have to weigh these scruples in the balance. In this place it
is enough to have shown that once more we have found an
operation, which is not three-term reasoning, and which yet
lays claim to the title of inference.
28. It is worth our while to pause for a moment, and to
see the extent over which this principle operates. Any judg
ment whatever may be turned into reasoning by a simple
change. For we have merely to suggest the idea of the oppo
site we have only to suppose that the truth is otherwise, and
at once the predicate, which we already possess, excludes that
suggestion and returns to itself as what must be true. It now
is real because it must be so ; and it is a necessary truth, for it
has entered the field of ideal experiment and has returned
victorious. The process seems frivolous, since it turns in a
circle; we return to the place from which we set out, and
CHAP. II FRESH SPECIMENS OF INFERENCE 415
the predicate of necessity but adds the idle form of " It is
because it is " (cf. Book I. Chap. V. 29). We first degrade
our judgment to a mere idea, and then assert the idea on the
strength of the judgment. But this process, circular when we
apply it to judgments, is very different when used on mere
ideas. Take any idea, no matter what it is, suggest it of the
real and find it compatible ; bring it into collision with the
other ideas which are discrepant with itself, see that it defeats
them in open competition, and then go on at once to assert its
truth this alarming process appears to have no limit. Yet
valid or invalid, it certainly is inference. Whether we ex
plicitly state the possibilities as exhausted, or simply ignore
their possible enlargement, we have in both cases reasoning of a
type that does not fall under any other head.
29. We may add the remark that apagogic inferences
belong to this class, for, whatever intermediate steps they may
employ, they in the end must turn on a disjunction. They
make a transition from the denial of one predicate to the
assertion of another. And that transition assumes that no
other possible predicate exists. The large amount of vicious
reasoning which attends the use of the indirect method, is
mainly due to forgetfulness of this fact. The bad logic which
abounds in philosophical discussions consists in great part of
conclusions based upon hasty disjunctions. 29 And perhaps no
writer can hope entirely to escape from this error, for the
process, in which we are most likely to slip, is at times un
avoidable.
30. (H) We have nothing now left but our old friends
the so-called Immediate Inferences. 30 And these have given
cause for scruple ; doubt extends not only to the nature and
principle of their procedure, but even attaches itself to their
actual existence. If they are mere tautologies, rearrange
ments of words without alteration of ideas, they can not be
inferences. And some of them appear to be little else. To
argue from " A is B " to " Some B is A " gives rise to sus
picion, and that suspicion is deepened if we infer that B is equal
to A because A is equal to B, or that A must be to the left of
B, since B is certainly to the right of A. We may ask in these
cases what new conclusion comes from the process. On the
other hand if, given that A is B, we are offered the assertion
4l6 THE PRINCIPLES OF LOGIC BOOK III. Pi. I
" Not-A is not B," we decline to receive this erroneous addi
tion. 31 We should call it a bad inference, and should hence
be compromised when invited to deny that the legitimate " Not-
B is not A " is an inference at all.
We need not enter on the thankless task of enquiring in
each case if the inference is real or is simply circular. For no
logical principle is involved in this controversy, and it will be
enough to show that, given the validity of the immediate
inferences, we have already laid down those types of argument
under which they will fall. In any case they will make no
addition to those classes of reasoning which we have already
reviewed.
31. Where the so-called inference repeats the assertion
from which it started, there is nothing to be said. From A = B
to proceed by proof to B = A is an impossible process. In
each case you possess the same relation of A to B, and the
order in which you take those terms is perfectly irrelevant.
Hence the alteration which is made is psychological, not logi
cal, and is concerned with nothing but the verbal expression.
Let us take another case where the process seems doubtful.
It is not easy to answer off-hand the question, if " No B is A "
is a mere repetition of " No A is B," or if " Some B is A " is
a real advance on " A is B." But suppose that these are
inferences, they both fall under heads which we know already.
If, given one truth, you perceive another implied or contained
in it, this process is analysis followed by abstraction. And
what falls outside this is an inference from disjunction. If
to perceive for instance that Not-B is not-A, an experiment is
required which goes beyond the inspection of " A is B," the
process in that case will be indirect and the reasoning apagogic.
I will illustrate these general observations by some remarks
on the detail of Immediate Inferences.
32. If we consider first the immediate conclusions from
affirmative judgments, we shall find a good deal which excites
our wonder. The ambiguity which besets the word " some "
brings disgrace on this part of the traditional logic ; and
behind this ambiguity there is something hidden which will
hardly bear the light. Let us take the judgment as assertorical,
"All A is B." What is it, we may ask, that the inference
gives us, save this same relation over again? Take the judg-
CHAP. II FRESH SPECIMENS OF INFERENCE 417
ment first in extension as " All the A s are all the B s ; " is it
any news to be told that also " All the B s are all the A s "?
Is it not the old relation once more? Or if you know that the
A s are a part of the B s, are you further advised when you
learn that a part of the B s are the A s? If again from " All
the A s are all the B s " I am ordered to conclude, that they
are at least a part of the B s, I must ask for information. To
what am I committed by this doubtful formula? If it means
that a collection, being taken distributively, is taken distribu-
tively, that, if I have seen a, and have also seen b, and also
seen c, I must therefore have seen each then where is the
inference? But if it means that what is true of a lot is true
of some or each component part of that lot then the infer
ence is vicious, and the lot again is perhaps hardly taken in its
extension. And if I am invited finally to argue that, since I
am certain of each, I therefore am certain at least of some,
since that may be true even though I can not be sure of each,
then I must answer that you seem to be suggesting that I
should doubt my premise upon the ground of its certainty.
If again you do not take the predicate in extension if you
argue Because all the A s have a quality B, therefore some
things which have the quality are all the A s I can not see
how you have advanced one step. You know already that
there are things which have a quality B with a quality A, and
what more do you learn? Your " at least some B s are A s "
is not a positive conclusion at all. If it is neither tautologous
nor downright false, it is a caution to yourself not to make an
inference of a certain kind. It says, " I have a certain relation
which I must not go beyond ; to dispense with the some
would be wanton temerity, and to say at most would be
unauthorized despair. The right state of mind is a doubtful
hope, or an expectant ignorance." But this is not to infer, or,
if this is inferring, it is an inference which in the same breath
concludes that we must not make an inference.
And if, while we keep its assertorical character, we try to
read the whole judgment according to intension, we fare no
better. It is a fact that the attribute B attends upon the
subject or attribute A. Can we proceed from this to anything
more than a vain repetition ? To bring in our " at least " is a
futile expedient, for it merely reminds us of what we did not
4l8 THE PRINCIPLES OF LOGIC BOOK III. PT. I
say, and of what we must not say, viz. that B is never to be
found without A. But this is not making a good inference :
it is forestalling a bad one.
And if you reply, " To forestall a bad inference is to infer.
For how else should I know that my inference was bad, unless
after making it I compared it with my datum in an ideal
experiment? My "at least some B is A " does mean that be
sides there is a mere possibility. And the knowledge of this
possibility, which to me is not more and must not be thought
more, how else should I get it but by an inference ? " then
I answer that I am ready to accept your contention, for you
now have yourself admitted that your conclusion is not asser-
torical, but is problematic.
33. The truth is that, if you keep to categorical affirma
tives, your conversion or opposition is not rational, but is simply
grammatical. The one conversion which is real inference is a
modal conversion, and that presupposes a hypothetical char
acter in the original judgment. I will not labour to prove
this last observation, but will proceed to show that a hypotheti
cal judgment can be converted modally.
It can not be converted in any other way. In " given A
then B " you experiment with A, and your result is B. But
you can not, by simply taking B, experiment with that, and so
get as a result its relation to A. This I think is obvious, and
if in despair we fall back on our old device and bring in
" some at least," we shall get no further. We shall succeed in
saying " Given B you have A, if you suppose the case where
A has given B." This is barren tautology.
The real conclusion is " B may be A," but this once again
may be reduced to mere words. If you start with " Arsenic
creates such symptoms," and conclude " The symptoms pos
sibly have come from arsenic;" or if you begin with "Any
dog is a mammal," and go on to infer "A mammal may be
a dog " it is possible that still you are drifting between the
Scylla of false inference and the Charybdis of verbiage. It is
assumed that you mean to go beyond the truth you started
with, and that you are not content with the impotent result,
that the symptoms are arsenical upon the condition that arsenic
has caused them. You really mean that they may or may not
be arsenical, but tliat you have some reason to judge that they
CHAP. II FRESH SPECIMENS OF INFERENCE 419
are so. And this is the point; for you do not judge directly
of the real facts; you do not conclude by a vicious extension
that, given some other drug, you might have the same symp
toms; nor again, by an orthodox but imbecile process, that,
since arsenic must be mortal, its administration at least may be
the cause of death. This is not your meaning, and you would
be sorry to be understood as conveying such frivolity. Your
real judgment is about your own grounds of belief and dis
belief, and is only indirectly an assertion about facts. That
the death may have come from arsenic can mean, that, among
the possibilities of death which are otherwise unknown, we can
specify this one. And you perhaps meant to say this ; but it
is more likely that you meant to say something else. For you
knew nothing before about arsenic as a possible cause of the
death, except that you had no more reason to believe in it than
in anything else. But now, from the knowledge that it does
produce death with certain symptoms, you can make an infer
ence. You have that reason in favour of its chance when you
seek the most probable cause of the death. Among all the pos
sibilities this alone has extra weight, and the weight turns the
scale. The symptoms may or may not be arsenical ; but in
favour of the former we have at least the consideration that
arsenic certainly would produce them. There is so much more
probability in favour of arsenic than there is in favour of any
other cause. And this, I think, was what you really intended
to convey.
And if the conversion has this modal character, it then
will imply an inference based upon the disjunction of possible
alternatives.
34. This argument from certainty to probability is, I
think, the real sense which underlies the conversion of affirma
tive judgments. We may be told, in answer to our charge of
frivolity, that such conversion and opposition are a valuable
agent in education, and that therefore the orthodox logic in
this point can not be wholly absurd. Most absurd, I reply, in
the doctrine that it inculcates, but possibly useful because mis
understood into something rational. It can not, I should say,
much profit a pupil to be taught that, if " every dog is a
mammal," he may argue that " some mammals are therefore
dogs," and from this make his way to the triumphant con-
42O THE PRINCIPLES OF LOGIC BOOK III. Pi. I
elusion "Some dogs are mammals" (cf. Lotze, Logik, 81).
I should have thought that it might have been better to tell
him that, unless he has special information before him, he can
not reason straight from the attribute to the subject or from
the consequence to the ground. He might be told, I should
have fancied, that the presence of the former was a sign to his
mind, which so far certainly increased the probability of the
latter, but still could not prove its actual presence. This is
what he must learn, if he really learns anything else than
folly, and this he has to learn in spite of his teaching. It is
here as elsewhere with the uneducated professional. He is
pledged to the creed that truth can not be imparted until lost
in a medium of superstition and nonsense.
35. If we pass to the conversion of negative judgments
and to conversion by way of contraposition, we must modify
these charges. It can hardly be maintained that in this new
sphere we have no frivolity ; but on the other hand it can not
be said that we have nothing else. From " A is not B " there
seems really a passage to " B is not A." This no doubt may
be questioned; we may be told that we knew before that A
and B were incompatible, and that now we but know that B
is incompatible with A ; we thus have the same relation with
a grammatical difference. But this view I take to be incor
rect. It is true no doubt that in negation we may be said to
experiment with both our terms, while in affirmative judgment
we have but the first. Still the result, arrived at by the nega
tive experiment, is not the incompatibility of A and B. We
find that, given A, B can not be there ; but as to what will
happen when B is supposed, we have no information. Hence
the relation arrived at is so far one-sided.
How then do we gain the other side of this truth? Most
certainly not by any general principle, for that principle itself
must first be got by the process in question. The process
must consist in another experiment, which takes B as real
and, suggesting A, again finds exclusion. The essence of the
inference is open to doubt. It might be treated as the ex
plicit perception of a new relation, got by abstraction from an
implicit whole ; but I should prefer to take it as apagogic.
Suppose B, then A is excluded or is possible. First let it be
possible, and then A may be B ; or again B may be not-B, for
CHAP. II FRESH SPECIMENS OF INFERENCE 421
B can be A and A is not B. Thus we prove indirectly that B
excludes A and that the two are incompatible. It is by
virtue of the same apagogic process, that we are able to
reason from the absence of the consequent to the absence of
the ground.
36. This brings us to contraposition, and here without
doubt we have real inference. Given " A is B," we can be
sure that not-B is not-A ; yet we can not be supposed to see
this immediately. The process is indirect, and rests upon
disjunction. Not-B must either be A or not-A, but A is im
possible, because, given A, we must have B ; and by conse
quence B might exclude itself, or, if absent, must be there.
This conclusion removes the alternative " Not-B is A ; " and,
since but one possibility remains, that is therefore actual, and
hence not-B is not-A. We might desire something better than
such an indirect reasoning, which depends on the mere ex
haustion of alternatives ; but the desire would not easily find
its satisfaction.
37. I may end by mentioning the so-called Inference
through added Determinants. If we are sure that a negro is
a fellow creature, we may go on to argue, A negro who is
in suffering is a suffering fellow creature. Modern prejudice
takes the truth as a tautology, and would deny the very exist
ence of the inference ; but against this we may set the moral
prejudice, which, admitting the existence of the reasoning
process, practically refuses the conclusion. The process is
certainly vicious in form, for the addition may, so to speak,
chemically unite with the terms it is applied to, and may form
two components which are incompatible. A lie is a bad
action, but it is only in rhetoric that a virtuous lie is a virtuous
crime. So " friends are welcome," but " friends in adversity "
may find their added determinant makes a change. The form
of this inference, it is clear, will not stand, and it is better
to reduce it to two main types. In one of these we say " A
under any condition is B, C is A conditioned, and therefore C
is B." In the other we betake ourselves to the Third Figure,
and abstain in the conclusion from elision of the middle. " A
is B, A is C, therefore CAB is true," or " This negro is a
fellow creature, and this negro suffers, hence we have in this
negro a suffering fellow creature."
422 THE PRINCIPLES OF LOGIC BOOK III. PT. I
The same liberty of leaving the whole construction gives
the rational solution of another puzzle. " Because a horse is an
animal, the head of a horse is the head of an animal " (Jevons,
p. 1 8. If this argument can not be reduced to syllogism,
is is because the syllogism has first crippled itself. The
attributes of having a head and being an animal are united in
a horse, and you conclude, in the third figure, that Under some
conditions an animal has a head ; or, without elimination, that,
In the case of a horse an animal has a head. But this differs
from the result given by Professor Jevons in nothing except
grammatical form. The whole difficulty has arisen from the
supposed necessity of eliding the middle.
I do not know what to say of that inference by way of
omitting a determinant which Mr. Venn notices (Symbolic
Logic, pp. 285-6), for I do not think that I understand it.
" Men are rational mortals ; therefore they are mortals :
Here we have omitted the term rational from our result,
that is, we have eliminated it. Or we might have omitted the
word mortal, by saying that men are rational. " But, if
we did this, we should surely be proceeding in a way which
we can not justify. If our conclusion is based on extraneous
information as to the irrelevance of one term, that informa
tion should have appeared as a premise. But if we mean to
rest on the bare statement that we have, then we are cer
tainly illogical. We may mean that men " before identified
with rational mortals are now identified with an uncertain
part of the larger class rational, or mortal : " (ibid. 287)
but, if so, I must repeat a former criticism ( 32). We shall
have argued from my certain knowledge to my uncertainty
and ignorance. We shall in effect say, because I am sure of
a thing, therefore, and for no other reason, I do not know it.
And this surely will not do.
We may object on other grounds. The judgment may
become false if you remove any part of it. " Religious
miracles are pretended facts that are necessary illusions ; " try
elimination here. Or test the process by Mr. Venn s own
instance. Men would not be rational if they were not
mortal, nor would they be mortal if they were not rational ;
for in either case they would cease to be men. Our argument
has illustrated a well-known type of logical mistake. For
CHAP. II FRESH SPECIMENS OF INFERENCE 423
men simply rational would, metamorphosed by no logical
change, have risen like the angels ; and simply mortal would
have lost that foreknowledge which divides them from the
beasts. Each alternative robs them of their human existence ;
they perish alike before the nudity of Reason, and la mart
sans phrase.
38. The list of the so-called Immediate Inferences has
not given an additional type of reasoning. They all fall under
the previous classes, and none of them can strictly be called
" immediate," for none gives a conclusion without an operation.
But, if we leave them and ask for the general result of the
present Chapter, we may state it thus. Apart from these last,
we have found a number of palpable inferences which can not
be brought under the formula we laid down in the previous
Book. The list of such processes may not have been ex
haustive, but enough has been adduced to show beyond ques
tion that the general nature of the reasoning process has yet
to be ascertained.
ADDITIONAL NOTES
1 " Is a fallacy of inference." It would be better to insert "(even
if it involves)" after "is."
2 The inference to the new quality depends of course and follows
on the construction of the whole, and this is a prior conclusion. The
many terms must have become one. Cf. on Bk. II. I. III. 6.
3 " Ideal experiment." The distinction drawn here is seriously mis
taken. See Bosanquet, K & R, pp. 296 foil. We have an inference
wherever, and so far as, the necessity of a conclusion is seen or felt;
and we have an inference nowhere else. In all cases alike, where there
is a " must," there is an " ideal " result. Cf. Note 5, and on Bk.
II. I. III. And see the Index, s. v. Experiment.
4 On Arithmetic see the references in the Index, and so again on
Spatial Construction, s. v. Construction. For the nature of the in
ference used in each see T. E. I.
5 " For though the quality . . . got by it." This repeats the error
shown in Note 3. Whether the arrangement is made ideally or is
found, is irrelevant. The inference in every case alike is ideal or is
non-existent.
6 " The construction follows from the data themselves." This it
never does or could do. Even where the identity of the terminal
424 THE PRINCIPLES OF LOGIC BOOK III. PT. I
points is given, an ideal whole is necessary for the inference. See
T. E. I.
7 " The conclusion is thus arbitrary." Cf. the references in the
Index, s. v. Inference. And, on the general question as to arbitrari
ness, see T. E. I.
8 I can not enter further here into the subject of degree or in
tensive quantity. But I would venture the remark that any attempt
to deny this of psychical facts is to my mind quite mistaken and
plainly indefensible. Cf. Mind, N. S., No. 13.
With regard to the experiment, on the magpie and on other ani
mals, it is of course not the facts which I reject but the conclusion
drawn often too hastily. With regard to the " savages " I regret to
have lost my reference, and the fact, I admit, is capable of more than
one interpretation. See Bosanquet, K & R, pp. 87 foil. All that I
insist on is that, with groups, we in many cases, without in the proper
sense counting, can and do distinguish between more and less. Cer
tainly I did not mean that the perception of more or less can be
merely qualitative. I fully agree with the opposite view urged by
Dr. Bosanquet (K & R, loc. cit., and Logic, I, Chaps. Ill and IV),
and I certainly accept in the main his statement as to the nature of
number, to which statement the reader is here referred. Cf. also once
more my article in Mind, N. S., No. 13.
The perception of more and less does, I agree, imply " something
and another," and so by consequence involves " units " and an
integral whole. What, however, I doubt is whether we should speak
of " counting " before we have reached the more abstract stage of
equivalent units, and the idea of " how much " or " how many " as
distinct from " much," " more," and " less." But this doubt does
not affect the main doctrine urged here, namely that units apart from
an integral and qualitative whole are an abstraction which in the end
is impossible and unmeaning.
10 On the question of arbitrariness see Note 7. It does not follow
that, if the operation is arbitrary, the inference is so also. The
inference is here not the " operation " itself but is the perception of
the logical ideal sequence which appears there (13). But as to
whether, and how, " one and one " not only " make " two but " are "
two (7), see the discussion in T. E. I.
11 " It does but remove an obstacle to my vision." Cf. 15, and see
the Notes on Bk. III. II. III. 5 and 9. It is wrong (I should now
say) to call any process an inference if it fails both to show and also
to be the self-development of a real object. See T. E. I. The ideal
operation which shows an object taken as unmoved, is hence not an
inference so far as that object in itself is concerned. It may, how
ever, be a genuine inference, so far as it shows, and is, the necessary
development of that object in my knowledge. But the real object
here is the process of the known, which under certain conditions does
and must develop itself into a certain result, a result which, if there
before, was not there for me. So in the case of " superposition "
CHAP. II FRESH SPECIMENS OF INFERENCE 425
( !5), imagined or seen, and used to demonstrate coincidence and
identity. This process is an inference so far as you take it as mean
ing that the thing must be so, because under certain conditions I
must otherwise see that it is not so. Cf. Note 24.
As to how far in Arithmetic and spatial construction the object
itself must be taken as actually moving, see above, Note 10.
12 " The ground of knowledge." Cf . Bk. I. VII. 49, and Bk. III.
II. II. 13. This problem involves the whole question of the relation
of truth to reality, and no final solution of it was offered in this work.
What we have seen so far is that in inference the ground of knowledge
is, and must be always, in some sense a real ground. But the converse
statement, that the real ground is always a ground of knowledge, does
not of course follow from this, at least immediately. Our answer here
will depend on our view as to how far reality is identical (a) with
truth, and (b) with knowledge knowledge in a sense taken more and
more widely, until in the end (c) it is the same as experience. But see
the Index, s. v. Ground.
13 Comparison and Distinction. See the Index. There are some
remarks on Comparison by me in Mind, O. S., Nos. 41 and 47,
and by Dr. Bosanquet in No. 43. I was concerning myself, so far,
mainly with what may be called processes subsidiary to the actual
inference. The nature of Comparison as inference, and again of
Distinction, so far as that falls under Analysis and Abstraction, has
been dealt with by me in T. E. I. The reader should, however,
consult Bosanquet s Logic, I, pp. 108 foil., and II, pp. 19 foil.
14 " The copulative process." This statement seems ambiguous.
An assertion that the use of " both " always implies comparison could
hardly, I think, be defended. It would have been better to say " The
copulative process, so far as this involves comparison, will be an
inference of the above kind."
15 " Truth new to us." We have here a serious error. The ques
tion, as to novelty to m-e, is wholly irrelevant. The real question is as
to whether the subject developes itself ideally into something different
or not. See Bosanquet, Logic, II, p. 8.
16 With regard to Distinction, cf . Notes 13 and 22. " It is for us
because of our activity." This, however, once again, is not itself the
main essence of the inference. See Note n.
17 Recognition (cf. Bosanquet, Logic, II, pp. 22 foil.) is an am
biguous term, and its proper meaning is a subject calling for discus
sion which, however, seems here not required. The point here is
this that, where recognition involves a " because " and a " must be "
(as at times certainly it does), it there is an inference. And yet, even
there, we need have no middle in the sense of a " premise " or datum.
18 Hypothetical Judgment (cf. Bk. III. II. III. 10). The point
once again is the same that, though in all hypothetical judgments an
inference is involved, yet there need be no middle which is before us
as a datum. On the Hypothetical Judgment see T. E. II, and again
Bk. I. II. Note 40.
426 THE PRINCIPLES OF LOGIC BOOK III. PT. I
19 " Is a heresy." But on this question the reader is referred to
Dr. McTaggart s Studies in Hegelian Dial-ectic.
20 On Dialectic as inference see T. E. I.
21 Abstraction. For references see the Index. And, on the nature
of abstraction, see T. E. I and IX; and cf. Bosanquet, Logic, II, pp. 20
and 144.
22 The inference itself, here once more, is not " arbitrary " ; and it
claims, at least, to be a real self -development, though of what object
is a question. See Notes 10 and n.
23 " Our data are pure universals." " Pure " here, as in the next
paragraph, means " free from the mass of detail " which there is
referred to. If A, B, and C were " pure and freed from all irrelevancy,"
in the sense of " unconditioned " they could not, as such, " appear "
together merely as ABC.
24 Disjunctive Reasoning. Cf. Bk. III. II. III. 16, and see the
Index. The statement in this work as to the nature of disjunctive
inference is vitiated by errors which must be noticed. Their presence
was pointed out by Dr. Bosanquet (K & R, pp. 255 foil.), and, so far
as I returned to the subject in my Appearance (see the Index, s. v.
Privation), I hope to have stood on firmer ground. But for a satis
factory treatment of Disjunctive Judgment and Inference I must refer
the reader to Dr. Bosanquet s Logic. In the present work I have
already (in the Notes to Bk. I. Chap. IV.) remarked on the above
judgment, and, in T. E. I, have pointed to the main defect of the
inference a defect not removable unless we pass beyond the limits of
mere Disjunction.
In what follows here I must attempt to distinguish the true Dis
junctive Inference from processes which fail really to fall under that
head. And with this object I shall begin by noting the assumption
which in all genuine disjunction is necessarily made. We have there
to take for granted, not only that we are dealing with the entire
Universe for so much we do, in a sense, and must do in all knowledge.
In genuine disjunction we have to make a further assumption. We
must, that is, also assume that the special reality (whatever it may
be) which is the subject of our inference is itself the entire Reality
in this sense that it is all with which we are here concerned or by
which we here can be affected. The above assumption may be ex
plicit, or, again, may be more or less tacit. It may, that is, consist,
and at first it does consist, in the mere ignoring of all else. But,
in either case alike, the above assumption is necessary; and, so long
as it stands, it excludes in principle (as lower down I shall note more
fully) any appeal to doubt based on Privation and ignorance.
In a Disjunctive Inference (to proceed) our subject has predicates,
such as a, b, c, which, though they all of course are real and determine
their subject (S), are on the other hand "incompatible." If, that is,
the subject is taken as, here for instance, specified and individualized
as Sa, it, in that character and so far, excludes itself as Sb or Sc.
On the other hand a, b and c all qualify S, and so determine the
CHAP. II FRESH SPECIMENS OF INFERENCE 427
contents of S no less positively than negatively. Hence the exclusion
of a, b, or c according to whatever conditions prevail in a given
case is ipso -facto the necessary assertion of whatever remains in S.
The denial of any one specification, Sa, Sb, or Sc, is the positive
qualification of the whole S as therefore, now and here, necessarily
expressing and individualizing its entire self in the residue. This
expression is still of course conditional, if more than one alternative
is left; but it becomes categorical when but one (whichever it is)
remains. Disjunction, in other words, assumes a whole which is
systematic, in the sense that its contents exhaust and complete it
fully by their character and connections at once positive and negative.
A disjunctive inference, where genuine, rests (i) on a whole of
the above kind, and it involves secondly (ii), as given or supposed
here, the specification of this whole in one part of its full character.
From this ground the conclusion follows necessarily, and in the above
lies the real "must" and "because" of disjunctive inference. The
process is defective so far as that specification of the whole which
here is given, is not itself the result of known and included con
ditions. For the ideal self-development of S is thus broken by an
intruding but necessary x (see T. E. I). But the argument, apart from
this, is free from logical flaw. The conclusion follows necessarily
from what is assumed. And, if you suggest that the conclusion depends
on an appeal to mere Privation, the answer is that anything of this
kind has been in principle excluded. The very ground of the dis
junctive inference is the presupposed impossibility of an interfering
" other " or " otherwise."
It is not the sequence but the foundation itself of our process
which is liable to an objection drawn from Privation and human
ignorance. Can we anywhere (this is the point) start from a basis
which truly is all-inclusive, and which admits no suggestion that it is,
or may be, essentially otherwise than as it is known? So far as our
knowledge is " absolute," we must, I maintain, answer this question
by Yes (see T. E. I and VIII). We have here no possible idea or
genuine suggestion of any " other." And, if our knowledge could in
the full sense be systematic, that knowledge would everywhere and
throughout be self-complete. There would hence remain no field open
for the merest suggestion that aught could really be otherwise. But
since, as things are, we have no such system, and since in concrete
detail all our knowledge remains but " relative," another answer must
be given. If we except (as we must) any truths which are absolute,
the body of our knowledge shows throughout incompleteness and de
fect, and opens everywhere within itself room for the rational sugges
tion of an " otherwise." Hence the assumption necessary for a dis
junctive inference may be said to rest, so far, on ignorance and
Privation. On the other hand we must not forget that, the more
our knowledge (though always incomplete) is enlarged and unified,
the less space and ground remains for legitimate and rational doubt.
It may be asked finally whether we can still speak of a disjunctive
428 THE PRINCIPLES OF LOGIC BOOK III. FT. I
inference where the possible " otherwise " is merely ignored. Ob
viously in this case there is no statement, or any explicit understand
ing, that in the field of what we have before us the possibilities are
exhausted. And can we claim to have made here, really though tacitly,
this required assumption ? We may assert such a claim, perhaps, where
our ignoring of anything outside is utter, and so is practically com
plete ; where we proceed, that is, from a positive ground which ex
cludes all doubt. But, on the ether hand, if the least suggestion of
an " other " is here present, there is an end, I agree, of genuine
disjunctive inference.
With this I pass on further to consider processes which may show
the appearance of disjunctive inference, but which still may be with
out a good claim to that title.
Where, having a subject R qualified as Ra, I attempt to find
some other determination of R, such as Rb, and then fail to find any
or, again, where, Rb being suggested, I discover on scrutiny that
Rb really is no "other" have we in these cases an inference? And,
if so, to what class does that inference belong? These questions
deserve, I think, to be considered carefully.
(a) If, in the first place, we bring nothing with us back from our
excursion, there is here certainly no inference. We are still left with
our Ra as it was at the start, and we have not, any more than before, a
conclusion that R must be a.
(b) But the case, secondly, may be otherwise. For we may have
reminded ourselves, as a result, that every judgment is really an
inference, and have reflected that what Ra should mean is that
Reality is such that therefore R is a. Here, if we have not actually
inferred, we have gained the recognition that our Ra is, and was,
an inference. But we can hardly add that, with so much, the inference
is specified as disjunctive.
(c) We may find, thirdly, that the "other" (Rb), which was
suggested or sought, is in some sense actually an " other." Still it
does not, as such, qualify our subject, and it hence, so far, leaves
unaffected our judgment Ra. Our judgment has hence been, so far,
neither weakened nor strengthened. Our result has been, in other
words, the discovery that Rb is an error. This error is, in the process
of our knowledge, something actual, and, taken so, has reality; while,
on the other hand, logically in the character of Rb, it is not taken
as real. As to our discovery, if the result of that is the mere dismiss
ing of an error, we have clearly so far no inference. But on the
other hand we have a " must," a conclusion and an inference, so far
as we take the suggestion and removal of the false Rb as a necessary
step in the process of our knowledge. This inference, further, will
be disjunctive, so far as our world of knowledge is viewed as a
system which contains the error, Rb, as an essential element. For
Rb thus has become something the negation of which establishes
for us the conclusion Ra. What of course we must not add is that
Rb, as such, is, or ever was, compatible with our logical subject,
CHAP. II FRESH SPECIMENS OF INFERENCE 429
or is logically a possible " other " than Ra. But for a treatment
of this problem of Error, I must refer the reader to my Essays.
(d) We may (lastly) assert that our subject must be Ra and not
otherwise, on the ground that, if there were an " other," we must
certainly have found it. And we may have an inference here which
is genuine and also disjunctive. I may, that is, assume here that
my knowledge is exhaustive, and that therefore any "other than Ra"
is, if anything, an error. But in the character of an error this
" something else " can, we have seen, be taken, in the world of our
knowledge, as actual. And, taken so, it may be regarded once more
as a positive element, which by its denial necessitates for us the
result Ra. And the result will, thus and in this sense, follow as
the conclusion drawn in a disjunctive inference.
We never (the reader will observe) do argue directly from priva
tion, from ignorance, absence or incapacity. No inference of any
kind can rest immediately upon these, and any idea that it could
so rest comes from misapprehension. The basis of an inference, if
and so far as it is a genuine inference, must everywhere be taken
as positive. The real and vital question is as to how far the positive
assumption or assumptions, which we must use, are vitiated by our
ignorance, and how far they are thus open to legitimate doubt about
the possible presence of an unknown " other." And to this question
I in this Note have referred already.
It is better perhaps to add here a few words on what is called
Elimination. On this process, so far as it appears in Arithmetic
and again in Abstraction, see Note 21, and, further, T. E. I, IX,
and the Index. All that need here be remarked is that Elimination
involves a disjunctive inference only where, and so far as, the removal
of an element takes place within a whole which itself is truly dis
junctive. For solely in this case does the element excluded become
(through the above whole) a positive ground for the assertion of the
residue as now necessarily real. How far, on the other hand, mere
Abstraction fails to reach such a result will be found noted elsewhere.
See the references given above.
It should be clear, I hope, finally, that the " axiom," given in 27,
is fundamentally wrong. We have here again that mistake as
to "mere ideas" which so much injured this work. But no idea,
if it actually is an idea, can possibly fail to be real somewhere and
somehow. Further, we have now recognized the genuine principle,
the place of which was usurped by this spurious " axiom." The
ultimate Whole, and again any subordinate whole with which
for our purpose we are concerned, is what we have to take as reality.
And the more that any determination of a whole contains and ex
presses that entire universe the more that any totality individualizes
itself specially in one part of what falls under it and within it the
more real everywhere does that special embodiment become. The
exclusion of the incompatible " other " or rather its exclusion as,
and so far as, incompatible has reinforced by so much what remains.
43 THE PRINCIPLES OF LOGIC BOOK III. PT. I
The "other" lives and shows itself positively in the greater share
of the whole which has now appeared as owned by the residue. The
process here is the real opposite of that abstract struggle where the
survivor is victorious through its own private and particular force,
or by the external accident either of designed interference or blind
irrational chance.
25 " This attempt would be futile, since &c." After " since " should
be inserted, " if for no other reason." Cf. 27.
28 " The residue is self-consistent," i. e. as containing no conflicting
possibilities. The following statement " One possibility . . . fact " is
wrong in principle. See Note 24.
27 " The earliest form, &c." We begin, that is, by, at once or in
the end, ignoring practically the possibility of an " otherwise." See
ibid.
28 " There is an axiom &c." This and what follows is erroneous.
Section 28 also is largely mistaken. See once more ibid.
29 If I may state the result which has come to me personally from
my own experience and errors, I should repeat that False Alternative
is that fallacy which, beyond all comparison, is most prevalent and
insidious.
30 " Immediate Inferences." My treatment of this subject is not
satisfactory. I would refer the reader to Bosanquet s K & R,
pp. 188 foil., and Logic, I, Chap. VII, and II, Chap. I. The main
point to my mind is this, that no inference is or can be really imme
diate. Unless there is a link of " why " and " because," unless there
is an ideal whole, and, through that, a necessary self-development,
there is no inference anywhere or at all. Where we come to perceive
another aspect of a given matter, that result is not an inference, unless
we take this second aspect as connected with the first, in, through,
and because of some whole which is concerned. And in the tradi
tional Immediate Inferences this essential feature, I should say, is
wanting.
31 " On the other hand . . . erroneous addition." With regard to
this point, and on the conversion of negatives, etc., the teaching of
this work is mistaken, here and in 311, 35, and 36. Exclusion is
essentially reciprocal; and the perception of this, I now agree, should
not be taken as an inference. Further, I now hold, with Dr. Bosanquet
(Logic, I, Chaps. VI and VII), that, in "A is B" or in " If A, then
B," the connection of A and B is in principle reciprocal. It is other
wise only so far as there is irrelevancy, so far as A and B, in other
words, are not pure, and an x is really implied in our assertion.
See Index, s. v. Cause, and T. E. X ; and cf . Appearance, p. 362,
note.
With so much, and with a reference once more to Dr. Bosanquet s
works, I will now summarily dismiss the subject of Immediate In
ferences. To study its detail further would (the reader may agree)
be more wearisome than profitable.
CHAPTER III
GENERAL CHARACTERISTICS OF INFERENCE 1
I. The position we now stand in is briefly this. It is not
every inference that gets a new relation of the original ele
ments, by means of a construction that interrelates them.
This is not the universal type of reasoning, and it obviously
does not present us with its essence. The ideal operation is
not always a synthesis based on the identity of given terminal
points. 2 The place of such a construction may be taken by
processes, the nature of which we have partly seen, but whose
general type we have not yet asked for. But we must delay
that enquiry till we reach another chapter. At present we
shall not take this diverse array of ideal operations, and try
to reduce them to common types ; for, before attempting this
scrutiny, we may pause with advantage and raise some
questions.
2. And the first of these is, Can we not at once say
something general about the nature of reasoning? Without
regard to the differences which we have brought to light, is
there not some account which holds true of all of them? And
we answer that we can see clearly such a common character.
No matter what the operation may be, there is always some
operation. This operation 3 is an ideal experiment upon some
thing which is given, and the result of this process is invariably
ascribed to the original datum. We have here an application
of the Principle of Identity; 4 for what is true of a datum
within the operation of our ideal experiment, is also in some
sense true of that datum without regard to the experiment.
This formula holds good throughout all our instances, and it
will repay us to consider them awhile from this side and
aspect of their nature.
3. In reasoning we have a starting-place that is given, a
subsequent operation, and a consequent modification of that
starting-place. In an abstract form we may represent it as
follows. First A, then A in ideal experiment becoming Ab, and
43i
432 THE PRINCIPLES OF LOGIC BOOK III. Pi. I
last the assertion that Ab is true, unconditionally or condi
tionally. 5 We have thus (i) Premises or premise, (ii) Opera
tion, and (iii) Result. 6 The first is A 1 , the second is A z b, the
last is A 1 ^. For what holds of A once will hold of it always,
and the quality, which A gets in the context of that process
which we represent by A 2 , belongs in some sense to A apart
from the process. Our present task will be to verify this type
throughout all our examples.
4. We may preface the enquiry by a reference to causa
tion. Without discussing the exact relation which exists be
tween the causal and the reasoning processes, we may refer
to something which they have in common. In causation you
first of all start with the elements called the " conditions," the
next step consists in the process of change which issues in a
certain result, and the whole is complete when that which has
resulted is ascribed to the original conditions. It is the same
with inference. The result of change that issues from the
process into which the original datum enters, is ascribed to
that datum. Both causation and reasoning depend upon iden
tity, sameness in spite of a growth of difference ; 7 sameness
again which preserves itself, not by refusing but by appropriat
ing that difference. Both are alterations of a datum which
is changed, but survives in its changes and makes them its at
tributes. In a future chapter we shall further discuss the rela
tion which subsists between the effect of a cause and the con
clusion of an argument.
5. Returning to the task we have now in hand, let us
proceed to the application of our general remark. And let
us try first those inferences which interrelate three terms, and
which so bring out a new relation. In these we have first the
elements of our construction existing apart, then we have the
construction, and last of all the new relation. Take for in
stance " A to the right of B, and B of C, and therefore A to
the right of C." We here have got (i) two spatial relations,
or rather two sets of terms in relations of space, and we may
call this starting-place reality qualified as these pairs of rela
tions. Let us pass to the second step 8 (ii) ; this gives us
the synthesis of those very same terms which we had at the
beginning. The contruction certainly is a difference, but it
does not make such a difference to our terms that they lose
CHAP. Ill GENERAL CHARACTERISTICS OF INFERENCE 433
their identity. We next (iii) perceive a new relation, the result
of the construction. But since the terms are the same not
withstanding the construction, they are the same in respect of
this further result, C A. Hence the real, qualified as C B
B A, is the real qualified as C B A, and that again is
the selfsame subject as the real which has the relation C A.
We have sameness both within and without the construction,
and we have appropriation of that construction s result.
Take another argument, " A is equal to B, and B to C,
and therefore C = A." The whole synthesis of these terms,
effected through B, is the second stage, on which follows
thirdly the separate perception A C. The result of the
construction is taken as its attribute, and is so predicated;
and the construction itself is in just the same way made an
attribute of the terms. A, B, and C are the same in the con
struction and with the result that it developes, as they were
apart from it. The issue of the operation is simply their own
being.
And we can verify this type in the common syllogism. In
" Mammals are warm-blooded, men are mammals, and so men
are warm-blooded," we find the same elements. 9 First the
separate judgments are given us as true; we have reality ap
pearing in the attribute of these two syntheses, " man-mam
mal " and " mammal-warm-blooded." Then the construction
follows, and from that the intuition of " man-warm-blooded."
But the relation which we predicate of these extremes, is not
a foreign compulsion of their nature. For the issue of the
process, the result of the change, has not removed their same
ness. They have remained through alteration, and accept 10
the difference as their proper attribute and native possession.
6. Where we go from the construction not to a new in
ternal relation but to a quality of the whole, our account still
holds good. The elements, which during our circular voyage
we received discontinuously each in isolation, first combined
themselves into a spatial whole, and then took on the qualities
we understand by " island." But the reality throughout has
maintained its identity. It moved before our eyes a changing
show, that came fresh from the unknown and slid back per
petually into nothingness. To our judgment it appeared as a
discrete series of spatial arrangements; and it was with this
434 THE PRINCIPLES OF LOGIC BOOK III. PT. I
series that our reasoning began. That, boldly relying on the
Identity of Indiscernibles, built up for us an intellectual whole,
and that whole presented us with certain qualities. We then
attributed these qualities to that very reality which was mani
fest in our fragments of successive coast line. The reality has
certainly both undergone experiments and suffered changes at
our hands. It is not what it was, and it yet remains the same ;
for it is itself and more. It is the original subject with addi
tional attributes, conferred upon it by our ideal operations.
We find the same when we pass to spatial arrangement.
Bricks and mortar with the builder are here our premises, the
compound action and reaction of the two may be called the
construction, and the conclusion is the appearance of the house.
It may be doubted how the elements, which we had at the
start, can survive in the result ; yet we can not but think that
somehow they have survived. For otherwise it would surely
be false to say that the house is the effect which has come
from these causes. I admit the difficulty which attaches to
identity, but it is still harder to believe in a discontinuous
existence and in a divided reality. For if in the house you
have not got the work done by the builder on a certain ma
terial, you have no right to speak as if you had. And you
could not even say that the house has appeared, without syn
thetic judgments which assume an identity. If the reality has
changed, the same reality must be there still, and if the reality
has not changed, there has been no change whatever; for a
sequence of mere differences would have nothing it could alter,
and could not generate even the show of alteration.
And in the same way when, not externally but simply in
my head, I rearrange elements by an arbitrary choice, 11 the
result, which I get at the end of my process, is true of the
basis from which I began. That foundation has survived and
has got a new quality without the loss of its own selfsame-
ness. The result is hypothetical, since my free action was no
more than possible. One element of the cause, apart from the
others, is but the hypothetical producer of the consequence,
and is no more than what we call a " condition."
7. We may deal rapidly with the operations of addition
and subtraction. We have the units arranged in a certain
manner, and these are our material 12 with which we begin.
CHAP. Ill GENERAL CHARACTERISTICS OF INFERENCE 435
Then follows a rearrangement of these units, and a consequent
perception of another attribute which also belongs to them.
Throughout the operation the units are identical, and they
appropriate the result of the experiment. And since it is
assumed that to them the experiment can make no difference,
therefore that difference becomes a categorical predicate. The
units with a quality of certain integers go into a process, and
come out in possession of another quality. Thus by virtue of
this change the identical subject is credited with both contexts,
or, in other words, the two different arrangements, which we
began and ended with, are taken as identical.
And it is clear that the same view holds good of geometry.
The data are divided or are rearranged or are compounded
with arbitrary fresh surroundings, and from this manipulation
comes out a result. But since the experiment adds nothing
to the data nor takes anything away, since again the data
remain the same throughout the experiment, the result becomes
their categorical attribute.
8. 13 In Comparison it is easy to recognize the same type.
A and B are first given us apart from their relation. The
next stage is the process, in which we bring them together,
and so perceive a relation of likeness. The relation is then
predicated of A and B apart from our comparing activity.
They are alike because their change to this relation was no
alien imposition, and because their identity has remained unim
paired throughout the alteration. The same remarks apply to
the inference of Distinction.
And they apply once more, with slight modification, to Dia
lectic reasoning, to Recognition, and to the Hypothetic judg
ment. In all these we have but one premise explicit ; we start
with AB, and, subjecting this to an ideal experiment, we are
given ABC. The original datum is met by a function which
produces a result. But it is assumed once more that the syn
thesis does not arbitrarily add from the outside ; and hence,
since the datum is the same in the experiment as it was before
hand, the result is taken as its quality and attribute.
Nor in passing to Abstraction do we find any change. We
start here with reality in the character of abed 1 . This same
content is subjected to an ideal operation as abed 1 , and then
presents us with a d. Upon this we conclude that abed 1 is
436 THE PRINCIPLES OF LOGIC BOOK III. PT. I
also ad, or, more directly, that the reality is ad. But our con
clusion would be false, did it not presuppose the identity of the
subject in two different contexts.
9. In Disjunction lastly we find once again this identity.
Whether we begin with the alternatives stated as exclusive,
or with a simple field of possibilities, 14 makes no real differ
ence. We start with a subject determined inside a certain area
of possible predicates. This subject then undergoes an opera
tion which reduces that area, and it ends by seizing on the
undestroyed remainder as its actual attribute. But it could
not do this, if it stood outside the process or were dissi
pated within it. Itself goes there and is active, preserving
its self, and emerging with a difference which it refuses to
give up.
The same character is seen in Apagogic reasoning, and
again in that qualification through rejected suggestion, which
(by employing the supposal of an opposite) turns " it is " into
" it must be." The identity within and without the experi
ment needs here no indication. And finally the Immediate
Inferences, which we were last concerned with, are not inde
pendent. They arrange themselves under the heads we have
discussed, and our foregoing remarks have already dealt with
them.
10. Our result so far is that inference is the getting a
new result from a certain datum. The result is procured by
an ideal operation upon this datum, and when procured be
comes its predicate. Reasoning thus depends on the identity of
a content inside a mental experiment with that content out
side. And so we find once again in the total process that need
for individuation, which we before discerned in the middle
construction. Just as that construction was insufficient to give
us a new relation of the extremes, unless it joined them in an
individual whole so here the full process would not get to a
conclusion, unless it possessed an individuality. And it is made
individual by the identity of that content which runs right
through it, and which joins the final result to the initial start
ing-point. So much at least we are now able to say in reply to
the question, What is an inference? And this beginning of an
answer we may go on to make clearer by laying down some
important distinctions.
CHAP. Ill GENERAL CHARACTERISTICS OF INFERENCE 437
ii. It is not any and every mental activity which can
properly be called reasoning. This claim could not, I think,
be seriously maintained, but it may perhaps be worth while to
examine its nature. We may be asked if our account, so far
as it has gone, has not tacitly admitted such a sweeping pre
tension. " Does not every ideal activity," an objector may
urge, " first begin with a datum, and, performing on that an
ideal operation, so produce a result? Take for instance judg
ment. Here we have the reality, and we qualify that subject
by referring to it a suggested content. That is an ideal action,
and it is an action again which brings about a change which
it does not create or manufacture. The result is ascribed to
the original datum, and ascribed by virtue of an ideal opera
tion." We must briefly reply to this mistaken claim.
12. There are two questions we must endeavour not to
confuse. Each of them asks if judgment is inference, 15 but
each makes that enquiry in a different sense. 16 The first asks
if all judgments imply an inference. That is, does judgment
presuppose and is it the conclusion of a reasoning such as is
described above ? That is the first question, and the second is
quite different. For the second enquires if every judgment by
itself is an inference, independent of and apart from any of
those processes which we have hitherto called argument. We
will begin by dealing with this latter claim.
Suppose for instance that we had an operation, which,
taking X, simply added on 3; as a mere suggestion that came
from the outside, and then judged X y. Could we call that
an inference ? No doubt it may be said to preserve an identity ;
no doubt again that it ends with a judgment, which may fairly
be said to predicate something new of the original datum. No
doubt once more it is an ideal activity. But, notwithstanding
all this, it is not an inference. The y, which in conclusion it
attributes to X, is not in any sense got from X by an operation
thereon. It is stuck on from the outside; and because the
result, ascribed in the conclusion, is not procured from the
starting-point, therefore this result is not a real conclusion.
13. In the arbitrary synthesis of a suggestion 17 with
reality the predicate does not really come from the datum. It
thus lacks an essential character of inference, the getting of
the product on and from the premises. We may try however
THE PRINCIPLES OF LOGIC BOOK III. PT. I
to renew the attempt in an amended form. Judgment, we may
say, is an inference of this kind; we have (i) Reality together
with a suggestion, and beside these two we have an arbitrary
power of junction. These three elements are our premises,
and we have (ii) the actual union of these elements, which
gives (iii) the synthesis of the predicate with reality and
this result is a conclusion. But this amended attempt is as
futile as the former. For the judgment in the first place will
not be categorical. In this it will be like free spatial arrange
ment ; so that the inference, if there is one, does not end in the
simple assertion X y. It can not go beyond, "If X is
treated in an arbitrary manner it will turn to X y." And
perhaps this is senseless. For in the spatial arrangement the
combination of the data produced a new quality, while here on
the other hand it produces their combination. We must end
by writing the result of our process, " X, if X be X y, must
certainly be X y." And there does not seem to be any in
ference here.
14. I offer no apology for pursuing these somewhat dull
enquiries, since it seems to me that every answer we elicit
throws some light on our general doctrine. We have seen so
far that judgment is not inference, and that a process which
was nothing more than a judgment would never be reasoning.
We may now approach the second question we asked : Is every
judgment part of an inference? Does, that is to say, judg
ment presuppose a process which must be called reasoning?
May assertion be always taken as conclusion ? This is really a
somewhat difficult problem, and, as we shall have to recur to
it afterwards (Chap. VI. 15), we may content ourselves here
with some brief remarks.
15. Some judgments, we know, do involve a reasoning.
We saw that this held of hypotheticals, 18 since the supposition
that A is real, is itself an ideal operation on this content.
For, in the union with reality, A is met by a function of syn
thesis and so developes a new connection. And again if we
take those common judgments which go beyond presentation
I mean those extensions of sense which supply us with the
past or with the unseen present they are all inferential. They
imply, as we saw, an ideal operation, and it was for that reason
that we called them " synthetic." Nay, when, leaving these,
CHAP. Ill GENERAL CHARACTERISTICS OF INFERENCE 439
we come down in the end to those judgments which assert
about present perception the class we thought fit to call
analytical " even here it may seem we are dependent on
reasoning. For these assertions are based on a process of
mutilation. They are all abstractions, and abstraction, we now
know, is a kind of inference. So that, resting on these grounds,
we clearly have got some cause to maintain that judgment is
never separable from reasoning.
16. But there is ground on the other side from which we
might deny this thesis. " Admitted," we might say, " that
every judgment can be turned into a kind of inference by a
suggestion of the opposite, 19 yet all judgments do not undergo
this operation. In the first place the operation may be wholly
circular (cf. Chap. II. 28), and hence illusory; and then,
apart from this objection, in very many cases it does not exist
at all. These cases so far will be free from all reasoning.
And now, passing from this point, let us take in hand a more
real difficulty. We admit that all judgments, though they may
not combine, at least must mutilate ; but it does not follow that
they therefore infer. Mutilation is ambiguous, for you may
perform the operation or may simply accept it. A judgment,
that is, may either start with something given, and by working
on this may extract an isolated and abstract product, and this
would clearly be inference; or on the other hand, instead of
selecting, the judgment may receive. If the original whole has
never been given to the judgment, if the judgment takes up a
foreign suggestion which itself is mutilated, then, although in
conclusion we affirm an abstraction, yet we have not abstracted,
and the result for us will not be a conclusion."
i/. 20 " For," we might continue, " you should consider it
so. You can not reason categorically unless you start with a
given, 21 and unless this given premise contains a judgment.*
If therefore all judgment depended on inference, you never
would get to an ordinary judgment. And the only way in
which to escape this circle, is to begin with judgments that
imply no reasoning. Nor is this impossible, for you may have
a result which involves selection, 22 and yet you may never your
self have selected. An abstracted content can be conveyed to
* This statement must be taken subject to the explanation given in
Chap VI. 15.
440 THE PRINCIPLES OF LOGIC BOOK III. PT. I
your mind, though you have not worked on the raw material.
The testimony received from others is an instance; and then,
apart from the reasoning of other men s intellects, you have
your own senses. Judgment rests in the end on suggestions 23
of sense, and these suggestions are never uniform. For we
do not feel one equable and steady flow, we are not in con
tact with a level surface; the judgment does not come down
unsolicited, and compose at random its spontaneous junctions.
This, if it were possible, would be to reason without reason.
But it is not possible. Before judgment appears there are
prominent points in the suggestions of the senses. A stands
above the level and with it stands B. Together they knock
at the door of judgment, which admits them together and
keeps back the rest. The result may thus present an ideal
synthesis, an intelligible abstraction; but the process is no
selection of the reason. It is bare natural selection, where
the fittest have survived and where the strongest are most fit.
And hence the conclusion, for the intellect, is the work of
chance. The mind has not embraced the persuasion of argu
ment, but has yielded to the insistence and the emphasis of
sense."
1 8. Such is the answer we might make to the claim of
all judgment to stand as inference; and in another Chapter
we shall have to weigh the worth of this denial. But we can
not pause to consider it here, and must be content with a
partial answer to our questions. All judgment is not infer
ence, if m-ere judgment claims a position as inference. So
much is certain. But when asked if judgment does not pre
suppose inference, if in short the two activities are not diverse
stages of a single function, we can not yet give an answer.
We have however shown some reason for considering them as
separate, at least for the present.
Judgment then is not inference, and reasoning is not the
same as intellectual activity. 24 We must now go on to con
sider a narrower claim. Has all Redintegration a right to
assume the title of inference ?
ig. 25 Every reproduction is clearly a function which
starts from a basis and gets a new result. And some repro
duction of course is inference. Where, AB being given, C is
CHAP. Ill GENERAL CHARACTERISTICS OF INFERENCE 44!
supplied and then attributed as a predicate to AB, we have a
kind of reasoning with which we are now familiar. An ideal
whole is produced by a process, and a judgment follows from
this ideal construction. 26 And if redintegration always had
this character, the question if it always might call itself in
ference, could be answered at once and answered affirma
tively.
But there are other reproductions which are far from ap
pearing to possess this character. Redintegration does not
always seem to result in judgment. An object may excite
vague feelings of pleasure or a dim sense of pain, but these
feelings need not be attributed to that object. Their content
is not always taken apart from their existence, and applied to
the thing as one of its adjectives. They may remain my feel
ings, mere psychical phenomena, which are together with the
object but form no part of it. Hence the process has no right
to call itself inference. For it does not end in a judgment ; the
starting-point does not survive in the process, maintaining its
identity and appropriating the difference. We simply pass
from it to another existence which is taken as existing on a
level with the first. This process is on the one hand ideal, 27 in
the sense that it advances on the strength of a connection be
tween universals. But on the other hand it is not logical, since
the universal, brought in by the ideal connection, is not used as
a content which is bestowed upon the original object and par
ticularized by that reference. The universal on the contrary is
allowed to become an independent fact, in which the content
is one with the existence, and where the particular character
is supplied psychologically from my whole state of mind.
There is hence no logical individuation. What unity there is
does not fall within a development of the datum through one
process of change. It falls simply within my feeling self; and
the result is a conjunction which is no connection. 28
It is useless to object that the result in the end may be a
judgment which affirms the existence of this mere conjunction
in my soul. For that result will be no inference from the
original datum. You may say that we certainly have got our
conjunction from the datum, but after all that datum does not
survive in it. And so we have not got a content, we have not
got a predicate, our result is not ideal, nor is it a conclusion.
44 2 THE PRINCIPLES OF LOGIC BOOK III. PT. I
And when starting again from this mere psychical fact you go
on to a judgment, then, let that be an inference, it has not been
inferred from the content we began with. It has come from
a fact whose existence has supervened.
20. This discussion, I fear, may prove hard to follow ;
and the reader who finds more than moderate difficulties, had
better pass on to the following chapter. For we are now
about to raise another question, both important and relevant,
but not essential to the understanding of the sequel. 29
There is an answer we might give to the foregoing section.
Admitted, we might say, that some redintegration exists, the
final result of which is not logical, yet the process itself, with
its immediate product, is still an intellectual inference. All
reproduction will in that case be reasoning.
We objected, in our Chapter on Association, to the formula
we found laid down by Wolff, on the ground that reproduction
went beyond perceptions. And on this very ground we have
just objected to taking the process everywhere in the char
acter of inference. The unity of the process we found might
be other than the individuality of cognition. But a doubt may
now be raised as to whether this result is after all not mis
taken, and it may be urged that, at bottom, the recall and recon
struction are purely intellectual.
Let us try to state this possible contention. It is admitted
on both sides that an object, once accompanied by certain
feelings, may, when it is either reinstated ideally or once again
presented to sense, bring in those feelings. The issue is this
Are the feelings, as such, reproduced or produced ? We have
assumed so far that the former is true, but our assumption
admits of being traversed thus. Feelings, it might be urged,
can not be recalled unless made universals ; and this uncon
scious abstraction suggests the presence of intellectual work.
For suppose that when the object was presented, it, together
with the feeling, engaged our attention. This mere attention
will be apprehension, it will imply selection 30 and rudimentary
judgment, and this alone and by itself will set up between the
elements a logical connection. It will make the whole per
ceptive, so that now, given one part, the rest will follow.
Hence the feelings are recalled as they are for perception, and
that process is inference. They certainly come to us as psy-
CHAP. Ill GENERAL CHARACTERISTICS OF INFERENCE 443
chical facts, but this final result falls outside the inference, and
is a mere psychological addition.
21. Let us further explain. We must remember that
every psychical phenomenon is complex ; for on the one hand
no perception is without some tone of feeling, and every feel
ing on the other hand is partly perceptive, and has a content,
a character, a quality that we recognize. 31 Now suppose that
this perceptive side of the feelings was attended to together
with the object, in that case the object will recall it by reason
ing, and will supplement itself by this inferred content. This
is inference, but it still falls short of what is wanted, for it
does not account for the side of mere feeling. How, it may
be objected, do you get back to that? If you do it by redin
tegration, then, after all and in the end, you have been forced
to admit the reality of what you denied, a reproduction that
was not logical.
And this is the issue. The view, which we are here attempt
ing to work out, would admit that such reproduction would
not be logical, but then it would deny that such reproduction
exists. It would urge in opposition that it is the perceptive
side of the feeling which is reinstated, and that this produces
actual feeling directly and not through reproduction. The per
ceptive side may be particularized first by the psychical con
text into which it is brought, but this is not the point. The
point is that it works directly on the soul, and by that working
causes an actual feeling which is like the original. Thus the
old feeling, as feeling, is in no sense reinstated; but the real
fact is that the soul is such, or has become such, that, without
restoration or redintegration, and by nothing at all but simple
reaction, it responds to the idea with an outcome of feeling.
And, if this account is true, a restriction has saved us. The
feeling is not the conclusion of an inference, but falls wholly
without it as a mere psychical effect. And, if so, the actual
reproduction is purified from feeling, and remains in the char
acter of intellectual connection.
22. I think that this view deserves careful attention, but
I must not be understood as adopting it wholly. It is not that
I doubt the reality of the psychical process which it describes ;
for I am sure that in some cases that process exists, and its
existence has somewhat important bearings. The confusion
/| /| /| THE PRINCIPLES OF LOGIC BOOK III. FT. I
for instance which in English Moral Philosophy besets the
word " motive," arises mainly from a false assumption on this
very point. And that confusion disappears when we dis
tinguish between the idea itself and its psychical effect (cf.
Ethical Studies, Essay VII.).
But it is one thing to hold that a process exists, and it is
another thing to deny the existence of any other possible
process ; and here I hesitate. We might explain perhaps every
phenomenon offered, on the view that reproduction is always
logical. This view in the hands of those who espouse the
cause of the intellect and are champions of its primacy, would
be a weapon perhaps not easy to withstand, and which
would make short work of many difficulties. But then in
some cases the explanation might force the facts. And
again any inference from the universal character of what is
reproduced to the logical nature of the reproductive process,
would appear to me to Ke questionable. The logical is
universal, but I am far from sure that the universal must be
logical.
And I doubt on another point. This simplification might
be premature; for suppose we got down to an ultimate true
doctrine of the relation between the elements of our nature,
and suppose we saw clearly how the intellect stands to the
emotions and the will (if there really is a will) are we
sure that this weapon would any longer be wanted, and that
the difficulties would keep the form that they now wear? To
this doubt 32 I can only allude in passing.
But however we settle the questions just raised, we are
certain of one thing in respect to inference. The mere result
of feeling, not attributed to an object, is never a conclusion.
Whether produced by reinstatement, or not so produced, in
neither case will it come straight from reasoning. For in the
latter case it will fall outside the process, while in the former
case the process is no inference. And with this we may
proceed to another enquiry.
23. A result of mere feeling we saw could not be an in
ference, since it was not ideal. But the result of imagination,
it may now be urged, is often ideal. It may keep itself dis
tinct from mere emotion and desire, and may present us with
CHAP. Ill GENERAL CHARACTERISTICS OF INFERENCE 445
a pure perceptional series. 33 In such a case as this can imagina
tion be called inference ?
We must deal briefly with this question, for it tends to
divert us to matters of great interest which may here be neg
lected. And we may answer at once, No result of mere
imagination can be an inference. It can not be a conclusion,
because it is not a judgment. The production of imagery
may no doubt follow strictly the logical sequence to a certain
point; but there it breaks off. For instance Ab may proceed
to a result of fancy through logical functions b c, c d; but
the result when obtained is now not integrated logically with
A. On the contrary it appears as an individual image D,
and that image is not a predicate of Ab. It certainly stands
in relation with Ab, but it falls into that relation through psy
chical co-existence; 34 and so once more we have conjunction
without connection.
We have no judgment, since the result is mere fact which
exists in the mind, and since it is not a symbolic content
referred away from its own existence. It exists and it stands
in certain relations, but it is not taken as an adjective which is
either true or false. And then the given A, with which we
started, does not survive in the result ; it does not appropriate
the content and use it as its attribute. That content breaks
its logical bond, and, wandering off into the psychical space,
begets by contact with beings external to A an independent
substantive D ; which, itself autonomous, has now a substan
tival relation to A. Hence we have no logical unity in the
object, no ideal individuation.
24. Imagination is certainly not free from logical pro
cesses. Its trains, no doubt, throughout a great part of their
length may consist of the strictest intellectual sequences. They
may contain few images, and but little save the purest sym
bolic ideas. Yet somewhere we find a solution of continuity ;
somewhere the identity of the datum is lost; at some point
we pass from the adjectival content attributed to our basis,
and slide into an image which is not its predicate. And with
this break, wherever it comes, we have left judgment for fancy,
and are not concerned with truth but with psychical fact. 35
It would no doubt be interesting to pursue this enquiry;
but the interest would, I think, in the main not be logical. It
446 THE PRINCIPLES OF LOGIC BOOK III. Pi. I
would in the first place be psychological, and then perhaps
aesthetic. But the broad distinction, that what is merely
imagined is not held to be true, removes imagination from the
province of logic. We shall however be forced to touch again
on this point when we deal with the early development of
reasoning (Chap. VII.).
25. Inference then, so far as we have seen, is an ideal
experiment which procures a result from a given basis. This
result is a judgment in which the new product is predicated
of the given. And in this whole operation we have found that
identity which our Second Book perceived to be essential to
the middle construction. But our enquiry so far has stopped
short of the goal. We are naturally still curious about this
middle process. We still ask Is there not some central iden
tity to be found in this? And we shall take up this question
in Chapter V. ; but, before we can answer it, it is necessary
to inspect our types of inference and to reduce them, if we
can, to some more general form.
ADDITIONAL NOTES
1 Chap. III. The reader is referred here throughout to T. E. I
for what, I hope, is a more correct view of the subject.
2 " Given terminal points " should have been " terminal points that
are given."
3 " This operation." The aspect of "operation" and "ideal experi
ment " certainly belongs to inference, but the essence lies always in
the ideal self-development. Cf. the Notes on the last Chapter, and
see T. E. I.
* " Principle of Identity." Cf. Bk. I. V. and Index. This principle
(the reader should note) is positive. It asserts that any given con
nection of content may be taken as a " law." Hence where (under
change) you infer or assume that the "law" is not counteracted the
old connection still holds under the new conditions.
B " Unconditionally or conditionally." The distinction, I presume,
is between what follows and does not follow from A essentially.
6 "(i) Premises, (ii) Operation." This separation is quite unten
able, unless the " premises " are confined wrongly to the datum, taken
in a narrow sense. See the Index, s. v. Premises, and T. E. I. As to
the Operation, this is not, itself, the " because." Cf. Note 5.
7 " Sameness in spite of a growth of difference." The whole thing,
CHAP. Ill GENERAL CHARACTERISTICS OF INFERENCE 447
I would once more repeat, depends, in a word, on self-development.
8 " The second step." But an ideal whole, containing (in some
sense) all schemata and this schema, is here a necessary "premise."
See on Bk. III. I. II. 6.
9 " Mammals . . . warm-blooded." The subject here is "Man,"
which, in and through an ideal whole, necessarily developes itself as
"warm-blooded." What the subject of an inference really is, does
not of course always appear from the formal statement. See Index,
s. v. Subject.
10 In " accept the difference," " accept " should be " claim."
11 " Simply in my head . . . choice." For " in my head " see on
Bk. III. I. II. 5, and for " arbitrary choice " see ibid. 6. For spatial
construction and Arithmetic, see again ibid.
12 " Our material," i.e. so far as given. Further it is hardly true
to say, in the next paragraph, that " the experiment adds nothing."
But, once more, the real subject of the inference and, on the other
side, the data can not be assumed to be simply the same. And (in
8, paragraph i) it might be well perhaps to insert "mere" before
" alien imposition."
13 For all these processes see the Notes on the preceding Chapter.
14 The " simple field of possibilities " ought to include an ignoring
of anything outside (see on Bk. III. I. II. 25). In the present Section
the question as to what really is the subject, is again neglected. On
Disjunctive Inference, including "rejected suggestion," see again ibid.
15 Judgment and Inference. On this difficult question the reader
is referred to T. E. II. Its treatment here is not satisfactory. Cf.
Bk. III. I. VI. II foil.
What I should have said here is (i) that a judgment certainly need
not be mediated in form; and that (ii), so far as it involves mediation,
this mediation, to make it an inference, must be a necessary self-
development under one of our heads. The mediation otherwise is
psychological, and is not logical. But see on Bk. III. I. VI. 15.
16 The first question put here is, " If you take inference as it has
been taken so far, is it implied in all judgment?" The second ques
tion is, " Can you take inference otherwise, so as to say that in all
judgment it is present?" To this the reply given here is No. For
(a) an " operation " is not an inference, if that operation remains
external and the subject is not self-developed. And (b) you can not
avoid that result by trying to include, within the subject itself, an
external operation.
17 For " suggestion," see the Index, s. v. Suggestion.
18 For the Hypothetical Judgment see on Bk. III. I. II. 18.
19 " Suggestion of the opposite." Cf. ibid. 27, and see ibid.,
Note 24.
20 On the whole subject of 17 see the references given above in
Note 15.
21 " Unless you start with a given." See on Bk. III. I. IV. 15, and
the Index, s. v. Premises.
THE PRINCIPLES OF LOGIC BOOK III. Px. I
22 " Selection." See Index, s. v. Judgment, and Selection.
23 It is certainly an error to speak of a mere suggestion, whether
from another mind or from one s own senses. No mere suggestion
is possible in fact. Any suggestion is really such because of the
mental world which receives and appropriates it. And the issuing
judgment, depending thus necessarily on an implied whole, is so far
always an inference. Certainly, so far as the particular conclusion
is due to force, the judgment becomes, so far, more impure. It con
tains and is based on a greater amount of external and unknown
conditions. But the aspect of mediation remains unfailingly, and the
"mere judgment" (of 18) is no more than an erroneous abstraction.
On the whole subject see T. E. II.
24 " Judgment then . . . activity." I should have inserted after
" then," and, again, after " reasoning," the qualification " so far."
" Intellectual " is used here in the sense of " logical." See Note 27,
and the Index, s. v. Logical.
25 Sections 19-24 possess, I think, a real importance, such as to
deserve the close attention of the reader. On the subject of them I
would venture to refer him to Mind, O. S., No. 47, and to Essays,
Index, s. v. Inference.
26 " This ideal construction." Add " as is stated more accurately
lower down in this Section."
27 For " ideal " and " universal " see the Index, s. v. Association and
Universal. For " logical " cf . 22. A process is logical where it has
an object which, as a subject, is therein and thereby self -developed
ideally.
28 The connection is always ideal and through universals, but, none
the less, the process at its end may re-particularize itself not as truth
but as fact. Hence in the result not only may the logical identity
be broken, but this result may even cease altogether to be before
us as "objective." The process, that is, where still "objective," may
in the end present us, not with a truth about our first object, but with
another objective fact. Or, again, the process may even result in
something which, wholly or partly, is not any object before us at all,
but is, on the contrary, felt as our mere emotional state. We have
here neither (a) a truth about our original object, nor (b) have we
a mere change of object, with a consequent breach of logical identity.
We have ended (c) in what may, in this connection, be called a bare
psychical fact.
29 The interesting question, noticed here (in 20-22) hardly tends,
I think, however it is answered, to affect the general conclusion. I
have touched on the subject again in Mind, O. S., No. 47, and N. S.,
No. 33 (in the last few pages of that article).
30 For " selection " see Note 22.
31 " A quality that we recognize." Add " or may recognize."
32 " To this doubt." The meaning is that the intellect is only one
specification and result of our general nature and its laws. The in
tellect therefore can not in the end be taken as something apart. I
returned to this point in Mind, O. S., No. 47.
CHAP. Ill GENERAL CHARACTERISTICS OF INFERENCE 449
33 " A pure perceptional series," i.e. a series that is before us
and in this sense is genuinely " objective."
34 " Through psychical co-existence." Add " or at least through
some connection which is not logical."
35 1 have treated Imagination here only from the negative side
and as mere wandering fancy. Of this we certainly can say that the
result is not the ideal predicate of a subject which developes itself
throughout. You can therefore for logical purposes treat the process
as a simple failure and as merely psychical. And so much is all that
needed here to be said. This " solution of continuity " which I
noted is of course always possible, and is the main reason for that
general fallibility to which in a later context I called attention
(Bk. III. II. III. 24).
We may, however, remark that even " uncontrolled " fancy brings
an object before us, and so far is "objective." And imagination,
when " controlled " in a certain way, becomes at once strictly logical
and is itself the same as "thought." (See Mind, O. S., No. 47, and
Essays, pp. 362-5.) Imagination, again, otherwise controlled, be
comes what we may call " aesthetic." Here again we have an ideal
development which must be called " objective," though on the other
hand it is not in the proper sense logical. In none of the above
cases can the process (when we speak strictly) be regarded as merely
psychical. Any implication or statement, made to the contrary in
this work, is certainly wrong, and is connected with the more general
error as to the existence of " mere ideas " that in no sense claim to be
real (see on Bk. I. I. 10). But aesthetic "imagination" (to take that
instance), like logical "thought," abstracts and must abstract always
from the psychical aspect of its process. Every process is necessary ;
but the necessity of the psychical series is other than that which is
aesthetic or logical or again ethical, all of which (by virtue of what
controls them and constitutes them) must be called superior.
The result of aesthetic imagination (we must remember) is not in
the narrow sense true. That result is not the adjective and predicate
of a subject which has developed itself in a merely ideal form. The
aesthetic product is true only in the wider sense of an idea which is
also a real object. But, because the aesthetic object must be called
self-existent and real, it therefore, though ideal, is not true. It has
more than belongs to any truth when truth is taken logically. But
on this subject see further T. E. II.
E
CHAPTER IV
THE MAIN TYPES OF INFERENCE
I. In our Second Chapter we detailed a number of intel
lectual processes, all claiming to be inferences. These pro
cesses present us with many varieties of that middle operation,
which we have seen is one essential part of reasoning. In the
present Chapter we are to neglect many questions. We are not,
for instance, to say anything about the validity of these
processes, nor to attempt to reach their ultimate nature. We
shall be content, if we can show throughout their detail two
or three main types of ideal experiment.
There are two general classes x we can at once point out.
The operations we mentioned seem to fall under the heads
of synthetical construction and analytic elimination. We may
at least say of these, that we find no inference which does not
contain one of them.
2. In that form of reasoning which is most familiar we
verify the presence of both these activities. Thus from A B
B C we go by a synthesis to A B C, and then use
elimination to bring out A C. The preparation which pre
cedes the final intuition, has thus two aspects. But on the
other hand this does not seem 2 to hold good with all types of
inference. When for instance we argue without elision to a
new quality of the whole (as was the case when we discovered
our island), we seem to employ construction alone; and in
abstraction again we do not seem to use construction at all.
There is no apparent synthesis when we analyze the given, and
eliding one part then predicate the residue. Yet this is not
the point we are at present concerned with. To ask whether,
and in what sense, the isolated employment of one function
is possible, would here be premature, and at present we may
be satisfied if one of these processes can be discovered every
where. We shall proceed to assign our list of operations each
to one head, but must not be understood to exclude it from the
450
CHAP. IV THE MAIN TYPES OF INFERENCE 451
other. Thus we shall call an inference synthesis or analysis,
according as each type appears more prominent in each case.
3. (A) Let us begin with construction and see what
processes will fall naturally under this, (i) Those syntheses
of relations which group themselves round an identical centre,
will take the first place. Whether they end in a new internal
relation, or remain joined in one whole, or proceed to a new
quality, in each case their most prominent aspect is synthesis.
The first class of constructions are those which are based on
an explicit identity, which so to speak forces the extremes
together.
As compared with these all the rest seem arbitrary. For
we have in none the bond of a given centre, while in some it
is doubtful if any kind of centre exists. The ideal unity is not
anywhere prescribed to us beforehand. In some cases it looks
as if the operation were capricious; and it is a question, to
which we must hereafter return, how far the conclusion can
stand either with or without this operation. Since at present
these constructions seem not necessary like the first, since their
middle term, if they have one, appears our mere choice, we
may distinguish them here as arbitrary syntheses. 3
4. As such (ii) we recognize addition in Arithmetic, and
the geometrical extension of figures. 4 In each, under differ
ences, we find the same process of free rearrangement. I
obtain a result by composition of elements, and that result is
held true of the elements themselves. The same holds with
Comparison. There I bring the terms together, I unite them
under a certain aspect, and I then see a quality which I pro
ceed at once to predicate of these terms. In the process of
Recognition I may seem less at liberty, and still less free in
Dialectic reasoning; but in both cases the main feature is the
construction of a whole a construction round a centre, which
is not given, into an unity not prescribed by the premises.
5. Our material so far has arranged itself under the head
of Construction ; and the synthesis seemed in some cases to
be necessary and in others arbitrary. We pass next to the
consideration of that other main type which is the counterpart
of the first.
(B) The essence of analysis consists in the division of a
given totality, and in the predication of either the whole or
452 THE PRINCIPLES OF LOGIC BOOK III. PT. I
part of the discrete result. In the latter case the presence of
Elision is manifest, but even in the former it is to be recog
nized. When reality first appears as a whole and then as a
number of divided units, something certainly is gained but
something else is eliminated. For the aspect of continuity or
unity is left out ; and thus mere analysis always involves and
must involve some elision.
The first example of this class may be found in Abstrac
tion. We are burnt, and proceed from this experience to the
result, Fire burns. We have first reality as giving the whole
complex, we have next the elimination of all content, save two
elements in connection, we have thirdly the predication of this
residue; Fire burning is real. The validity of the process is
open to grave doubt, but it consists in analysis followed by
elision.
Arithmetical subtraction shows the same features. Reality
gives us an integer five. We then divide this into units, and,
removing two of them, get an integer three, which we predi
cate of reality. And we assume here once more that the units
are not altered by the disruption of their context. This as
sumption may be false, but the process is clearly one of
elision.
In Distinction we seem to have a new variety, but we still
may find the same general outline. We are presented with
elements which are taken as one. Altogether, or with refer
ence to a part of their content, they come before us as a whole,
obscure no doubt but still unbroken. In the result of the
operation this whole has vanished. A and B fall apart and
appear as divided, entirely or in respect of one or more attri
butes ; and then this result is attributed to the original reality.
We shall once more neglect the suspicion which such an as
sumption excites. Confining ourselves to the general char
acter of the operation employed, we are able again to verify
our type. A totality is divided by a function of analysis, and
ignored in the product by an act of elimination.
6. We have seen so far that all our examples fall under
two heads. Can we advance to the conclusion that inference
consists in two main processes, construction and elision? Our
way is barred by an unforeseen obstacle ; for we have not yet
dealt with Disjunctive reasoning. 5 And it is impossible to
CHAP. IV THE MAIN TYPES OF INFERENCE 453
reduce this wholly to either process or to a mixture of both.
Both indeed are concerned in it, but they do not exhaust it.
If the alternatives are given us with an explicit statement
of their reciprocal exclusion, and of the sequence of each from
the absence of the other, in that case we do not find a new
principle of reasoning. For one of our data removes a pos
sibility, and that removal does, by virtue of another datum,
assert the remaining possibility as fact. In " A is b or c " and
" A is not-c/ by combining our premises we bring in not-c,
and so banish c; and, this affirmation of not-c being elided,
we can then join b directly to A. Thus where the " or " is
explicit, we have nothing which falls outside our two prin
ciples.
But suppose we start with possibilities not given as strict
alternatives. If, for instance, A may be b, and again may be
c, and can be nothing else; and if we further suppose that A
is not c, what conclusion can we draw ? Can we go to There
fore A must be b? We do indeed make this advance, but the
advance is made on the strength of the fresh assumption that
any unopposed possibility is real. And this means a new
principle. 6 For here what we predicate is not the residue of
truth, but the remainder of chance. We attribute to the real,
not something first given and then worked upon by our act,
but an issue from premises which afford nothing positive. We
do not go simply from the mutilation of a whole to the accept
ance of a part, but we also leap from the possibility of that part
to its unconditional existence. This principle, which we before
had need to mention (Chap. II. 26), and which will engage
us hereafter, will not fall under the head of either analysis or
synthesis.
7. Disjunctive reasoning may employ all three processes,
but it certainly need not do this. Where alternatives are
explicit, we have seen that it is content with the use of two.
And there is another instance 7 where two are enough. For
where the process is ponendo tollens where from " A may be
b, and A may be c (though not both), but A is c" we advance
on the strength of an ideal synthesis to " A excludes b " we
are not forced to cross from the possible to the actual. We
remain in the latter, and the exclusion of the possible is, as
such, no real quality of A (vid. Book I. Chap. III.). 8
454 THE PRINCIPLES OF LOGIC BOOK III. PT. I
But in other cases three movements may be seen. The
argument constructs and then eliminates ; and in the end the
residue is predicated with a vital change in its character.
Under this general type, which calls in the third movement,
we may point out several varieties.
In the first of these (6) the possibilities are given, not as
explicit alternatives, and yet as together exhausting the subject ;
and also along with these possibilities may be given the actual
exclusion of one. This is the first variety. In another we
are left to make a complete exhaustion for ourselves; and
again in another we may have no possibilities given us, and
may even have no statement of exclusion. In this last extreme
case we are reduced to operate with mere suggestions. 9 Thus
if on trial b is found possible, and A excludes the suggested
c, d, and e, and if in the end we can find nothing else which
we are able to suggest then we advance to the conclusion, A
must be b. We have conjoined b with A, have eliminated the
rest, and have boldly leapt from " may be " to " must be."
Here the exhaustion was not guaranteed, nor the exclusion
given. Our datum was A ; and it was we ourselves who con-
.structed the whole, assumed its completeness, elided one part,
and then sprang to the actuality of our product.
In all these latter varieties of disjunctive reasoning, we
have first synthesis and then elimination, the whole consum
mated thirdly by a transition to fact from mere possibility.
8. In this last section we have already provided for
Apagogic inferences (Chap. II. 29), and have finished our
rapid survey of the principal classes of reasoning. We may
now present the result in a tabular form, asking the reader to
bear in mind one thing. He must remember that, when a
process is referred to one head, he is not to assume that the
other type is absent. We are to class each operation by its
more prominent feature, and to neglect for the moment our
additional step from the possible to the actual.
A. Construction.
(i) Where the whole is made] (a) necessarily. 1
out of the datum ( (/?) arbitrarily. 2
(ii) Where the whole is made ) () necessarily. 31
beyond the datum j ( /5 ) arbitrarily. 4
CHAP. IV THE MAIN TYPES OF INFERENCE 455
B. Eliminative analysis.
Where, the whole being given, ) (a) necessary. 5
the elision is f ( /? ) arbitrary. 6
We may enumerate the processes here presented. We have
in No. i the three-term inference which we first discussed. In
No. 2 we find addition and comparison. No. 3 gives us recog
nition and dialectic movement. With No. 4 we reach deter
mination (positive or negative) by means of a suggested pos
sible synthesis. Thence we come in No. 5 to that disjunctive
reasoning where the possibilities are independent and one is
excluded. Then No. 6 closes the rear with abstraction, dis
tinction, and arithmetical subtraction.
We may append three remarks. The first of these is that
the Hypothetic judgment 10 may be assigned to No. 3. It may
be said, no doubt, that we are at liberty not to suppose; but
then on the other hand we also elsewhere are free not to think.
The premise is a datum not given as real ; I treat it logically,
and thus get a result which I conditionally predicate. But
nothing here is my choice, save the resolve to suppose and
then to see what logically comes. But so much choice as this
seems to exist in all reasoning, since everywhere it lies with
ourselves at least to think or not to think.
In the second place addition and subtraction will be neces
sary where the quantities are given marked with plus or minus.
But their result in this case is hypothetical. The signs do
not belong to the nature of the quantities (Chap. II. 6 and
10). And the reader must remember that free spatial re
arrangement falls under the heads of 2 and 6.
And the third remark we have to make is this. The
process of suggesting possible predicates, and of then proving
one by excluding the others, may be regarded as a mixture
of Nos. 4 and 5 ; it is not worth while to place it in a class
by itself.
We may end by stating briefly the conclusion of this
Chapter. The middle operation of every inference consists of
analysis or synthesis, or both; and in certain cases it invokes
besides an additional principle.
456 THE PRINCIPLES OF LOGIC BOOK III. FT. I
ADDITIONAL NOTES
1 " Two general classes." See further in Chap. VI.
?< " Does not seem " should be " does not at least seem."
3 " Arbitrary syntheses." Cf . the next Chapter, i and 2. The
syntheses are arbitrary in the sense that the points of connection, from
which the particular construction follows, are not given. On the other
hand we must remember that the ideal whole on which any and every
inference depends is never itself given completely. See on Bk. III. I.
II. 6.
4 For the processes mentioned, in 4 and 5, see the Index. And,
for Elision and Elimination, see further on Bk. III. I. II, Notes 21
and 22.
5 Disjunctive Reasoning. The account given here (in 6 and 7)
is to a considerable extent wrong. For correction in the main, see
Bk. III. I. II, Note 24.
6 "A new principle." See the Index, s. v. Possible; and, for the
error here, see the reference given in Note 5. The reader will note that,
for anything to be possible, it must be connected with the Real by
some ground. Hence, if all counter-grounds are removed, it is con
nected forthwith as actual to say nothing of any fresh positive support
that it has now gained. See, once more, ibid. And cf. T. E. XL
7 " And there is another instance, etc." But is the inference here
really disjunctive? To make it so strictly, would you not have, at least
practically, to include all possibilities, other than c, under &?
8 " No real quality of A." But see on Bk. I. III. 13.
9 " In this last . . . suggestions." For this error, see Bk. I. I. II,
Note 24.
10 " The Hypothetic judgment." The inference itself here is neces
sary, though not the whole process. From "A(x)b, b-c," you can not,
that is, reach " A is c," unless you have been able to remove the x.
For the Hypothetic Judgment see T. E. II, and on the nature o
Supposal see Bk. I. II, Note 40.
CHAPTER V
ANOTHER FEATURE OF INFERENCE 1
I. We must search into the nature of these general
processes, but there is a question which presses for immediate
answer in the present Chapter. We supposed first of all that
every inference was a construction round an identical centre.
We have since then discovered that reasoning demands a self
same subject, that appropriates the difference got by the ex
periment. But we must return to examine the middle opera
tion, the experiment itself. We now know that our first sup
position needs correction, since the experiment is not always
a construction through a given identity. But this result does
not satisfy us. We want to know if our middle process
can ever dispense with all identity. There clearly is not
always an explicit common term ; and when this fails shall we
say that everything has failed? Or can we still say, there is
an implicit centre, unavowed but active ? Our instinct leads us
to embrace this latter suggestion.
2. But how shall we support it ? There is obviously
some unity in the operation, but it is doubtful if this will give
us what we want. Mere togetherness (so to speak) before the
mind is clearly insufficient ; and we must hence take the mind
itself as a centre, not given but used, and see if on this line
we can make an advance. We may say, " In all relations,
where the terms are able to be separated in idea, the relation
may be considered as an interrelation. 2 The result is an infer
ence, a putting together of elements which before that infer
ence existed apart. And since those elements were all related
to one mind, and because of that unity now come together, the
mind may be taken as a common centre of interrelation." Is
this what we want? We must answer in the negative; for
though I believe it to be true, and a truth whose importance
can hardly be exaggerated, yet in its abstract form it is simply
irrelevant. It tells us that some relation of some kind exists
457
THE PRINCIPLES OF LOGIC BOOK III. PT. I
between all objects of thought, and that they are all inter
related. But then this knowledge must fall outside of any
special inference. Thus A and B are called equal 3 because I
have compared them; but, before I compared them, I might
have known that some relation must exist between them ; and
this knowledge is therefore not the reason why I now know
that they are equal.
3. From mere interrelation you can make no passage to
a special relation. It does not matter how actively the mind
may work; you may suppose an intense appreciation of the
fact that we have a common term in the mind ; you may postu
late any degree of attention, or the preferential application
of the intellect to this fact yet from these general premises
you never will get to the particular conclusion. For the centre
of the operation, if we are to find it at all, must be found in
the unity of that special operation. We can not settle such
a point by abstract reflections, which at the most serve to raise
a vague presumption in our favour. If we wish to exhibit the
identity in our processes, we must be prepared to show the
central point in each particular case.
4. Let us start with what we called Recognition and
Dialectic. The given here is Ay, and the mind meets this
with a function y-S, which extends A to 8. The central point
is here obviously y ; and round this point, and by virtue of its
identity, A and 8 are brought together. We must notice how
ever that y-8 is not given, and further that y-S may never be
explicit. Our consciousness may pass straight from Ay to 8.
It may never suspect the presence of that common middle
term on which everything depends. Hence we might say that
we have subsumed the original datum under a function of syn
thesis, which never appears except in its effects ; but this
statement would be incorrect, since the process is not a sub-
sumption at all. It is a construction by means of a hidden
centre.
This seems tolerably clear, and it gives us a principle to
which we must hold. But in its further application the truth
becomes much more difficult to see.
5. If we consider the operations of Comparison and
Distinction,* we are at first unable to perceive any middle.
The mind, we may say, is the point which compares, and the
CHAP. V ANOTHER FEATURE OF INFERENCE 459
centre which separates ; but such a mere generality, how
ever important, we agreed was not the answer that is
wanted. The question is whether in the process itself we can
find a special interrelation; and we shall now make this
attempt.
Both the processes exhibit a double aspect of unity and
diversity. In Comparison this fact is at once apparent. In
" A = B " we have of course the differences of A and B.
These differences are held together in relation, and are com
bined on the strength of a common point, since the quantity of
A and B is the same. Thus the relation of each difference,
A and B, to an identical quantity is the very ground of their
interrelation. Take that third term away, and the connection
vanishes ; reproduce it, and the mind requires nothing else in
order once more to construct the relation.
But is it so too with Distinction ? Take for instance, " A
is not equal to B," and where is the third term? I answer,
It is there, though we do not perceive it. For consider the case
thus; A and B, it is certain, are still related, since they are
taken as different ; and their difference is not abstract but
specific and definite. It is as quantities that we fail to find
them identical. But, this being grasped, observe what follows.
Just as the general perception of difference implies a mind
which distinguishes, and which serves in some vague character
as the base which supports that general relation 5 so it is with
every special difference. What is true in general will prove
true in particular. All objects of our thought in the first
place must have some relation because, as our objects, they are
all identical ; and again every distinction of special qualities,
such as sounds or colours, takes place on the basis of a special
community. For instance, the separation of red from blue
must imply the unconscious taking of each as a colour ; and that
felt common quality is the basis upon which the separation is
effected. It is thus too with quantities. A and B are per
ceived to be unequal, but inequality presupposes that both have
quantity. In this they are the same, and it is because of this
point that they can be seen as unequal. Thus identity in
regard to the possession of quantity is here the third term that
was required, and it is relation to this centre which inter
relates the quantitative differences. In short distinction can
460 THE PRINCIPLES OF LOGIC BOOK III. PT. I
never be effected except within an area of sameness; and,
once outside this area and common meeting-ground, the rela
tion would vanish.
6. Perception of identity and perception of difference
are two modes of one function or two functions of one process.
The result in both cases depends on a synthesis of diversity
with unity, but with this likeness there goes a striking con
trast. Take first Comparison. Here we start with the dif
ference, and at the end this difference has been partially lost,
and the identity of the terms has become explicit. 6 It is other
wise with Distinction. We begin here with a vague and undis
criminated unity, but in the conclusion the differences appear,
and the identity has passed away from our sight. In both
processes alike the sameness of the terms is the middle point
from which everything hangs; but that centre is used in two
diverse ways. In the case of Comparison it is the receptive
identity which, standing opposite to external differences, takes
them into itself. Content with a partial recognition of its
power, satisfied with a declaration made by the differents that
in some point they are the same, the unity slurs the remainder
of diversity, and becomes the mere relation of similars. But
the process of Distinction shows a contrast to this. The iden
tity here turns against its own unseen differences, and makes
them explicit. It pronounces the relation which sunders them
apart, and is led, by the emphasis of this its own activity, to
forget its own being. Thus the differents appear as indepen
dent varieties, which subsist and form relations in a passive
atmosphere. 7 The identity which has generated them, which
separates and supports them, is slurred even more than in the
former case diversity was slurred by Comparison. We might
say that one tends to think less of the relatives and more of
the relation; while the other quite sinks the active relation,
and keeps its eye on the terms related.
7. In the ensuing Chapter we shall return to this point,
but at present we may try to develope our meaning. In Com
parison and in Distinction we employ certain functions, and
you might say incorrectly that these processes consist in
subsuming the given under certain activities. What are these
activities? In a clumsy fashion we may represent them as
follows. 8 In Comparison we apply to the original datum,
CHAP. V ANOTHER FEATURE OF INFERENCE 461
X
A and B, a function of synthesis, /\ . Through the pos-
a b
session by A and B of the qualities a and b, we unite them in
relation to our common point X. The result may be depicted
x
as /\ ; but, since the unity is degraded and becomes a
A B
relation, the conclusion which appears is simply A B.
For Distinction we must bring in another formula. We
may be said to start with a vague totality, in which is latent
an internal diversity; and we may represent this datum as
X x
/\ . To this unity we apply a function of analysis /\ .
a b A B
Then on the one hand X, now identified with x, becomes less
visible ; while, as this fades away, the other side appears, and
a and b, developed by the application of the function, appear
x
as A and B. The immediate result is /\^ , but, since x is
A B
wholly slurred, A and B fall apart as separate facts which
show a distinction.
8. It would be interesting to enter into the finer meta
physical detail of these processes; but we can afford no more
than a mere passing remark in protest against an obstinate
prejudice. In answer to the doctrine that sameness and di
versity imply one another, at least -when perceived, we shall
be told that Difference is independent, and derives its origin
from the shock of change. And for the apprehension of this
shock, it will be added, no activity is required. Thus we have
no ideal operation at all, and may so dispense with the illusion
of an ideal unity. But this objection, I must reply, depends
upon a complete mistake. It partly confuses feeling with per
ception, and partly is wholly wrong about feeling. I will
take the second of these points first.
If a shock is intended to be felt as a shock (and I suppose
it must be so intended), then the feeling must be compound.
There must be some feeling to start with, in collision with
which the inrush of new feeling disturbs the mind. For if the
462 THE PRINCIPLES OF LOGIC BOOK III. PT. I
place were quite empty the new arrival might appear, but
could hardly make a striking sensation. Thus the shock pre
supposes another element, and it implies the felt relation
of both. 9 But, if so, once more we have found in this relation
a point of identity, a common sameness not of perception but
of feeling. In other words it will be the continuity of the
feeling which makes us sensible of the change and the shock ;
and this is our first point.
But we have not yet reached the perception of change, and
the failure to see this is the second point of error. Think
what you like about the felt shock, you are yet a long way
from the consciousness of difference, and you can not advance
without calling in an ideal identity. Take a sensation A, and
let it change to a wholly different C. This will give you the
succession of two psychical events, but not the perceived rela
tion of change, and the question is how this relation can be
given. It can not be given without retention, 10 and retention
is not possible unless what precedes and what follows possess
some point in common. But let AB (for example) be followed
by BC, and the problem is solved. Here the identical B
redintegrates A; or (if you prefer to say so) the retention of
AB gives us A with a point in common with C ; and, in either
B
case, we have a result which we may write /\ . No change
A C
can be perceived unless by means of an ideal continuity.
9. This ideal identity is a necessary element in the per
ception of difference. Without such a centre the extremes
would never be held together, and their relation would never
come before the mind. We may represent as follows the mode
^
in which this unity operates. In a whole , , as it passes
before us, the difference be is not at first noticed. Hence we
do not perceive b and c to be discrepant, till we try to identify
them. 11 But, in going from A& on to Ac, the self-same A
reproduces b, which, thus forced upon us in identity with c, is
rejected by it ; and then, A retiring from view, we perceive the
difference as B against C.
How then do we become aware of identity? We must
have differences Ba and Da, and we must feel, when we pass
CHAP. V ANOTHER FEATURE OF INFERENCE 463
from one to the other, that they are not all different. This
feeling comes from the presence of a, which is not yet explicit.
It rises to explicitness, through the reproduction of B, and
the consequent collision of B with D. By means of the alter
nate rejection of these discrepants, the common identity a is
set free; and the relation of similarity between B and D is
brought clearly before the mind. We may be said to begin
with an implicit sameness, then, by working with that, to make
our implicit difference visible, and from this visible difference
to return back to sameness, bringing out in our movement a
relation of similarity, and perhaps in addition a seen and ex
plicit point of identity.
We can not further pursue these enquiries. For our object
is attained if we have succeeded in showing that, alike in
Distinction and in Comparison, we obtain our result by an
active centre which stands in relation with both the extremes.
10. After leaving the perceptions of sameness and dif
ference, we come next to the processes which depend on these
perceptions. There are a number of remaining inferences which
consist in re-arrangement, in the new grouping of elements
within a whole. And here we may make a broad distinction.
If our fresh distribution starts from analysis, then the process
falls throughout within that whole which is given us at the
start, 12 and this whole will be the unity, relation to which
interrelates the elements. But if on the other hand our re
arrangement demands a construction outside the original datum
if, that is, we must first extend what is given by addition of
fresh elements, before we are able to find our conclusion in
this case our datum is not the whole required. 13 The entire
ultimate construction implies a fixed ideal centre of its own,
and the extension and re-arrangement will therefore take place
within a whole which includes our datum, a whole which,
though invisible, still is active. We must apply this general
truth to our detail.
ii. If we consider the free construction of elements in
space, we find at once that this movement implies a centre of
identity. Unless the extended parts that we deal with came
into one whole, our process would be nugatory. We should
begin and end with mere isolated fragments, indifferent to each
other, neither united nor yet sundered by spatial relations.
464 THE PRINCIPLES OF LOGIC BOOK III. Px. I
Our conclusion implies that the elements, we begin with, are
members of one space. But, if they belong to one extended
whole, they either must have identical points, or must all be
connected with some common centre. So much is clear, and
will perhaps be admitted. On the other hand a serious dif
ference of opinion would at once arise, if we asked where the
middle of space can be found. Is all motion merely relative?
Is there again an actual existing centre by which all else
is determined? Or is not this point of reference n^rely ideal,
something that does not and indeed can not exist? But we
need not answer these questions here. It is enough if we agree
that all spatial grouping, perceived or imagined, implies some
kind of common focus, whether that focus be before us
explicitly, or whether it be a mere unconscious implication.
But, if so, it is clear that our new relation springs from
interrelation, and depends upon a point of identity.
12. And the same thing holds when we come to Arith
metic. When an integer is divided the analysis takes place
within the limits of that unity, and the elements are separated
from that centre of dispersion. The point of interrelation
no doubt disappears in the product which we see. It becomes
invisible; but if you removed it wholly, you would find that
your discrete units had vanished. They would in this case have
lost the common relation which keeps them apart, and gives
them their show of independence. But just as here con
tinuity is active in the production of discretion, so again, when
the discrete returns once more to explicit oneness, an implicit
continuum is presupposed. If the units had no relation to a
common centre, they never could be added. Let us consider
this last statement.
Even if we adopt an erroneous view, the truth of our
statement will still be plain. Let us suppose that the units
have no relation amongst themselves, but are simply pushed
together by the action of the mind, or fall together in the
mental space. But, in the latter case, how could they all fall
towards one point, if they were not co-partners of one spatial
world? And how once more could that world be single, if
it had not got some kind of centre? And, in the former case,
where we suppose that the mind is an external agent which
forces the unity, it surely could not act upon all the units
CHAP. V ANOTHER FEATURE OF INFERENCE 465
unless each single unit were related to this one operator. Nor
again would this one special operation be performed, were it
not that the agent stood in one special attitude to all the pieces
of material. So that, even if we accept such mistaken views
about addition, we are still compelled to believe in an inter
relation.
But in reality the units are not independent, nor need we
invoke external violence to crush them together. For they
arise and they consist in the suppression of an integer, and
would not be many if they were not thus one. Their relation
to each other is the degraded form in which their ideal con
tinuity is manifest ; and, when we think out this onesided ap
pearance, we are forced to advance. The discretion of the
units implies a connection of each with an unseen centre of
repulsion ; but that means on the other hand their common
interrelation by virtue of this unity, which so reappears as the
integral whole in which they subsist. We can see this even
when we take at haphazard a number of units and increase it
at our pleasure. I will not ask how we are able to do this,
though the answer to that question might help us forward.
Suppose that somehow the new unit is got. Yet, before it is
added, it must have a relation to the units that exist ; and this
relation implies a common world of number, 1 * and a central
point. If this were not present the mind could not add; and
therefore the addition makes explicit an ideal unity which was
active though latent. It is on the strength of this idea that
the mind can work and can make the idea visible. Con
tinuity is no ghost, that is laid in the units and conjured up to
surprise us in the integer; it is the soul which unseen is felt
in the limbs, and returns to the centre with a fuller life.
I3. 15 Abstraction is the process which next claims our
attention. It first involves a function of analysis. In A we
distinguish b, c, and d, and we may say that we start from a
x
datum x\ and then proceed to a result /fX - This, we
b c d
know already, has been got by means of an identical centre
and still implies it, for the unity A has been sunk but
survives.
Let us proceed to the next step. We take b-c-d, and re-
466 THE PRINCIPLES OF LOGIC BOOK III. PT. I
arrange these elements, and so get, by fresh grouping, b-c on
one hand and d on the other; thus, b-c \ d. Now identify
the b-c and the d in / \ with the last-gained result, and
bcd
bc
we reach the conclusion x( > where each relation to *
\d
seems independent of the other. One or more of the elements,
which analysis showed within the whole, are identified with
elements that appear outside the whole, or are independent of
it. We have here Subtraction or the Method of Difference.
But our process still implies a centre of identity, since the
grouping, whether it conjoins or separates, must be carried
on from one common point of attraction or repulsion. That
point however will, according to the case, be manifest or in
visible.
14. And coming in the end to Disjunctive Reasoning,
under which head falls the Apagogic Method, we may verify
once more our general law. Where the possibilities are given
us within the unity of the given subject A, it is solely because
they are identified in this, that b, c, and d are found to be dis
crepant. 16 Their relation to this centre thus interrelates them.
And, in the further operation of removing one part so as to
predicate the residue, our construction and subsequent elimina
tion must rest on the basis of an ideal mid-point. We have
discussed this already by anticipation, and it is not worth
while to repeat the argument.
When once more the possibilities of A are not given us,
and when we make them ourselves by a free suggestion, 17 then
so far the process is constructive synthesis. We should not
think of c or d in connection with A, if there were no reason
for their appearance. And the reason lies in common points
of sameness y and 8. It is on the strength of these that c and
d are connected with A, and when we find that the suggested
connection will not hold, we can discover that it was a mis
taken inference upon the ground of identity.
15. The result of this perhaps too brief survey may be
summed up thus. Not only does inference preserve an iden
tity throughout the whole process, but in the actual experiment
itself we rest upon a central sameness. There is a point of
CHAP. V ANOTHER FEATURE OF INFERENCE 467
unity in every operation, and each special operation has a
special point of unity. We have thus recovered that earliest
view with respect to inference, which seemed torn away from
us. But it does not return intact. We cari not call the con
clusion in all respects the necessary outcome, and we have not
got a given point in two given relations, which thus inter
relates them to form our conclusion. That conclusion in some
cases, we have seen, is not made unless we choose to make it ; 18
and the arbitrary character inherent in these processes gives
rise to doubt and to grave suspicion. In the Second Part of
this present Book these doubts will be considered; but we
must first endeavour more exactly to apprehend the operations
we have just been passing in review.
ADDITIONAL NOTES
1 The main point insisted on in this Chapter is that all inference
depends on a whole, which not only is ideal, but is also individual
and special ; and that by this alone is secured that identity of the
middle without which is no inference. And, so far, the Chapter seems
satisfactory. On the other hand we must remind ourselves that the
required ideal whole is not anywhere (even in Analysis) given in the
stated premises. In inference we can not in one sense pass beyond
our datum, since we must keep to self-development. But, on the
other hand, if there is to be development at all, the datum must in a
sense be transcended. We, in other words, require, for a conclusion,
something in addition, while, if that something is merely added,
the whole inference is destroyed. But to leave this main principle
the question as to how much is contained, in each case, within
the premises given, and how much, in each case, must be supplied
from elsewhere, is a matter of detail. The whole problem is dealt
with in T. E. I ; also cf. the Notes on the last three Chapters, as also
the Index, s. v. Premise. The reader will notice that the formulas
used in this Chapter are subject, in accordance with the above, to
correction throughout.
2 " In all relations . . . interrelation." It would be better to have
said " In the case of any relation, where you can start with the
terms as separate, the resulting relation can be taken as an inter
relating."
3 " Thus A and B are called, etc." For " called " here substitute
" are inferred to be, etc."
4 For Comparison and Distinction see Bk. III. I. II, Notes 13-15.
The discussion, which follows here (5-9), is, I venture to think,
468 THE PRINCIPLES OF LOGIC BOOK III. FT. I
important and in the main correct, though ft certainly is insufficient.
See, once more, T. E. I.
6 "Just as the general perception, etc." "General" does not mean
that there really is in fact such a thing as mere difference. It means
that our actual perception (as distinct from feeling) may not go be
yond that result.
6 " At the end this difference . . . explicit " should be, " At the end
this mere difference has been lost to view, and the identity of the
terms (together perhaps with their specified differences) has become
explicit."
7 "A passive atmosphere." See Essays, Index, s. v. And, and cf.
Appearance, Chap. II. I ought perhaps to remind the reader that the
nature of " And " has been most elaborately discussed by Hegel under
the head of " Auch."
8 In 7 the formulas used should be amended in accordance with
T. E. I. I still think that the matter of 7 and 8 is right in the
main, though the detail, I agree, is more or less open to objection.
The reader may compare here the treatment in Mind, O. S., No. 47,
and I would refer also to Appearance, Index, s. v. Change, Succes
sion, Time.
8 " The felt relation of both." But this is, so far, not experienced
as a relation. We have, so far, a feeling which is altered, but still
remains one, and remains even the same feeling. Its diversity, to be
felt, implies its identity. But, with such mere felt difference, we
have not yet got before us a "one and another" or a "one and then
another," for these are relational perceptions. It is such perception
which is meant lower down by " the consciousness of difference."
On the nature of the Present, see Bk. I. II. n foil. And for Feeling,
as Immediate Experience, see Essays, Index, s. v. Feeling and Imme
diate.
10 Retention. The immediate experience of change and difference,
or a succession of such mere feelings, could not by itself generate
the relational perception which follows. But it leaves behind it what
we may call a tendency in the mind to move hereafter, under certain
conditions, in a certain way. See Mind, O. S., No. 47, and the Index,
s. v. Reproduction. However, I once more agree, the detail of the
process by which we pass from Feeling to relational consciousness
is open to question. In any case mere " after-sensation " (Appearance,
p. 99) could not possibly by itself account for this passage.
11 " Discrepant." This dependence of incompatibility (see the
Index) on an attempt to identify, is further explained in Appearance,
Appendix, Note A.
12 " The process falls . . . within that whole &c." But it never
does so entirely. See on i.
13 " The whole required." On the whole which contains the possi
bility, and in a sense the reality, both of this or that schema and of
all schemata, see T. E. I.
CHAP. VI THE FINAL ESSENCE OF REASONING 469
14 On Arithmetic generally, and specially as to the nature of the
" common world of number," see ibid.
15 On the processes mentioned in 13 and 14, and on the ideal
whole everywhere required, see, again ibid.; and cf. the Note on
Bk. III. I. II. 25.
16 " It is solely because &c." See Note 11.
17 "A free suggestion." "Free" (if it does not simply repeat
"not given") means, I presume, "proceeding from A itself, and not
from that which is external to A." And certainly this process is
mediated ; while a suggestion, so far as it comes to us otherwise, is
no inference. On Suggestion see the Index, and cf. Notes on Bk. III.
I. II. 25, and III. 17.
18 " We choose to make it." On this " arbitrary character " see
Bk. III. I. II, Notes 7 and 10.
CHAPTER VI
THE FINAL ESSENCE OF REASONING
I. If, considering once more the processes we have sur
veyed, we ask for the principles which underlie them, we dis
cover first of all the Axiom of Identity. 1 What is true in
one context is true in another, and what holds of a subject
within an experiment is valid also beyond that experiment.
And when, advancing from this, we approach our array of
ideal operations, we see that they fall under analysis and
synthesis. These, if we take in that other principle of move
ment, by which we go from the possible to the actual, seem
to cover the ground of all our material. On the Axiom of
Identity we propose to say nothing more at present, but there
is much in the rest which remains unexplained. Let us for
the moment dismiss the principle of transition from a sur
viving possibility, and let us turn our attention to analysis and
synthesis. Although at the cost of a partial repetition we
must try to penetrate their more hidden nature.
2. We may begin by asking an obvious question, Are
these two operations really two, and, if so, in what sense?
Are they unconnected, that is, and two alien species of a
single genus, or have they something in common beyond the
universal type of inference ? 2 The answer to this question
leads straight to the conclusion which we are to reach. We
shall try to show that analysis and synthesis have so much in
common that they are actually identical. They are two dif
ferent sides of one single operation, and you never can have
one without having the other. Hence though different they
are the same.
3. And they are the same in this way. Take an act of
analysis in which A becomes (A) bed. The elements in the
result come to us as separate, but this very separation involves
a relation. They are distinguished by virtue of a central iden
tity, and they stand thereby in some kind of relation with one
another. But this relation is synthetical. It did not exist
470
CHAP. VI THE FINAL ESSENCE OF REASONING 471
before the operation, and has resulted from it. Thus the
analysis, whilst analyzing, has shown itself synthesis.
Now take an act of synthesis. We have A B, B C,
and from this we go on to produce A B C. We have got
to a relation which before was absent ; but our process is also
an act of analysis. For A, B, and C are now related within
a whole ; 3 these terms and their relations are the constituent
elements of the whole A B C. And yet, as these mem
bers, they did not exist and could not exist till that whole
was realized. Thus the synthesis has analyzed while it seemed
but to conjoin.
Summing up the above we may state it so. Analysis is
the synthesis of the whole which it divides, and synthesis the
analysis of the whole which it constructs. The two processes
are one.
4. But with all their unity they are still very different,
for they are opposite aspects and sides of one movement, and
are held apart by three special diversities. In the first place
(i) the given material is different. In the second place (ii)
the product is not the same. And finally (iii) the operation
of which we are conscious differs in each case. Let us take
these in order.
(i) In analysis, first, we do not go beyond the area which
is supplied at the beginning. 4 The whole is given, and we work
upon that whole to produce a synthesis of elements within it.
We do not travel outside our explicit starting-place, and hence
we may say that analysis is the internal synthesis of a datum.
But in synthesis we find that the opposite holds good, for the
whole is not given any longer, but is made. Our act is the
analysis, not of our visible starting-place, but of something
implied, unseen, and ideal. In other words the totality emerges
for us in the product. Thus in analysis we operate upon an
explicit whole, and proceed to its invisible inside. In syn
thesis we begin with an organic element, or elements, not seen
to be such; and passing beyond each to w r hat is outside, so
bring out the invisible totality which comprehends them. This
difference of start is the first point of diversity.
5. And it leads to the second (ii). As the material sup
plied is in each case different, so again the product is not the
same. In one case the whole precedes and is followed by its
472 THE PRINCIPLES OF LOGIC BOOK III. PT. I
internal relations ; but in the other case external relations 5
come first and so produce the whole. Where the result ap
pears as the further determination of a given element by some
thing outside it, the process is synthetical. Where the result
gives a view of something that lay hid within the given, the
process is analytical. Thus it is analysis where your con
clusion falls within the boundary of your original premise ; but
it is synthesis where the conclusion falls beyond each premise
and transcends its limits. Analysis is the inward synthesis
of a datum, in which its unseen internal elements become
explicit. Synthesis is the analysis of a latent whole beyond
the datum, in which the datum becomes explicit as a con
stituent element, bound by interrelation to one or more ele
ments likewise constituent. This is the second diversity.
6. And the third is implied (iii). For with each we are
conscious of a different side in our one operation. In analysis
we do not keep sight of the synthesis, and in synthesis we
forget the act of analysis. In the former case we start with
an unity, we break this up by a function of diversity, and
ignore in the result both the unity that was given and the
function that was applied. The product presents us with
separate elements ; but these elements were got by ideal dis
cretion operating upon an original continuity. This given con
tinuity, and this ideal discretion, are not visible in our con
clusion ; though implied they are latent. But in synthesis the
unity, latent at first, becomes explicit in the end, and what we
ignore is its previous activity. The construction, that was
wrought on the original discretion, was the ideal function of
the final unity. 6 But this we forget, and at last are unaware
that the elements, which seem to have made the whole, can
more truly be said to have been found within it. Let us try
to state this otherwise.
We may say that in analysis the given becomes the con
tinuity of fresh discretes, while in synthesis it becomes one
single discrete in a new seen continuity. But our conscious
ness of this process is in each case fragmentary. For in one
we ignore the continuity of the product, and in the other we
forget its once helpless discretion. In analysis we employ a
function 7 of plurality in unity, in synthesis we use a function
of unity in plurality ; and we do not see either. In the result
CHAP. VI THE FINAL ESSENCE OF REASONING 473
of the first we throw away the continuity on which we worked;
and emphasize only that hidden discretion which before was
latent. In the result of the last we reject the original hopeless
discretion, and emphasize that continuity which, with its ideal
activity, we before ignored. In both analysis and synthesis
what is used is not seen. An unseen discretion is the agent
which procures for us known discretes, and an implicit con
tinuity makes behind our backs an explicit continuum. But,
if so, in these processes we have found difference with identity,
identity with difference.
7. If we do not object to clumsy forms, 8 \ve may sym
bolize our general doctrine thus. In analysis the given A,
plus a function / \ , gives a conclusion b c. But in the
J8 V
result we forget that ft and y have no validity except within
x; and that hence b c must imply the whole A. In syn
thesis again we start with A B, B C ; and this datum,
ft-y-d
plus a function NJ/ , produces A B C. But here we
x
forget that, without our function, A B and B C stand
sundered by a gulf ; and that in our result, where they appear
A B C
in unity, they are really the analysis of a whole
which before was latent. x
It is, I think, scarcely worth while to enlarge on this head.
We perhaps have said enough to show how synthesis and
analysis are essentially connected. With all their diversity they
are but different sides of one radical principle.
8. If this is true when we apply the principle uncon
sciously, it continues to be true at a later stage. We may de
liberately adopt the so-called Analytic or Synthetic Method,
and there is of course a real difference between them. But the
result is always a two-sided product. In the Synthetic Method
we begin with first principles, which are stated explicitly, and
work our way down to the individual facts. We thus con
structively build up a whole ; but all the while we are uncon
sciously analyzing. In carrying our principles out into the
detail, and in showing the detail as a consequence of those
474 THE PRINCIPLES OF LOGIC BOOK III. PT. I
principles, we are really breaking up the vague general idea
with which we started, and our whole development may be
taken as setting forth the particulars of this implicit whole.
The same twofold character exhibits itself when we apply
what is called the Analytic Method. Starting here with the
confused appearance of the whole, we break up and pierce
into its sensuous concretion. Thus we make our way to the
relations of elements more and more abstract, what in short are
termed Laws. But these Laws are syntheses ; and thus the
analysis which, if fully carried out, would be the entire de
struction of the first confused whole, 9 reconstructs that whole
as a world of abstract connections. It is everyday experience
that the analysis of a subject shows its internal unity.
This reflection may prevent our staggering at the truth of
a weighty paradox ; " Knowledge advances from the abstract
to the concrete." The confused whole, that is, which comes
before our senses and pours out its riches, goes bankrupt when
we refuse to accept such payment and insist on receiving uni
versal truth. Or, we may say, the felt concrete, when distilled
by thought, yields at first but a thin and scanty result. The
intellectual product, which first comes over, is a connection
whose actual truth holds only of a fraction of the subject. 10
It is not till we have gone further down to principles, that our
intellectual results spread over the whole field and serve to
unite the mass of detail. In becoming more abstract, we
gradually reach a wider realm of ideas ; which is thus not sen
sibly but intellectually concrete. What is abstract for one
world is concrete in the other.
9. At this point, when we remember some too hard say
ings on the comparative worth of these different currencies,
we feel tempted to digress and humbly to protest. But we must
hasten onwards, for we have now to make another remark on
the reciprocal implication of these two Methods. Induction is
of course considered to be " analytical " ; but, if we understand
induction in its primitive sense, and use it for that collecting of
instances which gives an universal, the synthesis is obvious.
For we not only get internal connections in our given material,
but, travelling far beyond it, we take it as one member in a
group of instances. Beginning with the individual case we are
investigating, we go on to others of the self-same nature. We
CHAP. VI THE FINAL ESSENCE OF REASONING 475
subsume under the universal which we have implicit in our
original datum. Thus unawares we are using a synthetic con
struction from an identical point; and, by the actual employ
ment of this latent universal, we make it in the end explicit
and visible.
We may find the same unconscious substitution of process
in our use of the Synthetic Method. When facts are explained
by the Synthetic Method, they are actually analyzed. We
reconstruct the phenomenon which we have under enquiry, and
build it up ideally by an union of elements, and thus show it
as the intersection-point of our Laws. And this is not all.
Our synthesis never quite exhausts the fact ; there is left an
unessential, sensuous element, which is put on one side as
irrelevant matter. And this residual product, left by the
analysis which dissects the fact, may be highly important. In
comparing it with our ideal reconstruction, we may find a vital
discrepancy, before unseen. In this way our rebuilding, with
its subsequent contrast, may disclose a feature in the case which
otherwise would have escaped perception. Our synthesis has
once more, and in this additional respect, turned out analytical.
10. It is not in principle alone that analysis and synthesis
are essentially one, but in practice also their unity tends to
show itself in the product. Performing one operation we find
that we have also accomplished the other; and we may err
in our estimate of the relative importance and prominence of
their aspects. As an instance of this blindness, I should like
once more to bring on the stage the so-called Analytical Psy
chology. 11 There is no doubt that this possesses a right to its
name; for its object is to resolve the phenomena of the soul
into groupings and blendings of simple elements. But it is
blind not to see that its procedure is just as much synthetical,
since, starting with certain elements and their laws, it attempts
to reconstruct and build up ideally the complex facts that are
actually experienced. And this process is of course the Syn
thetical Method.
This criticism holds even if we admit every claim put forth
by our English school. Even if the original elements and their
laws have been got by means of a preliminary analysis, it may
yet be true that in subsequent practice the analytical reduction
of particular phenomena is effected a priori by a constructive
476 THE PRINCIPLES OF LOGIC BOOK III. Pi. I
synthesis. The " analysis " for instance of visual extension
does not proceed by anatomy of what is given, but rather
by the selection of factors which together might have formed
it. Thus when the claim of the school is fully admitted, we
must still point to blindness ; and it is possible to take a more
unfavourable view. The elements, it may be said, if reached
by analysis, are reached by an analysis which ignores im
portant tracts of the subject. And again in part they are
not reached by psychological analysis at all. On the contrary
they are importations of coarse physical ideas, unacknowledged
borrowings from crude metaphysics, preconceptions introduced
without any warrant. The analysis is in short accused of rest
ing on a vicious construction a priori.
ii. We first saw that all inferences could be reduced
to the acts of synthesis and analysis, plus another function.
We have now seen that analysis and synthesis are branches
from a single stem. And it is time that we turned to search
for the nature of this other element. But we are tempted to
make first a fresh enquiry in connection with the processes
which we have just discussed. If analysis and synthesis are
thus entangled at the root of reasoning, what bearing has this
on another question which we asked before (Chap. III. n).
There was a doubt if every judgment was not an inference,
and the doubt seems now to have gathered strength. For it
may be asked, Does not every judgment involve a synthesis
and analysis, and, if so, is not each one therefore an argu
ment? We will begin with the first question, and then take
the second.
12. Let us imagine a judgment before any reproduction
has taken place. 12 Certainly no such judgment could exist,
since judgment proper appears long after redintegration has
been used, and is a consequence of that use but for argument s
sake let us suppose such a judgment which comes straight from
presentation.
Even such a supposed judgment would still exhibit both
analysis and synthesis. It would in the first place analyze for
this reason: the whole sensuous datum, the totality which
appears, never can be ideally mastered by thought so as to
be intellectually referred to reality. For apart from a native
CHAP. VI THE FINAL ESSENCE OF REASONING 477
tendency of the mind in an opposite direction, 13 we have a
sufficient cause in impotence. Do what we will, we can not
take up every single detail of the sensuous mass. We must
neglect something; but the dropping of part is the forced
selection 14 of the part which remains. Hence we have used
compulsory and unwilling abstraction, and that means analysis.
But this judgment is on the other side synthetical. The
content which it has selected is complex; it involves ele
ments in relation, which the joint selection binds together in
our minds ; and this is synthesis. Nor will it avail to object
that some predicates of the reality seem to be simple, and that
here at all events we have no synthesis within the ideal con
tent. For in all such cases an element of content would
be found in the reality which stands as the subject. The real
subject will appear in union with a certain general or special
appearance, and this appearance is implicitly a part of that
which we mean to say of the ultimate reality (cf. p. 114).
This is still true where we predicate of the whole given fact
(p. 56) ; for we connect some character of that whole with our
adjective, and take both as qualities of the real subject; 15 and
thus in effect, though not ostensibly, both fall within the
predicate. We can not have the given either as simple being
or as a sensuous felt mass without character or feature ; * and
hence, in referring to the real, we attend to and we mean the
real as qualified in a certain way. This quality can not be
said to become an idea, yet it is unconsciously united with the
ideal content. We may therefore say that, if we go back far
enough, all judgment does informally predicate a connection
which is synthetical, and which is the analysis of that real of
which it is predicated.
13. It would be no answer to reply that in many judg
ments we seem quite passive. For in all these judgments we
can show a selection and again a conjunction, and we may
argue that hence there can be no judgment in which we are
* In metaphysics it is necessary to keep this in view. 16 When, for
example, we argue that without a Permanent no change could be ex
perienced, we should remember that on the other side it may be urged
that, unless this Permanent were itself phenomenal, it could not be
effective, and that the fact of there being something stable in phe
nomena seems deducible from no principle.
478 THE PRINCIPLES OF LOGIC BOOK III. PT. I
not active. True, I admit, that we do not actively go about
to join and select. True again in some cases that we never
selected, nor should have dreamt of joining, and that the act
is little but the formal acceptance of a conjunction forced
upon us from without. I fully admit this, but it seems in no
way to shake my assertion.
Assume, as we must, that our intellect is not answerable
wholly for the matter which it perceives in our sensible judg
ments. 17 Assume that it has no intelligible ground for many
of the events which it is forced to register. Recognize the
fact that mere chance strength of stimulus, blind emphasis of
sense, is the reason why our perception was thus and was not
otherwise. Acknowledge, in the end, that whatever intellectual
assimilation by affinity you may fairly suppose to have worked
unconsciously yet at last the effective condition of the judg
ment is found in mere sensuous depression and relief ; that
it was by this that a part of the presentation was sunk, and
the rest left standing in a prominent conjunction. But, I re
peat, all this is nothing to the purpose; we here have got the
sine qua non, ls but we have got nothing else.
The intellect in judgment may be guided and led by irra
tional suggestions, and yet that judgment after all may be an
intellectual act. For the sensuous emphasis which prompts
and directs disappears in the result, and, however the mind
has come to its judgment, after all it has judged. The selec
tion and relation, which appears in the product, is not the
mere blurring and accentuation of sense. It may have been
influenced by it, and arisen from it, but its essence is now
diverse. Bare difference is one thing and distinction is an
other; solicitation and tempting prominence are still not recog
nition; and we may be forced to notice, but after all we
notice. Judgment is our act ; and the separation and integra
tion, which appear in its content, are the work of our own
analysis and synthesis, compelled, if you will, but none the less
active.
14. From mere strength and weakness of feeling on one
side, you can not cross to the other side by degrees, 19 and reach
without a break a relation of content referred to reality. The
distinction and separation, which appear first in judgment,
imply, as we have seen, both analysis and synthesis. The
CHAP. VI THE FINAL ESSENCE OF REASONING 479
perceived exclusion of one element by another involves their
relation, and hence their unity in an embracing whole. And
the existence of this central unity is obvious in every con
junction. Let that be ever so external, it still presupposes a
point of identity; and it is synthesis within a whole which is
so differentiated and therefore analyzed.
We may thus state our result. All judgment necessarily
contains a relation; but every relation, beside its pair of
related elements, presupposes an unity in which they subsist. 20
Hence the judgment, in so far as it is the synthesis of the
elements, is just so far the analysis of that whole to which
they belong. And, since the experience into which our sen
suous suggestions have to be translated, bears this character
a character not in the same way possessed by those sug
gestions themselves we may say that all judgment, however
near to sense, is essentially an act of analysis and synthesis.
15. Our first question has thus been answered affirma
tively. Let us now come to the second. If judgment is an
act of analysis and synthesis, is it true that therefore judgment
is an inference? 21
The answer which before (Chap. III. 12-18) we gave
in the negative, seems now threatened with reversal. In
ference so far has been found reducible to a double process
of synthesis and analysis ; and it seems that such a process
exists also in judgment. Must we not then say that, as reason
ing implies judgment, so judgment implies reasoning? We
can not say this, and a distinction remains which it is impos
sible to break down. Inference is an experiment performed
on a datum, which datum appropriates the result of the ex
periment. But in those judgments of perception, which we
have been just discussing, there is properly no datum. I do
not mean that, like the Deity of our childhood, they create
their world from nothing at all, and exert their activity on a
void externality or their own inner emptiness. What I mean
is, that the basis, from which they start, and on which they act,
is for the intellect nothing. It is a sensuous whole which is
merely felt and which is not idealized. It is not anything
which, as it is, could come before an understanding; and
hence we can not take it as the starting-point of inference, un
less we are ready to use that term in a somewhat loose sense.
480 THE PRINCIPLES OF LOGIC BOOK III. Pi. I
We needs must begin our voyage of reasoning by working
on something which is felt and not thought. The alteration
of this original material, which makes it first an object for
the intellect, is thus not yet inference, because the start has
not been made from an ideal content. Before reasoning exists,
there must come an operation which serves to transform this
crude material ; and this operation is both analytical and
synthetical. But it is not inference; for, though its result is
intellectual, its premise, so to speak, is merely sensuous.
Thus our primitive judgment falls short of inference in two
main points. 22 It is doubtful first (i) if the operation per
formed is not purely capricious. Psychologically, of course, it
does not come by accident ; but regarded logically it looks like
chance. We have no rational ground we can produce, in order
to justify our result. This is the first point; and secondly (ii)
the stuff, upon which the act is directed, is not intellectual.
16. Thus judgment is not inference. But though the
answer we have given is so far satisfactory, it ignores a
question which must now be raised. Both judgment and
inference are terms that can be used in more senses than one.
They may stand for these acts at the highest stage of their
most conscious development, or may point to the undeveloped
and early rudiment of their unconscious beginning. And the
question is whether this doubtful meaning has not seduced us
into a common fallacy.
The evolution of the mind and of its various powers
through different stages, and the survival and co-existence of
nearly all these stages, lead us everywhere into difficulty, and
threaten us with illusion. And the danger lies in the risk of
turning through a vicious circle. For two so-called faculties
stand to each other in such a way that each one, if you take it
at a higher stage, presupposes the other in a less advanced
form of development. Each therefore in some sense does
start from the other; and, if you forget that sense, you are
tempted to make the dependence absolute. While both are
co-equal, you may falsely place one in front of the other. This
is as common a mistake as can be found in psychology, and
we may seem to have given it a fresh illustration.
For we argued that judgment could not be inference, since
inference starts from an intellectual base, while early judgment
CHAP. VI THE FINAL ESSENCE OF REASONING 481
must begin with sense. And the doubt is whether a similar
proof would not show that inference must precede judgment.
Suppose both coeval, and progressing through stages, then
rudimentary inference will come before explicit judgment, just
as primitive judgment was required as a base for explicit
inference. And in this case we surely should have fallen
into error, for reasoning of some kind would be implied in
the very beginnings of judgment.
17. We did not make this mistake. When we said that
some judgment was free from inference, we knew the sense in
which our terms were used. What we spoke of was explicit
judgment and inference, acts both of which end in an asserted
truth, and one of which starts with a truth laid down as the
foundation of its process. And in this sense it is true that we
judge before we reason, since we become possessed of an
affirmation, when we can not produce any other affirmation
upon which this stands. Thus the distinction which we made
remains unshaken. Explicit judgment comes before explicit
inference. And supposing that both are really and in the end
two sides of one act, then the above conclusion is what we
might have expected. Here as everywhere the product comes
to consciousness first, and the process afterwards.
18. Explicit judgment is assuredly distinct from explicit
inference ; but if we like to go back to the origin of each, and
ask if the rudiment and beginning of one comes before or
after the rudiment of the other then, I think, we must give a
different answer. The earliest judgment will imply an opera
tion, which, though it is not inference, is something like it;
and the earliest reasoning will begin with a datum, which
though kin to judgment, is not intellectual. And from the
first these two functions imply one another. You can not
say that in development either comes first; they emerge to
gether as two sides and elements, implicit within one primitive
whole.
If we begin our enquiry from the physiological side, we
find there a process which consists of two parts, an action and a
reaction. We may agree to say that experience starts with
a stimulation coming in from the periphery; but then this is
but one side, for the stimulation must be met by a central re
sponse. I do not mean that experience first begins with a
482 THE PRINCIPLES OF LOGIC BOOK III. PT. I
motor discharge ensuing upon an incoming shock. That may
be true, but something else and more general is to be con
sidered here. Unless the nerve-centre answered to the afferent
impulse by some kind of reaction, whatever it may be, could
we say that there existed a physiological sensation ? 23 It
seems clear we should be wrong if we ventured on this.
And, if we consider the same thing from its psychical
aspect, we shall reach the same result. No doubt our inherited
superstitions have used us to the idea of sensations, which
simply walk into a mind which is nothing but empty space.
But is this idea true? Is it not being slowly but surely
exploded by the doctrine which sees in every sensation the
product of an active mental reaction? We may say then that
our senses give us sensations; but their gift contains traces
of something like thought.
19. I am aware of the difficulties which beset this sub
ject, and it is impossible here to enter into them. I may per
haps briefly state the question thus. At a certain stage we
should all admit that our presentations show marks of intel
lectual activity. Well, as you follow backward these presenta
tions to the earliest rudiment which you can say is given, at
what point will you draw your dividing line? Where will you
say, We have here the crude material, which would be exactly
what it is now, though there were nothing like comparison,
reproduction, or abstraction ? 2 * And non-success in finding
the proper place for this line, may lead to the belief that no
place is proper, and that no known material is wholly crude.
First experience is not intellectual, in the sense that we get
elements conjoined and parted by relations which explicitly
appear. It does not give us an ideal content marked off from
the mass of confused reality, and internally defined as quali
ties in relation. On the contrary it comes as a vague totality
which has nothing outside it, and which internally is felt as
an indiscriminate effect, in which the constituents are lost to
view. But it is intellectual in the sense that, when we come to
reflect on its datum, we find marks of activities, which, if they
had been conscious, and if they had not stopped at feeling, we
must have called intellect. And I regret to say that I must
leave the matter so.
20. But, assuming that the first thing, which we feel or
CHAP. VI THE FINAL ESSENCE OF REASONING 483
know, results from a reaction upon a stimulus, we must deny
two things. 25 We must refuse to allow that experience comes
from an operation on a datum, or yet is a datum without an
operation and so independent. Both assertions would suppose
that something is given, where nothing is yet given. The
beginning of experience is the resultant of two factors, a
stimulus and a response. And here we see how the rudiments
of judgment and reasoning are intertangled. The mere stimu
lus is not given, and so reasoning has nothing from which it
could start. But, on the other hand, a mental activity can not
be directed upon simple zero. We have two factors, the re
action and the stimulus, and in a certain and improper sense
these two factors may be taken as the premises of a judgment.
And the result again may be taken as a conclusion, not indeed
from data, but from an indefinite ground to a definite datum.
21. Nor can we fairly object that this conclusion is
capricious, that the activity is either an arbitrary handling
which makes its result, 26 or a formal registration which merely
accepts it. Irrational indeed the conclusion must be, in the
sense that the mind can give no reason for the sensation it is
forced to. But capricious or formal it certainly is not. It fol
lows from its premises with the strictest necessity, and com
bines in its result the character of both. 27 And again it is no
mere formal acceptance. For the organism, and with it the
empirical subject, has its peculiar nature which is impressed on
the product. We might say that our premises are the centre
and the incoming change, that the middle operation is the
synthesis of both, and that our result is the conclusion. And
in such a loose and incorrect sense of the term this operation
is inference.
Or let us take the same thing at a higher remove. Let us
pass beyond those factors which first produce feeling, and let
us say that the feeling has been produced and qualifies the
subject. But one feeling is, as we are told, no feeling; and
the subject, merely determined as a, is so far nothing. Then
while a remains, let ft supervene, and the result may now be
a sensation A, which is neither ft nor a, but is the consequence
of their union. This result is clearly no inference proper, yet
it possesses much in common with reasoning. We may be
said to have premises a and ft, then comes their synthesis,
484 THE PRINCIPLES OF LOGIC BOOK III. PT. I
and a sensation A is the new result. Nor is it easy to object
that at all events for consciousness a result must come first,
and then afterwards be used. For if one feeling is no feeling,
perhaps consciousness first wakens with a complex presenta
tion, and gets by a circular process the result together with its
premise. The first feeling, which is the reason why we ex
perience the second, itself becomes explicit in the product, and
is thus both starting-point and goal.
22. It is clearly unsafe, when we go back beyond ex
plicit judgment, to give priority to either function. It is better
to treat their rudimentary forms as two parts of one whole;
and it is this point of view from which it would be right to
consider the nature of our early experience. We should in
this case be led to ask some interesting and important ques
tions. 28 If in knowledge the subject and the object are
premises, is not every assertion, which confines itself to the
object, an illogical conclusion? No physiologist would believe
that colours or sounds were the properties of those stimuli
which act on the centres of vision or hearing. But, if so, by
what process are we to remove the influence of the subject in
knowledge ?
And there is another question, the importance of which
could not well be exaggerated. If in knowledge the subject
and the object may be called premises, then what are we
to say of the middle operation? We have seen that this
demands a central identity, and where is the central identity
here? But, without it, what becomes of the relation of the
premises and of the ensuing result ? This question would lead
to problems in metaphysics which we can not even glance at
in passing.
23. If we tried to pursue this line of enquiry, we should
soon be carried beyond the scope of our volume. But, if we
return to the immediate object of our scrutiny, the relation
existing between judgment and inference, we may show how
the circle, which we lately noticed, comes up in the process
of reproduction. Every judgment on the one hand seems to
imply redintegration, which itself on the other hand seems to
presuppose judgment. The explanation is that reproduction
implies a rudiment of judgment, but that this does not be
come explicit and show itself as judgment, until it has been
CHAP. VI THE FINAL ESSENCE OF REASONING 485
used as a basis of inference. The unconscious synthetical
activity brings its own principle or premise before our eyes,
and in a sense makes that actual. And we have here no
miracle. We are given ebf, which, by redintegration from
abed, turns to ebfd; and from ebfd an abstraction may supply
us with the judgment b d. But this b d, which is
thus the conclusion, was also the basis of our reproduction.
It will be objected no doubt that in abed there perhaps
may be no rudiment of judgment; that there may exist in this
foundation no intellectual act, no unconscious selection, or
notice, or preferential attention to b d; and that in short
there may be nothing but sensuous strength and prominence
of b and d. But in the end, as we have seen, this will make
no difference. For it is admitted that, out of the past abed,
b d is employed to qualify ebf. But, if so, we ask, In what
shape is this b d made use of ? 29 Can it, if you take it as it
comes to sense, be so employed at all? This would be quite
impossible. Beside its entanglement with the whole abed, it
has in itself a particular character, a special colouring, which
does not suit ebf, and which does not appear in the conclusion
ebfd. And thus the purification of b d is an intellectual act,
performed as part of the reproduction. It shows clearly that
function of selective analysis 30 which belongs to judgment
and to inference alike.
24. It is interesting to see how, when we qualify a per
ception through reproduction, our act is one common process
of analysis and synthesis. Let abed be given, and then ebf,
and let b redintegrate its complement d, with a final result
b d. The movement is synthetical, and yet it has analyzed,
since it has divided two wholes. In the first place, since b d
has never been given us, its use and explicit realization breaks
up abed, and is thus abstraction. In the second place, now
that we are aware of & d and have ebf presented, the dif
ferent contexts of b are a means for splitting up ebf. The
analysis of both these compounds emerges in the act of con
struction.
I will work out more in detail one part of the process we
have just observed. Let abc be presented, and then let b be
fixed upon and considered by itself. This of course is analysis,
and what I want to show is that construction can effect it.
486 THE PRINCIPLES OF LOGIC BOOK III. PT. I
For suppose that, on the strength of former experience, b is
now an element in other connections. Then here in abc the
b may redintegrate other elements, and may try to appear as
h p or b q or b r, all discrepant with one another and
with abc. A collision must follow between p, q, r and ac, with
the result that p, q and r are rejected. But this rejection may
have led to a distinction. The identity of b amid these
struggling differences may have caused the attention to be
centred upon it. In the process, so to speak, it may thus have
become free, and hence the synthesis will have been a condi
tion of analysis.
We are invited to pursue this subject further, but we have
done enough if we have shown the interconnection of both our
functions. We must return from our digression (if it really be
such), and must take up the thread we broke off before in
25. Beside the functions of analysis and synthesis we
found that reasoning employed a third principle. The leap
of transition from the possible to the real did not seem to fall
under either of these heads. We must try to see this third
principle more clearly ; and, if the reader will permit, will
approach it indirectly. We will try to show how the defects
of analysis and synthesis lead the mind beyond the limit of
these functions.
We have seen that they both are two sides of one process.
And it follows from this that the increase of one must add to
the other. The more deeply you analyze a given whole, the
wider and larger you make its unity; and the more elements
you join in a synthetic construction, so much greater is the
detail and more full the differentiation of that totality. We
have here the antipodes of that false relation of extension to
intent which we criticized before (Book I. Chap. VI.). 31 That
preposterous article of orthodox logic turned the course of our
reason into senseless miracle. The less a thing became the
further it went, and the more it contained the narrower it
became. Such a total reversement of our rational instinct
could spring from nothing but a fundamental error. And it
arose from our use of the abstract universal. That can not be
real, and in consequence our thoughts were all built on un-
CHAP. VI THE FINAL ESSENCE OF REASONING 487
reality and ended in falsehood. But in the concrete universal,
which has guided our steps, and which has appeared as the
identity of analysis and synthesis, we have returned to truth
and made our peace with reality.
26. If for metaphysics what is individual is real and
what is real individual, for logic too the rational is individual
and individuality is truth. And this is no paradox. Our prac
tical criterion s2 in every enquiry is the gaining all the facts and
the getting them consistent. But this simple test unconsciously
affirms that the individual is true and the truth individual.
For a fragment of the whole broken off abruptly, or a whole
that internally was at issue with itself, would alike fall short of
individuality. Unawares then we strive to realize a com
pletion, single and self-contained, where difference and iden
tity are two aspects of one process in a self-same substance,
and where construction is self-diremption and analysis self-
synthesis. This idea of system is the goal of our thoughts,
and to sight of this perfection we have been conducted.
27. But we have not reached nor entered. Our analysis
and synthesis have fatal defects, and their unity is poor and
but superficial. Our analysis has to begin with a datum, and
to divide its singleness into single components. But in the
first place this origin is not single. For the datum, with
which it begins, is limited, and is therefore defined by exter
nal relations. 33 These alien connections go to make it what it
is, and it hence involves them within its own being. But, if
so, its unity comes to an end. In its attempt at self-develop
ment it depends on the external; and therefore, even if its
analysis is successful, 34 it has not analyzed itself. And in the
second place the result of its analysis remains defective. It
fails not only to analyze itself, but it also fails to carry out the
analysis. For the components it produces are themselves
unstable. Characterized as they are by their external rela
tions and so impregnated with a foreign principle, their
own unity falls apart internally into relations of other in
cluded units; and hence we never reach anything which we
could rightly call single. Want of individuality in the datum
that we began with, absence of self-movement and impossi
bility of self-development, this is the first defect. Want of
individuality in the result attained, and endless dissipation into
THE PRINCIPLES OF LOGIC BOOK III. ?T. I
foreign relations, this is the second defect of our analysis.
It is ruined throughout by externality. The elements are
inwardly alien to themselves, and from without they each are
alien to the other and to their common origin. The analysis
in the end is hence not synthesis, if that means self-relation.
28. And our synthesis is no less defective. 35 We start
with one element and go on to another, and find them both as
constituents in a whole. But we can not say that we advance
from our datum by the analysis of that. The opposite is the
case, for our fresh constituent is dragged up and chained on
from the outside. To the original element this stranger does
not seem a part of itself, but a foreign arrival and importation.
The synthesis is thus not self-determination. And this same
fault has another side. For the whole, which you have
reached, is no system of differences; it is not an individual.
The differences are an aggregate, found conjoined together,
and no self-analysis of a single unity. The elements certainly
are united by a central point, and are thus interrelated; but
their relations remain external and forced. Instead of moving
freely from one to the rest, you are compelled to pass through
a machinery of steps, which seem to have no vital connection
with the elements you bring together. Thus the union is in
the end no inward bond, but a foreign coupling; and you can
not pass from the centre to the system of differences. It is
no living point that withdraws into itself the life of its
members, and flows forth into a body which it feels as its
own. It is the axle of a wheel where spokes are driven in,
and where the number of holes and spokes is indifferent.
This first fault of our synthesis implies a second and
counterpart. For the whole, which we make, is never com
pleted. It is determined from outside; and its unity is com
pelled to assimilate in relations to foreign bodies the seed of
dissolution. These bodies fall outside that whole whose
analysis we from time to time have procured by our synthesis.
The synthesis turns out therefore not to be the analysis of
the whole which we assigned to it, since that whole does not
include the foreign matter, which intrudes in the result. And
the perpetual effort to go on and to find the completion of
our synthesis, and to realize the unity which we demand in
our construction, proves a self-delusion. It leads to that chase
CHAP. VI THE FINAL ESSENCE OF REASONING 489
of the spurious infinite, where fruition, ever instant, is
baulked perpetually. Our synthesis is therefore no self-
analysis.
29. We have seen the defects in both sides of our opera
tion, and we naturally ask, Is there any remedy? Or, since
the sin lies so deep that to remedy the process would be to
change its nature, we may ask, What is it that we really
do want? What was it that guided our half-conscious
thoughts, and forced us to see failure where we desired suc
cess? To perceive imperfection is to judge by the perfect,
and we wish to become aware of this idea which has served us
as a canon and touchstone of reason. If we realized our
ideal, what then should we get?
We should get a way of thinking in which the whole of
reality was a system of its differences immanent in each dif
ference. In this whole the analysis of any one element would,
by nothing but the self-development of that element, produce
the totality. The internal unfolding of any one portion would
be the blossoming of that other side of its being, without
which itself is not consummate. The inward growth of the
member would be its natural synthesis with the complement
of its essence. And synthesis again would be the movement
of the whole within its own body. It would not force its parts
into violent conjunctions, but, itself in each, by the loss of
self-constraint would embrace its own fulfilment. And the
fresh product so gained would renew this process, where
self-fission turns to coition with an opposite and the merging
of both in a higher organism. Nor would the process cease
till, the whole being embraced, it had nought left against it
but its conscious system. Then, the elements knowing them
selves in the whole and so self-conscious in one another, and
the whole so finding in its recognized self-development the
unmixed enjoyment of its completed nature, nothing alien
or foreign would trouble the harmony. It would all have
vanished in that perfected activity which is the rest of the
absolute. 36
30. This crown of our wishes may never be grasped. We
may find that in practice it is not attainable, and is impos
sible for us to realize in detail. I will not say this is not so.
Nay, I will not deny that this ideal may itself be a thing
4QO THE PRINCIPLES OF LOGIC BOOK III. PT. I
beyond the compass of intellect, an attempt to think something
to which thought is not equal, and which logic in part refuses
to justify. I will not pass this sentence, nor will I gainsay it.
But one thing I will say. The idea may be a dream, or even
a mistake, but it is not a mere delusion. For it does not
wholly deceive us. It does set before us that which, if it
were actual, would satisfy us as thinking beings. It does
represent that which, because it is absent, serves to show
imperfection in all other achievements, takes away our rest
in all lesser productions, and stirs our reason to a longing
disquiet. There has come in to us here, shut up within these
poor logical confines, and pondering on the union of two ab
stract functions, a vision of absolute consummation. In
this identity of analysis and synthesis we recognize an ap
pearance of our soul s ideal, which in other shapes and in
other spheres has perplexed and gladdened us; but which,
however it appear, in Metaphysics or Ethics or Religion or
Esthetic, is at bottom the notion of a perfected individuality.
31. We may seem to have wandered away from our sub
ject, but in reality, I think, we have come straight upon it. We
desired to understand that remaining function, 37 which fell
outside our analysis and synthesis, and we began by seeing
how far these principles stopped short of and fell outside
completion. Their defect was, in a word, the lack of self-
development. Is it an idle fancy, if we see in the element
which we desired to understand, and which passed without
help from idea to fact, a trace of self-developing perfection?
Or is it actually true that in our every-day arguments we
must use an incomplete form of this principle?
We must, I think, in the first place admit this, that the
act of thought by which we assume that, given one possibility,
that one is real, can not be reduced to analysis or synthesis.
And this act exists as a normal function. It is a law that,
when we have a subject A, and with this a possible predicate b,
and when (either because other predicates are absent, or be
cause they have been suggested and excluded) this predi
cate b is left alone that then the subject appropriates this
predicate, and openly attributes it to itself as a possession. We
may not recognize this law, we might even like to repudiate
its claim, but we can not help obeying it. Where a sug-
CHAP. VI THE FINAL ESSENCE OF REASONING 4QI
gestion has been made,^ 8 if that suggestion is not rejected
by the fact which we start with, or again by some other sug
gested quality, if in short we are left, not with discrepant
possibles, but with one uncombated may-be that suggestion
must always be taken as fact. This is a process of thought,
and it does not seem to fall under any previous process, but on
the contrary to lie at the root of all our reasoning. On its
negative side you may give it the form of " I must because I
can not otherwise," and you may reduce every function of
inference to this form. But on its positive side, and that
is the truest, you may state it as " I must so because I will
somehow." The striving for perfection, the desire of the
mind for an infinite totality, is indeed the impulse which
moves our intellect to appropriate everything from which it is
not forced off.
32. And, if I may guess, it was this principle which,
falling from the sky, appeared disguised as Primitive Credu
lity (Book II. II. Chap. I. 23). Among the many services
which Professor Bain has done to our philosophy, we have to
thank him for this, that he is incapable of suppressing what
looks like a fact. 39 Here in the middle of the rest of his
theory, without any reasoned connection with his principles, he
points out this seeming irrational readiness to take ideas as
facts, so long at least as this process is possible. And with
this, if indeed it is not the same impulse, goes " the tendency of
an idea to become the reality " (Senses, p. 341). These primi
tive weaknesses, according to our author, should be counter
acted by experience and reason, and are a thing which perhaps
we may say should not be, and ought not to exist. From this
conclusion I dissent,* but I gratefully acknowledge the frank
acceptance of the mental tendency. For I seem to find in
these early superstitions a normal activity of the developed
soul, the increase of which does but add to its progress. This
double effort of the mind to enlarge by all means its domain,
* I must dissent again from the formula of Credulity, as given by
Professor Bain, and which I have italicized. " We begin by believing
everything ; -whatever is, is tru-e." This at all events we can not be
lieve, unless we are idealists of an extreme type. I must suppose that
Professor Bain means " Whatever appears, is r-eal," or " Whatever
seems, is true."
4Q2 THE PRINCIPLES OF LOGIC BOOK III. PT. I
to widen in every way both the world of knowledge and the
realm of practice, 40 shows us merely two sides of that single
impulse to self-realization, which most of us are agreed to
find so mystical. But, mystical or intelligible, we must bow to
its sway, for escape is impossible.
33- We shall hereafter discuss the validity of this with
other forms of reasoning, and we may here recapitulate our
present results. 41 Inference is an experiment, an ideal experi
ment which gains fresh truth. It employs divers modes of
synthesis and analysis; and, underlying all and in one case
apparent, is that aim of the intellect after perfect fulness
which leads it to appropriate all suggested ideas which are
not torn away. And reasoning depends on the identity of
indiscernibles ; for the middle operation must turn on a cen
tral point of sameness, and again the datum, with which we
begin, must survive through the process. It must go into the
experiment, and must appropriate the result which that ex
periment obtains. We have seen all this, and there is some
thing else which now becomes visible. The identity, which
we find in the middle operation, and the self-preservation of
the basis we start with, have been set side by side. But in a
sense they really are one and the same; and it will repay us
to see this. It shows that at bottom, and in a struggling way,
reasoning is really a self-development. Throughout the
process one subject is developed, and again to some extent
it developes itself.
34. I will begin with the first of these assertions, but will
not weary the reader with a repetition of detail. 42 For the
presumption is now so strong in favour of its truth, that we
may content ourselves with the removal of obstacles. All
depends on our looking in a proper way at the premises we
begin with. If for instance we have certain spaces and com
bine them, or two subjects and compare them, then in the
middle operation, it may be said, the unity is imported from
the outside. And so it is, if you take the spaces or the
subjects as they wrongly appear in complete independence.
But in that case you would never by any machinery force
them together. The true starting-point is the total space 43
as qualified by these points in relation, the common reality
CHAP. VI THE FINAL ESSENCE OF REASONING 493
which appears in both subjects, the one ideal integer in which
any given numbers exist as fractions, the underlying whole
which presents itself as complex, and by abstraction is shown
with a simpler predicate. This implicit subject is what sup
ports the change brought in by our process. And it also
serves as a centre of activity in the process itself.
With spaces and numbers this second truth is clear. But
in other cases, such as comparison, 44 we may still verify the
same rule. We begin with A and B, and we compare them to
find the relation between them. But the centre of this synthesis
must be a felt basis of quality common to both, and this com
mon basis was implicit in our starting-point. You may indeed
determine to compare two terms before you know the special
point in which they are comparable; but you can not perform
the actual comparison, until the terms have been unconsciously
apprehended under one aspect. Thus reality appears, not sim
ply as two terms, but as possessing an attribute or group of
attributes, which is given with two separate sets of qualities.
And in the result this basis through its own activity becomes
explicit. We may say here as everywhere, that the real sub
ject, implicit at the start, and active in the middle, shows itself
at the end by a development of some latent relation or quality
which it claims as an attribute.
35. And thus, in a certain sense, the movement of the
subject has been self-development. We have seen by how
much it falls short of true freedom. We have seen how
the capricious changes which we effect, 45 and the external
constructions which we introduce, stamp the character of our
reasoning with an arbitrary print, and raise painful suspicions
of its invalidity. But there yet remains something, which we
must examine later. It is assumed that, whatever in our rea
soning may be arbitrary, yet at least the conclusion follows
from the premises naturally and necessarily, without altering
or straining or even addition. If we can be shown of our own
free choice to have forged one link in the chain of inference,
then the connexion snaps and the ends fall apart. The as
sumption will trouble us enough in the discussion which ends
this work. But, if there is any truth in it, it points to our
belief that the conclusion must naturally grow from the
premises, and can not in any way be dragged or forced out of
494 THE PRINCIPLES OF LOGIC BOOK III. PT. I
them. Our apparatus of proof has been compared to a scaf
folding, which is removed when the edifice of reason has
been built; yet, if we have but placed the parts in conjunction,
there is nothing which will hold when the scaffolding is gone.
If our process is not to end in a ruin, the apparatus we have
used must be simply a prop, supported on which the argument
has grown up, till strong enough at last to support its own
fruit and to stand by itself. Or if this, as I fear, is too high
a comparison, we may say that our constructions must be
plasters or threads or splints or bandages, which hold together
for a while our broken perceptions, till we see them unite and
come together. Every inference we could make would prove
unstable, unless, at least to this poor extent, it were self-
development.
ADDITIONAL NOTES
1 " Axiom of Identity." See on Bk. III. I. III. 2. And, for " that
other principle," see on Bk. III. I. II. 25.
2 " Are they unconnected . . . inference." In this alternative
"alien" is objectionable. It should perhaps be "disparate." And,
after " beyond the," I should prefer to read " mere fact that each is
an inference."
3 " Within a whole." Before " whole " insert " visible " ; and
(two lines below) for "as" read "as."
4 "We do not go beyond" i.e. in our mere result. And (lower
down), in "the whole is not . . . made," insert, after "given," the
words "as a datum," and, for "is made," read "itself depends on the
inference." The text, as it stands, is really erroneous. See the fore
going Chapter, Note 15.
6 " External relations." " External " means here " not falling
within our datum" The relations can not of course be " external "
otherwise.
6 " The final unity." Add " which from the first, was, in a sense,
there."
7 " We employ a function." The " function " everywhere rests on
and implies an assumption. See T. E. I.
8 For the formulas used in 7 see once more T. E. I. In the second
of those given p-y-6 seems written by a mere mistake, for o-/3-y
9 " The first confused whole, reconstructs that whole as ... con
nections." After "confused whole" add "as such"; and, for "as,"
read " as and in."
10 " The intellectual product . . . ideas." It may serve to make
CHAP. VI THE FINAL ESSENCE OF REASONING 495
these words perhaps clearer and more correct, if, after " connection,"
we read them thus, " whose actual truth covers no more than a frac
tion of what is contained in our datum. It is not till we have gained
truths more special truths at the same time less sensuously par
ticular and general that our intellectual results spread over the whole
field, and can serve as principles to unite and comprehend the mass
of detail. In becoming more analytical, and so more abstract, we
gradually reach a wider realm of connected ideas."
""Analytical Psychology." Cf. Bk. II. II. I. 6.
12 " Let us imagine &c." On the priority of Redintegration to Judg
ment (proper) cf. Mind, O. S., No. 47.
13 " Apart from a native tendency." This is ambiguous. It should
be something like " apart from the presence of instinctive reaction
or apperceptive interest."
14 On Judgment being always Selective, see the Index, s. v. Judg
ment.
15 On Reality as the Subject being always qualified, and never
anything like mere Being, see the Index, s. v. Subject. And, on the
case where the whole Reality is the subject, see Essays, p. 41, note, and
Index.
16 The point here is that, without some stability in the content of
what comes in Feeling and Sensation, no orderly world would be
possible. For order could not be simply super-induced by or from
any mere abstract principle or function.
17 "Assume, as we must &c." Cf. Bk. III. I. III. 17. And, in the
next sentence, before " no intelligible ground," insert " for itself."
18 " The sine qua non." After these words read " but we have
got, so far, no more."
19 " You can not cross &c." See, once more, Mind, O. S., No. 47.
20 " Every relation . . . subsist." Cf. Bk. II. I. II. 10. This
fundamental doctrine I have done my best to preach, but, I fear, still
largely in vain. It does not surprise me, even now, to find it assumed,
in criticism of myself, that relations are ultimately real, and that the
only question, even with myself, is as to their character as so real.
Cf. T. E. IX.
21 Judgment and Inference. Cf. Bk. III. I. III. 12 foil., and
T. E. I and II. The answer to the question, whether Judgment comes
before Inference or Inference before Judgment, is that both emerge
together. Each appears first not by itself but as one aspect of a single
process. As, however, each may be taken at different stages, and so
in various senses, either can thus be shown plausibly as prior in time
to the other.
But Judgment is mediated from the first and is mediated essen
tially. Judgment issues from a felt whole, and this felt whole is
never left behind in the sense of remaining outside. It still is there
in one with that Reality of and within which the selected synthesis
of the judgment is affirmed. Hence from the very beginning the
form of Judgment is R (x) a, or S (x) P. And in this x is
496 THE PRINCIPLES OF LOGIC BOOK III. PT. I
essentially implied that " R is such that S is P." But, where you
have " such that," you have obviously a mediation and an inference.
On the other hand this irremovable aspect is easily ignored. It
is by a natural abstraction that judgment is taken often as simple or
mere. And certainly to a greater or less extent we may lack not
only the wish but the power, in the case of many judgments, to
show the special inference which is implied. In judging we may
ignore or may be unaware of the base of our judgment, and of
that system and ground on which really it rests. But our judgment
is, none the less, the expression of a system, however latent and
however imperfect that system may be.
" Your doctrine," it may, however, be replied, " takes no account
of an objection, an objection noticed in this volume (Bk. III. I. III.
17) and really fatal. "We admit," it may thus be urged, "that judg
ment never is a mere accident which supervenes. It is in every case
(we agree) a necessary result. It comes from a whole of conditions,
which, if you please, you may even call a system ; and in this sense
a judgment is always mediated. But, on the other hand, the necessity
involved here, may be, in a word, psychological, as is evident when
we consider a selection due to relative force (ibid.). And you
can not pass direct from conditioned psychologically to logically
conditioned. The necessity in the former case is external to the
logical judgment, when once that judgment has been produced. But
true logical necessity belongs to that, and solely to that, which is
contained now within the judgment itself, no matter how the event
of this judgment has happened. It is mediation in this latter sense
which you have to show, and which you can not show, as present
always where judgment exists."
The above objection is serious, I agree; but, when considered
more fully, it tends, I think, to confirm our conclusion. And I will
first notice the error involved in any attempt to separate wholly and
to divide the psychical from the logical process. For the psychical
process (we have seen) is implied always and everywhere, though
logic for its own purpose must abstract from this necessary side of
things (T. E. I). And this same process (we have seen again),
when controlled in a certain sense, itself becomes, so far, that which
we mean by thought (see on Bk. III. I. Ill, 23). And further this
very control is even itself an effective part of the psychical sequence,
since it is something which happens and which makes other things
happen in the mind. Hence an absolute division between what we
rightly distinguish, as logical and as psychological, must clearly be
set down as a dangerous error.
But, so much being premised, the above distinction must be ad
mitted and emphasized. It does not, however, consist in the separa
tion of diverse matters. It is based on that difference of interest
and of object with which the same matter is treated, on the one side
by psychology and on the other side by logic. The psychologist asks
how certain events, with such and such characters, occur in the mind.
CHAP. VI THE FINAL ESSENCE OF REASONING 497
And for this purpose he ignores, and he must ignore, all that otherwise
is implied in these characters. He has not to deal, for instance,
with the question as to whether and how far judgment and infer
ence are true. But the question of truth, the problem as to how,
and how far, the ideas used in judgment and inference hold good
of Reality, is essential to logic. And hence, aiming at its restricted
end, logic, if it is to exist, must abstract. It must ignore, in general
and in detail, that aspect of event which is really inseparable from
all judgment and from every inference (see T. E. I. And cf. Mind,
N. S., No. 33).
Are we then to insist that psychological conditions are excluded
from logic, and remain in every sense outside? To this enquiry
our answer must, after all, be No. Or this exclusion, we may again
reply, holds good rigidly, but only so far as the above conditions
seek to enter as such. And I will now point out how within logic
itself they still can appear, though never, whether generally or in
detail, in their own special character. We may return here to the
instance where the relative force, say of certain sensations, was the
cause which brought into existence a certain judgment.
This force, I repeat, remains, as force, external to the judgment.
It can not in its own character pass into the content of that judgment
and there claim recognition. But every judgment (we have con
vinced ourselves) must, on the other hand, contain and depend
on an internal x. It is never mere R, but always R (x), that in the
end we qualify as S P. Within this x falls every aspect that
belongs to our Reality, and thus, though not given in its special
character, every aspect is itself included in our judgment. Hence
every psychical condition, such as, for example, the force of a sensa
tion, can, in a sense, appear within that judgment which also follows
as its mere external result a result which claims for itself at the
same time complete independence.
This transformed appearance of the non-logical within logic shows
itself (we may note further) in more than a mere general form. Not
only does every judgment presuppose and contain an unspecified x,
which, except for convenience, it has no right to ignore. We have
also judgments where this x is specially recognized within that sub
ject which we mean to affirm. In the " This," of what is called
Designation, the judgment is qualified explicitly by what we take as
an x which is special and particular. A prevailing force, say of
sensations, can find here an admitted expression within the judgment,
and can itself, so far, become logical. But on the other hand, in
its own psychological character and taken as such, this force, whether
in general or as particular, remains excluded from logic. (On Des
ignation see further Essays, the Index.)
We have now, I think, disposed of the objection which seemed
to threaten our result. And our conclusion holds that, as there is
no inference without judgment, so, on the other side, there is no
possible judgment without inference. In principle the two are no
2321.2 H
498 THE PRINCIPLES OF LOGIC BOOK III. PT. I
more than inseparable aspects of one process. Apart from an ab
straction, at times permissible but in the end illegitimate, there can
be no mere inference or mere judgment. And the question of priority
can be admitted only when we limit it to those various stages which
appear as the development of one two-sided activity.
22 " Our primitive judgment ... in two main points." But, as
is pointed out in the following sections, the absence (i) of an ex
plicit, or even a producible ground, and (ii) the absence of an object,
in the strict sense, from which we start only show that inference,
if and so far as taken at a certain stage of development, is not yet
there.
23 "A physiological sensation." Cf. Bk. III. I. VII. 4. Before
these words insert " even." I do not know if the terms used here are
accurate, but the meaning is that, if the "incoming shock" were a
mere shock, it would not be in any sense a sensation, whatever else it
might be. The " inherited superstitions," spoken of lower down, refer
to what still flourished in England, more or less, even in 1883. And
the opening words of 19 should certainly have been, " I am, I hope,
aware."
It may perhaps assist the reader, if I, somewhat more briefly,
repeat the foregoing. It is objected that, though there are in every
judgment special psychological conditions, which do in fact mediate,
and which so make every judgment to be in fact what it is yet
these conditions do not appear, at least always, within the judgment
itself. They therefore may, in whole or in part, remain external
to the logical judgment. And hence it follows that not all judgments
are mediated logically.
In answer to this objection I admit the fact that, as above stated,
these special conditions do not, in their detail, appear in the judg
ment. And I agree that the judgment is so far defective. To make
the judgment perfect logically and complete, all the conditions, in
cluding those which are psychological, must appear in the judgment
itself. And, failing this complete mediation, the judgment is not
what it ought to be. It does not, that is, realize the character to
which, as a logical judgment, it is bound to lay claim.
On the other side logic itself marks this incompleteness and this
defect by insisting, everywhere in judgment, on the necessary inser
tion of an x. And, in the field of this internal x, it provides space
for the inclusion of all and of every condition required by the judg
ment. Hence the judgment contains within itself whatever comple
ment is needed for its own perfect mediation. And, though actually
this complement is included not in its particular but only in its
general character, none the less its inclusion is there. Any objection
which insists that the required mediation remains but external can
not, therefore, stand.
Further, wherever we fall back on Designation, we recognize,
and set down as present, in the judgment itself, something which is
there although it can not be specified in detail.
CHAP. VI THE FINAL ESSENCE OF REASONING 499
The conclusion then holds that in principle all judgments are fully
mediated. But, so far as the special mediation required is not made
explicit, every judgment fails so far to be complete, and is imperfect
logically. And it is in this sense only that a judgment can be char
acterized by that which can also be termed " external." In every
judgment all its logical conditions are included in principle, but there
are, on the other hand, particulars, which, as particulars, remain
outside of the actual judgment.
24 " Comparison " should certainly have been omitted, and its men
tion here amounts to a mistake. For Comparison see the Index. Cf.
Bk. III. I. VII. 2.
25 On the conclusion advocated in 20 cf. ibid., 3 and 4.
26 On the question as to how far inference in general is arbitrary,
see Bk. III. I. II, Note 7, and cf. the Index, s. v. Inference.
27 " Combines in its result . . . both." If this meant that the
effective detail of the " premisses " survives, as detail, in the logical
result, it would be open to objection. But cf. 23, and see Note
21. Not even in the result taken as psychological can the entire detail
survive. See Index, s. v. Reproduction.
28 " Interesting and important questions." Questions (I would
add) as important now as ever, and needing perhaps still as much
to be asked. The reader may observe, specially in this section, the influ
ence of Hegel.
29 " In what shape made use of." See Note 27. The reader may
notice that the account of Reproduction given here omits to notice
the formation of " Dispositions." This necessary feature of the
process may, however, be taken, I think, as here irrelevant to the
main argument.
30 On the selective analysis, present in all judgment and inference,
see the Index, s. v. Judgment.
31 " That false relation of extension to intent." But see on Bk.
I. VI. 6.
32 " Our practical criterion." For " practical," as applied to theory,
see Index, s. v. Practical. And for " criterion " see s. v. Criterion.
33 " External relations," not of course merely external but external
enough to vitiate the result. Cf. Notes 21 and 34. And see Index,
s. v. Relation.
34 Analysis. If the totality implied in the datum were included
there at the beginning, and, if this totality could, in and by the
analysis, itself develope itself independently and fully the result would
be satisfactory. But, as this can not be the case wholly, the result
is defective. See T. E. I and IX. And, for Data and Premises, see
Index, s. v. Premise.
35 Synthesis. Our datum, once more here, is not the entire whole
which is implied in our process. And, in any case, that whole is not
developed except in the imperfect form of an aggregate, where,
though the ends of the bricks (so to speak) are united by identity,
all the rest of them remains in principle external and but stuck on
500 THE PRINCIPLES OF LOGIC BOOK III. PT. I
by a foreign x. Hence, inside the whole, there is no binding con
nection throughout, nor again on the outside is there any real com
pletion. For there is no one single thing which, of and by itself, has
developed in the process its own proper self. See T. E. I. The mere
conjunction (we should note) of identity and difference is not a
solution of the problem as to how these diversities are able to be at
one. See Essays, pp. 240, 264, note.
38 On the Dialectical Method see the Index, and T. E. I.
In the words " that perfected activity . . . absolute," the reader will
note the difference between perfected and perfect. He may further
observe that, even in 1883, I seem to have been clear that " activity "
is not ultimate, and can not be taken to be real, as such, in the Ab
solute. See Appearance, the Index.
3T On the supposed " remaining function " and " law," see on Bk.
III. I. II. 26, and IV. 6. We have here an error resting on the gen
eral mistake made in this volume as to " mere " or " floating " ideas
(see on Bk. I. I. 4 and 10. As to the inference discussed in 31,
where there really is one, it consists in Elimination. And it will fall
under the general head of Analysis and Synthesis, since it explicates
both distinctions and connections in the subject. The statement "can
not be reduced " is therefore, so far, wrong. It would become right
only if we passed to the real from that which is sundered from it as
merely possible. See again the Note on Bk. III. I. II. 26.
On the other hand the general " impulse to self-realization " is
really fundamental. And this " striving for perfection " shows itself
everywhere in the aiming at " an infinite totality." And it appears
here specially in the desire for and postulation of Reality as an ideal
system, where all distinctions are related and connected at once posi
tively and negatively.
88 In " where a suggestion has been made " it would be better,
perhaps, to say " has been accepted as possible," and to insert " special "
before " fact." For " suggestion " see on Bk. III. I. III. 17, and
V. 14.
39 As my attitude towards the late Dr. Bain had so often to be
that of criticism, I should like to add here that it is now only too
easy to underrate or to ignore his merits and his work in psychology.
He was a man, I think, who tried to see the actual facts for himself,
and to recognize at any price anything that struck him as a fact.
And, wherever we have found that, the reader may agree with me
that our gratitude is due.
40 A critic seems literally to have taken me to be recommending
here a practical trial of every form of vice. I should have thought
that the distinction between the " infinite totality " and the spurious
infinite might have stood in the way of so gross a misunderstanding.
See Ethical Studies (1876), pp. 68 foil.
41 The importance of this " recapitulation " is such that clearly it
should have come at the beginning, as the thesis to be developed in
CHAP. VI THE FINAL ESSENCE OF REASONING 5OI
the account given of Inference. I would now refer the reader to a
summary treatment given in T. E. I. And on " experiment," opera
tion," " identity," and " self-development " see the Index, and cf . the
Notes on Bk. III. I. Chap. III.
42 On the detail of 34 see T. E., I, and cf. the preceding Notes
on Book III, I. II. Further on data and premises, see the Index,
s. v. Premise. And, for the apparent and implicit subject, see T. E. II,
and the Index, s. v. Subject.
43 " The total space," i.e. both as general and as in this case indi
vidual.
44 On Comparison see the Note on Bk. III. I. II. 16. Here for
" special point " we might substitute " special or more special point."
You can hardly compare (we might add) unless it is to compare
further.
45 On "arbitrariness" in Inference see Notes 7 and 10 on Bk. III.
I. II. And before " we effect " and " we introduce " insert the words
" seem to." For a construction, so far as really " external," could not
even make part of a genuine inference.
CHAPTER VII
THE BEGINNINGS OF INFERENCE 1
I. We have seen in what explicit 2 inference consists. It
is a conscious operation, aware that the activity which it
exerts is ideal, and ending in a judgment. This judgment
again is accompanied by the reflection, that what went in at
one end of the process, has come out at the other end. This is
explicit inference, separated, we shall agree, by an enormous
interval from the beginning of soul-life.
It is not the purpose of our volume to trace the growth
which in the end has bridged this gulf. But we can not fully
understand the highest form, unless we have at least given a
glance at the lowest. And we have been compelled already
in our account of judgment, to say something on the nature of
the primitive mind (Book I. Chap. I. 18), and to return to
that theme, when we tried to correct the vagaries of those
whom Association has victimized (Book II. II. Chap. I.).
Once again, and in the present Book, the entanglement of in
ference with judgment brought us face to face with the be
ginnings of reason. And, as we are nearing the end of our
labours, it may be well to sum up, and even to repeat, what we
have to say on the earliest intelligence.
2. That intelligence is scarcely to be recognized ; for it
lacks, as we saw, the chief marks of intellect. It can not judge,
for it has no ideas. 8 It can not distinguish its images from
fact, and so can not unite them consciously to the world of
reality. And thus it can not reason; for its inference, if it had
one, would end in a fact, and not in a truth. It would not be
aware of an ideal activity, but would blindly accept the trans
formation of an object. And even to this point it has not
progressed. As perceived by the dawning reason, the object
itself is unable to change ; since if the change is to be known, 4
the original must be retained, and its sameness held fast.
But such a process is too hard for nascent intelligence. And
502
CHAP. VII THE BEGINNINGS OF INFERENCE 503
so we must not say that it observes the fluctuation of the
object, for it does not as yet possess any object.
I do not mean that in this blurred and confused totality
there exist no differences, and no dim feelings of self as
against a not-self ; 5 for these characters, I believe, are there
from the first and also are felt. And, if it were not so, I do
not see how we could ever have advanced to the place where
we stand. But these differences, though felt, are not for con
sciousness. They are aspects of one feeling, they are not
two feelings, in the sense of two elements which present them
selves apart. They do not appear as two realities, for we
are still a long way from perceiving realities. Hence there
is change in feeling, not alteration in things. And, having no
things, to repeat it once more, we have got no ideas. And so
we have got no ideal processes. Comparison and distinction,
that bring with them a consciousness of agreement and dif
ference, are activities we have not yet learnt to recognize.
We can not even say of two elements that they are like al
though they still are two. There is no memory 6 or expecta
tion, since the past and the future are nought but felt colour
and quality of the present. And there is no world of imagi
nation nor play of fancy, since these presuppose a knowledge
that ideas can exist and be unreal ; while in the primitive
mind no suggestion is retained which does not integrate itself
with felt reality. Dream and waking again bring no known
diversity; for dreams are not recalled, and at a ruder stage
the very difference seems to be absent. We are ever awake,
or live out our lives in a prenatal dream.
We may say that at first the whole ideal side of our minds
is hidden from consciousness. 7 So far as we know it, it is the
mere dumb feeling of elation and collapse, which marks the
continuous flow of sensation.
3. So blind and unintelligent is the childhood of our
intellect, and we might think that no germ of intellect was
there. We might fancy that we saw the mere passive recipient
of external impressions, the sport of sense and of mechanical
suggestion. We might flatter ourselves that at last we were
quit of activities and functions, and had bored too low for a
fictitious reason any longer to trouble us. In this floating tide
of presentation, 8 where nothing is false and nothing is true,
504 THE PRINCIPLES OF LOGIC BOOK III. Pi. I
and where self-consciousness seems only the felt practical
relation with its manifestation of pleasure and pain we might
think that at last we had come upon a soul, which was free
from even the rudiment of those powers that have been
ascribed to the developed intelligence.
But, if we cherished this thought, we should fall into error.
For in the very lowest stage of psychical existence we still can
point to a central activity, and verify there a rudiment of
inference. And a soul, so far as we are able to see, would
be no soul at all if it had not this centre. It would be an
abstraction which can flourish in the heads, and can take its
rest on the shelves of theorists, but which never was actual
and never could have been actual.
4. Physiology gives no countenance to this false idea. 9
It would be presumptuous for a layman to rush in, where
special education gives the right to speak ; but I will confine
myself to a guarded statement. Physiology does not reject
the belief that the beginning of feeling implies the presence
of two bodily factors, a stimulus coming inward from the
periphery, and then a reaction on this from within.* But,
if so, we may be right if we say that the very first glimpse of
sensation is a result of two activities, is a conclusion, so to
speak, from two material premises, of which the central re
sponse makes one. And, if we considered the same question
by the light of introspection, we might find reason to think that
the lowest feeling, which we are able to observe, does exhibit
two aspects, one of which may be conveniently called self-
feeling. I will not venture to assert here what certainly de
mands a lengthy discussion, and I admit that this double aspect
in sensation is a very obscure and difficult point. But I
thought that in passing I might call attention to the fact, that
the mere passivity of our first sensations can be controverted
alike from the ground of psychology and the ground of
physiology.
5. It is better to move towards plainer issues. Let us
suppose, if you will, for the sake of argument, that the first
sensation is a passive impression. But no sober writer will
* I have purposely used the vaguest language, as I do not feel at
liberty to assume that psychical life does not precede the development
of nerves.
CHAP. VII THE BEGINNINGS OF INFERENCE 505
contend that this by itself is experience. The origin of ex
perience, we shall probably be agreed, is to be found in what
is called reflex action. But unfortunately here we are still
in the region of doubt and controversy. When we desire to
know how the physical reflex gets a psychical expression, our
progress is barred. It seems not known, for instance, if the
efferent side of the circuit is ever represented in consciousness,
or, if it is represented, how it comes to be so. The so-called
" muscular sense " appears to be as doubtful an article in
physiology as it is in psychology, and in these pages we are
compelled to avoid it wholly. And our only course is, I
think, to content ourselves with an unfavourable view. 10 Let
us say that experience begins with a reflex which comes to
consciousness, and that, on the psychical side, this reflective
circle starts with a simple passive sensation. Then follows a
discharge which moves our limbs, and brings forth a change
in the immediate environment. This alteration is represented
by another sensation (however produced), which for conscious
ness simply ensues on the first. From this modest beginning
we have to see how the activity of the centre begins to develope
the rudiment of inference.
6. Let a feeling A somehow cause a reflex action /?, with
an altered feeling C. This feeling C comes indirectly from
the reflex, since it arises from the change, in my body and in
the object, which that reflex produces. Suppose now that a
modified A recurs, then by mere reproduction it is followed
again by the action /J; but let us suppose in addition that /?
fails in its former relation to the environment. Then C will
not ensue. The sensation from the object, and the enjoyment
of possessing it, will in this case be absent. But something
else will be present. For part of C consisted in certain feel
ings, arising from changes in the muscles, the skin, and the
organs of secretion. These changes are produced once more by
the reflex; and therefore, although the object is not there, their
feelings will come up. And this is important : for, part of C
coming up, a redintegration will supply us with other parts.
Hence, though the object is not present, though the full sensa
tion and pleasure of possession remains untasted, we yet are
visited by fainter suggestions out of harmony with presenta
tion, and that do not satisfy. This gives us a collision, a
5O6 THE PRINCIPLES OF LOGIC BOOK III. PT. I
contrast between the new presentation and the feelings excited
by the inappropriate reflex action. And in this contrast there
lies an undeveloped inference. 11
We have not yet got anticipation baffled and disappointed
hope; for the mind has not yet reached the stage of expecta
tion. It does not know that its suggestions are mere ideas.
But, for all that, we have already both sides of a process
which must lead in the end to this great distinction. We have
first a modification of sensation by ideal suggestion. We have
next a failure in correspondence and a collision of these
elements. And the pain of accident or unsatisfied desire will
force the soul to consider this contrast, and to make explicit
the difference which it must feel. Both in theory and in
history, it is mishap and defect on the practical side which
gives birth to speculation. 12
7. For the early soul-life (it is a truth we can not repeat
too often) is immersed in practice. 13 It is wholly directed to
the satisfaction of its appetite, first for food and then for the
continuance of its species. The selective attention, with which
it meets the series of sensations, is guided by these heads,
and is governed throughout by the dominant ideas of feasting,
war, love, and social attachment. 14 For the sake of these ideas
it neglects the main part of the offered suggestions. And the
intellect is so unfree, that the very first start that is given to
redintegration may consist, as we saw, in a reflex action which
seems merely physiological. This rule of the " passions,"
and bondage of the " reason," comes down very late in the
scale of evolution, and it is hard to say where intellectual free
dom begins first to show itself. The curiosity shown by the
lower animals, and their apparent love for beautiful objects,
are phenomena which I could not venture to interpret. It
seems probable that pure theoretical curiosity appeared before
man had been developed ; 15 though it no doubt may be argued
that the impulse still remained at bottom practical. But, what
ever we may think on this interesting point, what is certain is
this, that at the beginning of progress the intellect is sub
ordinate, and that afterwards it becomes at least partially
free. And the conclusion I would add is, that the intellect
would never have appeared on the scene, if it had not been
present and active from the first. We may start with a reflex
CHAP. VII THE BEGINNINGS OF INFERENCE 507
that follows unfelt upon a sensation; and the feeling that
ensues may so far be taken as a passive result. But, together
with this feeling, are recalled by a synthesis other elements
which co-existed with it. And this recall has no immediate
practical link. 16 On its psychical side it is assuredly a rudi
ment of intellect and reasoning.
From the first it is a function of undeveloped inference
which enlarges the given by ideal suggestions. The selection
of these suggestions begins with being practical. There is,
so to speak, no attention but appetite. But gradually the
interest becomes more remote. It is held to appetite by a
longer chain of links. And it possesses at last, not a mere
activity, but an end of its own. When this is accomplished
the reason is emancipated ; and the history of the intellect
would recount the setting free of that ideal function which
was present from the first.
8. Such a history would be hindered by many difficulties, 17
and obstacles would arise upon every side. It would find in
secure metaphysics, one-sided psychology, a physiology in
great part unsettled, and a study of the ruder forms of the
soul not long attempted. It was not our object to trace even
the barest outline of development, but to call attention to one
cardinal point. The beginning of intellect, the first rudiment
of reason, is present at the outset of psychical life. In what
is called " association " is involved the vital principle of the
highest logic. 18 For we must repeat once more what we have
insisted on so often. Universals are what operate in the very
lowest minds. We may say the line of least resistance is too
narrow for facts, and that in passing they are stripped and
thinned down to generals ; or that this line, like our fore
fathers ghostly bridge, is no way for more than bodiless
spirits. But, however we phrase it, the result remains that
from the first what works is the universal. It is never the
whole object, it is that in the object which corresponds to the
inherited predisposition, 19 which excites the reflex. It is never
the whole feeling, which by redintegration calls up those
sensations which accompanied the past. It is always an ele
ment particular to neither, but common to both and uncon
sciously typical. The anticipated image is itself again an
implicit universal ; for otherwise how could it ever be identi-
508 THE PRINCIPLES OF LOGIC BOOK III. PT. I
fied with a reality not the same as itself? We need not here
recall the detailed discussion which we entered on before.
If there is any result we may be said to have established, it
is this, that from the first similarity is not a principle which
works. What operates is identity, and that identity is an
universal.
9. In the view which we take of the primitive mind we
have to battle with two counterpart mistakes. On the one
hand we see in the lowest life functions higher than those
which some assign to the highest. The degradation of the
soul to an impossible pitch of decentralization is one of the
prejudices against which we protest. But, on the other side,
we must take our stand against the undue exaltation of early
intellect. With the most debased theory of the beginnings of
the soul go the wildest beliefs in the high capacities of the
lower animals. Now I do not for one moment profess to be
able to fix the limit reached by non-human intelligence ;
but I think some views may safely be rejected. When
animals, confessedly far inferior to man, are represented as
inferring in a manner in which no man does reason, save
when working at his most self-conscious level then, I think,
we may be sure that this idea is erroneous, and that the fact
must here have been wrongly interpreted. 20 We may perhaps
have no real knowledge, but still we have probability.
10. We may illustrate this tendency to an overhigh
estimate by the classical instance of disjunctive reasoning.
The dog, who follows his master s traces, comes to a spot
where the road divides. He approaches the first of his possi
bilities in a spirit of doubt; but, when that doubt is ejected
by disbelief, his mind is made up. He runs confidently down
the remaining alternative ; for he has reasoned reflectively.
He is certain of this that, if one has proved false, the other
must be true. But the instance, I think, is largely fictitious.
The facts are uncertain and the interpretation vicious.
With respect to the facts, I venture to assert that the
ordinary dog does not first examine tentatively one road, and
then confidently and undoubtingly go down the other. What
he visibly does (in a case of ignorance) is to approach both
outlets in much the same way ; or if he hurries to the second,
he does not, with that hurry, show any sign of confidence or
CHAP. VII THE BEGINNINGS OF INFERENCE 509
elation. And the true interpretation is, I think, very simple.
When he comes to the division he does not say, " See here
are two ways and I know one must be wrong, I have therefore
two exclusive alternatives." He does not, I think, enter on
these introductory reflections, but the road which is nearest
suggests the idea of his absent master, and he acts on this
suggestion. Then he fails, and, seeing the other road, repeats
the same process, except so far as delay has increased his
eagerness and hurry. There is nothing to show that he ever
has before him more than one idea at a single time. One
suggestion follows and drives out another, but different sug
gestions are not held together. And we should remember that
the retention of an idea, which, by being denied, forms the
basis for a further positive advance, is a very late acquisition
of the mind. It is hard to believe that, where speech is
undeveloped, this function can be present.
And, if I am told that from examination of the first road
there are dogs who will at once go down the other without
any examination, and that therefore they must use explicit
disjunctive reasoning I will not take back one word of the
foregoing. Admitting the fact, I should consider the interpre
tation absurd. The fact to be explained is the appearance of
the last road as the path of the master, and it is gratuitous to
explain this by the retention of and reflection from the negation
of the residue. It is, I presume, agreed that each road tends
to suggest the master; but, if so, provided only that the
failure of the other roads prevents them from coming before
the attention, the whole fact is explained. They cease to be
suggestions, because they are now made one with the feeling
of failure. They are hence excluded as soon as they are called
up, and the remaining suggestion must therefore seem fact
immediate and simple. I have presumed that, in explaining
the acts of the lower animals, we should not postulate more
intelligence than is wanted in order to account for the
phenomena.
ii. It would be interesting, if it were possible, to dis
cuss in greater detail the intellectual phenomena of the
primitive soul. But, apart from other reasons, we are forced
to confine ourselves here to the general, and may sum up
what we have to say in these words : in the infancy of reason
5IO THE PRINCIPLES OF LOGIC BOOK III. Pi. I
there is no necessity. 21 The nascent intelligence goes to its
result, not because of the premises A and B, but because it
can go forward in no other direction. And even that is
incorrect. It advances, not because it can not do otherwise,
but because it advances. The ideal change takes place be
fore it and is effected by its act; but it has not reflected on
the existence of that change, and still less on its ground.
Thus it sees, not at all because it must see, but simply because
it happens to see. And for this reason disjunctive inference
is impossible. 22 There are no possibilities between which to
choose, since every suggestion is taken as fact or is straight
way excluded. There can properly be no choice where the
mind is not conscious of any ideas. Thought follows the
line of the least resistance ; but it knows nothing of resistance
and nothing of other lines, and it does not know that it is
even thinking. The primitive mind has troubles of its own,
but as yet it has learnt neither its strength nor its weakness.
And there remains an observation I may be allowed to
make. It is possible that the upward growth of the mind may
so have changed or coloured its simplest functions, that we
can not any longer find in ourselves the psychical phenomena
of the lower animals. This is possible, and with respect to
certain special functions it is much more than possible. But,
if we take it broadly, 23 I confess that I see no ground to
accept it as probably true. In the disparaging estimate, if it is
disparaging, I may seem to have formed of animal intelli
gence, I may say that I have done nothing but estimate my
self. Without doubting my own title to rationality, I observe
in myself at my less conscious moments those processes and
those feelings which, with certain exceptions, seem to explain
the acts of the lowest creatures. And these processes are
united to my highest functions by one steady advance of one
single principle, first unconscious, then reflective, but always
reasonable.
12. My excuse for these poor yet repeated remarks is
on one side the great importance of the subject, and on the
other side the cloud of prejudice which darkens it. It must be
difficult in any case to study the minds of the lower animals ;
and it is more than difficult when we come to the task with
false preconceptions. It will perhaps be no unfitting end to
CHAP. VII THE BEGINNINGS OF INFERENCE 511
this chapter, if we try to signalize the most mischievous of
these.
I may mention, as a leading cause of error, confusion of
ideas as to general psychology. An investigator will discuss
such questions as. Have dogs got " self-consciousness," or
Have they " the power of abstract reasoning," when the ap
proximate meaning of these terms is not fixed. Now in our
selves we can observe a number of stages, beginning with
the dimmest feeling of self, and ending with reflective intro
spection. It is idle then to argue about the dog s " self-
consciousness," when we have not tried to settle, even within
limits, what the word is to stand for. So again with the
power of " abstract reasoning." If we begin our enquiry
without asking in what way, and by what steps of develop
ment, such reasoning is divided from the inference which
simply serves to qualify further a present perception how
can we expect to go right in the end ? One very great obstacle
to the study of animals is defective psychology propped by
bad metaphysics.
This vitiates interpretation, but observation itself is largely
vitiated. There is a tendency in the lovers of domestic animals
towards credulity and exaggeration. As we approach the
facts, we too often find that their stories dwindle, like the
tales of ghosts. And the tendency, I think, is not hard to
account for. The mere unlikeness of the other animals to
ourselves suggests something unknown, and the unknown is
mysterious. And, besides, there are powers possessed by these
animals, which we do not possess and find hard to explain.
This suggests the possibility of marvels without end. And
another common source of mistake co-operates. The observers
of animals too often forget to note the occasions where
stupidity is shown. These they pass without remark and as a
matter of course ; and thus they escape the difficulty they would
find in showing how such different grades of intelligence can
exist in one being.* For, if you interpret the successes of a
* For some years, while noticing the habits of my dogs, I observed
the views taken by others of their conduct, and was impressed by the
general readiness to accept any kind of explanation, provided only it
supposed a high degree of intellect. In speaking above of powers that
we do not possess, I mainly allude to what (perhaps not very happily)
512 THE PRINCIPLES OF LOGIC BOOK III. FT. I
lower animal by direct analogy from the highest functions of
the human intellect, you should apply the same principle to all
his failures. The total consequence would be a strange com
pound.
13. The two obstacles, which we have noted so far, are
a crude basis of theory and then uncritical observation. We
pass from these to the doctrinal prejudices which rise from
the idea of evolution. These prejudices show themselves in
the desire on one side to minimize the difference between man
and beast, and on the other side in the wish to suppress their
points of similarity. But, in each attempt, there surely is a
want of understanding. If we believe that the highest has
come from the lowest by the operation throughout of a single
principle, it is surely a derogation from that principle, when
we are fain to help it by shortening its course. If its triumph
is to pass from one extreme to the other, then by moving the
goal you must abridge the triumph. And again, since in any
case the actual genealogy has not been recovered, I confess I
do not see the object of hurrying the historical progress, and
of straining oneself to reduce the chain by some links at one
end or at the other. We must agree, I think, that in combating
prejudice, the theory of descent has itself used prejudices.
But, on the other side, what are we to say of our would-be
conservators of human dignity? How can those, who are not
slaves to a childish mythology, persuade themselves that any
real interest of their souls can be jeopardized by an ape-like
ancestor? For consider, although you deny this parentage,
yet the basis of your being is too plainly animal. Though
more than a beast, yet, however you have come here, you
assuredly are still a beast among beasts. But you will say,
" This more, that divides me from the rest, is lost if my first
beginning is beast-like." Most foolish rejoinder, for what
do you fancy is your own private history? If the coming
has been called the " sense of direction." There seems no ground 2 * to
doubt that some animals are aware of distant objects, in a manner not
explicable by smell, vision, or hearing. There is obviously no great
antecedent improbability in the idea that different animals may have
diverse senses. And, at the cost of a digression, I should like to sug
gest that this " sense of direction," if properly established, would be a
ready explanation of most forms of second sight among human beings.
These phenomena, if we suppose them real, would arise from the sur
vival and abnormal reappearance of a sense in general aborted.
ClIAP. VII THE BEGINNINGS OF INFERENCE 513
together of two miserable microscopical pieces of matter was
in any case your origin, what worse is left behind to destroy
or threaten your immortal aspirations? If you do not blush
to acknowledge the spermatozoon, why scruple to own the
paternity of the ape? It is a sensitiveness which seems irra
tional, and which history will mark as a ridiculous prejudice.
And it is the more ridiculous, since the question of the
temporal union of each soul with its proper body was a topic
for dispute long before Mr. Darwin fluttered the Church.
It is hence not obvious to the mere stander-by how this in
teresting uncertainty about our ancestors can add much ma
terial to the former dispute, or how it can have closed that
pathway of salvation which, I presume, the Church must at
some time have found. And, until we have some explanation
on this head, I think we must conclude to one of two things :
if the present outcry is not ridiculous, the former calm was
not very creditable.
But it is absurd, so long as in every man s history the
transition has been made from the lowest to the highest, to
think that by exaggerating the differences which exist between
man and beast, you tend to disprove a transition of the
race from one to the other.
14. The prejudices, which up to this point we have re
viewed, may fairly be classed as intellectual mistakes. But
there remain at the bottom of the wish to disparage and be
little our inferiors the threatened hopes of a privileged class.
What seems threatened is man s heritage of a life after death.
For, if the beasts are his kin, then, since the beasts perish, he
may perish with the beasts, and his claim to that after-land of
pure torture and delight seems greatly shaken. But, on this
ground once more, I confess that I see no just cause for alarm.
And I would first recall to the orthodox Christian champion
of human nature something he may have forgotten. The new
dispensation knows no natural claim on the part of man to
anything but unpleasantness. And hence, if we can not hope
in our own nature, we can certainly have no reason to dread
that nature s abasement.
And then from any point of view that is not quite ortho
dox, and that attempts to be even a little rational, what loss
is threatened in the other world, if we admit our kinship with
the lower animals? There are difficulties in the way of their
2321.2
514 THE PRINCIPLES OF LOGIC BOOK III. PT. I
immortality. But are there none in our own case? Are
there much more or less in one case than in the other? You
will answer perhaps, " I can not draw any line within the
animal kingdom." Will you draw me then a line in the life
of a man, and mark one period in his strange development as
the birthday on which he is given his immortality? When
such questions as these are once discussed by daylight, the
answer is certain. Our relationship to the beasts would not
lessen any hope, save that which comes from superstition or
prejudice.
15. But, as we set ourselves free from our selfish hopes
and brutalizing fears, we free ourselves too from the belief in
our isolated origin and destiny. The same joy in life, the
same helpless mortality, one common uncertainty as to some
thing beyond draws us nearer to all the children of earth.
The frank recognition of a common parentage leaves us still
the rulers of our poor relations, but breaks down the barrier
which encourages our cruelty, our disregard for their miseries,
and contempt for their love. And, when this moral prejudice
is gone, our intellectual prejudices will not long survive. We
shall not study the lower animals with the view to make out a
case or a claim, but for the pleasure of finding our own souls
again in a different form; and for the sake, I may add, of
understanding better our own development. If such a study
would tend on the whole to inspire us with a warranted self-
confidence, it would call up some feelings of self-reproach and
pity and shame.
We must return from this digression. We have described
the general nature of inference, as it appears in the special
kinds of reasoning. We have shown how the principle remains
the same throughout all stages of psychical evolution. And,
while protesting against the confusion of these stages, we
have used the occasion to point out some prejudices. I would
end with the remark that, if we will but keep hold of and
be in earnest with the idea of development, we shall lose
all wish to pull down the higher or to exalt the lower. We
shall ask throughout for identity of principle; and, above all
things, we shall not try to get that by diminishing the wealth
of varieties and stages of progress in which the single prin
ciple has found realization.
CHAP. VII THE BEGINNINGS OF INFERENCE 515
ADDITIONAL NOTES
1 1 may perhaps be permitted to call attention to the real importance
of this Chapter. The reader will not, I trust, regard it, together with
the criticism of Association (Bk. II. II. I.) as a mere deviation into
psychology. Certainly psychology for its own sake has always at
tracted me. And, merely from this side, I should have been forced
to reject the doctrines which I found most current in my youth. And
I judged, further, that a philosophy, if wrong fundamentally, must
also be unsound at its psychological basis. I could not, from the
other side, accept the idea that a psychology could hold good up to
a certain point and hold good no higher. And one aim of this book
was hence to show that a truer logic must imply a diverse view of
psychical fact. Judgment and Inference in other words, when in
terpreted rightly by logic, must show their essential nature even at their
psychical beginning. They must in an undeveloped form be actually
there, and must be really effective at the earliest stage of mental life.
This is the conclusion at which the psychological enquiries of this
volume are aimed and which they endeavour throughout to enforce.
My interest in psychology led me early to consider Hegel s views
on this subject. But I have never pretended to be, either here or
anywhere else, a Hegelian. There is much in Hegel s psychology
which I do not understand, and there are things in it from which,
as I understand them, I am forced to dissent. Still it was here that
I found that help which I needed the most. To learn that Association
holds only between universals was to pass from darkness into light
(see Bk. II. II. I, Note i). And Hegel s doctrine of Feeling, as a
vague continuum below relations, seemed and seems to me to have
an importance which really is vital. Against an exaggeration of this
importance Hegel often, and perhaps too sweepingly, protests. But
his main doctrine here was to myself the formulation of that which
I had felt to be the fact. The reader must be referred here mainly
to Hegel s Encyk., 399 foil. And the information in Volkmann s
Psychologic (Ed. II or III, 127) may perhaps prove useful. My
knowledge of the history of modern psychology does not, I regret,
enable me to say how far here Hegel has followed others, as, I pre
sume, he has followed Aristotle.
If I am asked why I then did not in this work refer to Hegel s
psychology, I would refer the reader in general to what he will find
in the Preface. I did not, and do not, know the limits of my indebted
ness to Hegel; and, if once I began to acknowledge what I owed, I
felt that I might be taken to deny or to ignore, wherever such an
acknowledgment was omitted. I feared to fall into at least a tacit
claim to originality, a claim which through my whole career I have,
I hope, everywhere avoided, and with regard to which I entertain a
feeling of something like contempt. Still I admit that, in the present
case, another course might perhaps on the whole have been better.
5l6 THE PRINCIPLES OF LOGIC BOOK III. PT. I
1 will not try to recall other writers on psychology from whom
also I got help, but I am now forced to add that Prof. James (much
as I value his work) was not among them. He himself even credited
me here with an originality which I had to disclaim (Essays, pp. 152-3).
Since his death, however, Dr. Schiller has (as I understand him)
suggested, in Mind, No. 95, pp. 348-9, that the unacknowledged source
of the following Chapter is to be found in two articles published by
Prof. James in Mind in the year 1879. He seems to intimate that
I, as being (according to him) a faithful reader of Mind, must have
read and used these articles. Now not only would anything at that
date have found the doctrines of my Chapter already familiar and
established in my thought, but, in addition, I had never in 1883 so
much as seen or heard of the articles in question. I did not, at the
time when they were published, read or see Mind regularly and con
stantly (as seems intimated), but, on the contrary, seldom and ex
ceptionally. And I can assure the reader that there is nothing in
the whole volume of Mind for 1879 with which in 1883 I had any
acquaintance. As to Dr. Schiller s further assertion or sugges
tion (ibid., p. 347) that what I say I derived here from Hegel is not
to be found in his writings, the reader will perhaps permit me to
take this as at once characteristic and negligible.
Passing from this point, and in view of the defects of the follow
ing Chapter, I must ask the reader not to forget the date at which
it was published. I have left it with almost no attempt in these
Notes to mention, much less to remedy, its shortcomings. And I
wish that I could add that, even if space permitted, such a perform
ance would be within my power.
2 " Explicit inference." The word " explicit " appears to be used
here so as to imply not only " consciousness " but even " reflection."
But to include the latter aspect seems certainly indefensible.
3 " It has no ideas." Add (here and again lower down) "known
to be such"; and after "it can not reason" add "consciously." Cf.
11. Further, after "an ideal activity," add "though that certainly
is there." For what is called " ideality " see Appearance, the Index.
4 "If the change is to be known," i.e. in its proper character as
change, and is to be more than merely felt. See, once more, Appear
ance, the Index, s. v. Change.
5 " No differences . . . not-self." Felt differences might of course
be there at first without the above specific " dim feelings," and this
is the view which I took later in Mind, O. S., No. 47, and to which
I still incline. This very difficult question is fortunately for the
present purpose irrelevant, and may here be ignored. It has, however,
great importance in its bearing on the nature of our experience of
Activity. For this see Appearance, Index, and, specially, the references
to Mind given on p. 607.
The view which was taken by me in this Chapter may be stated
as follows. Every change in feeling is an incoming disturbance which
involves a reaction on the side of that which is changed. This re
action shows itself within every feeling as an integral and also dis-
CHAP. VII THE BEGINNINGS OF INFERENCE 517
tinguishable aspect. And the felt group which habitually reacts is
a central core which is later the basis of what we call self. I can not
now be sure whether, and, if so, how far, the " feeling of elation
and collapse" (2) and "the felt practical relation" (3) are in these
pages taken as precisely identical. But see Note 13.
6 " Memory." See Appearance and Essays, the Indexes.
7 "The ideal side," which, however, is there and is felt (cf. Note 3),
though not recognized as such (cf. 7 and n).
8 " Presentation." By this I meant simply " what presents itself "
in the sense of " what comes." But this use, I found later, caused
difficulty, and it would have been better avoided. In the same way
" Sensation," in 2 and 4, was not used as distinct from " feeling,"
but as one aspect of the felt. For the " felt practical relation " see
Notes 5 and 13.
9 Physiology. The reader will content himself, I hope, with taking
what follows here for anything that he may find it is worth. Cf.
Bk. III. I. VI. 20 foil, for the above, and for the " two material
premises."
10 " An unfavourable view." What, for the sake of convenience,
is supposed here is that, in reflex action, a passive sensation comes
first, and that the final result of the reflex is to show this sensation
altered. But the reader will note how much in this (I need not point
out how much) is mere imaginary hypothesis, offered simply to make
the main argument more plain.
11 " An undeveloped inference " which in itself is not practical.
Cf. Notes 13 and 16.
12 " Mishap and defect." Cf. Bk. I. I. 20, and I. II. 73.
13 " Immersed in practice" (cf. Bk. I. I. 20). "Practice" and
"practical" (the reader should know) are terms used too often am
biguously and blindly (see Essays, Index). The differentia of
"practice" is alteration of existence (Bk. I. I. 15), and "mainte
nance " should fall here under the head of " alteration " (Essays, p. 83,
note). Hence whatever I do is practical, so far as I do it; for so far
it obviously alters existence. To lose sight of this aspect, and to treat
ideal activities as lacking a practical side, is a serious error. And it
may lead to that counter-error, no less serious, for which whatever I
do is practical mainly or solely. But the question, in every case to be
asked, is What is here my special aim, and how far does the product,
when the end is gained, qualify the resulting existence as its adjective?
Now clearly an affirmed truth is, in its essence, not the adjective
of its affirmation. As truth, it is true obviously of something else,
and so far (like beauty) it is ideal and transcendent, and is, so far,
not practical. And, from the other side, in " practice " everywhere
is involved mental activity which itself is not practical, except in the
sense that here it subserves practice. " Practical " and " ideal " activity
are in short not two things that you can view as existing separate,
each apart and by itself. An activity is practical or not practical
according to that aspect of itself which predominates, and which you
take as here the end and the essence of the matter. And, without
5l8 THE PRINCIPLES OF LOGIC BOOK III. PT. I
denying that " practice " offers a difficult problem, I am convinced
that in the above lies its one possible solution, and that this is the
only way of escape from one-sidedness and from dangerous error.
On " practical," as used for the " working " aspect and detail of
what is theoretical, see the Index, s. v. Practical. And on the whole
of the foregoing see T. E., No. XII.
Passing now to " early soul-life," I think that it was right to call
this practical, as aiming mainly at the conservation and alteration of
existence, though the existence may, as in sexual activity, be that
only of the species. On the other hand, even in the earliest psychical
activity, we find a side which is not itself practical (cf. Note 16).
And again at what point, in animal life, ends other than practical first
appear, is a question not to be ignored.
If we turn now to the doubt, raised above (Note 5), with regard
to the " feeling of elation and collapse " this feeling will always be
practical in one aspect; but still that aspect may, in a given case,
be merely subordinate, while the main essence is ideal. And the same
thing holds again ( 3) with regard to pleasure and pain and what is
called " self-feeling." It would be a ruinous mistake to regard these
as being practical solely, or even, in their main essence, as practical
always. And I do not think that anywhere in the present work that
error was made.
14 The reader will note that I am speaking here of life in general,
and not merely of human life. Hence such terms as "feasting" and
" war," &c., used below are in part metaphorical only.
15 " It seems probable." I should now think it safer to qualify
this statement by " perhaps."
16 " Has no immediate practical link." See Note 13.
17 " Many difficulties." The reader will remember that this refers
to the year 1883.
18 For Association and Universals, see Index, s. v. Association.
19 " The inherited predisposition." This is a point which is not
essential here, but to which psychology would of course attach a very
serious importance.
20 I was thinking, here and lower down, of the vertebrate world.
To deal with the problem of insect-intelligence was and is beyond me.
21 " There is no necessity," i.e. conscious necessity. Cf. Note 3.
22 On Disjunctive inference see on Bk. III. I. II. 25, and on Choice
see on Bk. I. IV. i.
23 To insert " enough " after " broadly " would be safer. See
Note 20. In the " special functions," mentioned above, as in the
" powers " spoken of in 12, I, no doubt, had in view what is referred
to later in 12, footnote.
24 " No ground " may, as to higher animals, be perhaps too strong,
but the insertion of " great " before " antecedent improbability " was
not called for. I can not now recall the actual origin of the following
suggestion with regard to " second sight " ; but it may well have been
borrowed from what I found in Hegel s psychology.
BOOK III. PART II
INFERENCE CONTINUED
CHAPTER I
FORMAL AND MATERIAL REASONING
i. The words matter and form have an ominous sound.
They tend to waken echoes from unknown windings of for
gotten controversy. But we mean to be deaf, and these mur
murs must not stay us, now our logical voyage approaches
its end. We must neglect the metaphysical questions in which
these terms would entangle us, and even their logical bearing
we shall not try to deal with exhaustively. Nor again do
we purpose directly to discuss all the claims of the so-called
Formal Logic. Our object in this chapter is to make such
remarks, as may tend to clear up what has gone before.
And we hope in the process to dispose of some prejudices, and
finally to get rid of some clinging illusions.
2. If " formal reasoning " meant that we use a bare form,
and that we work with this, as it were with a tool, on the
matter of our premises, this assertion might very soon be dis
missed. For we have no bare forms we can so take in hand.
The principles of Identity, of Contradiction, and of Excluded
Middle, are every one material. Matter is implied in their
very essence. For without a difference, such as that between
the letters A and B, or again between the A in two several
positions, you can not state or think of these principles (Book
I. Chap. V.). And the nature of these differences is clearly
material.
It is no answer to object that the matter here is not
special, that the form will work with any material, and that
the given material in each case does not formally affect the
result obtained. It will not do to argue that, since with all
matter the identical form reappears in the end, and in every
52O THE PRINCIPLES OF LOGIC BOOK III. PT. II
case its action is the same hence the matter is passive. That
would repeat a fallacy which has wrought havoc in meta
physics, and which in particular is one main support of
Materialism. You can not conclude, because a male proves
fertile with every known female, that he therefore supplies the
principle of fertility. That would be quite absurd; and it is
always absurd, when a result appears from a pair of elements,
to argue, Because the specialty of the element on one side does
not affect the general type of the result, the other element is the
sole cause of this type. For something common to all the
different cases may exist and may work from its material side,
and hence some matter after all may belong to the essence of
the formal activity. The " bare " form may be nothing with
out " bare " matter, though indifferent to the varieties of cloth
ing and colour.
3. If formal reasoning means reasoning with a naked
form, then it has no existence. It is a sheer illusion and
impossibility. The form, that we use as a principle of ar
rangement, is not form that can dispense with every matter,
but that is independent of this or that special matter. 1 The
material element, which remains indispensable, is a general
quality which can exist in any number of instances. Thus
the form is no longer form absolute but relative.
Now, if we understand form in this relative sense, can
we say that reasoning has a formal character? Or rather
let us ask what we should mean by such a statement. We
might mean, that an inference, if it is to be valid, can be
shown as an instance of a certain type. We might mean,
that is, that the relation, which is brought out in the con
clusion, results from the relations given in the premises, and
that all these relations in their proper connection can be antici
pated in theory and reduced to formulas. And we might add
that, although for actual reasoning you must possess special
matter, with which to fill up the blank type of these formulas,
yet this matter which falls outside the blanks is wholly inactive.
The relation, which unites the terms in the end, is hence not
specialized by the particular premises. It is simply the old
relation of the formula which, supporting a load of extraneous
content, has come out unaltered. Upon this view we may
say that the type is a vehicle.
CHAP. I FORMAL AND MATERIAL REASONING 521
If this is what we mean by reasoning being formal, then I
will not say outright that we speak of the impossible. 2 For
by a stretch of fancy we perhaps might conceive a realm in
which this logic would be adequate. But it does not corre
spond to real experience. It is not merely that the syllogism
has broken down, and that it covers at its best but a portion
of the subject. It is that no possible logic can supply us with
schemes of inference. You may have classes and kinds and
examples of reasoning, but you can not have a set of ex
haustive types. The conclusion refuses simply to fill up the
blanks you have supplied. It may show a term not given
in the premises. It may produce a relation not anticipated in
the scheme, a special connection that arises from the indi
vidual synthesis of the elements. And the attempt to pro
vide for these endless varieties is, as we have seen (Book II.
Chap. IV.), irrational and hopeless. In this other sense of
formal reasoning we can see no more than another illusion, a
mistake which is increased if we confine ourselves to the
figures of the syllogism, and aggravated if we read those
figures in extension.
4. Formal reasoning so far has turned out a mere blunder.
Let us look at its opposite, and see what we can make of
material inference. If this meant that the conclusion was
really not got by work on the premises, 3 but required the
addition of some other matter, then of course it would not be
reasoning at all. But if material reasoning merely means such
reasoning as is related to fact and refers to reality, then this
is an essential quality and mark of every kind of inference.
That judgment and reasoning could be confined to ideas was
an error which long ago we got rid of. So that if " material "
is a name for what transcends mere " concepts " and commits
itself to truth, then of course all logic must be material.
But if, leaving such clear truths and such plain mistakes,
we understand our term in a different sense, we may get
some fresh light thrown upon the subject. Material reasoning
might mean such an inference as neglected wholly the form of
the premises. It might be taken in the sense of a conclusion
which comes from the data when used in their full particu
larity. Given certain elements in a particular arrangement, it
might be urged that we get to a fresh result, though we have
522 THE PRINCIPLES OF LOGIC BOOK III. PT. II
used our starting-point as this arrangement. The conclusion
has come from the whole special case, and not by virtue of
anything it could have in common with another arrangement.
5. But, if we made this attempt to rehabilitate reasoning
direct from the particular, we should once more end in failure.
All arguments, as we saw, fall under certain heads, and to
this extent must forgo singularity. But this is not all. In
every inference there must be in the premises something which
does not co-operate in the work, 4 something which is carried
by the process into the conclusion, but which itself is not
active in carrying that conclusion. There must after all be in
every argument a matter w r hich is not relevant to its form.
I do not mean to repeat the most evident truth, that to
reason from mere particulars is impossible. 5 That delusion, if
not dead, for us is done with. It is palpable that, starting
from sensuous images, you denude them by an unconscious
selection and use them as types. It was not this I meant;
but I wished to assert that, taking your premises in their proper
character, and reducing them to that logical content which you
really use, you still everywhere have something which stands
to the form of the argument as its matter. You have on the
one side a process which is able to exist with another different
context. On the other side again you have a concrete detail,
which appears in the basis and the result, but which does not
seem to contribute a special character to the process. In this
sense all reasoning is both material and formal, and in each
case we can separate the matter from the form. We can find
in each peculiar arrangement an arranging principle which is
not peculiar.
6. We should all admit that an inference which did not
hold in another example, was not a good inference. We
should agree that with every argument there must always
be some imaginable case beyond the present, 8 in which the
principle of the argument would hold. And we use this as a
test and trial of our reasonings. We do not merely apply the
argument itself, as an abstract form, to more concrete in
stances, with a view so to prove it by detailed results. We
do more than this. We make variations within the content
of our argument. Thus we clear the principle from the
matter that accompanies it; and, by verifying this principle
CHAP. I FORMAL AND MATERIAL REASONING 523
in a parallel instance, show that our conclusion was not got
by making use of irrelevant matter. But this process implies
a belief that all reasoning has a passive detail, which does not
co-operate in producing the result. 7
And the belief is well founded. In " A south of B, and C
west of B, and therefore C north-west of A," the relation of A
to C is not got by virtue of the A and the C. These are
carried by the spatial interrelation, but they contribute noth
ing special towards it. Their differences fall outside the
form of the argument. Take another example, " D = E, and
E = F, therefore F D." Once again the letters, which we
use, make no difference to their own arrangement. You must
indeed have some terms or you could have no relations, but
the specialty of these terms is quite inactive. It is simple
matter arranged without regard to its private claims and
peculiar character. If we take even such an abstract instance
as " one and one = two," still here we can verify the same
distinction. It may be said rightly that the units are com
bined to make the integer, that the integer is perceived to have
a new quality, and that finally the identity of the units
on both sides is affirmed in an equation. And it may be fur
ther asked, Is there anything irrelevant in the whole of this
process? Beside the general principle of addition have we
not the activity of a special experiment, to which the whole of
our datum contributes? But, I answer, two units can hardly
be conceived quite naked and pure. Some shade of quality,
some lingering touch of exclusive relation in time or space is
obscurely present, and it makes a difference between these
units and other possible units. But, if so, such differences
will be immaterial to the argument, and they will stand out
side what may be called the form. And in Dialectic reasoning
(if we do not pass this by) we shall find the same feature.
I can not believe that the ideas, which we employ, are ever
quite pure. We may indeed use that element in each which
is strictly relevant, but I think we shall find that other elements
are there. And these passive diversities, which vary or might
vary, can be called once more the matter of the argument.
If we had an inference in which all the qualities of our
content were active factors in producing the result, in that
case the matter and the form would be inseparable, and we
524 THE PRINCIPLES OF LOGIC BOOK III. PT. II
could no longer distinguish them. The argument would in
deed belong to a class more general than itself, but its work
ing principle would be confined within itself. 8 There would
be nothing that was passively carried into the conclusion ; and
so, in this sense, there would be no matter.
But if such reasoning is an ideal 9 which we can never
realize, then everywhere we may speak of the form of an argu
ment, as distinct from its matter.
7. Let us sum up the result. There is no absolute
divorce of matter from form, but there remains after all a
relative distinction. All reasoning is formal, and is valid
solely by virtue of its form. Every inference not merely
belongs to a class, or a head of synthesis, but each has a
principle which is, so to speak, its soul. In each we can
distinguish 10 between passive and active, between the part that
carries and the part that is carried.
But, having gone so far, if we please we may go farther.
Having distinguished we may separate. We may extract the
active principle of the inference, and may stale it in the form
of a general axiom, exemplified and instanced in the actual
argument. We may write it at the top of this actual arrange
ment, and call it, if we please, the major premise (cf. Book
II. I. Chap. IV.).
8. It is not a major premise; it is not any sort or kind of
premise; for it never has appeared before the mind. It is a
function, not a datum; nor will any way of treatment trans
form its character. The major premise, we have seen, is an
illusion (Book II. Part I.). We have already exposed it,
and return to it here that we may finally show its root in
the truth. It is worth while to repeat ourselves, if we only
in the end can get entirely clear of this obstinate prejudice.
The defender of the syllogism may wish to take advantage
of our latest result. If every inference has a matter and form,
then, by using this form as a major premise, we can show
every inference in the shape of a syllogism. But this possi
bility of reduction, he may urge, is a proof that the syllogism
is the normal type. And I will add a few words on this
exhausted theme.
In the first place I may remark that all valid arguments
may as well be reduced to the shape of equations. If success-
CHAP. I FORMAL AND MATERIAL REASONING 525
ful torture is a source of evidence, then torture will disprove,
as well as substantiate, the claims of the syllogism.
But this is a mere argumentutn ad hominem; and it is better
to expose the root of the mistake.
9. We have proved that there are reasonings without
any major premise. We have proved that to abstract all the
principles of these reasonings, and to set up a complete and
exhaustive collection is quite impossible. We have proved
again that the principle of an inference, when procured and
explicitly stated as a major, may be something quite strange
to us, that we do not recognize, and that we never could have
used as a premise in argument. I will not do more than allude
to these points, which I think have been made evident, and I
will go on to consider the last defence of the syllogism. It
may be said that, if in the end all reasonings will take this
form, it must be in some sense a general type.
Let us consider this claim. It rests on the fact that, having
used an inference and obtained a result, you can then abstract
the form of that inference. You did not use this form as a
premise, since it was not a datum. But you can use it, now
that it has come into your hands. And, so restated, the
inference after all will be a syllogism. This, I think, is the
claim, and we now have to show its utter worthlessness.
10. It is worthless for this reason, that your major, when
you get it, may do no work. It may stand above the actual
process, and contribute nothing to the production of the result.
What will happen is this, that your minor will contain the
real operation, and the major will be simply not used at all.
Let us take the inference, " A precedes B, and B is con
temporaneous with C, so that C must be later in time than A."
We have to make this take the shape of a syllogism, and we
do it by abstracting what we call the form. " What is prior to
anything is prior to that which co-exists with the latter," or,
" When two events co-exist, and a third precedes the first, it
stands also in the same relation with the second ; " this be
comes the major. In the minor, of course, we have to bring
the instance under the principle ; and the minor therefore will
be simply the whole of the former premises. Then what is
the conclusion? That of course asserts of the instance in the
minor the predicate given in the major premise. The predi-
526 THE PRINCIPLES OF LOGIC BOOK III. PT. II
cate is a relation of antecedence and sequence, which, when
transferred to the instance, is the relation which holds be
tween A and C. And the result is undeniable; it is certainly
correct; but then it does not result from the major. It is
simply the old conclusion from the old premises, which are
now restated in the minor. The minor unassisted did get out
the result, and it is natural to suppose that the minor still con
tinues to get it; while the major remains inactive and but
idly presides.
Let me further explain. We are offered something in the
shape of a syllogism, and are supposed to use a function of
subsumption. Do we use this function? Do we, holding the
principle, then fill up the blanks with A, B, and C, and so get
our conclusion? Or is it not rather true that we do precisely
what we did before, that is make a construction of A, B, and
C, and so get the relation? But, if so, the major will be
simply otiose. I do not say that its presence makes no kind of
difference. For at first our construction was not reflective; it
was performed unconsciously. And now we, consciously and
with some foreknowledge of the outcome, apply the same func
tion. But still we apply it; we do not cease to arrange A, B,
and C in our minds. We do not pass into the category of
subject and attribute, 11 and so get a predicate A-C by a mere
subsumption.
Take another example. We have two pairs of equals, AB
and BC. By holding these together we perceive that their
quantity is the same throughout. From this we go to the prin
ciple, " When two terms are each of them equal to a third, all
these terms are equal." We then construct a syllogism with
this axiom as the major, and bring out the old conclusion,
A = C. But, in getting this result, do we cease to obtain
the relation of equality by holding A, B, and C together, and
by perceiving their identity ? Do we say " A and C are equal
to the same," and then, without any synthesis through B, go on
to our conclusion by a mere subsumption? Is not the other
course more natural, and is it not more rational? If we keep
to those cases where the subsumption is possible, is it not some
what frivolous?
ii. It is in most cases possible. If you do not mind
frivolity, you can torture most inferences into a syllogism of
CHAP. I FORMAL AND MATERIAL REASONING 527
the kind which we have just described. Nay, there are some
cases where no torture is required. For where an operation
has been repeatedly performed, the connection between end
and beginning grows familiar. We can dispense at last with
a lengthy process, and, using the axiom, go at once to the result
by a mere subsumption. And I will not deny that the axiom
of equality may be so made use of. But the subsumption in
these cases will be rarely explicit. Even here what we use will
not be a syllogism. Still we do here use a function which,
when stated explicitly, would be syllogistic.
In these cases the major may be said to do work. The
function which established the axiom does not operate; and
the conclusion is reached by an act of recognition, which,
when you make it explicit, and so gain another premise, will
fairly take the shape of a syllogism. We admit that (in these
cases, which still are not syllogisms) the reduction is rational;
and we admit again that in most other cases the reduction is
possible, though utterly frivolous.
12. But for all that the claim of the syllogism is worth
less, for the reduction is not always even possible. You must
come to a point where the attempted subsumption proves
wholly illusory. For consider a regular syllogism itself. This
contains a function which is not a premise. If I argue, because
any man is mortal and John is human, that John must die,
the general form of the synthesis is not given. We must write
the whole of the argument as minor and conclusion, and for
major we must take such an axiom as " What falls under the
condition of the rule falls under the rule." Under this major
our former inference is subsumed as a special instance. But
now mark the difficulty. This fresh subsumption is an active
function, and hence its principle should find expression in a
major. But what is this major? Suppose we agree that our
last axiom was ultimate; then once more this same axiom
must be written at the top, and it thus will figure as the
principle of itself.
What I mean is this. If you will reduce to subsumption,
in the end you must come to something final, and your sub-
sumption will consist in the use of a principle, in order to
bring another use of this same principle under itself. You
have first an argument based on a certain function of syn-
528 THE PRINCIPLES OF LOGIC BOOK III. PT. II
thesis; you have then the connection of this argument with
its function, based once more on a function of synthesis;
and the first and the last of these functions are identical.
They are absolutely the same. But, if so, I would ask,
is your reduction not worthless? If you use in the end the
precise form of synthesis, which you used at the beginning,
why not be willing to stop at the beginning? Why not openly
say, I used a function but did not subsume under it; and my
further reduction has simply made me conscious of what I did
do? It has not changed the function; it has but given it self-
consciousness.
Reduction to the shape of a syllogism makes explicit the
function of the inference, and it does not substitute another
function. But from this we may proceed to a result unwel
come to the friends of the syllogism. For if the function we
begin with is not syllogistic, we deceive ourselves in thinking
that, by going back far enough, we transmute its character.
Suppose that A may be b and may be c, but nothing beyond;
and then we argue from the absence of c to the presence of b.
This clearly is not syllogism. But you say it is syllogism,
when you write " Where I can not do otherwise I must," 12 and
repeat the inference as a case of this major. Entire delusion;
for how is it that you know that your minor comes under the
condition of the major? By a function of subsumption. And
the principle of this subsumption is whatever axiom you agree
to take as the basis of syllogism. But then that principle itself
is not so ultimate as the axiom that you must where you
are unable to do otherwise ; and hence it must stand and be
based upon this latter axiom. What is the consequence?
The consequence is that in the syllogism, which you manu
facture, you really do use the more ultimate principle which
you used before. But, if your reasoning actually were syllo
gistic, you would have to use the subordinate principle. This
would mean that the use of a higher function is taken as the
use of a lower function, and in the end, if you carry out
your process, must appear as one case of a subordinate prin
ciple.
13. You can not transmute all inferences into syllogisms
by extracting- their general function of synthesis. For that
function, when exhibited in its abstract form, continues in
CHAP. I FORMAL AND MATERIAL REASONING 529
most cases the very same work which it performed before;
and in some cases it can not do else than continue. The
difference, which we have made, has been therefore no differ
ence to the action itself. It has been a difference to our
knowledge of the action. We have not changed the nature of
our function ; we have simply made a reflection on that nature.
But, if so, we must say that the syllogism, which we have
constructed, if taken as showing the actual process, is a blun
der and mistake. It is instructive only if you take it as a
mere mode of reflection, by which we explicitly state and lay
down the function which we use apart from that reflection. 13
This final exposure of an old superstition shows the root
by which it keeps hold of our minds. There is in our argu
ments a form more abstract than the arguments themselves.
And it may be useful to separate this form from its matter,
and so perform self-consciously the very same act which we
accomplish unawares. And if this extracted major be under
stood as the statement of a principle which operates in the
minor, and if we remember that it is the minor, and the minor
alone, which in these cases gets the conclusion, there is then no
harm in our continuing to use a logical tradition. But, since
we are certain not to remember, and since others (if we re
member) will forget, my voice, if I have one, is for putting
under ground this much decayed object of unpleasant war
fare. 14
14. Let us cease to pretend that the principle is a premise.
Let us try to call things by their real names; and, instead of
applying for the production of a major, simply ask for the
form and principle of an argument. This is rational and
useful ; it is good alike for theory and for practice. 15 By find
ing the functions made use of in our proofs, we can classify
them with a view to a further understanding. And we may
thus avoid some mistakes in the actual work of reasoning.
For by an exhibition of the abstract principle we can dis
tinguish what is relevant from irrelevant detail. When doubt
ful of an inference we may desire to know how the conclusion
is got. We therefore ask for the active function, and we make
this explicit, by direct abstraction from the inference in hand,
or indirectly by a previous comparison with other instances.
In this way we can test the form, either by a simple scrutiny
2321.2
53O THE PRINCIPLES OF LOGIC BOOK III. Px. II
of itself, or by seeing how it works in fresh applications
and further deductions. And this process is useful as well as
rational.
15. There are two parallel mistakes, which we must try
to avoid. We must not fall into thinking that our actual
inferences are proved by deduction from a general form.
And we must shun the idea that this principle itself is proved
by the collection of working examples. The universal neither
demonstrates, nor is demonstrated by, its particular applica
tions.
It does not demonstrate them for this reason. It is not
a statement which is believed when received, but a function
which must be worked in order to be seen. And it can not
be worked quite pure in a vacuum. Some matter must be
used. And hence, when we lay down the abstract principle
we really are using a concrete instance, though we distinguish
in that instance the matter from the form. But this shows
that in the end our criterion must be an individual operation.
Take for instance the axiom, that things equal to the same
are equal to each other. The only method of perceiving this
general truth is to make an experiment in which you distinguish
the equality from the other attributes of the terms, and observe
what each element contributes to the result. We must use in
the end this individual test.
" But," it will be said, " this criterion in its use is universal,
and our particular reasonings are proved by subsumption under
its conditions." This is the old mistake. Our fresh cases,
as we saw, are themselves proved true by a renewed experi
ment. Our criterion serves merely to show us the essence of
the act which we perform, and to give us in the operation
the distinction between its form and matter. But the con
sciousness of this distinction, I must repeat, is not the proof
of the actual conclusion. You might just as well say that the
fresh use of the function was a proof of the axiom.
1 6. And this last remark leads us to the parallel mistake.
No amount of mere instances, where the function is used,
would demonstrate its principle. Their number and their
variety are precisely that part of them which is not relevant
to the principle itself. When operations, that look like analo
gous instances, all have consequences which square with the
CHAP. I FORMAL AND MATERIAL REASONING 531
nature of things, this affords a presumption that some valid
principle is present though unknown. But the proof of this
principle comes solely from abstraction ; 10 and the number and
the differences of our applications help us only so far as they
help us to this goal. They work not by the support but by
the destruction of each other. 17 They prove the axiom by dis
carding themselves, and they all unite to demonstrate each by
reciprocally discounting their private irrelevancies.
We may so put the result. A principle will neither demon
strate its applications nor can it be demonstrated by them.
The principle is demonstrated when we see it in, and as the
function of, an individual act. The instance is demonstrated,
first by the concrete performance of the function ; and secondly
it is shown to be an instance, when in that performance we
distinguish the form from the passive matter.
17. You can not reduce all reasoning to syllogism. Every
inference is necessary, and the necessity of the process can
be formulated as an universal truth. This principle is more
abstract than the inference itself, and more abstract than the
conclusion which the inference reaches. But then itself is not
one of the premises. It is that which developes the conclusion
from the given, but it is not given itself; and the attempt,
as we saw, to get it into the given, conducts us to a process
that is simply idle. It is this confusion between principle and
premise which has served to protect the old age of the
syllogism.
And on this basis we saw that we might effect an under
standing. If it were admitted, on one side, that the syllogism
supplies no general type of the reasoning act, it might be
allowed, on the other side, that it is a mode of stating the
principle which is used in that act. It is universal as a form
for showing the explicit and conscious exercise of a function.
But, for myself, I must repeat that, friendly as I am to
the friends of the syllogism, I can not venture to support this
compromise. When I think of the futile and fatuous per
formances enjoined upon the student, when I think of the
nature of too many of his instructors, I feel sure that the
syllogism, if it continues to be taught, will be taught as a
form to which we must reduce every valid argument. It would
never be taught as a form in which we may state our know-
532 THE PRINCIPLES OF LOGIC BOOK III. PT. II
ledge of an argument s principle. And, then, even if the ortho
dox logic might be learnt in this heterodox spirit, we should
cover in the end but a part of our subject. I can not speak
from experience of the more active side in the educational
suffering, but still I must venture to offer a suggestion. 18 Most
humbly I would submit to all teachers who are resolved to
stand by the syllogism, that they are teaching what is either
incomplete or false. And if they care not for truth but for
practical results, then I think for the sake of their much-
enduring pupils they are bound to make at least some trial of
the Equational Logic. There is reason to think that it might
answer better, and I hardly see how it could turn out much
worse.
18. We have now finished all that we desired to say on
the relation of matter to form in logic. We have seen that
no reasoning is absolutely formal, but that in logic, as in
deed in all other sciences, there is a relative distinction of form
and matter. We then entered a repeated and final protest
against the idea that action was subsumption under a form of
activity. And we expressed, not a hope, but a pious wish
that together with this false notion the syllogism might be
banished.
We may end these inadequate remarks by a warning, that
both matter and form bear other senses, which we have not
mentioned. An inference may be good in point of form, when,
though the substance is incorrect, the conclusion follows from
the premises given. An argument again is formal, when its
steps are drawn out in regular detail ; or, possibly, when the
principle is explicitly stated. Substantial again or material
may mean much the same as implicit. A process once more
is merely formal, when it effects an arrangement which is not
material to the substance of the case. But, where the form is
the essence, mere material alteration is likewise irrelevant.
The further question how the form stands to the universal,
turns upon the categories of relation and quality, and can
hardly be discussed outside Metaphysic. And with these dis
jointed statements we must pass to a theme which has long
been awaiting us.
CHAP. I FORMAL AND MATERIAL REASONING 533
ADDITIONAL NOTES
1 " But that is independent." Here, and in " is wholly inactive "
(in the next paragraph), we should substitute, for "is," "can be taken
as." Cf. on 5 to 7.
2 " The impossible." I should have said " what is, everywhere in
Logic, impossible practically." For we have here, certainly, what in
the end may be called impossible in principle.
s " By work on the premises " taken, that is, in the very widest
sense. See on Bk. III. I. III. 3, and the Index, s. v. Premises.
4 " Something which does not co-operate " and " which itself is not
active." The " does " and " is " should here be taken as qualified.
See Note i. Otherwise we push an abstraction, which is necessary
in Logic, beyond its due limits. Cf. Notes 7, 8, and 9.
5 " To reason from mere particulars." See Bk. II. II. Chap. II.
6 " Some imaginable case." Even if in one sense the case is unique
necessarily and in principle as it may be when we reason about the
One Universe still in another sense it is never so. The same argu
ment, used yesterday, to-day and again to-morrow, will also be different
cases of the same argument. The possibility of a " unique " argu
ment is, however, ignored in the text, which therefore so far, calls for
correction.
7 The expressions " passive," " does not co-operate," and (in the next
paragraph) " is quite inactive," must all be taken as subject to quali
fication. Cf. Notes I and 4. From this qualification, however, Logic
has the right to abstract, and to treat the unused as if it were inert
absolutely.
8 " The argument . . . itself." Cf. Notes 2 and 6.
8 We have here an " ideal," even for Logic, because all truth, to
he quite and wholly true, must include every aspect of itself. Cf. on
Bk. III. I. VI. 15, and Bk. III. II. II. 13, and see T. E. I. On the
other hand the realization of this ideal would carry us beyond truth
as such. And hence Logic, in order to exist, must more or less ignore
its own ideal.
10 " We can distinguish." It would be better to insert " for our
purpose " before " distinguish."
11 " We do not pass . . . category." " We do not pass normally
into the mere category " would certainly be more correct.
12 " Where I can not . . . must." For the nature and more
correct form of this principle see the Note on Bk. III. I. II. 25.
13 On the question as to how far subsumption is everywhere essen
tial to argument, see Bosanquet, K & R, pp. 274-283. We may agree
that to reason with a consciousness of the principle actually used is
both higher and more rational. But it does not follow from this that
such an awareness is essential and necessary. The recognition that
one s operation is an instance of a certain principle does not, even
534 THE PRINCIPLES OF LOGIC BOOK III. PT. II
if the recognition accompanies the operation, transform that so that
it becomes itself subsumptive. And even if we, while reasoning,
could perceive the necessary place in the whole system of the Uni
verse which, with all its connections, is filled by our inference, I
should still persist in my denial. For neither the rational scheme of
the world in general, nor every particular consequence falling under
and within that system, can, I think, be subsumptive in its main
essence. Hence, while it may be right for certain purposes to apply
to the Universe the category of Subject and Attribute, it is another
thing to regard the Universe as a system whose contents are deducible
throughout under that mere category, and to take that category as
containing the working principle of every inference.
14 The expressions used, here and again in 17, are perhaps ex
aggerated. After all, this question must, I presume, be left to those
who (unlike myself) possess actual experience as teachers of Logic,
or who (again unlike myself) make use in their own practice of logi
cal rules.
15 " Practice," i.e. theoretical practice. See the Index.
16 " But the proof . . . abstraction." " Proof " should here be
" perception " or " apprehension." Abstraction can hardly amount to
proof (see Bk. III. II. III. 11, and the Note on Bk. III. I. II. 23).
The criterion must really everywhere consist in system (see the Index,
s. v. Criterion). This truth has again been too much ignored above
in 15-
17 " They work not by the support." This is one-sided, though it
holds as against the mistake which is being noted. A principle is
shown to be more true the more widely it holds. The criterion (once
more) is system. See Appearance, and Essays, Indexes, s. v. Criterion.
18 I think this suggestion both generally and with regard to Equa-
tional Logic was too hasty. See Note 14.
CHAPTER II
THE CAUSE AND THE BECAUSE 1
I. We have seen that an inference is an ideal operation
which gives us a result. The conclusion comes because of the
process, and it is natural to imagine that the process must
therefore answer to the cause. If so, we should be led by a
very short cut to a far-lying goal. In reasoning we should
always be knowing by causes, and, at least for our knowledge,
the connection of truths and the course of events would be one
and the same. But such a rapid success is itself enough to
awaken suspicion. Great results in metaphysics are not
reached so easily, and a promise of short ways is almost
sure to conduct us into error. We should find that enquiry
would confirm the doubt excited in our mind by this general
presumption.
Is the middle in reasoning always the cause? No doubt
we have some ground for taking this as true. For wherever
we say " because," there must be an inference. Wherever we
ask " why," we ask for a reason ; and a reason, when given, is
once more a because. And so we might conclude, since to
infer is to reason, and since in reasoning we always make use
of a reason which gets the result, that the middle in an argu
ment represents the cause, and that the conclusion stands for
the effect of the premises.
2. It would be irrational either to affirm or to deny such
a general assertion. For we can not say at once what it
signifies. The word " cause," we know, has a great many
meanings; and its ambiguity does not lie in mere verbal
looseness, or rest on the chance obscurities of language. It is
the cloud that arises round the common source of many great
problems; and, if we tried to penetrate, we should at once be
lost in the mist of metaphysics. The " cause " may not be
distinguished from the " principle," and then every universal
connection will be a cause. On the other hand " cause "
tends to pass into " substance." It appears again as " energy,"
535
536 THE PRINCIPLES OF LOGIC BOOK III. PT. II
" force," and " power," accepted by some as the essence of
reality, while rejected by others as absolute illusion. 2 The
controversy, that springs from this radical difference, would be
fought over the fields alike of metaphysics, psychology, and
physiology, and would embroil us everywhere in debate and
uncertainty. We should ask in vain for any harmonious
finding as to the bodily process which conditions my feeling
of energy put forth. 3 We should find no answer if we desired
to know the actual deliverance of consciousness itself, 4 and
begged for an account of what we feel as will. And lastly,
when we enquired if Force or Energy is anything conceivable,
if it is an idea self-consistent and so far possible, or a coarse
delusion that breaks up before scrutiny we should receive
once more conflicting responses.
If we mean to ask here how the grounds of our reasoning
stand to the causes of our real events, we must begin by
limiting the meaning of our term. Cause must be confined
to the antecedent member within a law of the sequence of
phenomena. 5 I do not mean that the cause is to be the
unvaried event, that it is something which, throughout a col
lection of instances, has happened in time before something
else. We must take it in the sense of the invariable event.
It is that to which, supposing that it happens, something else
will succeed. In other words it is the hypothetical datum from
which there comes a necessary consequence. It is an universal
element in an ideal law of the sequence of phenomena.* (Cf.
Book I. Chap. II.)
3. If by cause we understand the antecedent in a law of
the succession of phenomena, we can at once proceed to dis
cuss the question, Are the cause and the reason always the
same? And we may divide the enquiry into these two parts.
* The term " unconditional " would merely express this same idea.
If B comes invariably from A, it must come unconditionally ; 6 for the
introduction of a condition would modify A, so that B would no longer
come from it. And again, supposing that we could say no more than
that " B follows from A, when A is conditioned," I do not see how in
that case we could assert that B follows invariably from A. We could
not assume that an alteration of the conditions is impossible, or that
no possible alteration would affect the sequence. I do not ask if the
knowledge of the invariable and unconditional is possible in fact. Cf.
14, and infra, Chap. III. n.
CHAP. II THE CAUSE AND THE BECAUSE 537
(i) Is the cause, as we know it, always a because? (ii) Does
every because appear as a cause ?
(i) Is causation, in the first place, known by inference?
Can we say there is a cause, when we do not reason? This
would surely be impossible; for, in perceiving the cause, we
must perceive the law, and, possessing the law, we have at
once in our hands an universal connection. And to judge,
Here is a cause, is to take the antecedent as an instance of
this law, and to take the result as a necessary consequence.
But this process is reasoning.
It is useless to deny it. It may be said that the actual
process of causation is a real chain of existing things, and is
no ideal construction formed by our minds. But this objection,
if true, would be quite irrelevant ; for we are talking of cause
and effect as we know them. And without such a reconstruc
tion it is impossible to know them.
4. I mdy be told that the cause and the effect are pre
sented, that they are given to sense. Well, for argument s
sake let us suppose that the sequence is confined to a single
sense-perception. It does not follow from this that our senses
present it to us. We surely never could see that mere B fol
lows mere A. We see a complex, a tangle of details, from
which we separate this thread of succession. The so-called
fact, that mere A comes immediately in time before B, is an
universal connection, which is reached by a process of intel
lectual abstraction. Itself is ideal; it is nothing that by any
possibility could exist. For A is not a phenomenon, nor is
B a phenomenon, but both are abstractions. Their relation
again is no phenomenal sequence. It is purified from a mass
of irrelevant details, it is removed from the flux of actual
events. It is a truth that is true, not anywhere but in the
region of universals and the world of hypotheticals. And the
result of this is that to know the law is to know the product of
a reasoning by abstraction; to know the instance is to recon
struct this case as a synthesis of the law with a particular
element; and to know the so-called particular fact, that A
comes before B, is either to perceive something which in part
has no connection with the mere and pure antecedence of A to
B, or else must be really in a particular instance to apprehend
the very law itself. (Cf. Book I. Chap. II.)
538 THE PRINCIPLES OF LOGIC BOOK III. PT. II
For example, if I see a man fire at an animal and say,
The shot was the cause of death the cause is here clearly a
because and a reason. For I have isolated this thread from the
sequence of phenomena, and now unconsciously take the par
ticular fact as an instance and application. Thus let the
whole act of firing be A (cdc), and the fall of the animal be
B (fgh) ; the apprehended connection will be A B, and it is
because we perceive this that we are able to say, A (cde) and
therefore B (fgh). The inference is probably not explicit,
but it certainly is there. For how could I use the observed
succession in other cases, if it was not universal? And how
in this case could I speak of causation, as distinct from mere
succession, if I did not take this sequence as having a
principle which connects its terms ? But that is reasoning and
inference.
5. Causation is no mere phenomenal sequence. It im
plies a principle felt in the succession of the elements ; and that
principle is a connection which can not be presented. Let us
dwell on this truth. We have seen that it holds with a simple
succession, but it holds still more with a true process of causa
tion; for that (if we go on to understand it rightly) can not
possibly be a simple relation of sequence. It is a change in
time, and no change would take place unless it arose from
a meeting of elements. To apprehend causation we must first
distinguish the elements, before they have come together. And
thus we get to perceive what may be called the " conditions "
(p. 210). 7 But these conditions, when asunder, are not yet
the cause. To make the cause they must come together ; and
their union must set up that process of change which, when
fixed artificially, we call the effect. Hence to know causation
we must (a) first have the elements in ideal separation; we
must (&) then ideally reconstruct their meeting, and from that
(c) perceive the issuing change. But such a knowledge surely
can not come from presentation.
To repeat you can not properly talk of causation, unless
you can say first that something was, then that something
happened to it, and that so something else appeared in time.
The full " conditions " are not the elements apart, but the
elements together with the change which unites them, and
combines itself with them. It is in the moment when this
CHAP. II THE CAUSE AND THE BECAUSE 539
nnion is realized, that the process begins ; for otherwise the
" cause " might exist for ever, and not begin to produce its
effect. But this process of change is itself the effect, and
nothing else can in strictness have a right to that name. We
have first the elements apart, then their union, and lastly the
product.* You can not even think the law of your instance
without an ideal synthesis through identity.
Thus to experience a definite relation of succession de
mands the separation of irrelevant and relevant. But this is
abstraction, and therefore inference. And to experience that
succession as following a change implies a reconstruction by
identity and a further inference. But the main point is this.
To recognize a succession as a causal sequence means to per
ceive the facts as a presented law. And to see the law in the
facts is to unite the facts by an ideal principle ; and this is to
reason. In other words to say, This phenomenon B was the
effect of A, implies the perception of an ideal connection be-
* Hence we see that a cause demands previous change. It can not
exist without producing its effect, so that, if the effect is to have a
beginning, the cause must have a beginning also. To produce the
effect it becomes the cause ; and that becoming is a change in time,
which naturally calls for another cause by which to account for it.
Hence first cause is pure nonsense.
Again the effect is the change which issues from the union of the
conditions. It is a passing event, and it is only by a licence that we
(allow ourselves to treat it as a permanent product. Being a phe
nomenon in time it can not persist. Once more the effect must follow
the constitution of the cause; it can not begin until after the moment
when the synthesis is complete. It is impossible it should ever co-exist
with its cause, and the belief that it does so arises from confusion. For
we forget that both cause and effect are events, and we tend to think
of them as substances maintaining an identity in spite of events.
But, though the effect succeeds, it succeeds immediately. Causa
tion is really the ideal reconstruction of a continuous process of change
in time. Between the coming together of the separate conditions and
the beginning of the process, is no halt or interval. Cause and effect
are not divided by time in the sense of duration or lapse or interspace.
They are separated in time by an ideal line which we draw across the
indivisible process. For if the cause remained for the fraction of a
second, it might remain through an indefinite future. Permanent cause,
unless you take cause in another meaning and treat it as substance, is
simply nonsensical. I should be glad to discuss some of the difficulties
which arise in connection with causation, but the questions raised
would hardly be logical. 8
54-O THE PRINCIPLES OF LOGIC BOOK III. PT. II
tween A and B. But to know by means of an ideal connection
is to know that the fact is a result of that connection. And
thjs must be inference. It may be latent and unconscious, yet
still it is there. The mere conjunction has become a connection,
felt as such. And this connection is now used with other
conjunctions. But, if so, the facts are united in my mind be
cause of an universal.
6. The thread of causation is nothing visible. It is not
seen till it is demonstrated; and it is demonstrated solely by
the ideal decomposition and reconstruction of events. It is an
ideal unity which we discover and make within the phenomenal
flux of the given. But it has no actual existence within that
flux, but lives first within the world of universals.
And from this we may proceed to draw a consequence
which serves to transform a worn-out controversy. To ask if
the belief in cause and effect results from the mere repetition
of sequences, is to put the question in a form which ensures
and necessitates an erroneous answer. For, if the definite
sequence has once been perceived, what need can there be for
further repetition ? 9 The knowledge that mere B has followed
on mere A, would itself be the very goal which we desire to
reach. But on the other hand if this pure sequence is never
experienced by mere sense-perception, then, with all our
repetition of innumerable perceptions, we do not ever repeat
the experience of that sequence. The true point at issue is
the way in which, from impure presentations, we derive the
pure intellectual sequence of B from A. And we have seen
that the process is in principle abstraction, and in its essence
consists of ideal analysis. The repetition serves merely as a
help to the abstraction (Chap. I. pp. 530-1).
7. Since to recognize a case of cause and effect, is to
apprehend the instance of a law universal, and which can not
be presented in sense perception, we are safe in saying that,
in order to know causation, we are forced to reason. And in
this connection we may perhaps be excused, if we pause to
consider a radical mistake. Reasoning, we are told, consists
in a seeing with the eye of the mind, by which we perceive
" details now unapparent to sense." It is " a mental vision
reinstating unapparent details." " What is termed the ex
planation of a phenomenon by the discovery of its cause, is
CHAP. II THE CAUSE AND THE BECAUSE 541
simply the completion of its description by the disclosure of
some intermediate details which had escaped observation." *
It would be difficult to find any statement more opposed to the
doctrine which we embrace.
And it is a statement which collapses before the smallest
scrutiny. For suppose the whole mass of detail to be
present, suppose not the smallest element to fail is this huge
congeries an explanation? Or what is explanation? Does it
not rather consist in finding within this mass the threads of
connection? But these threads are no details, 10 and they
unite no details, apparent or unapparent. For they are made
by abstraction, by a getting away, from the details of sense
and their sensuous relations, to universal laws which subsist
between elements too pure to be presented. The sequences
of science may be got by observation, and may be given by
description; but it is an observation which mutilates phe
nomena, and a description which shears off all those details
which belong to the very essence of presentation.
8. To explain a fact you must exhibit it as the instance
of a general principle or meeting of principles. The mere be
holding an intermediate something would be by itself no kind
of explanation. It is an old superstition to look for causality
in a something coming between the first fact and the second
one. You can explain without any sort of intermediate, 11
and, when you have intermediates, you may still have not
explained.
I am far from wishing to write down these platitudes, but
they may serve to dispel a thoughtless mistake. Suppose
that I place a glass bottle on the fire and it presently breaks.
"If you had better eyes," I shall hear the remark, "you
would see the molecules, and see them irregularly increasing
their distance the one from the other. Then the bottle would
separate, and this has been explanation. For you have seen
the intermediate hidden phenomena." But, I reply, I have
seen an enormous number of other details, and, if I fail to
make the right connection, I have not perceived the cause.
This connection is moreover a preparation of mine, which iso-
* G. H. Lewes, Aristotle, p. 76. I do not raise the question how far
Mr. Lewes s later (and, I presume, borrowed) utterances are consistent
with this view. It is a typical mistake, and as such may be examined.
542 THE PRINCIPLES OF LOGIC BOOK III. Pi. II
lates one thread from the tangled whole. Is it really not
possible to have, as we say, the cause before our eyes, and then
fail to perceive it? Is presence of a mass of detail in percep
tion, and apprehension of the relation between two elements,
exactly the same thing? If one is left at the end of one s
devoted labour incapable of making such a simple distinction, I
almost think it would be better not to talk of having " toiled
through modern German philosophy" (ibid. p. 80). 12
Presentation to sense of intermediate detail is in itself
no explanation; and without an intermediate you may still
explain. If the case is taken as the instance of a rule, even
that by itself is some explanation. I know it has been said,
and by those whom I respect, that we have nothing here but
bare tautology; that it is frivolous to tell me that this bottle
breaks because all bottles break. But I confess I never could
see the bare tautology. For the particular nature of our one
bottle is in this way connected with a general law. It does
not break because it is a black bottle, or a quart bottle, or a
bottle made by an infidel and on a Sunday, but because it
possesses an unstated quality common to other bottles. And
this quality is a reason why it breaks. The explanation of
course does not satisfy our desires, since we want to make the
quality explicit; but, so far as it goes, it does give us some
principle, and it can not fairly be condemned as tautologous.
In just the same way an apple falls down because of gravita
tion, and this knowledge connects the other qualities of this
falling body with a general attribute of material things. The
explanation, I admit, leaves much to be explained; but I can
not see that it gives us mere words. On the other hand,
however, I do not perceive that it presents us with any inter
mediate details.
9. But what is the truth which underlies this error
which we have been considering? It is the mediate char
acter of all explanation. You show that a connection, which
seemed immediate, is not what it seemed. You point out
the link which serves to unite the second element with the
first. And, starting with this truth, the mistake we are
discussing goes on to turn the link into one constituent part
of the chain of events. It confuses that which is mediate
ideally with that which is separate by an interval of time.
CHAP. II THE CAUSE AND THE BECAUSE 543
Thus, if Protestants commit suicide more often than Catho
lics, we explain this fact by showing that suicide is increased
by civilization, 13 and that in the main Catholics are more
ignorant and uncivilized. Higher culture is mediate between
Protestantism and suicide, but it surely is not a detail which
always intervenes in time.
No doubt in a very large number of cases, in order to
find the true immediate connection, you are forced to enlarge
the presented phenomena. Where analysis fails, you supple
ment the given by ideal synthesis, and find in that supplement
the true connection. But this is accidental, and it is not
essential. The essence of the explanation of phenomena
consists in getting the relations pure, and by analysis of the
facts connecting their detail with those pure relations. It does
not consist, and it could not consist, in the mere unintelligent
gaze through a microscope.
10. It is not my object to ask in the end what it is to
explain, or to discuss the ultimate metaphysical nature of a
law or principle (Book I. p. 88). But our rational instinct
prompts us to assume that we explain by offering something
universal and something real. Now the " laws " of phe
nomena are assuredly universal; they give not the facts but
a garbled extract. 14 And their truth is hypothetical; they do
not even pretend that the elements, which they connect, have
actual existence. 15 Hence the unfortunate holder to sensuous
reality is driven to face a desperate alternative. He must
explain the real by what is not real, or he must assert that
reasoning and all explanation never go beyond mere sense-
presentment. He must persist that it makes a mere addition to
the detail which comes to the senses or the sensuous fancy.
But we have seen that his alternative is a common-place
blunder. For causation, as we know it, is never the sequence
of actual phenomena, or of anything that could exist in the
phenomenal series. No imaginary detail, added to the given,
could do more than increase the existing confusion. If the
history of a thing is ever its explanation, this is true because
history can never be sensuous. By design, or even against
its design, it must mutilate the facts, and substitute for them
a thread of connection which never could have been visible.
Our reasoning and our knowledge of causal sequence is not
544 THE PRINCIPLES OF LOGIC BOOK III. Px. II
ideal in the sense of an imaginative resurrection, or a miracu
lous increase of the sensuous supply. It is ideal because it is
intellectual, because it demonstrates a connection between
universal elements, because it substitutes for fact, and con
nects the facts by, a rational construction.
II. Even where we explain by assigning the cause, we
must rise into the world of ideal arrangement. For inference
is never a mere presentation, and the knowledge of causation,
we have seen, must be reasoning. The first of those ques
tions, which we raised at the beginning (3), has been
answered affirmatively. To know the cause is to know the
because. But the second enquiry remains unanswered. When
we know the because, or the reason why, have we learnt the
cause? Are both one and the same? We must now en
deavour to find an answer to this question.
(ii) If cause were understood in the sense of principle,
then every reasoning would rest upon causation. It would be
a cause in each argument by virtue of which we proceeded to
get the result from the premises. But this identity of prin
ciple and causal law is the very point which is under discussion.
And if causation is confined to sequence in time, the way to
put the question is this, Can the principles of reasoning be
all exhibited as laws of sequences? Must the principle of
knowledge be a principle of becoming?
Is the because in reasoning always a cause? Most clearly
we can not make any such statement. 16 When, from A = B
and B = C, we conclude to the equality of A and C, it is hard
to see how any common relation of both with B is the cause
why A comes to be equal to B. And the enquiry, once opened,
lets in a torrent of kindred objections. Is the proof in
geometry the cause of the conclusion ? Does the result turn true
because of my construction, or does it only turn out true for my
knowing mind ? Two coins are proved to have similar inscrip
tions, because they each are like to a third, but the cause is not
found in this interrelation. The cause is the origin from a
common die. If a vessel has sailed for London or Liverpool,
and we know that it has not sailed for the former, we argue
that its course is shaped for the latter. But is our middle a
process of actual causation? We can hardly say this, and we
CHAP. II THE CAUSE AND THE BECAUSE 545
could give no reply to an endless variety of similar questions.
So far is the middle from always presenting us with the cause
of the conclusion, that, given an inference, we can draw no
presumption in favour of that view. The truth is in general
perhaps more likely to lie with the other alternative.
12. The question " Why " is always ambiguous. It asks
indifferently for the cause of the thing, or for the ground of
my knowledge. And the answer " because " repeats these two
senses. It gives us alike the reason of the fact and the reason
which has led me to believe in its existence. And it offers no
sign by which we may distinguish these radical differences.
The presumption, if there is one, is against the identity of
the cause and the reason. We can not in any case treat them
as one, if we have not some special ground for our assumption.
Wherever the premises represent a reality in time, which,
actually and by its own necessity, goes into a construction
wherever that construction itself is real, and the quality or rela
tion, that appears in the conclusion, is its immediate result in
these cases, and in these cases alone, the because and the cause
must be identical. Wherever, on the other hand, 17 a division
or a junction is made by the arbitrary choice of our minds,
there the reason for knowing and the reason for being fall
hopelessly asunder.
13. We shall return to this theme in a following chapter;
but for the present we may endeavour to close some sources
of dangerous fallacy. 18 And the first of these rises from an
obstinate confusion. Every conclusion possesses two char
acters (p. 226). It is a psychical event and a logical judg
ment, and what is true of it in one of these aspects, may be
wholly false if you take it in the other. Now, if you consider
the judgment as a mental occurrence, the premises are always
part of its cause. The presence of these elements, together
with a mind in a certain state, at once sets up that psychical
change which gives the conclusion. The logical grounds are
psychological conditions, and as such they do work in bringing
about the existence of the result. But we turn this truth into
absolute error, if we go on to say that the premises are the
cause, or even part cause, of the existence of that which the
conclusion affirms. For it is not the content of the final judg
ment which thus has issued from the synthesis of my mind
2321.2
546 THE PRINCIPLES OF LOGIC BOOK III. Pi. II
with the premises. It is not the relation of A to C which is
caused by the apprehension of AB together with BC. What
is caused is nothing but an act of judgment, and that act is
a genuine psychical result, though the content it affirms may
have no kind of reality. It is the bare event of assertion, and
not the truth of the matter asserted, which follows as effect
from the psychical conditions. The cause in psychology and
the ground in logic must be carefully distinguished. The two
series may run parallel, and may partly coincide, but they are
never identical.
14. We may notice in passing a possible objection to this
coincidence of causes and grounds. 19 It might be said that
a cause must produce its effect, while logical grounds may be
idle in the mind, and fail to produce a logical result. But the
objection would rest on a misunderstanding. If we consider
the logical process from its aspect of a psychical movement,
then no doubt we may say that the consequence does not follow
from the premises, unless another condition is presupposed.
We have to assume a mind, not merely present but specially
active, and therefore intervening. But, we may urge in reply,
that the conclusion can still be said to follow, since the func
tion exerted by the mind is regular. When we say " it
follows," we mean that it follows given the activity of a normal
intellect, which abstains from exercising arbitrary choice.
And our assertion is thus elliptical but is not really incorrect.
For this same elliptical character, we may add, is found in our
judgments as to cause and effect. We never exhaust the
whole mass of conditions which produce the effect. The event
never comes, and it never could come, from the abstract selec
tion which we call the cause. We imply the presence of un
specified conditions, but since these are normal, we omit to
mention them. Our full statement would run, Given such con
ditions in relation to the real, and not counteracted, and we
have the effect. In just the same way, Given certain premises
in relation to a mind, not blinded or biassed, and you have
the conclusion. And this answer may for the present be taken
as sufficient. Logical grounds may be considered as psychical
causes, as long as you keep out one supposition. But, if you
suppose the intellect of its own free choice to superadd a
foreign and irregular factor to the premises before it, then the
premises cease to cause the psychical conclusion. It was this
grave suspicion which underlay and gave its strength to the
CHAP. II THE CAUSE AND THE BECAUSE 547
objection ; 20 and it will rise again to give us other trouble in
the following chapters.
15. And finally we may point to an obvious mistake. 21
You may suppose that the consequent is more concrete than
the ground, or the effect more complex than the cause which
produces it. These are parallel delusions. If you understand
by " conclusion " the whole construction, this is certainly more
complex than each of the elements, since it is the union of
these separate elements. But if " conclusion " stands for one
part of the construction, then not only is the synthesis of the
premises more concrete than the consequent, but the premises,
if taken each by itself, may none be more abstract. So with
cause and effect. The effect, if you take it without isolation,
has endless connections with other phenomena, and may be
said to influence all succeeding history. But then, on the other
hand, why should you choose to isolate the cause? That also
exists by virtue of relation to the existing universe, and is just
as complex as you please to take it. If you were to isolate
effects and not to isolate causes, you might emulate an achieve
ment of Mr. Spencer,* by a proof a priori that history must
needs begin with the complex and advance towards the homo
geneous. The one demonstration would, logically speaking,
be as valid as the other.
16. Let us return from our digressions, and gather the
result obtained in this chapter. We have seen that, in order
to perceive causation, you must always use reasoning. The
cause, as we know it, must be the because. But there we are
stopped. We can not assume that the reason, where we have
one, is the cause of the consequence. In some cases, no doubt,
it does appear as the cause, but in others we can not see how
this is possible. And we concluded that no general presump
tion could be raised. But one thing we could see by anticipa
tion; wherever the mind makes an arbitrary choice, wherever
it seems to operate at will (as in distinction, comparison, and
again in abstraction), that capricious operation can hardly
represent the course of events. And a dire suspicion was then
whispered within us. If in inference the conclusion is made
what it is by an arbitrary act, how can any such process be
true of reality? Our knowledge of the cause will itself be
* See his Essay on Progress. The remark in the text is a criticism
of the proof as it appears in that Essay.
548 THE PRINCIPLES OF LOGIC BOOK III. PT. II
dragged down in the common ruin of all our reasoning, and in
the end we must doubt if there is such a thing as a valid
inference.
ADDITIONAL NOTES
1 In this Chapter the meaning of " cause " is fixed arbitrarily.
Causation is taken here as holding only among events and as a law
of their sequence. See Appearance, Index.
2 " Energy," " force/ " power." See again ibid.
3 " We should ask in vain." This statement is, I presume, still
correct.
4 " We should find no answer," i.e. no accepted answer. I have
dealt at length with this difficult problem in the articles referred to
in Appearance, p. 607.
5 For the meaning of a " law," see on p. 543 and the Index.
6 There is an ambiguity which attaches itself to the terms " in
variably " and " unconditionally." These may be taken not absolutely
but as qualified by " in fact " as holding, that is, only within the
limits of a certain area of facts, and as subject therefore to an
unknown x. This ambiguity attaches itself, however, to both of the
above terms alike and equally.
7 " Conditions." See the Index, and cf. Appearance, Index.
8 For a discussion of the subject of this Footnote see once more
Appearance, Index.
9 " For, if repetition." It would be better here to write " had "
for " has " and " could " for " can." And cf . the Note on the pre
ceding Chapter, 16.
10 " No details." Here (as below) " mere perceived details " would
be better. And (lower down) "all those" should be omitted.
11 " Without any sort of intermediate," i.e. in this sense. On Ex
planation and Mediation see further on 9. And cf. Essays, p. 154.
12 " Toiled through modern German philosophy." I hope that at
this date there is no need to warn the reader that any such claim
by the late Mr. Lewes should be ignored. I could say far more than
this if it were now desirable.
13 " Civilization," " Higher culture." I much regret not to have
written here " modern urban life," and not to have simply added
(what I meant) that a larger proportion of Catholics live outside of
large towns. The instance otherwise will serve, because, though, in
the case of an individual, you could say that he was first a member
of no denomination, and then grew up to become one this is not
what is meant. And obviously Protestantism can also be taken rightly
as itself a consequence from a " higher culture," which, far from
following, precedes it in time.
On the whole matter the reader should ask himself, first, whether
he is prepared to limit explanation to what we call the series of
CHAP. II THE CAUSE AND THE BECAUSE 54Q
events which happen. And next, even if he is ready (as I think
mistakenly) to do this, he should consider whether, even with this,
he is brought to the conclusion against which I have argued. The
main question, I think, is What do we mean by a Law ? Can even
the Laws of Co-existence be all resolved into Laws of Sequence?
And, generally, is it the pointing to an intervening event in which
all explanation by a Law consists? Where you have things with a
certain original nature or even an acquired disposition, and where
you explain an event by the reaction of this nature or disposition
on an occurring change how is it possible to take the " law " or
"tendency," to which your explanation appeals, as itself always an
intermediate occurrence? The whole enquiry as to Explanation will
be brought to a point in the answer which we give (or at least are
called on to give) to the question, What is a Law?
14 "A garbled extract," i.e. from the point of view of the Phe-
nomenalist.
15 " Have actual existence," i.e. as such, and as themselves facts
and not mere aspects of fact.
16 This paragraph contains some inaccuracies. In " of both with
B is the cause," for " is " read " must be." And lower down I appear
to have wrongly assumed that the construction is the real proof (see on
Bk. III. I. II. 5). But this question is fortunately here irrelevant.
As to the two coins, I should have written " The cause so far is
unknown. It may, or may not be, the origin from a common die."
With regard to the vessel the question should have been put thus, Can
we say that the exclusion of the alternative an exclusion which (as
we now know) happened in fact was what in fact operated in directing
the particular voyage? "
17 " Wherever on the other hand, etc." The alternative here seems
faulty. We should write " Wherever on the other hand there is no
question of a temporal process of events, or wherever, again, the
conclusion comes from something which does not itself make part
of the self-development of the inference, but is imported from out
side ( 14) wherever, e.g. a division, etc."
18 There is some detail in this section which calls more or less
for amendment, (i) In " wholly false " and in " absolute error," the
" wholly " and " absolute," though not perhaps indefensible, would
be far better omitted. (ii) After " that which the conclusion
affirms " should be added " where, that is, it affirms existence."
(iii) In "It is not the relation . . . conditions" the division is too
absolute. It would be better to add " as existing " after " A to C,"
and to omit nothing but," and to substitute, " as such, no existence "
for " no kind or reality," since the latter statement is false. On the
other hand (lower down), in "partly coincide," the "partly" should
remain standing in view of the " grave suspicion " of 14.
The main point of 13 is as follows. Every conclusion is a
mental occurrence. As that, it is an event and an effect. And the
premises, as concerned in producing this event, are therefore, so
far, themselves part of the psychical cause. But the psychical exist
ence of the conclusion is not the truth or reality which that conclusion
55O THE PRINCIPLES OF LOGIC BOOK III. PT. II
asserts. And, from the other side, the truth and reality affirmed in
and by the inference, taken logically, is not the psychical event of
the conclusion, which event has been caused in my mind concurrently
and (we may add) incidentally. And, further, that which may vitiate
the conclusion, taken as logical, need not impair the sequence of that
vicious conclusion as a caused occurrence.
The above distinction, legitimate and necessary in Logic, is, how
ever, in this Section taken too much as a sheer and absolute separation.
But the abstraction, which holds good here for the purpose of Logic,
possesses no more than a relative validity. There is, generally, no
truth without an aspect of existence, however much for our purpose
that aspect may be ignored. And, in particular, there is in the end
no truth which is not true for a mind, and does not enter from this
side into some process of psychical events. Thus a conclusion as to
the angles of a triangle is not possible without an aspect of existence
here and now as a mental occurrence. And, sundered from this ele
ment of its being, its truth in the end can not even be called true.
This inseparable aspect, from which Logic must abstract, demands
recognition in Metaphysics. But for Metaphysics to exhibit its neces
sity and truth in particular and in detail, is, I think, impossible ; and
I even doubt if in the end we can get to understand what may be
called its general " How." The problem of the relation of truth to
Reality, and again specially to psychical existence, is, however, far
too difficult for discussion in these Notes. See on Bk. III. I. II. 14,
and cf. Essays, Index, s. v. Truth, and T. E. I.
19 " A possible objection." This objection certainly did not come
merely from my own mind, but I am unable now to specify its source.
20 " This grave suspicion," i.e. that in certain inferences what we
call the conclusion really comes from an intervention by my arbitrary
choice of (cf. 16). Here it is not the premisses, plus the normal
activity of a normal mind, which can be said to produce the result.
And, if so, the " logical " sequence here not only fails to be identical
with the causal process, but can not be said even to coincide with it,
at least altogether. For in the causal series is nothing that could
regularly answer to mere mental irregularity.
The above statement, however, is wanting in clearness, and we
may express ourselves, I think, more correctly as follows. There is
no difficulty in principle as to mental irregularity, when viewed as
psychical ; nor, once more, is there in principle any difficulty as to
the coincidence of the psychical and the logical, so long as the logical
sequence is a regular consequence from its beginning to its end.
But, on the other hand, once admit anything like caprice into the
logical sequence, and then, as logical, that is destroyed; and hence
the question of its correspondence, as logical, with anything else dis
appears. On the subject of arbitrary choice in inference, see the
Index, s. v. Inference, and T. E. I.
21 Section 15 seems to be really irrelevant here. I wished, I pre
sume, to call attention to Spencer s characteristic mistake.
CHAPTER III
THE VALIDITY OF INFERENCE x
i. The title of our chapter, welcome though it be, excites
foreboding. We are glad when we see the harbour so near,
but the approach brings with it an ultimate risk and a final
anxiety. We have escaped some perils, but our safety has
perhaps been dearly purchased. In the course, which we have
taken, the worst lies at the end, and that end is before us. We
shall hardly sail in with vessel unscathed, and with colours
flying ; and, did fortune consent, we would gladly compromise.
We would change all hope of a triumphant entry for the trust
that our voyage might not end at sea. We are resigned to
shipwreck, if only by any means something may be saved.
The validity of inference has two main senses. When we
ask if a process of reasoning is correct, we may have in our
mind two different questions. We might ask if in argument
we possess a strict counterpart of the nature of things, if our
mental operation truly represents any actual process. 2 And
this would be the first question. The second would ignore
this correspondence with reality. It would content itself with
asking if the premises do logically prove the result. And this
latter enquiry is the theme we shall discuss in the present chap
ter. The first and the more difficult we still keep to the end.
2. But, when we have confined the question of our reason
ing s validity to the formal consequence of conclusion from
premises, we still find ourselves threatened by a double mean
ing. Our enquiry might be limited to a search for types, or we
might consider as well our practical necessities. And the
answer, it is possible, might vary with the question. For
conceivably our minds are dowered with a form of ideal
reasoning, pure and impeccable, while in practice our argu
ments are tainted with vice. And so to the question Is reason
ing valid? we should have to return a double answer. It
would be valid so long as you made it to order with condi
tions that never occur in practice ; while each actual inference
552 THE PRINCIPLES OF LOGIC BOOK III. PT. II
might be fatally unsound. We intend to lose sight of this
latter enquiry. We do not mean to ask what sound perform
ances of reasoning are practicable, but what types of argument
are flawless in themselves, without regard to the question if
any one, or no one, can use them in his work.
But, before we enter on our doubtful search, a word of
caution must be given to the reader. He must not look for an
ultimate solution. In the present chapter, and still more in the
next, we abut upon provinces which we dare not enter. It is
impossible to free logic from doubt and difficulty, until meta
physics first has cleared up its own mysteries. And so we
must come in the end to issues which really lie in the heart of
first principles, such issues as we can not pretend to deal with.
Our immediate question will therefore not find an uncondi
tional answer. Inference, if valid, in the end must be valid on
a certain hypothesis. The conclusion will follow, given a sup
position. Thus we can hope for no more than to arrive at
postulates, 3 assumptions whose truth we can not here scrutin
ize, but on which our intellects are forced to embark, if they
mean to serve us in the voyage of life.
3. Every inference, as we saw, falls into three parts. We
have first a datum, then comes an operation, and then follows
the result. And our question really asks how the last of these
is related to the first. What is given appropriates the result
of an experiment; and we demand the title on which it
proceeds. We enquire how it justifies the taking to itself of
this new possession.
For consider, we agreed that the result must be new.* If
we had nothing fresh we should have no inference. But, if
so, what was given us has suffered a change ; it is altered and
made different, and made different, we must admit, through
our mind s operation. And yet in the conclusion this most
ominous fact is quietly suppressed. We unblushingly assert
that the consequence follows; but we know that it follows
since we know who has dragged it. We protest that C is the
property of A. How else, when our hands first stole it and
then secretly placed it in his house? And the doubt that
now rises, and the suspicion that points at us, all start from
this ground. If it is you, they murmur, who have made the
conclusion, then it can not be true that you also have found it.
CHAP. Ill THE VALIDITY OF INFERENCE 553
The new attribute does not truly belong to the subject, if your
choice and caprice is the bond of their union.
We must begin with a frank and ready admission. If we
really did make of our own free will the conclusion which we
come to, if the result did not " follow " of itself from the
datum, but were pushed and thrust on by our arbitrary force ;
if (to use a perhaps still more grateful metaphor) we did not
" draw " the consequence from the bowels of the premises, but
inserted a product prepared by ourselves if we even chose so
to influence our subject, that changed by that influence it modi
fied its attributes then assuredly the process is invalid and
vicious. The conclusion in these cases would not come from
the premises. 5 It would come from the premises under a
condition, and its truth would depend upon that condition.
Or, more properly, the premises would be wrongly laid down ;
for they should have included the action of our minds. And,
just as failing one condition the others are powerless, and in
no sense are any a cause of the effect, so, failing the element
of our arbitrary choice, the premises we assigned are no
premises at all. The conclusion, if it comes, is merely pre
carious; it is hypothetical. It must wait upon chance, and
the result that ensues is given but not claimed.
4. If this is agreed on, then the question that remains
seems limited to one issue. Is there reasoning where the
conclusion really comes from the unhelped premises ? Is there
any where the truth of the consequence does not rest upon our
interference? Let us proceed at once to a particular example.
We will begin with what seems to be the strongest instance.
In a synthetical construction without elision, we appear to be
free from arbitrary choice. Given A B B C, then, by
virtue of the common identity B, we perceive A B C ; and
the conclusion seems wholly inherent in the data.
But there comes an objection. The process of inference
consists in putting the premises together. Of themselves they
lie idly apart in the mind, and by themselves they would still
remain asunder. It is surely your mind which supplies them
with an unity, and which gives them a connection which they
never possessed. You are held in this dilemma. If you say,
A B and B C are not really apart, then you falsify your
premises. But if they are apart, then one of two things ; they
554 THE PRINCIPLES OF LOGIC BOOK III. PT. II
come together of themselves, or you force them. If you force
them, the conclusion is admitted to be false. And they do not
come together, since experience shows that they may continue
separate, and since their change to union demands something
effective which falls outside their discontinuous state. But
this agency must lie in the motion of your mind.
Our answer to this charge may begin by rebutting a false
assumption. Did the premises change before our eyes into the
consequence, it would not follow that therefore we changed
them. For the premises are held in relation to reality, and
reality itself might supply the condition which moved them
into union. 6 But, passing by this, let us address ourselves to
meet the charge of interference. We may fairly enquire, "If
we have interfered, what is it we have done ? Have we taken
A B and B C from the outside and coupled them to
gether? But where is the thong or the chain that restrains
them? What glue or what nails have been used to fasten
them? And, if their attachment is part of their substance,
what is it that we have done to strengthen it ?
Our objector might not find an easy rejoinder, and yet we
have hardly replied to his difficulty. For assuredly we did
something, and that deed was the addition which brought out
the consequence. If a change was not made, then we had an
illusion; and if passively we stood spectators of a process,
then once more we were cheated. And we are fast in the
dilemma If nothing was altered, then there was no inference;
but if we altered aught then the inference is vicious. And we
admit that we were active.
5. We must meet the dilemma by a saving distinction.
We have here nothing to do with the real validity of our
reasoning process, but solely with its soundness as a logical
transition. And hence at present we need to regard our reason
ing as simply a change in our way of knowing. But this
breaks through the circle which threatened to be fatal ; for it
shows a possibility which was overlooked. If, by altering
myself, I so am able to perceive a connection which before was
not visible, then my act conditions, not the consequence itself,
but my knowledge of that consequence. 7 It goes to make the
consequence in my recognition, but stands wholly apart from
this truth which I recognize. Though the function of con-
CHAP. Ill THE VALIDITY OF INFERENCE 555
eluding depends upon my intellect, the content concluded may
be wholly unhelped, untouched, and self-developed.
And a logical postulate, to which we alluded, assures us
that this possibility is fact. Whether rightly or wrongly, all
logic assumes that a mere attention, a simple retaining and
holding together before the mind s eye, is not an alteration.
If the logical function does not touch the content, if it leaves
A B B C untampered with, then no viewing them at
once or one after the other, nor any attention to one of
their elements, makes the smallest difference to the truth
itself. My vision is affected, but the object is left to its own
development.
Thus, in A B B C, the identity of B is the bond of
construction. If I made that identity, I should certainly in that
case have manufactured the consequence. And it may be con
tended that it lies in my choice to see or to be blind, and that
hence my recognition does make what it perceives. Against
such a contention I can here attempt no further answer. I
must simply fall back on the logical postulate, and leave further
discussion to metaphysics.
6. But another objection remains to impede us. Though
our action is confined to the knowledge of the truth, we are
summoned to justify the truth of our knowledge. For the
content, which we know, becomes different in the sequel, and
it does not appear how truth can thus change. 8 We may say
that the premises perhaps are not true ; we may confine our
scrutiny to the soundness of the consequence ; yet the puzzle
does not vanish. Though the premises are false the conclusion
may be valid ; but how if the end contradict the beginning ?
If the premises are true, they surely would not alter; and if
they do alter their first state must be false. But even then the
last state will not square with the commencement. It destroys
the ground in which it is rooted, and, removing its own base,
must abolish itself.
Shall we meet this objection by embracing it wholly? Shall
we say that our reasoning is a process of correction ; that we
start with an erroneous view of the truth, and that the conse
quence is a necessary emendation, which arises from the error
when our reflection illumines it? If so, the conclusion in each
valid inference contradicts its own premises. It is no extrane-
556 THE PRINCIPLES OF LOGIC BOOK III. Pi. II
ous opposite which removes its contrary, and perishes itself in
that common ruin. It is the opposite which appears in the
decease of its parent, and presupposes a contrary which disap
pears into itself. The conclusion abolishes the truth of the
premises, since, by internal change, they pass into a product
which contradicts them.
This doctrine might stagger the traditional logic, but in
the main it would not seriously tend to disturb us. Yet we
can not wholly embrace its conclusion. It is true that all
inference is a process of correction. It is true that it can not
ever leave its starting-point quite unmodified. But it is one
thing to say this, and another thing to admit that every valid
inference contradicts its own premises. No doubt, if all
change were itself contradiction, and if knowledge is changed
in the act of reasoning, we could not infer without self-con
tradiction. But I venture both to doubt the general p rinciple
and to discern an error in the special application. I admit that
in the premises the terms A and C appear separate from each
other, and that this appearance is removed in the conclusion.
But I can not see that the premises do assert the actual sepa
ration of A from C. They fail to affirm their interrelation,
but they certainly do not go on to deny it. Thus the judg
ment, " A and C have no connection," would be made by the
transformation of a privative absence into a positive exclusion
(p. 117). It would turn a mere psychical matter of fact into
a logical judgment with respect to content. The appearance
of A-B without any C is denied in the conclusion which gives
their union; but the judgment A-B was not that appearance,
nor is this judgment in any way otherwise denied. It is
increased but not abolished. There is nothing abolished but
our own false prejudice, that what does not appear as the
element in a whole is therefore independent.
7. In the example, which we have taken, my arbitrary
choice does not influence the result. I may choose to attend
or not to attend ; I may retain and consider, or pass by blindly.
And so much as this is left to my caprice. 9 But suppose that I
consider, then the premises themselves pass into the result. In
what sense my mind co-operates in that passage, is a question
of first principles which we can not discuss. But it is clear
that my private desire and preference have no part in the issue.
CHAP. Ill THE VALIDITY OF INFERENCE 557
Once resolved to see, I am powerless to alter the object of
vision.
If we come next to those inferences which use an elision,
and where the result does not stand as the whole A B C,
but is lessened to A C, we must speak with more caution.
The elimination of B depends upon our choice. We must join
A B C, but to strike out B is by no means compulsory. If
so the conclusion will in part be arbitrary. Is it therefore
unsound ?
It may be unsound. If we ventured or forgot ourselves
so far as wholly to ignore the middle, if we stepped from the
construction to the absolute assertion of one part of its
content, we might make a common and most dangerous mis
take. If we intend to set up A C by itself, we must avow
the transition and be ready to justify it. And tacitly to assume
the independence of A C is a logical mistake.
But elision does not need to involve this error. It should
mean no more than the assertion of A C, subject to condi
tions left unexpressed. Since, A being given, there follows a
construction in which we are able to perceive A C, we may
say that A C is the mediate consequence. Or it follows
hypothetically at once, if B becomes implicit and is thrown
into the base which underlies the connection (cf. Book I. pp.
88-90). Our assertion is elliptic, 10 but in this case is not
vicious. On the other hand it becomes unsound, if we pass
from the privative, " I perceive mere A C," to the exclusive
" I can not see anything else, and so nothing else but A C is
real."
8. We shall return to this point when we come to discuss
the validity of abstraction. But at present we must mark a
division in our subject. There are certain reasonings in which,
as we see, we do nothing but attend or consider logically.
And it is a postulate that such perception does not alter the
object. These reasonings may go on to employ elimination,
and this addition is arbitrary. But the conclusion is still sound
if the addition is recognized. It becomes to that extent hypo
thetical, and, though elliptic, it may stand; for it does not
affirm that mere A C exists, but that A C is known. 11
But, after escaping this first wave, we are met by a rising
sea of inferences which all seem arbitrary from first to last. 12
558 THE PRINCIPLES OF LOGIC BOOK III. PT. II
For I need not compare, and I need not distinguish. Again
neither in Arithmetic nor in Geometry am I compelled to con
struct or forced to analyze. I now do more than attend to the
development of the object. My own hands have interfered,
and have procured the experiment which gives the result.
And, if so, the conclusion must surely be capricious, or at
least must be laid down quite conditionally.
Let us take the instance of free spatial construction. If I
move A, B, and C, and arrange them so as to stand in certain
relations, I can not proceed to predicate this result of A, B, and
C. Hurdles by themselves will not make a sheep-fold, and
you can not go straight from the one to the other. The
activity of the shepherd must be added to the grounds ; it must
be supposed and then implied in the consequence. For the
shepherd himself does not follow from the hurdles, and we can
not regard him as a condition involved in A, B, and C. Hence
we must transform our experiment either by adding something
to the original data, or by recognizing a condition when we
state the result. Otherwise that result is palpably vicious.
And the doubt may arise if this fatal alternative stops short
with our instance of free spatial construction.
9. It threatens to ruin in the first place comparison. For
that is a process, and the data compared are surely quite
passive. Can we say that A and B work out their own like
ness, any more than hurdles work into a sheep-fold ? Are they
like? Is it they which I see to be similar? Is it not some
product of my work upon them, and some capricious addition
which really owns the predicate? And the same with distinc
tion. Does my process but colour an element which already
was there in the premises, or have I added an agent which by
combination has produced a new result? If all I know is that
something not seen has, by virtue of my act, become plainly
visible, by what right do I claim to have simply made visible
and not rather to have made? Nor will arithmetic escape.
For, as we saw long ago, one and one are not two ; they be
come the integer, and their becoming seems no change that
arises in themselves. But, if so, they are not the actual sub
ject which appropriates the sequel : our hand is responsible and
can not be disowned. And geometry follows to a common
doom. Do those wonderful constructions grow out of the data,
CHAP. Ill THE VALIDITY OF INFERENCE 559
like branches from a tree ? Are those necessary pictures mere
sketches of the object? Were we not more right when we
likened them to builder s scaffolding, and should we not think
here of those diagrams of operations, 13 where we see depicted
the hand and the knife? The processes of distinction, com
parison, and construction, all show logical presumptions where
mistake is ruinous, and where nothing supports the ground
which we stand on.
10. And so once more we have to fall back upon a
postulate. Metaphysics alone can judge if we are right, but
in logic we are forced to assume that some processes do not
modify their consequence. We work round the content and do
nothing upon it. Thus retention and joint notice were sup
posed not to influence the object of vision. And here once
again we assume that comparison and distinction and synthesis
do not touch or alter the content of the given, but simply re
move an obstacle to our sight, or aid that sight by artificial
reflection. It is not with these as it was with our sheep-fold.
The position of the hurdles made the sheep-fold itself, and the
act of the shepherd did alter that position. But here it is
something in the hurdles themselves, their quality, or their
number, or again their magnitude, which appears no doubt
when the sheep have been folded, but itself can not have been
made by the shepherd. Apart from correction by the study
of first principles, the shepherd must predicate the sequel of
the origin. 14 He would not be right, if he inserted an inter
mediate condition. Assuredly, without his capricious act, he
might never have come to see the conclusion ; but, seen or
unseen, the conclusion was still there. The process has but
altered an imperfect vision ; 15 his want of perception has been
changed to plenty. It is he that has chosen to let in the
light ; but the object, our logical postulate assures us, was
there from the first and there unconditionally. Where we state
the mere truth, we are bound to eliminate the middle opera
tion.
And our postulates give us the same right of confidence,
when we take an idea and suppose it to be real, or when
suggestion of predicates brings out a response on the part of
the subject. 16 In these cases once more, though our viewing of
the sequel is conditioned by our choice and our arbitrary act,
560 THE PRINCIPLES OF LOGIC BOOK III. PT. II
yet the view, which we perceive, we must take as unconditional.
The process once more has not modified the content. It has
placed it in experiment and prepared it for observation, but
has left its essence unchanged and unbiassed.
ii. It is different when we come to the process of ab
straction" Where we separate ideally one element from the
whole, we not only perform an operation on the given. We
not only make a leap from the known to the unknown, when
we attribute to the given the result of the act, but we also make
this venture on our own responsibility. It is a logical in
stinct that prompts us to the act; but no logical postulate
guarantees the outcome. Reasoning by abstraction has a fatal
defect.
For how shall we tell, and what justifies our confidence,
that our element remains when the rest is removed? We are
burnt and we go from this to " Fire burns." We strike out
the mass of accompanying detail, and treat the residue as
belonging to the real. But who goes surety that the roots are
not twisted, that, in cutting between the reality and its detail,
we have not severed some fibres of the selected element? If
we find that a b is true within x, on what ground do we rest
for our desperate leap to the assertion that a b is true with
out condition? It is one thing specially to notice a member.
It is one thing to say that this member at any rate is certainly
here. It is quite another thing to take that member apart,
and to assume that, by itself, it remains what it was when it
lived in the whole. This fatal confusion between theory and
fact, this blind assumption that our intellect s work must
always present us with the nature of things, is a special trait
of the " Philosophy of Experience." Bad metaphysic supports
it against logic and the cry of facts.
12. If we mean to keep clear of a dangerous venture and
really to prove the conclusion which we reach, then, unless by
way of an elliptical statement, 18 we can not eliminate where we
fail to analyze. If you wish to remove one part from a whole,
and maintain it away from its original context, you must find
what elements constitute that whole, and you must find exactly
what each contributes. For you can not tell otherwise what
it is you are taking, and how much is left. Your cutting may
not merely loose the string of a bundle. It may have utterly
CHAP. Ill THE VALIDITY OF INFERENCE 561
destroyed the connection which maintains the parts in exist
ence. And the result of this is that correct abstraction is
guaranteed by nothing save actual experiment. In fact, or
ideally, you must divide the whole into certain elements, and
you then must make trial with these several factors. You may
find that the whole falls asunder into parts, you may find that
this whole can be reproduced, when experiment puts the parts
together, and that the parts all remain unchanged in the
process. You may find that with any arrangement the parts
maintain their character, and that the qualities of the arrange
ments make no difference to that character. And if you were
able finally to isolate a, 19 you then would see if indeed the con
sequence were really b. Wherever this process is taken as
possible, elision and abstraction will demonstrate truths. But
elsewhere their result is precarious and doubtful. It suffices to
suggest, but it can not prove.
13. If I begin to reason with the integer four, I can divide
this integer into separate units, and, by combining these units,
I can once more produce the quality of the whole, while every
unit remains unchanged. By a number of specific ideal ex
periments I satisfy myself that the units are indifferent to their
junction in this integer, and may be freely treated as inde
pendent elements. For example I can show that, first taking
one unit and then adding another, I get the integer two, and
that I am safe in ignoring and abstracting wholly from the
totality four. All this is quite obvious, and the important point
is that my abstraction rests on specific experiment. I neglect
the given whole and eliminate its detail, because, within my
actual experience, I have destroyed that whole, and have seen
that the residue will stand without it. If I take two from four,
I know that two is left, since I have proved that the integer
does not inter-connect the units in such a way as to qualify
them. But, failing this experiment, my abstraction might be
vicious. In removing one half of the integer four, I might
have sapped and ruined the other half.
This is not the place, nor am I sure that it belongs to
logic, to discuss the limits of demonstrative proof in the
sciences. What logic may hold fast is the assurance that,
without a priori experiment, arithmetic could not start. And
it is certain that soon we arrive at provinces where such
2321.2 M
562 THE PRINCIPLES OF LOGIC BOOK III. PT. II
experiment is impossible. 20 In dividing the wholes, if we could
divide them, we should modify the parts; and in summing
these parts we should not regain the wholes. We are here as
powerless to construct the facts a priori, as we are to dissect
them by ideal analysis. And when these regions are reached,
as they very soon are reached, then our logical abstraction
becomes a venture, and its result can never amount to
proof.
14. I must return once more here to a fashionable error.
The idea that, apart from specific experiment external or ideal,
you can start with the individual and go on to prove an ab
stract universal, is wholly erroneous. The so-called " Method
of Difference " involves a downright logical mistake. It is
subtraction employed where arithmetic is not known to be even
possible (cf. Book II. p. 365).
From the given total AB df, by removal of B /, we
abstract A d, and we argue that A d is true of reality.
But our reasoning depends on the unwarranted assumption
that in AB df, we have nothing but units. Take the simple
example, " 2 -f- 4 i makes the integer five, and two units
apart from that whole integer are two, therefore 4 i has the
quality of five, or is at least a part of the cause of that
quality." 21 This strict application of the boasted method, unless
you confine its result to the individual instance, brings forth
what to me appears an absurdity. And the reason is obvious.
The Method identifies, in the whole and outside it, both B and
/. And, standing upon the Identity of Indiscernibles, it is so
far right. But then it goes on to assume the absence of dif
ference. It takes for granted that A and B make no difference
to each other. It takes for granted that df is nothing beyond
a mere sum. It assumes that the threads, from AB to df,
neither cross nor are twisted, but run side by side. And this
enormous presumption has no sound base. It could be justi
fied by nothing but a specific experiment, ideal or external,
which would show that AB df is this bare addition of
units. 22 Without this it is precarious, most useful as a tenta
tive means of enquiry, but unsound and imposturous if you
take it as proof. We feel tempted to re-christen the Method
of Difference as " the method which shuts its eyes to dif
ferences."
CHAP. Ill THE VALIDITY OF INFERENCE 563
15. Probability is increased with the number of
examples. 23 If to " AB df, B /" you go on to add
"AC dg, C g" "AE dh, E h," and "AF di,
F i" you approximate towards the certainty of A d. But
you never can demonstrate ; you never can show that d follows
from A with any condition, and still less that, if A were given
by itself and unconditioned, the result would be d. For you
can not presume that, apart from correlatives, A could even
exist.
And I venture, in this connection, to raise a doubt which
deeply affects some views of first principles. We are some
times asked, in accents of wonder, how we come to believe
that Reality is one. That enquiry is quite reasonable, but in
my turn I sometimes feel inclined to wonder what possible
ground could assure us of the opposite. For not all of us
follow the " School of Experience ; " we are not all equipped
with an a priori principle, which tells us that to every dis
tinction of the mind a division corresponds in the actual world.
We some of us still like to start with facts, and still keep up
some prejudice for regarding them. And, if so, it is difficult
to see what argument from fact could secure our conclusion.
For in actual experience we never can find a thing by itself ;
it is obvious that some context will always be present there.
And if, with indefinite variations, the thing remained visible in
all our contexts, that could hardly prove that without any con
text the thing would exist. If we showed that our changes all
made no special difference to the element, would that tell us
that everything contributed nothing whatever and at all ? And
the doubt that arises is, whether our conclusion does not rest
on the vicious abstraction we have noticed ; whether, in short,
supposing that single elements were real by themselves, it
would be possible to get to know this truth by anything else
than an unsound reasoning.
We saw, indeed, that analysis and abstraction were often
legitimate. But then consider the difference of the cases.
Quite apart from the fact that arithmetic deals with unreal
abstractions, 24 what is it that is shown with respect to the
units? Is it proved, or can it be proved, that units are inde
pendent of every integer? Did we not, on the contrary, merely
show their complete indifference to any particular integer?
564 THE PRINCIPLES OF LOGIC BOOK III. PT. II
But it is one thing to be free from this or that complex, and
another thing to stand entirely absolute. And, if we tried to
show that an unit could possibly exist by itself, we should
pass from arithmetic to bad metaphysics. For the isolation
implies an ideal integer, an invisible whole; and it implies
definition by relation to other excluded units. If we recog
nize these elements our unit is not solitary ; if we ignore them
we fall into vicious abstraction.
Where analysis is possible, there always remains an implicit
condition. 25 And this rises as an obstacle whenever we attempt
to raise our result to absolute existence. But where analysis
and construction can not be effected, there abstraction is always
a hazardous guess, and can never amount to a logical proof.
And with this last warning we may leave a most dangerous
source of widespread, insidious, and fatal delusion.
1 6. We may go on to deal with other difficulties. The
Disjunctive argument 26 consisted, as we saw, in the passage
from a single possible predicate to its assertion as actual (p.
413). This transition depends on a logical postulate, and I
do not propose to discuss it farther. It would be easy to raise
metaphysical objections, but they would fall beyond the limits
of this volume.
When we have once got to a sole remaining possibility, our
inference is then to be taken as valid. But how can we be
sure that we ever have reached this ground of inference ? We
saw that, in the end, disjunction depended upon our impotence
to find any other predicate. It seemed to rest on the experi
ment, " I can not otherwise and therefore I must." And this
process calls up the gravest suspicion. To state and settle
the doubts, which it gives rise to, would imply the discus
sion of some subtle questions that would lead us too far into
metaphysics. Omitting these,* we must content ourselves with
trying to consider the problem from its logical side.
17. In disjunctive reasoning we have a subject A. This
subject possesses a quality x, and x is determined as one of
the discrepants a, b, and c. We go from the denial of a and
b to the assertion of c; and this process assumes that x is
* In my notes for this chapter 27 I went somewhat more fully into
this question, but found I should occupy too much space with ques
tions I was not sure were logical.
CHAP. Ill THE VALIDITY OF INFERENCE 56$
exhausted by a, b, and c, and that any other predicate will fall,
not outside, but within these areas. But how do we know
that x is exhausted? How can we tell that no other predi
cate, such as d, is possible? Our inference is ruined unless
this condition is fully satisfied.
Now in subordinate reasonings, where we start from and
rest upon preconceptions, it is easy to have a complete division.
The division is complete because we have taken certain things
for granted. But this postulated omniscience, this factitious
totality, must come to an end. When we reach those assump
tions from which we proceed, we have then to face the
general problem, How can we ever exhaust possibilities, and
how can we know that they ever are exhausted?
Suppose that, in the end, we are forced to avow that we
rest upon impotence, that we are unable to find any other
suggestion, and that certainly nothing else will appear. Is
not this the admission that we stand on nought but a privative
judgment? And is not this foundation hopelessly unsound?
18. There is one way of escape. The rejection of an
other and opposite predicate may perhaps after all not be
based on privation. It may really spring from exclusion by
means of a positive attribute. For suppose that our subject
has the quality c, and that this quality is unseen. The experi
ment by disjunction might succeed in making us apprehend c.
It might cause what is latent to turn explicit, while the real
ground we possess for the existence of c might not lie at all in
the process of exhaustion.
To explain when a and b are rejected, the base of rejec
tion may not be any defect in A, but rather the presence
of c which operates although unseen. And this principle
goes further. When we ask, Is there anything possible but c,
it may be once again the presence of c which excludes the
idea of an opposite alternative. But, if so, our conclusion
would be fully guaranteed. We are assured that nothing but c
is possible, since the attempt to find a discrepant suggestion
has made c explicit. And, if c were not real, we should
find ourselves left with a conditional judgment, in which the
predicate would deny the subject. But the consequence is
that our impotence is not the real cause of the conclusion to
c. It is c on the other hand which has caused our impotence.
566 THE PRINCIPLES OF LOGIC BOOK III. PT. II
Its strength does not lie in the weakness of our minds, though
the experience of our weakness proves its strength. In other
words our knowledge of its presence depends indeed on our
failure to banish it, but its covert agency it is which procures
our open failure. The essence of our reasoning does not
really consist in tollendo ponere. Ostensibly tollens its ex
haustion and elision are a useful show provocative of truth.
From a tacit position it works tollendo, to attain thereby an
explicit ponere of this latent quality. It is thus a threatened
contradiction which compels our subject to reveal a hidden but
virtual pretension.
It is scarcely worth while to add an illustration. I may
deny that an actual number can be infinite, not because I am
unable to form the idea, but because it contradicts a quality of
the subject " actual number." I may be sure that a " Per
sonal Devil " is nothing, not merely because of the absence of
reason for belief in his existence, but because he implies a self-
contradiction. An immoral agent, who was utterly wicked,
would fall outside the sphere of morality; for badness, like
goodness, involves a collision, and ceases to exist when you
make it absolute. 28
19. Where this kind of disjunctive inference can be
practised, the conclusion it procures is logically certain. For
the predicate, which emerges, is not won by exhausting every
possible antagonist. The subject has not actually been altered
by the choice of our ideal experiment. It remains what it
was. Our own eyes are the real subject which has suffered
the operative process, 29 but nothing is removed save impedi
ments to vision. If we keep to the limits already laid down,
then logic is pledged to bear us unharmed through all logical
objections.
We are open to attack from another quarter ; for we may
fairly be charged with the sin of desertion. The process, which
we adopt, may be saved from every assault of the enemy;
but what, it may be asked, has become of the disjunction?
For this suggestion of an opposite, which leads to reflection on
what lay in our minds this going from the experience of " I
can not otherwise " by an inference to the ground of our
incapacity (however sound and however ultimate the process
may be) does not seem a disjunctive argument at all. Since
CHAP. Ill THE VALIDITY OF INFERENCE 567
the residue is in fact a preconception, since the exhausted
alternatives were never possible, the conclusion does not de
pend on exclusion. It is not in effect the mere assertion of
a residual element, and this show and pretence is a hollow form
which is simply deceptive.
There is truth in this objection. The disjunctive argument,
if you take it seriously, is not the process we have just
sketched and defended. This process does appear in the form
of disjunction. An exhaustion is the mode in which we clothe
it, and the shape which it bears, if you take it as a fashion of
opening our eyes. But the exhaustion itself is not that which
demonstrates. The possibilities banished were never possible.
And the experiment is so far from serving as a ground, that
the process consists in its total rejection. But the objection
may perhaps find its answer in a doubt. ao If disjunctive
reasoning is not willing to take the place which we have offered
it ; if it aspires to be more than a road to vision, and a way of
reflection which brings the actual ground into light, is it likely
to maintain its claim to existence? Is our seeming desertion
not a counsel to throw off a character assumed, and that leads
to condemnation?
20. For, taken in the guise which it prefers to wear, the
disjunctive argument will not bear a trial. Apart from a
borrowed assumption of completeness, the ground it stands on
is wholly rotten. If it really goes from the absence of a and b
to the presence of c, and if it takes this step because it has
failed to find other possibilities, then it sins against a cardinal
logical principle. It treats a mere defect in its knowledge as
equivalent to a positive quality in the content. The fact that
A, as it now appears, is wanting in d, is no proof that A d
is a false proposition. You can not identify the subject, as
it stands under psychical conditions, with the subject as fully
determined by content. You can not in short, by any kind of
handling, make a privative judgment become an exclusion (cf.
Book I. Chap. III.).
If my reason, for thinking that A d is false, is simply my
failure to find d in A, then the subject, which I deal with, is
the subject as qualified by my mental defects. It is not the
mere content A which excludes, but it is A taken together
with that stage of ignorance, at which my psychical history has
568 THE PRINCIPLES OF LOGIC BOOK III. Pi. II
arrived. But this absence of knowledge does not logically
determine the content A. It is an abstinence which reveals no
actual quality within the subject ; for there can not be virtue
where temptation as yet has not happened to assail.
To put the case otherwise, if d is not impossible, if it is
simply unreal ; or, more strictly 31 (since everything unreal is
impossible), if d is not impossible because, if it were, a quality
of the logical content A would be contradicted if d is im
possible, because otherwise our knowledge of A would be
altered, and if this is the only reason we can give for d s non-
existence then our inference is precarious, its process is un
sound, and its conclusion but begged. We may be forced to
put up with it, but we must not try to think that logic guar
antees it.
21. We may sum the matter so. If, in saying "I must
because I can not otherwise," we mean " I must not otherwise
because I do thus, and I know that I do thus because I can
not do otherwise," then our inference may not bear the name
of disjunction, but it is thoroughly sound and faultless in
principle. But, if, on the other hand, the essence of our argu
ment is " I must do this, because I do not perceive that I can do
aught else," then that argument may not reach a false con
clusion, but, considered as a proof, it is thoroughly vicious.
And, if this is what we mean by disjunctive reasoning, our
process in the end is based on a fallacy.
And this opens the door to a sceptical doubt. Must not
both these varieties, if we determine to go back, resolve them
selves into cases of the second? Does our proof depend on
anything beside the ignoring of another discrepant alternative?
This doubt does not cease with the province of disjunction;
it attacks the whole system of our judgments and inferences.
If all judgment in the end becomes an inference, when reflec
tion suggests an excluded predicate, and returns to the subject
from that repulsion if this, as we saw, is the ultimate infer
ence does not every judgment in this way become a vicious
inference? For it either is held for no reason except that it
has not been questioned, or, when attempted, it succeeds in
keeping its virtue for no other reason than the absence of sug
gestions fit to corrupt it. And this absence is assuredly the
chance of privation. We are forced to admit a theoretical
CHAP. Ill THE VALIDITY OF INFERENCE 569
possibility of our knowledge being otherwise, if our ignorance
were less. And, if so, with each predicate, we can not deny
the possible existence of unknown alternatives. To dissent is
to assume something like omniscience, and to agree is to vitiate
every inference.
22. We might reply that, even if we did not merely as
sume, but really possessed, entire omniscience, we should still
by the argument be compelled to doubt and to disbelieve. And
this consequence, the legitimate offspring of scepticism, shows
features distressingly like credulity. But it is better to at
tempt a direct refutation. The sceptical doubt, here as else
where, will at bottom be discovered not to be sceptical. It
assumes a foundation on which it stands to batter down its
dogmatic antagonists, and that foundation itself is always un
critical though covert dogmatism. We can see this at once in
the present case. We found (Book I. Chap. VII.) that the
possible must rest on the real. Possibilities exist in hypothetic
judgments, and consist in the assertion that, given some condi
tions, a subject would certainly possess some attribute. This
simple reflection has important results. For if you say that,
with every piece of our knowledge, we are bound to admit that
it might be otherwise, you assume that with every subject you
can frame a valid conditional judgment in which it acquires a
discrepant predicate. Thus, given A b, you assume the
existence of a possible c; and since the pair, A and b, are
coupled not by virtue of any special attraction, but solely
because b happened to be there when A was unoccupied, hence
the relation A & is itself but possible.
Now the answer is this, 32 that, if your conclusion is true,
you either have failed altogether to prove it, or have proved it
by means of a false assumption. For you yourself have ig
nored a possibility. Suppose that your effort, everywhere to
find a discrepant suggestion, were somewhere unsuccessful.
Suppose that, attempting to make a judgment in which the sub
ject developed a predicate inconsistent with the character al
ready possessed, you somewhere found your impotence and
the limits of your thought. If you wish to be sceptical, you
must cease to ignore this fatal alternative. For seeking a pos
sible quality c, incompatible with the present judgment A b,
you may end for ever in a blank defect, or for ever arrive at a
57O THE PRINCIPLES OF LOGIC BOOK III. PT. II
c, which seems to be discrepant with b, but which falls on
scrutiny within its area. And, if this is the case, then to doubt
A & is presumptuous dogmatism. You can not assert that
its opposite is possible, until you are able mentally to represent
that opposite. 33
To doubt where you have but a single idea, to balance op-
posites where one opposite is lacking, to suppose that the
inconceivable is true, would be surely mere forms of one self-
delusion. The question at issue turns on the fact of there
being these opposites. The real existence of these ultimate
doubts, the very possibility of these possibilities is the point
where you are met by a flat denial. You can not escape a
metaphysical discussion by metaphysical dogmatism in the
garb of scepticism. And, whichever way we may decide this
question, we certainly can not decide it off-hand by a simple,
argument a priori. We must meet the sceptic by a deeper
scepticism. His conclusion, if true, has been merely assumed.
Whether right or wrong in the ultimate result, his process has
consisted in begging the question at issue between himself and
those who dissent from him.
23. The actual question belongs to metaphysics, and we
can not attempt to consider it here. A logical enquiry must
remain content with a simpler result. If the subject of priva
tion be identified with the true and real subject, then, on that
assumption, disjunction is valid. The formal consequence of
conclusion from premises is then unimpeachable. But the
premise which maintains complete exhaustion is merely pre
carious. 34 If, on the other hand, we wish for a process which
is free from doubt, then, while it assumes the form of dis
junction, it must really proceed by exclusive assertion. It
must argue from presence and not from defect.
And, with this, the remarks which we are able to offer,
may come to an end ; and we shall say no more on the formal
validity of our types of inference. Dialectical reasoning has
not been discussed, but would not present us with new con
clusions. Our main result may be so summed up. Argu
ments, so far as they amount to demonstration, have been
found to depend upon logical postulates. It is assumed
throughout that some operations do but change our power
of perceiving the subject, and leave the subject itself un-
CHAP. Ill THE VALIDITY OF INFERENCE 571
altered. And this holds even where our wilful and arbitrary
choice selects the process and procures the result. The
gain which the subject appropriates in the end, is here its
original and rightful possession; while the loss and the
struggle from defect to growth is the lot which falls to our
finite intelligence. But these postulates in the end we left
unexamined.
24. We have still before us a very grave question. In
our final chapter we must ask whether inference is really
valid; if, that is, beside making good the conclusion, its process
has a claim to be true of facts. We may here, and in passing,
allude very briefly to another difficulty. 35 We saw that,
though our types might all be flawless and formally accurate,
we might still be quite unable to use them. The conditions
required for a demonstration might never occur in actual
practice. Our types might be ideals, visible in heaven, but too
far and too pure for human attainment.
We may indicate the principal source of our corruption.
What we use in logic is ideal content, and that content, we
have seen, can have by itself no mental existence. It must
always appear under psychical conditions, and hence comes a
continual tendency to error. If we confuse the context with
the actual content, we are sure to vitiate the whole logical
process. For since we do not know exactly what we have in
our hands, what we actually use and what we neglect, we
turn a judgment, that should be categorical, into a judgment
that depends on a latent condition. The form, in which the
conclusion comes out, will depend on the presence of impurity
in the agents. Take for instance A B and B C as prem
ises, with a result A C. The construction here depends on
the identity of B in both these premises. But suppose that,
in the second premise, C is not really connected with B ;
suppose that it really belongs to B;r, and that we have neg
lected to notice x. The relation with C will then depend upon
the context, while we have assigned it to the bare and simple
content B. Thus a condition has crept in and has destroyed
our reasoning. And hence to reason rightly demands a purity
which is based throughout on elimination. Since we must
have identity, and can not but have difference, we depend for
our success on preserving the material, while eliding the
572 THE PRINCIPLES OF LOGIC BOOK III. PT. II
irrelevant elements of our premises ; and this process is sub
jected to the risk of error.
25. We can not any further pursue this theme, but may
end our chapter with another word against the sceptic. We
are bound to admit some degree of probability in favour of
the badness of any one inference ; 3G and the sceptic once more
may urge his objection, If every argument is probably false,
how can any argument be certainly true? But the answer is
simple. Considering my reasoning as a number of acts, I con
clude that I am fallible throughout the series. But this chance
is mere antecedent probability. It may become unmeaning
when the instance is present and actually before us ; as un
meaning as the chances against a die giving six, when the
actual throw has been observed. And, if so, the presumption
of our fallibility may warrant a general feeling of diffidence ;
but it can not affect any actual inference which has once been
seen to exhibit the type required for demonstration. If in the
present instance you can show me no ground which justifies
doubt, your mere general probability is quite irrelevant.*
Whether it is true that in every case we have actual cause
for hesitation, is a question of fact to be settled by itself.
This question of fact, which perhaps underlay the objection,
and which has appeared in the answer, can not here be dis
cussed. We must concentrate our thoughts, since we are
summoned to encounter our ultimate problem.
* There is a somewhat similar fallacy in Mr. Spencer s Psychology,
vol. ii. p. 430. You can not argue from the general probability, that a
longer argument has more chances of mistake, direct to the conclusion
that a short argument must be more trustworthy than a longer one.
In order to do this, you must assume besides, that arguments differ in
nothing material except their length.
ADDITIONAL NOTES
1 " Validity." For the meaning of this ambiguous term see Ap
pearance, Index. We have to distinguish three senses here. See
Note 2.
2 " Actual process." " Actual " should be " real," or (if we keep
to the view more generally recognized in this work) " existing."
Further, the terms, " represents " and " correspondence," are am-
CHAP. Ill THE VALIDITY OF INFERENCE 573
biguous. They are taken here as implying identity, together with its
appearance in another region or embodiment. And this will be the
first of our three senses of Validity. The second will be " good
formally " ; and " good practically " will be the third sense. " Prac
tical " (see the Index) means here " for working purposes in reason
ing." This third sense in spite of the words " We intend . . .
enquiry " comes up again in 24.
3 " Postulates," see the Index. The question as to how far and
in what sense Metaphysics also depends upon postulates is not raised
here. See Essays, pp. 2, 16, 311.
4 " The result must be new." See on Bk. III. I. II. 17.
5 " The premises would be wrongly laid down." This is certainly
the case. For (i) a whole beyond the premises is always implied.
And (ii) so, again, is our agency. But, on the other hand, this agency is
not merely ours, nor does it in its sequence involve necessarily our mere
choice or arbitrary caprice. See Bk. III. I. II, Notes 7 and 10. Hence,
if the subject of the inference is taken in its full sense, i.e. together
with its implications, its self-development is intact. See T. E. I, and
Index, s. v. Premises, and Inference.
6 " Reality itself might supply, etc." This is what it does do,
for it is itself an agency in union with mine.
7 " If by altering myself, etc." The objection to this view is that
it destroys the inference. There is now no process of aelf-develop-
ment, and hence no real " therefore " or " must." A mere correction
of an unaccountable mistake is hardly an inference. See on Bk. III.
I. II. 13, and below, Note 15.
Apart from this, the argument is as follows. If attention does
not alter its object (as we postulate), so, more generally, other
mental activities need not do this. On Attention see Essays, the
Index. The reply to the above argument is " If no alteration, then
no self-development, and hence no inference." On the " logical
postulate " see further Note 15.
8 In inference does the conclusion necessarily contradict the prem
ises? This result is to my mind in the end unavoidable, (i) If
the " premises " are really all that is there at the start, then that is
altered in the result ; and by the result it is, I should say, contradicted.
And (ii) if it is urged that the beginning is denied, not as it is but
as it appears (cf. on Bk. III. I. II. 13), a dilemma awaits us. For (a)
the process will still be a self-contradiction, though what contradicts
itself will now be no more than an appearance; or (b) there will now
be no real process and hence no inference at all. Further (iii), if
the " premises " are widened so as to take in all that really is im
plied at the start, then (as before) either (a) you have included
so much that the process, and therefore the inference, disappears;
or (b) the end, as I think, still contradicts the beginning. The ques
tion in the end is whether the idea of self-development, though neces
sary for Logic, is, when you insist on a final answer, a consistent
idea. Does it, or does it not, depend on an x, which dependence,
574 THE PRINCIPLES OF LOGIC BOOK III. PT. II
so far as we can see, implies that, as such and as itself, the above
idea is not real? Cf. T. E. I., and (below) Notes 15 and 32. In this
work (the reader is reminded in 7) I was not attempting to deal with
first principles (cf. 10).
9 " Is left to my caprice." The real solution of the difficulty here is,
while accepting " agency," to distinguish that from " caprice." See
Note 5.
10 " Our assertion is elliptic " as is all judgment more or less.
See T. E. II.
11 " But that A C is known." The word " known " is ambiguous.
It should mean that mere A C can be taken as true subject to an
unexpressed condition.
12 " A rising sea of inferences." For these see Book III. I. Chap. II,
and the added Notes. Cf. also T. E. I. There are two main
questions here, (i) How far in each case is the process arbitrary?
(ii) How far, and in what sense, is this process the movement of
what really is the subject of the inference, and can so deserve to be
called self -development?
13 " Those diagrams, etc.," i.e. in some old books on surgery.
14 " The shepherd must predicate the sequel." The qualification
" here " should be inserted before " must."
15 " The process vision." The difficulty which arises here has been
noticed already (see Notes 7 and 8). So far as the process is not
a necessary development, and hence an alteration, it can not be an
inference, though doubtless it may serve as a help in inferring. Every
inference is the necessary self-development of a real subject. You
may take that subject (i) as real simply, or (ii) as real in the sense
of known so far by me, or again (iii) as real in the sense of a mere
psychological fact. Hence (iii) your conclusion may be as to some
thing that must happen necessarily in me under certain conditions.
I may conclude, for instance, that under such and such conditions
I shall perceive a certain result. But here, though we have a genuine
inference, we have, so far, no inference with regard to the object
itself which I perceive. On the other hand we may go on to arrive
at that result by a further process. For we may proceed to reason
from what happens in me to what in consequence must be true of the
object itself.
Having, for instance, attended to an object I may conclude that
the object, as I now perceive it, is and was the real object itself;
and my inference here is as follows. The development effected by
me is assumed to have made no change in the object. And hence
either that object has remained unchanged; or, if altered from out
side, has been altered by something other than my process. But we
can (we think) assume the absence here of any such latter alteration;
and therefore, finally, my object is either now what it was, or it has
developed itself.
The above assumption is (i) negative, so far as it excludes altera
tion from outside either by my process or by anything else. It is
CHAP. Ill THE VALIDITY OF INFERENCE 575
on the other hand (ii) positive, so far as it asserts the persistence
or development of the object, and takes its stand on what I have
called the Law of Identity (see Index, and Appearance, p. 602, and
Essays, the Index). And on the negative side (to speak only of
that here) the character of the inference so far as we have a
genuine inference will be disjunctive (see on Bk. III. I. II. 25).
With regard to the truth of the postulates given in the text I
can not in any case admit that it is ultimate. These postulates are
true only, I should say, in the sense that for certain purposes they
can be taken to hold. And we have here (I should further add) really
no more than one postulate, though that can be used in various applica
tions.
16 On Supposition and Suggestion see the Index.
" Abstraction." Cf . Bk. III. I. II. 23, and see T. E. I and IX.
18 " Elliptical," and so also " conditional." And after " where we
fail to analyze " is to be understood " completely, which is not possible
anywhere."
19 " If you were able finally to isolate," which (we should add)
is impossible. No analysis it does not matter whether the experi
ment is " ideal " or otherwise is in the end conclusive if taken as un
conditional. All that can thus be shown is that for a certain purpose
you may find that you can ignore that whole which everywhere, in
some sense, remains still vitally concerned. As for getting units
apart from some integer, this is clearly impossible ; though for the
purpose in hand the integer may of course be put out of sight. Cf.
15, and see T. E. I and IX. In the following sentence, " Wherever
. . . truths," the word " taken " should be emphasized. " Taken as "
should be understood here in the sense of " assumed to be."
20 We arrive . . . impossible." But it would be an error to take
the "a priori experiment" as holding good except on the strength
of an assumption, and so as subject to conditions. With one excep
tion no possible experiment can give truth which in the end is more
than relative. This exception is found in any case where the contrary
of the result is inconceivable. And by " inconceivable " I mean that
the " other " not only in fact is not found, but that you have no right
to regard it as even possible. For, if you know of no field in which
this "other " can be taken to fall, and, if you fail to give to it any
positive meaning, it is clearly nothing that can be called possible.
With the above exception no experiment can give more than relative
truth, and the criterion here, as everywhere else, must be found in the
idea of system. On the above see further T. E. VII and VIII.
With regard to isolation (cf. 15) I would repeat that this never
exists as the mere positive presence of one single element. There is
always present without exception a many in one, felt at least in the
mind if not also an object before the mind. Hence isolation must
imply the negation of an " other " which actually is also there. And
this relation of exclusion must (on my view) take place within and
depend on a whole. It is a common fault in Realism and Pluralism
5/6 THE PRINCIPLES OF LOGIC BOOK III. PT. II
to fail to recognize the above doctrine, even as a view which exists
( 15). But as to the nature and justification of the particular
assumptions used in experiments of various kinds, this is not a topic
to be discussed here.
21 " Is at least a part, etc." This conclusion is correct, if you
make certain assumptions, which, for a certain purpose, may be
justifiable. See T. E. I. But, as the "Method of Difference" leaves
out these assumptions, and tries to be absolute and unconditional, it
hence falls into grave error. For this Method, cf. Bk. II. II. III. 13.
82 " A specific experiment" which (once more) is impossible, if
taken as unconditional, and which is valid or not, according to the
conditions which can or can not properly be assumed, in a case of
this or of that character.
23 " Probability, etc." The greater the number of instances in
which accompaniments of A are shown with a consequence other than
d and the greater the diversity of these instances the less becomes
the chance of an accompaniment of A which is relevant to the pro
duction of d. This, I presume, is here the formal principle.
24 " Unreal abstractions." By " unreal " I meant here, I presume,
" not existing as such." On Arithmetic see Bk. III. I. II, Note 4.
25 " Where analysis . . . condition." Cf. Notes 19 and 20.
26 " Disjunctive Argument." The difficulties connected with this
have in the main been dealt with already in the Note on Bk. III. I. II.
25. Cf . Bk. III. I. IV. 6. And see T. E. I.
The condemnation of the Disjunctive judgment and inference which
follows here is (I may remark at once) conditional on their being
taken and used as self-supporting and self-sufficient. It is consistent
with the view that a Disjunctive Whole is the form into which our
knowledge should (so far as is possible) be brought however un
attainable is this end, and however imperfect must remain the system
which has to contain and support our disjunctions.
27 These notes, I believe, are lost. But it is not likely that they
contained anything which has not been used in my later writings.
28 " Badness like goodness." Goodness is taken here in the nar
rowed sense of moral goodness. Further, badness and goodness (taken
in any sense) were certainly not intended here to be put on the
same level. See my Ethical Studies.
29 " Our own eyes, etc." See above, Notes 7 and 15.
30 " But the objection, etc." Yes, but the question still remains
whether the process, now described, is an inference at all. See the
references in Note 26, and cf. the Notes which follow here.
31 " Since everything . . . impossible." It would have been better
to have inserted, after " everything unreal," the words " can be taken
as in a sense impossible" (instead of "is"), or to have omitted this
parenthesis. See T. E. VII. And after "impossible" it would be
well to substitute " in the sense that " for " because."
32 Obviously there is no disjunction where the supposed other
possibility is not possible, but is on the other hand self-contradictory
CHAP. Ill THE VALIDITY OF INFERENCE 577
or quite meaningless. For the difference (so far as there is one)
between the self-contradictory and the unmeaning, see T. E. VII.
Given A, the claim of a possibility other than A may be excluded
in two ways, (i) We may, first, have in our knowledge a field outside
of A; and the idea of a something, other than A, which falls within
this area of reality, is, so far, a sound idea. Hence an assertion
of its exclusion and absence must either in the end rest on an as
sumption, and will thus be admitted to be, so far, subject to doubt,
or else will be grounded in the end on mere privation. But (ii) we
may be without the knowledge of any such area outside of A. And
in this case the idea of an "other than A " is in the end senseless
and is wholly inadmissible. Hence there can be no disjunction here,
nor, again, is there any privation, since privation itself depends on a
known positive field of reality. What, however, may have been
gained here, in and through our futile attempt, is a better perception
of A s character This improved recognition is, however, the result
of an increased attention to A, and it involves, in itself, no inference.
I will go on to deal next with the question (raised in the last para
graph of 20) as to the difference between alteration and contradic
tion. If a suggestion that A is otherwise does not alter A as we
know it, then this suggested " otherwise " is in the end nothing. But,
if on the other hand we have an actual idea of an " otherwise," then
this must, so far, contradict A, since it is contrary to A, as itself and
A stand. But again, further, this idea need not be contrary, but may
be accepted as a change of A, if A is taken more widely, or if A and
itself are regarded as together qualifying (under some condition) a
wider reality. And in this case an " otherwise " that alters is an
admissible idea. For " Contrary " and " Contradictory " see the Index.
But obviously, where our A is taken as ultimate Reality, the sug
gestion of an "otherwise" becomes quite untenable. An "otherwise
than A," whether as a contrary or as an alteration, is here, alike in
either case, no idea at all, but is wholly senseless. Cf. Notes 8 and 15.
33 " Mentally to represent that opposite." The term " represent "
is used here in the widest possible sense.
34 " Is merely precarious." It is precarious (if I may repeat this)
so far as it rests merely on the fact that I do not find something
else, something else which on the other hand I can not refuse to call
possible. The more, however, our knowledge becomes systematic,
the less becomes the area within which this idea of an " otherwise "
holds good. But the question as to how large this region of the
Universe still remains, is in the end, I think, unanswerable. Absolute
knowledge is assured only by the nothingness of anything other than
its own positive and, in a sense, " exclusive " self-assertion. Cf. the
foregoing Notes, and see T. E. VIII.
35 The doctrine of 24, with regard to the risk of error in inference,
has been anticipated in Bk. III. I. III. 23, 24, to which a reference
should have been given. On this doctrine cf. Mind, O. S., No. 47, and
2321.2 N
THE PRINCIPLES OF LOGIC BOOK III. Pi. II
Essays, pp. 362 foil. The main point is that logical thinking is the
result of and consists in the exercise of a certain control, and in the
subordination of that which, apart from this or some other control,
would be mere wandering. And, since any control is naturally liable
to lapses, the identity of the subject is thus itself liable to be de
stroyed and the inference to be broken. The above view belongs,
I presume, to that general mode of thought which I adopted. And,
as for claiming originality here, such an idea (I may be permitted to
add) never so much as occurred to me.
I regret to be forced in this connection to call attention to a
statement made by Dr. Schiller (in Mind, No. 95, p. 350 note).
He allows himself (referring to my Essays, p. 368, note) to speak
of my " claim to have anticipated Mr. Sidgwick s difficulty about the
ambiguity of the middle term," i.e. in the present 24 of this Chapter.
Now, if the reader will turn to the passage in my Essays, p. 368, note,
he will find no reference made to any writer but myself. And I may
add that, as I have almost no acquaintance with Mr. A. Sidgwick s
writings, I could not pretend even to know in what his particular
difficulty or discovery consists. I will now ask the reader to refer
also to the Note on Bk. III. I. VII. i of the present work, and will
leave it to him to judge as to the amount of credit to be given to any
assertion or suggestion proceeding from Dr. Schiller.
36 So far as you take an inference simply as this or that inference,
there is certainly some probability against it as so taken. But this
antecedent probability itself rests on the assumed certainty of that
doctrine on which it is based where, however, we have again, so far,
the same general chance of error. On the other hand, when you
take an inference not merely as this or that, but as a concrete in
dividual case, the above abstract probability may be in various degrees
reduced or may wholly disappear. Obviously, if there is any case
where doubt is not possible, the above probability vanishes, since its
foundation is incomparably less secure than is that position which it
attacks. And you can not (to speak in general) take some particular
assertion by itself, and then argue a priori about its degree of prob
ability. Its real probability depends on the amount of its connection
with the whole body of your knowledge. See Bosanquet, K & R,
p. 266; and, on the whole subject of Probability, cf. T. E. VIII.
The reader will notice that in "another word against the sceptic"
the reference is not to 24 but to preceding Sections.
CHAPTER IV
THE VALIDITY OF INFERENCE (continued) * 1
I. In the foregoing chapter we limited the question of
our reasoning s validity. We discussed the possibility of get
ting an inference which amounts to demonstration. We asked
whether any conclusion does follow, when the premises are
assumed. To this limited question we were able to return
an affirmative reply. If we admit certain postulates, then
there assuredly are types of necessary reasoning. It may be
difficult to practise the rules which they enjoin, but we may
say at least that, given the conditions, the consequence must
follow. And so far, though relying on the strength of postu
lates, we have succeeded in holding the position which we
occupied.
But we now must await a more dangerous attack. Our
inference may be valid, if valid is to bear the sense of con
clusive; the consequence may follow and be true, if the
premises are not false. But what shall we answer, when asked
if our reasoning is true in reality, and valid of fact throughout
all its process ? It is not enough to reply that surely it comes
out true in the end. For the outset and the journey might
both lie in a region of convenient falsehood ; and the question,
which is pushed and which can no longer be fenced with,
directs itself to this fatal weakness. If truth is the ideal
counterpart of fact, 2 can we say that the process of our
reasoning is truth ? Can we venture to assert that our mental
operations are the same with any actual process in things?
Is the intellectual experiment the parallel of a movement in
the real universe? Our reasoning, we know, does answer to
the facts,* but that is not enough. Can we call it the literal
expression of those facts? Is reflection the double of an out
ward change, that shows feature for feature in an answering
element? Or is it an indirect process, which results in a
* Cf. Lotze, Logik, Buch III. Kap. 4.
579
580 THE PRINCIPLES OF LOGIC BOOK III. PT. II
picture, but which, taken in the middle, could not be recog
nized? We may doubt if the end, when we get it, is a copy;
and we may doubt still more if the means is a copying, or in
any sense a counterpart.
2. We can not dwell on this question in its ultimate form.
We can not decide if an activity, which appears in our reason
ing, is one with a force that alters reality. 4 It is not that I
think the question improper, but that in this volume it could
not be discussed. For the very existence of any force or
activity is itself a point which we are not able to assume ; and
without this assumption, the question we have mentioned would
of course have no meaning.
But, if we lay no stress on the question of activity, 5 and
confine ourselves mainly to the actual change, the problem in
hand may thus be stated. In our reasoning a datum suffers
alteration; undergoing a change it appropriates the whole, or
at least some part of the new result. And does the reality
transform itself in unison? Do the facts themselves exhibit
alterations parallel with the series that appears in our argu
ment? Is this aways the case, and again, if not always, is it
ever the case in any possible argument?
3. The result, we have reached, forbids us to accept the
first of these alternatives. Where the middle of our process
does not answer to the cause, where it is not the reason of the
conclusion s existence, but merely the ground which we have
for belief in it, in every such case our mental experiment does
not even pretend to reproduce fact. The equality of A and
of C to B is our cause for the judgment " C is equal to A,"
but we can not suppose that this change in our knowledge 6
has an answering birth in rerum natura. The last relation does
not spring from the original pair. The result in our minds is
no actual result, 7 the change in our minds is no change in
things, the mental experiment, if you compare it with the fact,
has no existing counterpart at all. If the real world is not far
other than it seems, then the course of our ideas, at least in
this case, can not possibly be true.
The conclusion does not really result from the function;
for if it were not there before, we admit it would be false. 8
On the other hand it can not be given, already and at the start,
for in that case we should have no inference at all. But, if
CHAP. IV THE VALIDITY OF INFERENCE 581
so, then both movement and issuing change are false appear
ances; they belong to our minds, and are not true of things.
This fatal consequence affects all inferences, where the middle
does not represent the cause. And then the middle, we may
go on to urge, can be wholly capricious. It may arise from
nothing but our arbitrary act.
For consider the processes of distinction, comparison, and
again abstraction. I need not perform these ; I experiment or
not, as it happens to please me. But is it possible that when
ever I happen to be pleased, the things have somehow changed
themselves harmoniously? How frivolous an idea, but how
inevitable ; and yet once more how wholly indefensible. We
have hitherto concluded from our logical postulate (which
assured us that our change did not alter fact) that the con
clusion was there and came out to be seen. But now we seem
confronted with three alternatives. 9 Our actual process may
be foreign to reality, and falls outside it in our mental world.
Or an actual and answering change has taken place, and the
facts are transformed by our caprice. Or lastly the course of
things runs parallel by an overruling harmony. Any one of
these alternatives seems attended with ruin.
4. (a) Suppose first that our arbitrary choice has modi
fied the facts themselves, that no quantities are equal 10 until we
have compared them, nor anything different before we have
distinguished, and that these functions make the object which
they contemplate. If so we of course must surrender our
postulate, and allow the result to become conditional. The
things, if you leave them alone, are not equal, since equality
depends upon your caprice. But, with this result, we not only
give up what before seemed true, but we can not accommo
date our view to the facts. Unless the world is quite different
from our common beliefs, unless we turn upside down our
ideas about reality, we therefore can not accept this first
alternative. And if (&) we next make trial of the har
mony, 11 we find ourselves still immersed in difficulty. For
suppose that, when I argue, the world is changed, and a process
takes place conformable to my movement, then, unless we
think that the world goes by chance, there must be some kind
of reason for that change. But the conclusion, as we have it,
is then incorrect; for the condition of the process is com-
582 THE PRINCIPLES OF LOGIC BOOK III. Pi. II
pletely ignored. We must therefore set down, not A by itself,
but A -|- x as equal to C. But what is this x? If it is other
than our act, then once more the things diverge from the course
which is taken by our thoughts.
5. " But the x" I shall be told, " though it is not the
act of our intelligence, is still the function of an under
standing. Phenomena are ruled by a reason not mine, and
my argument, capricious in regard to its existence, is com
pelled and subject in respect of its content. If I make it, I
must make it on a certain model, and this model is the work,
long done or now doing, of an inference precisely the same
as mine. This double process of a two-fold mind unlocks
the puzzles by which we are enclosed."
I should be sorry to seem to persist in unbelief, but I am
compelled once more to repeat the dilemma : If the reality in
this way corresponds to logic, then reality itself has been
wholly transformed. One may perhaps accustom oneself to
regard events as the reasoning sequence of the divine under
standing, but it is not so easy to bring under this head any
sameness and difference that is thought to exist. We are
forced to wonder, if things by themselves are really not alike,
how God himself can find them the same; or how even God
goes on to distinguish them, if they themselves are not really
different. It is indeed possible here that a distinction might
save us, that a sensuous ground, which is not different, when
taken together with a function of the intellect, produces alike
both distinction and difference. And yet this solution is
partial, and leaves a worse puzzle behind.
We might perhaps agree that reality is the work of a
reasoning mind, but how can we submit to the belief that my
reasoning must represent reality? How can we suppose that
each trivial argument, 12 every wretched illustration that we
may have used in these discussions, provided only it be free
from flaw, must have its direct counterpart in the nature of
things. You may suppose that, whenever we reason, we
retrace the solidified logic that is organic in the world; you
may believe that a mind, in union with our own, brings out
by one process, that to us seems double, the separate sides of
existence and truth. But, on either view, we are troubled with
CHAP. IV THE VALIDITY OF INFERENCE 583
this consequence; every possible piece of mere formal argu
ment, every hypothetical deduction from an idle fancy, all
disjunctive and negative modes of demonstration, must each
have its parallel counterpart in reality. This consequence may
be true, and I will not deny it. But, if true, to me at least it
is portentous. Our logic will have secured correspondence
with fact, 13 but the facts themselves have been strangely
translated.
6. If we mean to keep to a view of reality which is any
thing like our common ideas (and apart from a system of
metaphysics we can not, I think, do anything else) we must
come in the end to our third alternative (c). We must admit
that, although a valid inference in some way must answer to
the nature of things, yet at least some reasoning does not
show that nature. It exhibits a process essentially different
from the actual course of real eixstence. Even if you believe
that it comes right in the end, yet throughout its movement,
it diverges from the truth. Unless you revolutionize your
belief about reality 14 (and perhaps you ought to revolutionize
that belief), you can not maintain the strict correspondence
of thoughts and of things.
We have seen so far 15 that, at least sometimes, our move
ment does not answer to the course of reality. But we are not
allowed to get off with this compromise. We must prepare for
a still more fatal sentence. We shall have to see that our
mental experiment can never represent the actual event. And
our conclusions also are threatened with falsehood; for our
arguments can not even finish with a truth. Both process
and result diverge from given reality. They no doubt may
be valid in the sense of serving, they may go near enough to
convey the meaning, but neither can be called correct trans
lations.
7. If the result seems strange, it is strange because we
have not remembered our account of judgment. It is in a
judgment that our reasoning must end; and our natural im
pulse is to think that ideas are divided and joined like the
things which we know. But we saw that this notion could not
be verified. Our hypothetical, disjunctive, and negative judg
ments were none of them found to represent facts. There was
584 THE PRINCIPLES OF LOGIC BOOK III. Pi. II
nothing left which, if truth is a copy, could possibly be true,
save only the class of categoric judgments. And, seeking for
these, we failed wholly to find them, so long as we kept to the
series of phenomena. All our ordinary truths, every single
affirmation we were able to make about the course of events,
turned out in the end to be hypothetical. We tried in vain
to get right down to the facts ; we were always left with an
artificial extract and a fragment got by mutilating things.
And this product failed of truth in two ways. It left out
details which it ought to have copied, and it depended on de
tails which did not exist. However you took it, it turned out
hypothetical, and the elements which it connected lacked actual
existence.
8. And this failure was a symptom of our logical disease,
a weakness not passing, nor local in its area, but deep-rooted
in the system. For judgment and inference, if we are to have
them at all, must both be discursive; they must work with ideas.
But ideas do not exist, 16 and they can not exist, if existence
means presence in the series of phenomena. I do not mean
merely to press the obvious consequence that a thing can not
be in two places at once. I do not mean that ideas, being
inside my head, can not also and at once be found outside it.
I mean much more than this. Neither outside my head, nor
yet inside it, can ideas have existence; for the idea is a con
tent, which, being universal, is no phenomenon. The image
in my head exists psychologically, and outside it the fact has
particular existence, for they both are events. But the idea
does not happen, and it can not possess a place in the series.
It is a mutilated content which, as such, can not claim to be
more than an adjective. And the functions, that work with
these unrealities, can not possibly reproduce the flow of
events.
9. This discursive nature of judgment and reasoning is
fatal to their claim of copying existence. The process of the
inference can never be true, and the result can never represent
the fact. We will not waste time on less mortal objections
that destroy weaker forms of logical thought, but will at
once proceed to the strongest instance. Even where the middle
seems to answer to the cause, and the conclusion to exhibit the
actual effect, yet even here the movement in the mind is not
CHAP. IV THE VALIDITY OF INFERENCE 585
the same thing as the movement of facts ; the premises can not
exhibit the conditions, and the conclusion is very different from
the consequence in time.
In our inference we have first the elements apart, then
follows their union, with the issuing result. But the elements
that occur in the course of phenomena do none of them pos
sess an isolated being. They can not exist every one by itself.
Apart from one another they indeed may be found, but none
separate and divorced from all other existence. Yet this con
text, which makes them real as events, and without which they
could not appear in the series, is ruthlessly stripped off in our
mental experiment. And so, what we use in that ideal syn
thesis, is nothing but an artificial preparation. We operate
with content and not with existence. Our elements are noth
ing in the world but adjectives, and adjectives whose sub
stantives we fail to state. We indeed treat them as actual,
we attribute them all to the ultimate reality; but reality, in
the sense in which we have chosen at present to take it (the
sense of a being that exists within the series of phenomena),
refuses to maintain the existence of our elements. It sup
ports them hypothetically, and on the strength of conditions
which we are powerless to fulfil.
10. And as the separation of the elements is not true, so
also their union and construction is fictitious. I will not raise
again a former objection, though it weighs, I admit, in the
adverse scale. If our minds did not work by way of con
struction, the premises would hardly come together of them
selves ; and can we say that, in the outward movement, there
is anything like an answering activity? We will suppose that
this question has been answered in a way which favours the
claim of our inference to truth. But, be this as it may, the
movement in our mind remains discursive, symbolic, and ab
stract. If the facts come together on just the same principle
on which we unite our ideal elements, yet they can not come
together in just the same way. The real is divided from the
mental union by an insuperable difference. The synthesis of
facts may be partly the same as our mental construction ; but
in the end it diverges, for it always has much that we are not
able to represent. We can not exhibit in any experiment that
enormous detail of sensuous context, that cloud of particulars
586 THE PRINCIPLES OF LOGIC BOOK III. PT. II
which enfolds the meeting of actual events. We may say
indeed that we have the essential ; but that plea reiterates the
charge brought against us. It is just because we have merely
the essence, that we have not got a copy of the facts. The
essence does not live in the series of events; it is not one
thing that exists among others. If reality is the chain of facts
that happen, then the essence is a creature which lives only in
the thought which has begotten it. It could not be real, and
it can not be true. Our construction is as false as our sepa
rate premises.
And our conclusion can hardly fare much better. Be
gotten of falsehood it can not so far be misbegotten, as to
show us in the end the features of fact. The parental disease
still vitiates its substance. Abstract and symbolic it mutilates
phenomena ; it can never give us that tissue of relations, it can
not portray those entangled fibres, which give life to the
presentations of sense. It offers instead an unshaded outline
without a background, a remote and colourless extract of ideas,
a preparation which everywhere rests on dissection and recalls
the knife, a result which can not, if events are reality, be
aught but unreal.
II. And no possible logic is exempted from this sentence.
If we recur to that type, which we found or fancied, where
the real and the logical seemed wholly one, if we come in the
end to the Dialectic process, 17 we can not escape the point of
the objection. For, if the starting-place we leave were real by
itself, if it were actual so as it first comes before us, what
sufficient excuse can we plead for leaving it? Why do we
correct and supplement it, if it is true ? You may say that a
parallel alteration and amendment is the actual course of the
genuine reality, but I confess to my mind that solution is a
failure. If you think that the element, with which you began,
was apart by itself in the field of reality and within that
vacuum began to develope, then to me the whole question is
lost in darkness. But if you admit that a movement took place
by virtue of the action of the total system, then surely we must
add that, apart and by itself, our element was not real. Both
its isolation and its subsequent evolution took place within a
completed universe, 18 and without that universe would have
been nonentities. And, if so, our process is but partially true.
CHAP. IV THE VALIDITY OF INFERENCE 587
It depends on conditions which it fails to state. It does not
answer to the working reality.
Both our starting-place and our process of advance and the
provisional goal at which we arrive, are none of them true of
the actual world. If you take them by themselves, they can
hardly be more than our way of thinking. Our knowledge and
reality would never be one, until in our minds the self-con
scious Universe were to follow itself throughout all its pro
ductions, and comprehend itself in the whole of its detail.
And, if that pass were reached and that hope consummated,
it is doubtful if then our knowledge would be logical, and if it
could still bear the form of a discursive process. 19
12. It seems hardly worth while to follow any further
this line of objection. We may however recall a further point,
with which we will bring the discussion to a close. Even if the
process of our logical movement seemed ideally to counterfeit
the course of phenomena, and to present us with the actual
changes of events, yet, if this by any means could be believed,
we still fall at the end into hopeless confusion. For if it were
not for our inferring, we never should have had this series of
phenomena. It is not merely the separate strands and fibres of
causation, but it is the whole continuity of the total series
which is absolutely based on ideal reconstruction. By means of
this function, and this function alone, we have connected the
past in one line with the present. It is by this alone that we
have acquired our knowledge of phenomenal changes ; and it is
this creation we approach with that series of inferences which
attempts to exhibit the threads of causation. But if reality is
not to be the work of our reasoning, if it is to lie within mere
presentation, then the train of events are themselves not real.
They themselves are nothing but a false construction; and a
mental sequence that portrayed them truly, as we believe them
to exist, would itself be therefore untrue to given reality. 20
For unless we think that phenomena can be real, though
they appear to no one, we must hold that the past, at least as
we know it, has no existence outside reproduction. But we
know what is past by synthetical judgments, and they are a
function which depends on a ground. This ground is the prin
ciple of the Identity of Indiscernibles ; it is because the ideal
content seems the same, that we therefore assume it to be
588 THE PRINCIPLES OF LOGIC BOOK III. PT. II
really identical, and identical in spite of change and diversity,
despite the difference of its two presentations. But how shall
we dare, on the strength of this principle, to treat the ideal as
if it were real? What help could we expect from the School
of Experience, if our only way to rehabilitate their fact is
to violate their most sacred and continuous tradition? Can
we safely go from the appearance of sameness, within the
mind which compares, to a real identity that connects events?
Can we pass from ideal redintegration to actual continuity of
fact? If we can not, then forthwith the series of phenomena
becomes unreal, and our reasoning which follows the chain is
illusory. But, if we can, then at once our idea of reality is
quite transformed. Our reasoning will be true because the
facts are themselves inferential. We thus either have relin
quished the presumption that reality lies in what is given to
sense, or are compelled to admit that a serial reality is itself
a bad inference. On either alternative we have ended in con
fusion.
13. To sum up the result if reality consists in an actual
sequence of sensuous phenomena, then our reasonings are all
false because none of them are sensuous. And still more if
reality is wholly confined to the given in presentation, then the
inferences which try most thoroughly to follow the facts, are
therefore and on that account the most false. And reality, it
would seem, must be thus confined, since its prolongation is
merely ideal. It is lengthened on the strength of the Identity
of Indiscernible Content, and it ends in a link which is ideal
also. The past can not be restored in its sensuous fulness ; the
detail is not literally present to the mind. It is judged to be
there; but such judgment is nothing but a general indication, a
symbolic reference to a context, whose main character and
import still survives, but whose complex particulars have
perished irrecoverably. And in the end we are forced to hold
to one of these conclusions ; our reality is not that which ap
pears to our senses, or else, if truth is to present us with facts,
our reasonings are every one of them false.
14. It is idle to urge the argument from success. It is
useless to reply that the mass of our results is enough to prove
the truth of our presumption, and to show that our reason
ings are identical with fact. You can not plead that, because
CHAP. IV THE VALIDITY OF INFERENCE 589
logic works, logic can not be wrong. For the answer is simple.
If logic succeeds, then logic is not wrong to work as it does
work. It is practically right beyond all suspicion, but for all
that it may rest on theoretical error. It must answer to facts
so far indeed as to answer our purpose, but withal its assump
tions may be downright false, and its principle may turn on
unblushing fictions. You can not assert that, if a science goes
right, that science is unable to start from false premises. Have
not brilliant results in the study of nature been obtained by the
help of such working hypotheses as hardly pretended to be
more than fictions? And why should not logic, if it shares the
success, share also in the falsehood? We should surely be
satisfied if discursive necessity, though itself nothing real and
not strictly true, runs parallel with reality, and is throughout
corresponding to our practical needs. 21
15. For this seems the dilemma to which we are brought.
If we keep to the ordinary belief as to fact, or to anything that
is like that ordinary view, then either our account of the nature
both of judgment and reasoning must be radically wrong,
or else these processes are no proper counterpart of the ac
cepted reality. 22 We can not at the end of these toilsome
marches accept the failure of our whole expedition ; and we are
led to seek for a place of provisional rest in the second alterna
tive. And perhaps it is not our reasoning that will suffer a
loss of dignity. Why should not that view, which finds reality
within the series of temporal events, be itself degraded to the
rank of an illusion ? Why should not the result of the deepest
philosophies after all be the truth, and our sensuous present
ment 23 be misrepresentation that can not give fact ? In this
case, if our logic diverged from the given, it perhaps after all
has been wiser than it knew of. Unawares it has followed the
hidden reality, and against itself has throughout been true.
Possibly this may be, and, if so, an old dream would gain
fulfilment. But too probably, again at this final moment, a
rival alternative 24 might shatter our hopes. Although the
reality is, for certain and assuredly, no series of phenomena,
may it not still be something other than thought, or contain
at the least an alien element? Then, if so, this genuine fact,
when we found it, would remain out of oneness 25 with dis
cursive intelligence, or intelligence altogether. Our logic after
59O THE PRINCIPLES OF LOGIC BOOK III. Px. II
all may turn out to be false, if truth means complete identity
with the real, or implies an accurate unfalsified copy.
1 6. But what is it guarantees this presumed identity of
truth and fact? We have an instinct, no doubt, that leads
us to believe in it, but our instincts, if they can not be in error,
may at least be mistranslated and misunderstood. And here
we seem placed between rival promptings, that contend for
mastery over our reason. It is an old preconception that reality
and truth must contain the same movement of a single content
that, by itself not intellectual, then doubles itself in the glass of
reflection. On the other hand it is a certain result that our
intellect and the movement of our intellect s content is ab
stract and discursive, a mere essence distilled from our senses
abundance. And this certainty has inspired an opposite con
clusion. Since the rational and the real in truth must be one,
and since these vital essences are the life of our reason, then,
despite of seeming, the reality too must consist and must live
in them. If the real becomes truth, then so without doubt the
truth must be real.
In the face of these promptings, I must venture to doubt
whether both have not branched from one stem of deceit,
whether truth, if that stands for the work of the intellect, is
ever precisely identical 2G with fact, or claims in the end to
possess such identity. To the arguments urged by the reason,
and which demonstrate that an element which is not intelligible
is nothing, I possibly might not find an intelligible reply. But
I comfort my mind with the thought that if myself, when most
truly myself, were pure intelligence, I at least am not likely to
survive the discovery, or be myself when I wake from a pleasant
delusion. And perhaps it may stand with the philosopher s
reason, as it stood with the sculptor who moulded the lion.
When in the reason s philosophy the rational appears dominant
and sole possessor of the world, we can only wonder what
place would be left to it, if the element excluded might break
through the charm of the magic circle, and, without growing
rational, could find expression. Such an idea may be senseless,
and such a thought may contradict itself, but it serves to give
voice to an obstinate instinct. Unless thought stands for some
thing that falls beyond mere intelligence, if " thinking " is not
used with some strange implication that never was part of the
CHAP. IV THE VALIDITY OF INFERENCE 591
meaning of the word, a lingering scruple still forbids us to
believe that reality can ever be purely rational. 27 It may come
from a failure in my metaphysics, or from a weakness of the
flesh which continues to blind me, but the notion that exist
ence 28 could be the same as understanding strikes as cold and
ghost-like as the dreariest materialism. That the glory of this
world in the end is appearance leaves the world more glorious,
if we feel it is a show of some fuller splendour ; but the sen
suous curtain is a deception and a cheat, if it hides some colour
less movement of atoms, some spectral woof of impalpable ab
stractions, or unearthly ballet of bloodless categories. Though
dragged to such conclusions, we can not embrace them. Our
principles may be true, but they are not reality. They no more
make that Whole which commands our devotion, than some
shredded dissection of human tatters is that warm and breath
ing beauty of flesh which our hearts found delightful.
17. But be this as it may, one result is most certain.
If these pages have not erred from beginning to end, there is
at least one thing which we are safe in rejecting. No cheap
and easy Monism can stand before an enquiry into logic. The
parallel series of sense and of thought, phenomena presented by
simple observation and reasoning that retraces the chain of
presentations, may both be banished to the region of illusions.
If the string of appearances could possibly appear, if conceiv
ably their sequence could be given as fact, yet assuredly logic
could never reproduce them, or supply us with a truthful
counterpart and copy. The desire to comprehend our Universe
as the double outgrowth and revelation of a single principle,
depends on a genuine impulse of philosophy. It will hardly be
fufilled without patience and criticism, and never if we start
with a blind acquiescence in the coarsest prejudices of popular
thought.
ADDITIONAL NOTES
1 The attempt, made at times in this work for the sake of con
venience (see on Bk. I. II. 4), to identify reality with the series of
facts, and truth with copying was, I think, misjudged. It arose from
my wish to limit the subject, and to avoid metaphysics, since, as is
stated in the Preface, I was not prepared there to give a final answer.
But the result of this half-hearted attempt was an inconsistency, which
592 THE PRINCIPLES OF LOGIC BOOK III. PT. II
in this Chapter is admitted. The real world," as the series of facts
in time and space, is neither a given presented fact, nor is it a con
sistent construction. And obviously it can not be taken as ultimate
Reality. Hence the " actual process in things," as identified with
what is real, depends on an assumption which more or less is arbitrary.
On the other hand the reader was warned, as I thought, sufficiently,
that this view of reality, as the "real world " of Common Sense
which is copied in truth, was not accepted by myself. And I will now
point to warnings in this Chapter which some critics appear to have
overlooked. The reader is referred to 3, " If . . . seems," 4, " Un
less . . . reality," 6, " If . . . ideas," and (ibid.) "Unless . . .
reality," 9, " But reality . . . take it," 10, " If reality . . . happen,"
and 15, " If . . . fact."
2 " Truth the ideal counterpart of fact." I think that (notwith
standing the last words of this Section) " counterpart " is used here
throughout in the sense of " copy " or facsimile, and not anywhere
in the sense of " complement." It seems to signify here " the same
process and result, present in another piece of reality, and differing
only as an exact copy may differ from its original." On the doctrine
of truth as copying see Essays, Chap. V.
3 " Does answer to the facts," i.e. does in a sense correspond.
" Correspondence " is of course an ambiguous term, but it may be
taken as the keeping, as to sameness with the original, near enough
to work or " serve," and so at once to answer our purpose while
answering to the facts (6). See Index, s. v. Truth. Everywhere,
in order to exist and to reach its end, correspondence must imply
some identity, though how much is a question not discussed here.
For "correspondence" see further Essays, pp. 118-20.
* " Is one with a force." The expression " one with " is ambiguous
(cf. Note 25). Two things can be in one, and so have an identity,
while at the same time they may differ greatly. But far more than
that was meant here.
B " But if we lay no stress, etc." As, however, there is verifiable
activity on our side, we can hardly get rid of the problem by leaving
the presence of activity on the other side doubtful. The true answer
is that there is one joint activity on both sides. See T. E. I.
6 " That this change in our knowledge has, etc." The word
" always " should here be added after " has," and, again, after " does
not."
7 " Actual result." " Actual " means here " in the series of events,"
and for "things" we should substitute "the things that are its object."
8 " We admit it would be false." After " admit " insert " that, at
least in some cases." The argument here is as follows. If the infer
ence is not true of reality, it is not true at all. But, if it is true of
reality, then its change and its whole process belongs to the reality,
and this if reality is the world of Common Sense is, at least in some
cases, false.
Then, further, the fact of the inference depends on my caprice.
CHAP. IV THE VALIDITY OF INFERENCE 593
And, though you may reply that this fact (whatever its origin) can
be, and is (according to a postulate), taken as making, at least in
some cases, no difference to the real things yet this answer is not
enough. For it lies open to the fatal objection that, if and so far
as there is no change, there is no inference at all. Cf. the Notes on
Bk. III. II. III. 6 and 10. And for the question as to arbitrariness
and caprice, see on Bk. III. I. II. 6. For the " postulate " see Index,
s. v. Postulate.
" Three alternatives." The reader will note that these are dis
cussed in a different order, the first being taken last.
10 " Suppose, etc." It would be better to write here " that the
quantities need not be equal, etc." ; and, for "nor any thing," to write
" nor the things."
11 " The Harmony." The argument here may be put as follows.
On the above hypothesis the causation on the real side must include
a condition answering to the condition of the change on the mental
side. But the real world of Common Sense either does not include
such a condition, and so the parallel breaks down. Or, if such
a condition is included in the " real world," it threatens now to be
left out on the mental side, because it must, as present in such a
" real world," be taken as something which diverges from your act.
Further, if you suppose at the back of the " real world" a Mind, that
will not help you, unless you credit this Mind with any and every
movement of your own mind so long only as that is logical. But,
with this, you have not only perhaps upset your view of the Mind,
but are also now in conflict with the Common Sense view as to the
course of the " real world."
The words (at the end of 4), "If it is other than our act," were,
I think, meant to offer the following dilemma. Either, to make part
of the "real world" (as we are taking that), the x must be so other
than our act as to diverge from it ; or else we have to accept a para
dox which is too monstrous to be entertained, at least in Logic.
12 " Each trivial argument, etc." The view which we are discuss
ing might reply that the triviality falls merely in the fact of my selec
tion, and not in the arguments themselves. But the difficulty remains
that, if the Mind does not reason throughout as I reason, the parallel
is broken; and, if it does so reason, then, at least in certain cases,
its movement diverges from that of our "real world." And, if you
modify your view of the Mind, then, though it may be now the
Reality of each side of your parallel Harmony, neither of these sides
will now, as such, any longer be finally real. On the point as to
triviality, see T. E. I and VI.
13 " Correspondence with fact." " Correspondence " is not to be
taken here merely in the widest sense. See Note 3.
14 " Unless you revolutionize." See Note i.
is " We have seen so far, etc." The argument here makes a fresh
start and becomes general, as follows. Not only where the middle
does not answer to a cause, but everywhere else inference diverges
2321.2
594 THE PRINCIPLES OF LOGIC BOOK III. PT. II
from " fact." And inference must in principle so diverge, because
it is discursive and consists in an ideal process. Now an idea, as an
idea, is not an event, and an ideal process of content is not itself
a sequence of events though on its psychical side it may, or rather
must, imply such a sequence. Thus, as ideal, an inference leaves
out the detail which makes facts what they are, and again it depends
on conditions which it can not say exist actually in the facts. Hence,
as a process, it is not the same as any process which is " real."
The reader may notice here the absence of any direct reference
to inference so far as its character is intuitive. Certainly at this time
I was well acquainted with the claim of the "intuitive understanding "
or " intellectual perception," having been some years before struck
by what Schopenhauer, especially, has urged on this head. I should
perhaps have contented myself with the remark that, so far as we
fail here to end in a judgment, such intuition falls outside Logic;
and that, otherwise, in its conclusion it must diverge from fact as
given (see the last sentence of n). And for the purpose in hand
this remark perhaps is enough. The subject in any case is too
large for me to attempt here to deal with it in passing.
16 " Ideas do not exist," and (lower down) "the idea does not
happen." " Ideas " and " idea " should be here qualified by " as such."
17 See the Index, s. v. Dialectical.
The argument, in n, is as follows. No process which starts
with isolated elements and developes itself from that basis, can answer
to reality. For it ignores the Whole, apart from which its elements
and their process are unreal and untrue. The above argument,
however valid, appears no longer to concern itself with what is " real "
for Common Sense.
18 " Completed universe." If "completed" is to be pressed, then
no process could be true. But I doubt as to more than " complete "
being meant here.
19 " And if that pass . . . process." The reader will see that what
was already here in my mind as Reality, was some form of ex
perience higher than and beyond any discursive process, or even any-
process which can be called merely intellectual. See Note 24.
20 The view of reality as the course of phenomena is here no
longer, even for the sake of argument, taken as true. It is now,
on the contrary, argued to be false. If the real is what is "given,"
then the phenomenal series, being not given, is therefore unreal.
And hence, if our logic did copy it, that would prove our logic to
be false. And, as to our logic copying the "given" itself, that is
obviously impossible.
21 " Practical," " practically." These terms are of course ambiguous.
See the Index, and the Note on Bk. III. I. VII. 7. I should say that
in this Section they refer merely to theorizing as put into practice, and
recall the "convenient falsehood," of i, and the "valid in the sense
of serving," of 6.
22 " Accepted reality," i.e. the " real world " of Common Sense.
CHAP. IV THE VALIDITY OF INFERENCE 595
23 " Sensuous presentment, and (in the next sentence) "the given,"
are used here to cover both what is actually given and also the " real
world " of Common Sense.
2 * " A rival alternative." This would consist in the fact that
Reality is still other than thought, at least so far as to involve a
difference between the two not reducible to mere appearance in diverse
media. We might have, therefore, a fundamental identity, underlying
both sides, and a demand on each side for the complete and explicit
realization of this identity. And yet, notwithstanding this demand,
enough difference might be left to make truth, even at its best, not
wholly true, because still in part unreal. The ideal of truth might
thus still be left unrealized and unrealizable.
25 " Out of oneness " is ambiguous. Cf. Note 4. It means here
identity, either as absence of difference, or as the presence of only
so much difference as is involved in the existence and appearance
in two diverse media or regions. The above is also what " complete
identity " seems to stand for here. Cf. Note 26.
The solution of the above problem I did not attempt in the present
work. But later, in my Appearance and Essays, I tried to deal with
the whole matter. The answer which I gave is briefly this, that,
while Reality is Experience, thought and truth are merely one aspect
of the whole Universe. This one-sided being like all other partial
appearances is dimly aware of its own one-sidedness, so as not to
be content with itself so long as it remains but partial ; while, on the
other side, unless partial, this one-sided being must disappear, as itself
and as such. But, on the other hand, any " reality " which excludes
thought is no less one-sided, and, offered as such, is itself no more
than an unreal abstraction. For further explanation the reader must
be referred to the two volumes just mentioned.
26 " Precisely identical with fact." "Precisely" is here emphatic.
It means the presence of " complete identity " as defined above in
Note 25.
27 " Purely rational." " Purely " is here emphatic.
28 " Existence " is taken here widely in the sense of " reality."
TERMINAL ESSAYS
ESSAY I
ON INFERENCE
In treating of inference, judgment and ideas, whatever
order we adopt has its own disadvantage (p. 641). If some
thing like inference is everywhere the concrete fact, then sim
ple judgment, and still more again mere ideas, are unreal
abstractions. And hence, when we start from these distin
guished aspects, and go on to build on them as fundamental
and independent elements, our error seldom fails to have dan
gerous results. On the other hand, if we attempt to enter
first on the one actual and entire fact, another trouble awaits
us. In order to understand this whole we are led to make use
of distinctions, the sense of which seems to depend on a
previous enquiry. Hence in logic no one order of discussion
is either necessary or excluded. But, however that may be, I
am about to begin here with some remarks on inference.
Inference being a process, I will state at once what I take
as its essential nature. This may be set down as the ideal
self-developement of an object. And, starting with this, I will
go on to show how the one main type appears in various kinds
of reasoning. Further with each of these kinds I will point
out the failure and the shortcoming that is involved in each.
Everywhere inference, I shall argue, must be more or less
defective, and, since logic must be abstract, the defect, I shall
go on to urge, is in principle irremovable. I must dwell on
our inability in logic to take account of the psychical aspect
inseparable from all thinking, and, in connection with this,
will remark on the relation of logic to psychology. Passing
on I will deal next with the question as to how far all infer
ence is arbitrary, and again how far it is unreal. Its reality,
I shall contend, is genuine, but on the other hand that reality
is relative only. Every inference, I shall further point out, is
597
598 TERMINAL ESSAYS I
in principle fallible, and there is no remedy to be found in
any search for Forms of reasoning. The Criterion, it follows,
is to be found not here but elsewhere, and I will conclude by
remarking on the true aim and purpose of logic.
I. In attempting here to state briefly what I take to be the
nature of Inference I am forced to assert dogmatically what
I myself have been led to accept, (a) Every inference is the
ideal self-development of a given object taken as real. The
inference is " necessary " in the sense that the real object, and
not something else, throughout developes its proper self, and
so compels or repels whatever extraneous matter is hostile or
irrelevant. And the inference is " universal," not because it
has got to be made by more than one person or to occur more
than once. It is universal in the sense that it has an essence as
opposed to a particular accompaniment of more or less ir
relevant detail. Every inference is, in other words, something
beyond its " this," " here," and " now." It contains a " reason
why," a " principle," a " because," and a " must." As against
the resistance of the irrelevant or hostile, we have seen that its
self-development may entail and may show the character of
compulsion.
(b) The given object is an ideal content before us, taken
to be real as being in one with Reality, the real Universe. And
our inference, to retain its unity and so in short to be an in
ference, must, further, remain throughout within the limits of
its special object. But what in any particular case this object
is, and how its limits really are defined, cannot be taken as
appearing in those forms of language which serve as its ex
pression. The above question (to which I shall return) can
be answered only by an examination of the inference itself,
in and with its individual meaning and purpose.
(c) The inference, if it is to remain an inference, must
not cease to be ideal. Its goal and the conclusion in which
it ends must still offer itself as a truth and as a judgment
about its object. Where in inferring we have been led to
perceive a new fact, or where our conclusion appears as or
in what may be called an intuition, we have, so far here,
something less or more than the inference itself. We may
have an object which, though itself more than an idea, is used
ON INFERENCE 599
as the vehicle of an idea which expresses and subserves our
judgment. Or, again, we may have a process terminating in
a result which, if on the one side it contains a judgment and
inference, is itself on the other side something more concrete
and beyond their mere truth. But on this point I will enlarge
later when dealing with Judgment (pp. 626-7).
(d) I have now to lay stress on what perhaps may be called
the essential puzzle of inference. I refer to the problem in
volved when, here or anywhere, we speak of self-development.
If, on the one hand
