OUTLINES OF PHILOSOPHY
ENCYCLOPEDIA OF PHILOSOPHY
ENCYCLOPEDIA OF PHILOSOPHY
LECTURES OF HERMANN LOTZE
TRANSLATED AND EDITED BY
GEORGE T. LADD
PROFESSOR OF PHILOSOPHY IN YALE COLLEGE
GINN & COMPANY
Entered according to Act of Congress, in the year 1887, by
GEORGE T. LADD,
in the Office of the Librarian of Congress at Washington.
J. S. CUSHING & Co., PRINTERS, BOSTON.
EDITOR S PREFACE.
THIS volume is a translation of the second Ger
man edition of Lotze s " Outlines of Logic and En
cyclopaedia of Philosophy," which appeared in 1885.
The second edition differed from the earlier one
chiefly in the abbreviation of certain parts of the
Encyclopaedia of Philosophy. The matter thus
omitted consisted largely either of opinions ex
pressed elsewhere in the Philosophical Outlines, or
of a somewhat special criticism of certain views of
Schelling, Fichte, and Herbart. It has therefore
been thought best to take for translation the more
recent but somewhat less voluminous German text.
Although Lotze dealt with the subject of Logic
in a large and technical treatise, which constituted
one of the two volumes of his System of Philosophy,
completed by him before his death, it must be said
that his contributions to it are perhaps less distinc
tive and valuable than those to any other of the
several branches of philosophy upon which he wrote
and lectured. Notwithstanding this, his views upon
some important topics under the general subject will
be found very suggestive and valuable. This seems
VI EDITOR S PREFACE.
to me particularly true of the chapter on the " For
mation of Concepts." There can be little doubt that
the distinction between the association of mental
images and the definitely logical processes of the
mind is far too little drawn and too loosely held by
certain English writers on Logic.
Part Second, which treats of the " Encyclopaedia
of Philosophy," so-called, will be found to contain a
number of articles which throw considerable addi
tional light upon the author s general philosophical
position. His peculiar doctrine of "Values," as dis
tinguished from a knowledge of what is necessitated
or real, his view of the general method of philosophy
and of the relation in which the Theory of Cognition
stands to the whole of Metaphysics, and his attitude
toward philosophical Scepticism and Criticism, will
doubtless receive some elucidation from the careful
study of these sections.
A first draught of the translation of 6-38 of the
Pure Logic was made by John F. Crowell, graduate
student of Philosophy in Yale University, 1885-86.
The rest of the work upon the volume is by my
own hand. With this sixth number of the series
of Lotze s Philosophical Outlines, I regard my task
GEORGE T. LADD.
NEW HAVEN, March, 1887.
TABLE OF CONTENTS.
FIRST PRINCIPAL DIVISION. PURE LOGIC.
^ CHAPTER I. The Formation of Concepts . 9
CHAPTER II. Of Judgments ....
A. Preliminary Remarks and the Customary
Division of Judgments .... 24
B. System of the Forms of Judgment . .31
C. Immediate Inferences from Judgments . 48
CHAPTER III. Of Syllogisms .... 56
A. The Aristotelian Figures .... 56
B. The Forms of Calculation .... 75
C. Systematic Forms ..... 84
SECOND PRINCIPAL DIVISION. APPLIED LOGIC.
CHAPTER I. Application of the Forms of the
Concept ....... 97
CHAPTER II. Concerning the Adducing of Proof, 106
CHAPTER III. The Process of Thought in Discovery, 120
II. ENCYCLOPEDIA OF PHILOSOPHY.
SECTION I. Theoretical Philosophy . . .155
SECTION II. Practical Philosophy . . . 179
SECTION III. Philosophy of Religion . . .182
l. According to the combination in which the
external stimuli happen to act upon us, there arise
within us manifold ideas, simultaneous or succes
sive, which do not always have an interior coherence
that agrees with the nature of their Content. And,
further, since memory and recollection retain and
reproduce these ideas in the same connections which
they had at their origin, certain ideas that are quite
foreign to each other and without any interior cohe
rence, very often appear in our mental train in a
connection which, although it is matter of fact, is
without any real reason.
2. Besides, perception by the senses affords us
the impressions of at least one sense, namely, that
of sight, in an arrangement with reference to each
other which has space-form ; and this arrangement is
not, like the connection referred to above, a merely
accidental coexistence of the single colored points,
OUTLINES OF LOGIC.
but undoubtedly depends upon the peculiar nature
of what is perceived. Nevertheless, we do not call
this thought but * intuition/ and for the very
reason that, while we discover the arrangement of
the single points to be unalterable, we yet perceive
it as a bare matter of fact without understanding
the reasons on account of which each point has its
position toward others.
3. We are accustomed to distinguish thought
both from the aforesaid train of ideas and also from
such process of intuition, as a higher and self-coher
ing activity, which elaborates, shapes, and connects
the material of ideas furnished by both of the others.
Its essential tendency can be expressed as follows ;
that the thinking spirit is not satisfied to receive
the ideas simply in those combinations in which
what is accidental to the physical mechanism has
brought them to it. Thought is rather of the nature
of a continuous critique, which the spirit practises
upon the material of the train of ideas, when it sep
arates the ideas whose connection is not founded
upon some such justification for the combination as
lies in the very nature of their content ; while it not
only combines those ideas whose content permits or
requires some connection, but likewise reconstructs
their combination in some new form of apprehen-
THE TRAIN OF IDEAS.
sion and expression, from which the justification of
this connection admits of being discerned.
4. If we assume (not as a positive assertion, but
only as an aid to the exposition of the subject) that
the animals, although possessing the train of ideas
alluded to, do not possess thought specifically ; then
the distinction between these two achievements would
lie in what follows.
In the animal, with the idea of the stick when
swung, the idea of the pain that follows thereupon
is connected ; and the renewal of the first alone is
sufficient to reproduce in anticipation the second
also, and to determine the behavior of the animal
in some purposeful way.
Practically, therefore, the animal obtains fairly well
from the mere association of ideas the same service
as though it had, by thinking in the strict meaning
of the word, expressed its experience in the form of
judgments and conclusions, as follows: The stick
strikes the stroke smarts therefore, etc. Still
in each of these logical judgments there would be
involved an apprehension of the state of the case
quite other and more profound than is involved in
such mere association. That is to say, when we
apprehend the stick as the subject or cause from
which the stroke proceeds, we do not merely repeat
OUTLINES OF LOGIC.
the psychological fact that the ideas of the two
occur in connection, but likewise express the adjunct
thought that both belong together by an inner bond
uniting their content, in this case, by a causal
relation. The same thing is true in all cases, as will
subsequently be shown in particular.
Thought, therefore, carries the merely subjective
association of ideas that is, their mere occurrence
together in consciousness as a matter of fact back
to principles that govern the objective synthesis of
5. In order that the process of thinking may
be able to accomplish such an achievement, it must
have in its possession the principles for it, that
is to say, certain universal rules or grounds of right,
according to which, in general, the content of differ
ent ideas may, or may not, be capable of connection.
Or, to express the same thing in another way : if we
are to be able to distinguish truth and untruth, then
there must exist within us some absolutely valid and
universal standard determining what is permissible,
and what is not permissible, as to the connections
of ideas. Moreover, the general principles contained
in it must stand in a very close connection with the
presuppositions which we are compelled to make
concerning the nature and the reciprocal relations
of all Things.
THOUGHT AND "THINGS.
These latter we are accustomed to style metaphys
ical principles. And, accordingly, a near relation
ship would exist between logical and metaphysical
truths. This Introduction is not the place to treat
this relationship exhaustively; the following remark
is sufficient at this point.
We assume that the process of thinking is deter
mined so as to lead to the knowledge of the true
nature of Things. Now every means must be
directed, on the one hand toward the object which
it is to work out, and on the other hand toward
the nature of that which is to employ it. On this
account, the forms and the laws also, in which and
according to which thought connects the ideas, must
be such that by means of them the knowledge of
truth can be conclusively attained ; but they need
/ not be such that the ideas shall directly copy the
essence of the Things themselves. The rather,
since it is man who, by means of them, is to arrive
at the truth, must they attach themselves to the
nature and stand-point of man ; and accordingly they
must have peculiarities which are comprehensible
only from this fact, and not from the nature of the
Things which are to be known.
In other words (to answer, at least in a prelimi
nary way, a question which is not to be exhaustively
treated in this place) : The forms and laws of thought,
OUTLINES OF LOGIC.
with which we are to become acquainted, have neither
a merely formal nor a perfectly real significance.
They are neither mere results of the organization of
our subjective spirit, without respect to the nature
of the objects to be known, nor are they direct copies
of the nature and reciprocal relations of these objects.
They are rather * formal and real at the same time.
That is to say, they are those subjective modes of
the connection of our thoughts which are necessary
to us, if we are by thinking to know the objective
FIRST PRINCIPAL DIVISION.
FIRST PRINCIPAL DIVISION.
THE FORMATION OF CONCEPTS.
6. It is well known that most of the operations
of thought consist in acts connecting together differ
ent simple ideas. Wherever, then, some such f con
nection is spoken of, the question at once arises,
How must the simple elements themselves be formed
in order to be able to enter at all into the connection
designated ? Out of purely spherical elements it is
impossible to make a coherent structure. That can
be done only by means of prismatic elements which
present to each other surfaces that are definitely laid
out. Just so, from mere impressions, in so far as
they are nothing more than our affections (moods,
that is, of our feeling), no logical connection is to
be established ; but each individual impression, in
IO OUTLINES OF LOGIC.
order to be capable, in the logical sense, of being
combined with another into a thought, must be already
apprehended by the spirit in such a quite definite
form as renders this combination possible.
7. This, the first work of logical thought, be
comes most distinctly apparent to us in the circum
stance, that almost all languages divide the whole
stock of the content of ideas into definite, formally
different classes ; and that even those languages
which do not distinguish externally this difference
between substantives, adjectives, verbs, etc., still
cherish, in forming each one of their words, the
adjunct thought, that its content must be conceived
of either substantively, as something in itself valid,
permanent, independent of every other; or adjec-
tively, as quality dependent and presupposing some
other to which it adheres ; or verbally, as a move
ment or relation passing between different contents.
In the first place, by means of these forms in
which they are cast by the act of thinking, ideas
become elements of a thought ; and, like the pris
matic stones in the comparison made above, they
turn toward one another definite surfaces which
allow a connection in the logical sense. So long,
on the other hand, as ideas are only different modes
of being apprehended in our consciousness, although
LOGICAL ACT OF THOUGHT. II
they can, of course, like tones in music, be signifi
cantly connected with one another in other ways
(in this case, cesthetically) > yet as such no thought
arises from them.
8. The next question seems necessarily to be,
How must thought always proceed in order to ac
complish this arrangement of any content whatever
in one of these forms taken by the parts of speech ?
Since the question relates quite generally to every
content, simple as well as composite, this second
logical act of thought must consist in a very sim
ple process which can occur in both cases.
Now it does consist in the following : As often
as language forms a word for some content, which
is to be ascribed to this particular content and to it
alone, it necessarily expresses therewith the presup
position that this content is something which holds
good of itself, is identical with itself, and different
from others ; that, on this very account, it is able
to bear a name of its own. That is, when the sec
ondary thought, which occurs along with the act
of thinking, forms in speech a word for a thing
(that is, apart from speech, when it fixes some con
tent, and distinguishes it from others), it consists
particularly in this, that it conceives of it as a whole
which in itself belongs together, and as thus belong
ing together is marked off from every other.
12 OUTLINES OF LOGIC.
Expression in speech permits this act to be man
ifest in different classes of words with different
degrees of distinctness. An adjective, as blue,
expresses least of this logical import. Verbs sig
nify by means of their ending, that the content
indicated by them is thought of as a unity in a def
inite sense, namely, in that of the verbal relation.
In the case of substantives, certain languages make
it most palpable that the content designated should
be thought of as something identical with itself,
exclusive, one and entire, by means of the prefixed
9. This logical form of the idea (so we will
call this second act of thought) accordingly appre
hends its content, be it simple or composite, only in
such a way that it comes in general to be regarded
as unity or as totality.
In reference to simple content, that which admits
of being realized at all stands highest. For exam
ple ; the impressions, blue, sweet, warm, cannot
undergo any other logical elaboration than that of
being apprehended as having a content which is
identical with itself, different from others, and of
course adjective in its nature.
For the composite content, on the other hand, this
form of the idea which asserts in a general way
GENERAL IDEA AND CONCEPT. 1 3
nothing more than that its parts belong together,
without rendering cognizable the kind, the ground,
and the rule of the same, is an unsatisfactory mode
of apprehension ; although we very frequently cannot
get beyond this in the ordinary course of thought. 1
The words nature/ life/ state/ government/
indicate for the majority of men nothing but the
consciousness that in every case a manifold of phe
nomena and events is united into a totality ; without
their being able to specify the definite plan, the laws
and the forces, according to which and through
which this totality is produced. These same words,
however, will indicate a higher apprehension of their
content, a concept of the same, in case, besides the
bare fact that the parts of the content belong to
gether, some reason for the latter is also thought.
10. Now it is this principle of belonging to
gether which thought seeks to discover; since it
has regard either to that which, in several ideas
that differ from each other, appears as common
and homogeneous (the universal} ; or to that which,
throughout all changes of one and the same con-
1 Especially useful kinds of expression for anything thought of merely
in the form of idea, are such as these: in the Greek the neuter plural,
TO. fyvffiKa., TO. riOiitd, TO TToAtTtKa; in the German, compounds
with . . . wesen, Miinzwesen, Zollwesen, Heerwesen, etc.
14 OUTLINES OF LOGIC.
tent, continually remains homogeneous (the constant).
For there naturally seems to lie in both, somewhat
which coheres together more firmly and legitimately
than the other changing and heterogeneous marks,
and which, just for these marks, composes the prin
ciple of their coexistence and determines the kind
of their combination.
Should a composite content be thought, however,
in such a way that somewhat universal or constant,
but distinct from the sum-total of its marks, be
thought along with it as the determining law on
which that whole circle of marks is dependent ; then
is that content thought in the form of a concept.
The name linden, oak/ and the like, moreover,
designates for the ordinary course of thought a con
tent apprehended in accordance with a concept. For
everyone conceives of the general image of tree,
or the still more general image of plant, as the
outline, the schema, or the norm, according to
which all parts of the afore-mentioned individual
ideas are bound together into a whole. So, too,
all nomina propria of persons are real concepts.
Alcibiades/ or Napoleon, never means merely
a totality of parts ; but both are explained and
conceived of under the accompanying universal men
tal image of man.
CONCEPT AS UNIVERSAL. 15
11. Very rarely will such a general image admit
of being produced from several comparable individual
ideas through the retention of their marks that
are completely alike, and the simple omission of those
unlike. For the marks of ideas are not wont to be
alike and unlike, but similar and dissimilar. If
indeed we should merely retain what little is pre
cisely alike, we should arrive at a meaningless uni
versal which would sustain a relation of complete
indifference toward the omitted constituents, and
not that of a principle regulating them.
But in fact we do not so proceed. The compari
son of several bodies does not result in the general
image of body, because one is blue, hard, elastic,
light, and the other is yellow, soft, ductile, and
heavy, by omitting all of these properties ; as
though the idea of body would have any meaning
at all regardless of color, cohesion, and weight.
Of these dissimilar marks the comparison omits
merely what is different, but retains what is common
to them (for example, in this case, color in general,
weight in general ) ; and it combines these general
marks themselves into the desired general image of
a body, to which it is therefore quite essential that it
should have some color, some cohesion, some weight,
l6 OUTLINES OF LOGIC.
12. The ordinary theory of logic is accustomed
simply to teach that, from comparable individual
ideas (uotiones speciales) we ascend to the more uni
versal one (notio generalis) by abstracting from
the unlike marks (iiotae) of the former, and retain
ing only the like ones. This theory adds the
statement, therefore, that the content (matcria corn-
plexus] of a general idea is poorer, that is, can
count fewer marks than that of the particular ones
out of comparison of which it arose.
The foregoing remark must at all events be im
proved upon to this extent, that each universal has
exactly so many marks, which it is indispensable
should be thought together, as belong to the indi
viduals corresponding to it. Nevertheless, while all
these marks are perfectly denned in the particular or
in the individual, as respects both kind and quantity ;
in the universal, certain general or undefined marks
have taken the place of many of them. The universal,
as compared with the particular, is therefore poorer r
in defined marks, but not poorer in marks in general.
13. We distinguish, therefore, two different kinds
of universals. In the first place, there is the afore
said general image, through the entrance of which
into the group of marks belonging to an idea, this
idea is itself raised to a concept ; and, besides this,
FORMATION OF THE CONCEPT. I/
those universal marks out of whose connection to
gether the general image itself arises.
These latter, the universal marks, in the simplest
case require no special logical work of thought for
their origin, but arise out of the immediate impres
sion without our logical assistance. That green,
blue, red, for example, have something in common,
is a matter of immediate experience ; and although
this common possession may not admit of being sep
arated by a logical operation from that by which
these impressions are distinguished ; still the name
* color points to this as to the something experienced
as common. So, too, differences of magnitude are
immediately perceived as true ; and the general name
of magnitude expresses, side by side with these dis
tinctions, the common characteristic.
In this manner there arise from the consideration
of the different marks, which are presented in the
individual ideas, the general marks as the elements
out of which the aforesaid general image is then
composed ; and the latter holds good for those
individual ideas as a common type comprising
14. For the formation of a concept it is not
sufficient that its general marks, nor indeed for the
formation of the idea, is it enough that its indi-
1 8 OUTLINES OF LOGIC.
vidual marks, be merely present in general ; but the
essential thing is their mode of combination. No
idea, and no concept, consists of a mere summation
of marks in such a way that every first one should
enter into combination with every second one just as
the second with every third ; but in the universal
( the marks limit, define, or determine one another in
such manifold and characteristic ways, that a first
one is connected with the second otherwise than the
second is connected with the third, or the third with
In the case of mere ideas which only combine
marks in general into, a totality, without logically
characterizing the way in which they belong to
gether, the intuitions of time and space take the
place of such strictly logical work. Through
these intuitions we then know in what way, for in
stance, the distinctive marks of an animal color,
skin, head, swiftness, etc. are to be brought to
gether and combined. If, on the other hand, we
form an abstract concept of motion, for example,
and designate it as constant change of place, then
it is seen that no one of these three marks is thought
as of like species with the other ; but, strictly speak
ing, simply the general idea of change, in so far as
it is restricted by reference to the idea of place,
and through the mark belonging to it is defined
THE CONCEPT AND ITS NAME. 19
as constant, forms the content of the concept of
The general image which arises out of the com
parison of several individual ideas is formed, not
simply when the general marks are put in the place
of the particular, but also when a general mode of
connection corresponding to them is put in the place
of the particular modes of connection among the
The general mental image metal for instance
connects together the general marks of color,
weight, etc., in a form, or according to a scheme,
of which the modes of combination are only par
ticular examples, wherein gold combines the color
yellow, its specific gravity, etc., copper the color red,
and its specific gravity, etc.
15. To recapitulate the foregoing ; we give the
name of concept to an idea whenever, in addition
\ \ to its group of marks, a universal is thought along
with it as an explanatory law. Gold or Caius
is thus thought as concept, in so far as the marks
of both are regulated by the general schemata,
metal and man, respectively.
The universal itself, by whose entrance into it the
idea becomes the concept, is not necessarily nor
always itself thought as concept, but frequently only
2O OUTLINES OF LOGIC.
as idea. It is then, indeed, concept only when its
own marks also are not merely thought in general
as a whole belonging together, but as combined by
means of a new universal in accordance with some
There are accordingly just as much individual,
singular concepts (notiones singulares] like all
names of persons, for instance as there are uni
versal concepts (notiones generates] in manifold gra
The name of higher general concept is given to
that one, which is thought as an explanatory schema
in addition to the marks of another concept, which
latter is then the lower of the two.
It is then said that the content (materid) of the
higher general concept (genus] is contained in the
content of the lower (species] ; that is, that all the
marks which are essential to the genus occur also
in the species. But, conversely, the content of the
species is not entirely contained in that of the genus ;
but the former possesses, besides the particular
marks of the latter, certain ones peculiar to it as
species. On this matter a corrective remark is made
above ( 12).
It is further said and rightly, too that each
higher general concept occurs in a greater number
of kinds or individual concepts (or holds good of
RELATION OF EXTENT AND INTENT. 21
them) than the lower concept. The name of extent
(ambitus] is given to the number of these lower
concepts, of which the higher holds good. And
since to the latter there is ascribed, as previously
remarked, a smaller number of marks or smaller
content (materia complexus] ; therefore it is said that
"the extent and the content of two concepts are
in inverse ratio to each other " : the one poorer in
content that is, the more general commands a
greater aggregate of individual cases ; the one richer
in content occurs in fewer kinds, perhaps only in a
According to the foregoing, this proposition would
correctly run thus : A concept with clearly defined
marks is always individual. In case it has undefined
or general marks besides the defined ones, then with
Uhe number of the undefined marks (or, conversely,
with the number of the defined ones), the number
of cases increases in which it is valid, that is, its
16. Two relations of subordination, since they
are essentially different logically, are to , be held as
excluding each other. That is to say, every concept
can be ranked in respect to one part of it, under its
higher concept of species, for example, gold (G)
under metal (M) ; in respect to another part, under
22 OUTLINES OF LOGIC.
any one of its marks at pleasure, for example,
gold (G) under fusible (F).
Fig. i. Fig. 2.
The first of the foregoing relations (Fig. i.) is
called subordination. In this case the whole nature
of O is included in the universal M, in such a man
ner that there is in G no part, no mark and no com
bination of marks, which may not be essentially
comprehended by means of the universal principle
M ; for example, the yellow of gold is a certain
lustrous yellow peculiar to the metal, which does
not occur otherwise. Within this M, finally, G is
found co-ordinated with its natural kindred (copper,
lead, silver, C, L, etc.) ; that is, it stands in the
same logical relation to M with all the rest of them.
The other species of arrangement of one concept
under another (Fig. 2) is called subsumption. Here
G touches upon the universal concept F with only
one part of its content; the remaining parts of its
content lie outside F and are not defined by F. Be
sides, G (gold) is found in this case to be co-ordi-
SUBORDINATION AND SUBSCRIPTION. 23
nated, in reference to F (fusible), not merely with
its own related species, but also with other con
cepts of content altogether heterogeneous (sugar,
pitch, sulphur, S, P, etc.).
17. If we ascend by continued abstraction to
more and more general concepts, we shall, accord
ing to a frequent assertion, reach one single highest
general concept, that of the thinkable. Such
an abstraction, however, would only be performed
through subsumption (Fig. 2), if the concept should
have entirely let go of the characteristic content of
the concepts, and confined itself simply to a common
mark through which its content is not denned.
If we proceed by way of subordination, then it
is found that our system of concepts does not ter
minate in one point, but in several independent
points. The substantive concepts lead to one
highest concept of Being ; the verbal to that of
Becoming; the adjective to that of Property, etc.;
and there is absolutely no concept still higher, to
which these fundamental concepts may be referred
as to a common principle of their content. As for
the rest, it is obvious, and the reason why it
must be so needs no explanation, that these
fundamental concepts are nothing more than the
meanings belonging to the different parts of speech.
A. Preliminary Remarks and the Customary Division
18. The consideration of the subject up to this
point leads to a new problem. In the concept we
have distinguished the universal and the special
circle of marks. Concerning the reciprocal rela
tions of these two members we had, however, only
expressions characteristic of like species. The uni
versal served us only as a nucleus, as a normative
principle, as a rule for the disposition and combi
nation of the marks. The questipn now arises ;
what this means, when taken strictly, and what
power the universal can exercise over the marks,
and in what way.
We consequently seek for an explanation of the
relation of the two members to each other. Every
assertion which thought can utter on this question,
and by means of which it can answer the same,
must consequently take this form ; that it connects
two members S and P through the affirmation of a
definite mode of relation X. This is essentially
NATURE OF THE JUDGMENT. 25
the form of a proposition or a judgment, in which
S is subject, P is predicate, and X copula between
19. The ground of the fact that different im
pressions belong together, however, we have sought,
not merely in somewhat universal which is common
to the different impressions, but likewise in some
what constant which appertains to one and the
same content of the idea, while it experiences
changes in other respects by accession or diminution
of its marks. This relation, too, of an unchanging
nucleus, which is at once the ground of the possi
bility of the changing marks and the law of their
connection, requires a similar investigation. We
must know how any P can adhere to an S, and
how it is possible that it disappears again and
another mark, P , occupies its place, and every
assertion on this matter must bear the form of
20. Apart from such systematic coherency, the
doctrine of judgment may be introduced as fol
lows : In the train of ideas it must frequently
occur that, in the first place, two impressions a
and b, which have for us become united in part
(as, for example, the shape of a tree and its green
26 OUTLINES OF LOGIC.
color), are apprehended as a whole whose distinguish
able parts are not actually distinguished, because
all reason for it is wanting. If now, by a second
experience, the tree is shown without leaves, then,
in a third instance in which it is again seen to be
green, the two ideas of its shape and color will
no longer form an undivided whole in the same
nai ve way ; on the contrary, the recollection of
their being separable will keep them apart from
each other; and therewith arises the idea of two
impressions which are combined, instead of that of
one impression, in which there is no inner difference.
This process of the simultaneous association and
separation of two ideas without doubt takes place
in animals also. It supplies for them the place of
the logical judgment of human thought ; yet it is
not such itself, but only the occasion of a judgment.
If we, for instance, affirm in judgment, the tree is
green or is not green, then we interpret the co
existence of separable ideas and do not simply
express over again the fact of such coexistence.
When we conceive of the tree as subject (or in this
case as substance) and the predicate green as attri
bute or accident, we point to that inner connection
in which, according to our view, the property stands
related to the Thing or the accident to its subject,
as in each case constituting the legitimate ground
CLASSIFICATION OF JUDGMENTS. 2/
according to which both of the ideas ( tree and
green do not merely exist together, but belong
together precisely as they are together, to wit,
as separable yet conjoined.
21. The essential part of a judgment is, then,
precisely this secondary thought which the process
of thinking has, when it connects subject and predi
cate in definite form. As many as are the essentially
different points of view, grounds, or models, to which
this process of thought rightly refers the combina
tion of S and P, that is, as many as the essentially
different meanings of the copula actually are ; so
many are the essentially different logical forms of
the judgment which are to be systematically devel
oped later on.
We previously made mention of a classification of
the judgment usually given, namely that by Kant.
According to him, every judgment must at the same
time be determined in four different respects, and
must in each of these have one of the three mutually
exclusive forms ; namely, is
1) According to quantity either universal or par
ticular or singular.
2) According to quality it is either affirmative or
negative or limitative.
3) According to relation, that is, the meaning of
28 OUTLINES OF LOGIC.
the connection between S and P either categorical
or hypothetical or disjunctive,
4) According to modality, that is, the relation of
the whole content to actuality either problematic
or assertory or apodictic.
22. These differences are not of equal value :
1) To begin with, in the three quantitative forms :
This S is P,
Some S are P,
All S are P,
the kind of combination between S and P is entirely
the same ; and they differ simply in respect to the
number of the subjects, and consequently in respect
to the material, to which this entirely identical con
nection is extended. Accordingly, although the quan
titative differences remain of great importance for
other purposes, for example, the drawing of con
clusions from judgments, they are nevertheless not
essentially different steps in the development of the
judgment as such.
2) As to what further concerns the qualitative
forms, it is obvious that the affirmative and the
S is P,
S is not P,
must understand the kind of combination that takes
QUALITY OF JUDGMENTS. 2Q
place between S and P, in the same manner.
For the negative judgment could not be the exact
opposite of the affirmative, if it did not deny pre
cisely what the latter asserts. This judgment is there
fore fitly presented in such a way that, to one entirely
identical thought of a combination of S and P, there
is added the two secondary judgments; it is true,
or it is not true. They differ then in their content
very essentially, but not in their form. The limita
tive judgment should attach a negative predicate to
S by means of a positive copula, and so have the form
S is non-P.
On the other hand, it must be kept in mind that
non-P is a definite idea and not of any use at all to the
predicate, only in those cases where it does not merely
indicate that which is in general not P, but that
which is co-ordinated with P under a higher general
concept, and therefore has a meaning of its own,
as for instance, not-round in so far as it must still
always have some form, either straight or angular
and the like. If, on the contrary, non-P is intended
to comprehend everything that is simply not P in
general, for example, the not-round is to include,
besides the angular, things like the bitter, the
future, the cheap, etc. ; then non-P is no longer
an idea at all, such as could be apprehended and
given to some subject S as its predicate. The
3O OUTLINES OF LOGIC.
attempt to do this invariably has in time this issue,
that S is excluded from the circle of the predicate
P, and the judgment consequently, according to its
meaning, is negative.
3) The third distinction, that according to rela
tion, is of such essential significance that it is passed
by here in order to be thoroughly examined later.
4) The differences of modality, likewise, have no
essentially logical value ; since the possibility of the
combination of S and P in the problematical judg
ment, and its necessity in the apodictic judgment, is
expressed only by means of the auxiliary verbs,
S may be P,
S must be P.
They are both therefore, after all, properly speaking,
only assertory judgments ; that is, they affirm, exactly
as does the strictly assertory judgment,
S is P,
an actuality in the former case, that of possibility ;
in the latter, that of necessity.
But neither of the two admits of being brought
forward immediately as a consequence of the pecu
liar mode of relation of S and P. This kind of
modality, therefore, belongs to the content, but not
to the logical form of the judgment ; and there may
be set beside it yet many other forms of precisely
equal rank ; as, for instance, S should be P, S ought
SIMPLEST FORM OF JUDGMENT. 3!
to be P, S will be P, etc. Now, in what way the
judgments are capable of expressing, by means of
their form, at the same time a claim to the possi
bility, actuality, or necessity of their content, will be
shown by what follows.
B. System of the Forms of Judgment.
23. In the classification of the forms of judg
ment, we start from the point of view that thought
should declare itself as to how it conceives of the
coherency of that previously so-called nucleus of an
idea with its own circle of marks ; or, in other words,
of an S with P. Every such declaration will be ex
pressed by a separate form of judgment ; and the
series of the forms of judgment must therefore form
a series of increasingly better attempts at the com
plete and adequate expression of the aforesaid rela
tion between S and P.
24. The simplest form of judgment is the
impersonal. In the propositions, It lightens, * It
thunders, etc., the whole content of the judgment
is completely contained v* the predicate. The indefi
nite pronoun it adds nothing thereto, but formally
marks the place of the concept of the subject, which
is missing. But just this alone that the process of
thinking is not satisfied with the bare reproduction
32 OUTLINES OF LOGIC.
of the simple content which stands in the predicate,
that it consequently does not employ for its expres
sion the infinitive to thunder, but inflects the word
and joins it as predicate to the it proves most
evidently this fundamental necessity of analyzing
every content of an idea into two component parts,
the one of which is the regulative principle, and the
other the phenomenon dependent on it. Of course,
this requirement is here only formally satisfied. For
the case does not admit of specifying any subject,
with complete content, to which the phenomenon is
attached. We are, therefore, under the necessity
of joining the phenomenon taken as predicate to
itself taken as subject. 1
25. The next advance must consist in this, that
the separation of the ideated content in S and P,
which is here only indicated, is brought to comple-
1 According to their modality, the impersonal judgments are naturally
assertory; that is, affirmations of actuality. In the natural process of
thinking, they uniformly express perceptions. The it in the subject is,
according to its content, either nothing more than the predicate, or, if it is
to be distinguished from it, is only the thought of the universal Being, which
in the different phenomena is defined now in one way and now in another.
One might therefore say, instead of it lightens, the Being is [now] light
ening, or conversely, the lightning is. That is to say, it is possible to
convert the impersonal judgments into existential propositions, in which
to be is the predicate. Such conversion is, however, an artificial work of
the schools. The natural process of thought never apprehends the indi
vidual phenomenon as subject and the Being as predicate, but only univer
sal Being as subject and the phenomenon as a single predicate of the same.
THE CATEGORICAL JUDGMENT. 33
tion by the rise of a special conception of the subject
as different from the predicate.
This gives the so-called categorical form of judg
ment, S is P, in which P is unconditionally and
without further justification asserted of S (KCUIYOPCITCU,
Aristotle). The only available justification of this
connection, namely, that it takes place according
to the type of the relation between * Thing and
property, Substance and attribute (Kant) does
not suffice ; since, metaphysically considered, this
relation itself is not a perfectly clear truth but an
We can then distinguish two kinds of this judg
ment. One, the so-called analytic, connects with S
a P which is itself included in the very concept of
S; as, for example, Gold is heavy. For the con
cept of gold is not a completed product of thought
until it includes the mark heavy. Accordingly, this
judgment, strictly speaking, simply asserts that, when
we think the concept S, we think along with it that
of P as a constituent part of it. But how the con
tent of the P as a matter of fact adheres to the con
tent of the S, in such a way that, just in order to
think S, we must think P along with it, this the
form of judgment does not explain, but merely asserts
as a fact.
The second kind, the so-called synthetic or histor-
34 OUTLINES OF LOGIC.
ical judgment, connects S with a P that does not
lie thus within the concept, and consequently is a
changeable mark of it ; for example, Caesar fled,
The dog is mad. Here it is far less clear through
the form of the judgment, by what right two concep
tions which stand in no constant relation are brought
into such a relation. But here also the combination
is expressed unconditionally as a fact to be taken for
26. On occasion of this doubt arising and as the
ground of it, the first universal law of thought comes
to consciousness : The law of identity and of con
tradiction (Principium identitatis et contradictionis).
Its simplest logical expression is this : In a cate
gorical judgment of the form S is P it is absolutely
forbidden to combine unconditionally, as subject and
predicate, two different concepts S and P, whatever
they may be. The rather can only the two propo
sitions S is S and P is P always hold good ; but
never S is P or P is S.
The usual form of the proposition *A = A , (Propo
sition of identity), and the negative A not = non-A
(Proposition of contradiction) both express this sim
ple truth, that every thinkable content is equal to
itself and different from every other one.
This simple logical meaning of the proposition
PROPOSITION OF IDENTITY. 35
must without fail be distinguished from other theo
rems, partly true and partly doubtful, which, although
they spring from the application of the universal logi
cal proposition of identity, still do so only from its
application to a definite real content, and are not on
a par with the proposition itself. For example, that
every Thing is like itself, or that it is unchange
ably like itself, is a metaphysical proposition which
arises from an application of the logical proposition
of identity to the concept of the * Existent/ The
logical proposition itself says nothing at all of
Things. It is also valid of events that happen,
of conditions that take place, of the real as truly as
of the unreal. And of all of them it merely says,
that to be is to be, the changeable is changeable,
the contradictory is contradictory, the impossible is
27. Briefly expressed, then, the proposition of
identity asserts, that all categorical judgments of
the form S is P are false and inadmissible. Now
since such judgments nevertheless very frequently
occur, and we are sufficiently convinced of their
admissibility, their defect can only consist in the
fact, that they express a correct sentiment with
formal imperfection. And an interpretation of them
must be given by which they can be justified before
the law of identity.
36 OUTLINES OF LOGIC.
Attempts were first made at this in such a way
that a distinction was made between predicates com
patible, and those incompatible with the subject.
And as no one is capable of knowing from purely
logical laws, what P is compatible with what S,
therefore the general meaning was given to the
proposition of identity : Of two incompatible predi
cates only one can belong to one subject. This
proposition, correct in itself, nevertheless does not
justify the categorical judgment at all. For it in
turn always presupposes that an S can be a P.
And it is just this which the proposition of identity
forbids without exception, no matter in what the
P may consist.
Another attempt at justification makes prominent
the fact, that in the proposition S is P (gold is
yellow), S and P are by no means interpreted as
identical in such a way that the one could be sub
stituted for the other, and consequently the judg
ment be inverted and read, yellow is gold. Between
both, the rather, another relation is maintained which
is fitly expressed by S has P. Against this rela
tion, that a mark is had by its subject, or a
property by the Thing, the proposition of identity
raises no protest. This view, also, although it
alludes to something that is quite true, does not
reach the end desired. It indeed removes the diffi-
PROPOSITION OF IDENTITY. 37
culty of combining with S the content of P which
differs from S. But it does not explain how it is
possible to combine with S the conception of hav
ing (although it does explain what is had). For
since S is obviously able to have as well as not
have, having is itself in turn a predicate deter
mination differing from that of the mere Being of
S; and the question recurs concerning this predicate,
how it is compatible with S. The proposition of
identity simply says, S is S. Every proposition,
S has something or other, therefore declares some
thing different of the S, from the mere proposition
that it is S ; and, consequently, is itself defective
as respects the proposition of identity.
28. The solution of the above-mentioned diffi
culty lies approximately in this, that all categorical
judgments are according to their intent and meaning
identical but express this intent in a formally im
perfect way ; since they allude to only single parts,
sometimes of the true subject and sometimes of
the true predicate.
For example ; Gold is yellow means (as in Latin
the neuter of the adjective shows) the same as
gold is yellow gold, an observation which has
been for a very long time expressed in such a way
that, in the judgment, the subject is not merely
38 OUTLINES OF LOGIC.
defined or determined by the predicate, but likewise
the predicate by the subject. Yellow, for instance,
means here not simply yellow in general/ but in
The proposition Some men are black is ambig
uous in German. The Latin Nonnulli homines
sunt nigri* shows that in the predicate homines is
to be supplied. Now * nonnulli homines and nigri
homines undoubtedly seem to be two entirely dif
ferent conceptions. But still it is not meant, that
every some men you please, taken out of the
totality, so far as they are some, would be black ;
but we understand a perfectly definite some,
namely, the negroes. Therefore S and P are wholly
identical as respects content, and only indicate in
different ways, that in P one instance (S) is char
acterized as part of a more general concept by
means of its properties.
Finally, the historical judgments for example,
the dog drinks, Caesar crossed the Rubicon
that is, all which express particular facts but not
uniformly valid relations, have for their true subject,
not the concept simpliciter, which appears at this
place, but always such concept together with a multi
tude of secondary ideas, sometimes suppressed and
sometimes indicated, which we will call X ; so that
they properly have the form S-f-X = P. Thus in
THE HYPOTHETICAL JUDGMENT. 39
the foregoing examples, it is not the universal dog
which is drinking, but some specific one whose dif
ferences from other dogs are not pointed out ; but
which, when we add in thought all its peculiarities,
for instance, its temperament, the nourishment
it has previously had, its thirst, and the tempera
ture in which it lives is then exactly the same
dog which in the predicate cannot be thought of as
any other than the dog which is drinking.
These secondary ideas X, in the customary expres
sion of categorical judgments, are wont to be desig
nated mostly through the particular quantity of the
subject : for example, this S is P ; some S are P ;
or by particular denotation of the predicate, as S is
sometimes P ; S was P ; and the like. On. this
account we give to this entire grade the form of the
29. What these particular judgments indicate, is
more expressly alluded to in the more developed form
of the hypothetical judgments. Here the accessory
circumstances, which are in the previous form sup
pressed or only indicated, are designated in some an
tecedent proposition as the condition which must be
fulfilled, if P as predicate is to be capable of being
adjoined to the concept of the subject S.
The simplest form will be this : If to S an X be
4O OUTLINES OF LOGIC.
added, then S has the predicate P ; that is, antece
dent and consequent propositions have the same con
cept of the subject, which in the antecedent is
completed by means of X so as to become the real
subject to which in the consequent P must be
attached. In the usage of thought, other forms may
arise by suppression of the middle terms ; for exam
ple, If B is an X, then S is a P/ Nevertheless they
always depend upon the foregoing original form.
In this form, the antecedent proposition being-
according to its nature problematic, the consequent
is in a conditional way apodictic : it is necessarily
true if the antecedent, which is in itself only possible,
is true. If we wish to express therewith the truth of
the antecedent, then the assertory form comes into
use: Since S is an X, S is a P. If we wish to
designate that the antecedent is not the condition of
the consequent, the negative form arises : Although
S is an X, still S is not therefore a P.
30. If now we make prominent the fundamental
thought which the process of thinking has betrayed
through the elaboration of the hypothetical form of
judgment, we discover in it the second fundamental
law of logic : The principle of sufficient reason (Prin-
cipium rationis sufficient**).
The process of thought, as it were, says : You uni-
PRINCIPLE OF SUFFICIENT REASON. 4!
formly express a necessary truth when you put S =
S and P = P, in an identical judgment. You are
uniformly in error, when you put S = P, in a cate
gorical judgment; that is, if you suppose it were
ever possible for an S to assume for itself alone a
property which does not belong to its concept, or
which it did not have previously ; or that, out of a
single principle, a single substance, a single power, a
single thought, it were ever possible for a multiplicity
of substances, developments, or ideas to emerge,
in general anything manifold out of a unity. It
is, on the contrary, uniformly necessary, if, out of
one subject diverse new existences are to proceed,
that as many conditions differing from one another
should have to be brought to bear upon this sub
ject as there are different results to be derived
The principle of sufficient reason therefore asserts
negatively (and in this respect is in agreement with
the law of identity) the impossibility of an immediate
connection of the two different contents of the idea,
S and P ; affirmatively, on the other hand, it asserts
the possibility that, to a combination of two ideas, S
and X, which somehow determine each other, there
should be given a predicate P which is not given
either to the S alone, or to the X alone. The exist
ing relation between S and X, whereby this becomes
42 OUTLINES OF LOGIC.
possible, is the ratio sufficiens of the connection of S
The universal logical meaning of this concept of
sufficient reason (Grund} consists simply in the
supposition, that the manifold content of everything
thinkable is not a relationless and dispersed multi
plicity ; but that there is a truth that is, a sum of
such valid relations through which a definite form
of uniting the single elements of the thinkable be
comes of itself the equivalent of other elements. In
what, on the other hand, those relations consist, in
the particular instance or in single large domains of
the thinkable ; in what, therefore, the definite reason
for a definite combination of a certain S, or of a cer
tain class of S, with a certain P, or a certain class
of P, is not a matter of logic.
On this account, the principle of the ratio suffi
ciens should not be confounded with that of the
causa efficient, the law of causation ; or with such
other general rules as relate to what is actual or to
particular classes of what is actual. A Cause (Ur-
sache), for instance, is the power that produces some
thing actual, which previously did not exist. A
reason (Grund} is always simply some valid truth
by virtue of which it happens, on the one hand, that
a definite effect is attributed to a certain cause ; and
by which also, on the other hand, in those provinces
PRINCIPLE OF COHERENCE. 43
of thought, in which there is no happening, for
example, in mathematics the combination of the
two contents of the concept depends, in respect to
its validity, upon the combination of two others,
regardless of time. How this comes to pass, and
what is, strictly speaking, involved in the fact, that
a condition can be the condition of that which is con
ditioned by it, of this no general logical explana
tion is possible; with the exception of a single
meaning of this question, in which meaning the
question is now indeed to be answered.
31. Although we do not ask in Logic to know
what consequences follow on what grounds, and by
what means the two cohere together, still, if the
process of thought is to be able to develop new
truths from given ones, we must possess some uni
versal and purely logical principle, independent of
our knowledge of the thing to which it has merely to
be applied ; and according to this principle we must
be able to judge whether one proposition may be
rightly considered as the consequence of another.
Such a principle we do in fact possess. It con
sists in this, that everything special must conform
to its general concept ; every individual case to the
rule of the general case. Had we not this formal
logical principle, then all special knowledge of in-
44 OUTLINES OF LOGIC.
dividual conditionating relations which actually exist
between any of the elements of existence, would be
of no help to us. We should not be able to apply
them, and deduce any new truth from them.
32. This thought gains expression in the form
of the general judgment. Such form is to be dis
tinguished from that of the universal judgment.
The latter, of the form
All S are P,
only asserts that, in fact, all instances of S have P,
for example, All men are mortal/ but does
not tell why. Perhaps it may be on account of a
combination of unfortunate accidents which have
no real connection with each other.
The general judgment substitutes the general con
cept alone for the subject : Man is mortal ; or it
indicates by the other form, Every man is mortal,
that the predicate is to be considered valid, not
merely of all actual but also of all thinkable exam
ples of S ; and therefore is so by virtue of this
same general concept S, and not on other accidental
More accurately considered, the general judgment
must besides be included in the hypothetical form.
For it is not the general concept S (the universal
man) which is to be considered as P (mortal) ;
THE DISJUNCTIVE JUDGMENT. 45
but every individual, because he is man. Therefore,
the general form, strictly speaking, is : If any A
whatever is an example of the universal S, then
such A is necessarily P.
33. The form of the general judgment is, never
theless, still inexact in another way, namely, in
this, that it attributes to the subject the predicate
of the general concept, although this subject is not
the general concept itself, but only the example sub
ordinated to it ; for instance, the proposition, Every
material body has some color, is untrue in so far as
the particular body never has color in general, but
is either red or green or blue, etc.
That is, the general judgment passes over into
the disjunctive or divisive, of the form, Every S,
which is an example of the general concept M, re
ceives from every general predicate P which is
attributed to M, one of its kinds, q, r, t, . . ., to the
exclusion of all others, as its own predicate. The
disjunctive judgment, therefore, furnishes S with no
definite predicate whatever, but only dictates to it,
as it were, the necessary choice between different
predicates ; and these, taken together, are individual
modifications of a general predicate P that is re
quired by the higher concept of the genus M, to
which S is subordinated.
46 OUTLINES OF LOGIC.
The next step forward would have to consist in
concluding this choice and making an actual selec
tion between q, r, t, etc. But this cannot occur, in
so far as S is a species of M, because this reason
leaves such choice wholly indeterminate ; but must
take place on account of the fact that S is S, that
is to say, because it is such definite species of M
and none other. For making a decision, therefore,
two propositions will be employed ; the first of which
states what is true of S, so far as it is in general
one species of M, the second what is true of S, so
far as it is this species of M. These two proposi
tions are obviously the so-called premises of a con
clusion, to which new logical form we now pass
over. The series of judgments ends herewith, and
is not to be extended farther.
REMARK. The ordinary abbreviated form of the disjunctive
judgment is as follows :
) Affirmative : S is either q or r or t or ...
b) Negative : S is neither q nor r nor t nor . . .
34. The interpretation of the disjunctive judg
ment just adduced expresses two laws of thought
combined, which have commonly been brought for
ward as separate formulae :
I. The Dictum de omni et nullo 1 makes promi-
1 On the history of this, compare the Zeitschrift fur Philosophic u.
philos. Kritik, edited by Fichte, Ulrici, and Wirth, vol. Ixxvi (Halle, 1880),
pp. 48 ff.
PRINCIPLE OF EXCLUDED MIDDLE.
nent positively the dependence of the particular upon
its universal. The expressions which we frequently
hear, " What is true of the universal (or of the whole)
is also true of the particular (or of the part)," are
evidently false. The scholastic formula, "Quidquid
de omnibus valet [negatur], valet [negatur] etiam de
quibusdam et de singulis," is indeed quite correct ;
yet it no longer expresses the relation as one of
dependence of the particular upon the universal to
which it belongs, but only as one of subordination of
the unity under the totality with which it is numeri
cally included in the same conception ; in this way
the proposition becomes, fundamentally considered, a
2. The second formula, the Principium exclusi
medii inter duo contradictoria, is a special case of
the more general one which is expressed in the pre
That is to say ; if we presuppose, in the first place,
that the general predicate P has three or more spe
cies q, r, t . . ., and that one subject S must, so far
as it is a species of M, make a choice among these
species of P, then the choice of one predicate q will
exclude all the rest, r, t . . . ; whereas the negation
of q does not involve the affirmation of a definite
one of the remaining r, t, etc. Of these predicates
q, r, t . . . it is said, that they stand in contrary oppo-
48 OUTLINES OF LOGIC.
sition for an S, which is an M, to which M again P
But furthermore, if P (gender) is separable into
only two species q and r (masculine and feminine),
then these two predicates stand in contradictory
opposition for every S which has any necessary re
lation to P (for every living being) ; that is, not only
does the affirmation of the one deny the other, but
also the negation of the one affirms the other.
Finally, if we wish to avoid the condition, that the
S have a necessary relation to P dependent upon
its peculiar nature ; and if we therefore wish to
establish two predicates which are contradictory for
every S whatever ; then such relation can only con
sist in some Q and non-Q, whereby the latter com
prehends all that is not Q. But precisely for that
reason non-Q is not an independent concept, which
can be attached as predicate to any S whatever ;
and, strictly speaking, we no longer have a case of
an opposition between two concepts, but of an oppo
sition between two judgments, one of which ascribes
a predicate Q to S, while the other totally denies
the same Q to it.
C. Immediate Inferences from Judgments.
35. According to an ancient mnemonic coup
let, Asserit A, negat E, verum generaliter ambo,
Asserit I, negat O, sed particulariter ambo,
SUBALTERNATION AND OPPOSITION. 49
we designate the universal affirmative judgment by
A, the universal negative by E, the particular affirm
ative by I, and the particular negative by O. If we
conceive of these four forms as applied to one and
the same content* S-P, the following relations occur
among them :
A Oppositio Contraria E
I \ y i
_ (*\ i i
& X X *
0-9* % m
1 Oppositio Subcontraria O
i. Between A and I (All S are P some S are
P), as well as between E and O (no S is P some S
are not P) Subalternatio that is, subordination of
the individual to the universal takes place. The
validity of the general case always includes that of
the particular instance, the validity of the particular
not that of the general case. The invalidity of the
general case does not carry with it that of the par
ticular ; the invalidity of the particular (which is
always understood as meaning that there is no partic
ular instance whatever in which the content of the
judgment is valid) involves, on the contrary, the
50 OUTLINES OF LOGIC.
invalidity of the general case. Consequently, we
conclude ad subalternatam l from + A to + 1, from
+ E to + O ; but not from A to I, not from E
to O. Further, we conclude ad subalternantem,
from I to A, from O to B; but not from
+ 1 to + A, or from + O to + E.
Both of these prohibited conclusions namely,
from the particular instance to the general case, and
from the invalidity of the general case to the like
invalidity of the particular belong to the most
frequently occurring fallacies in logic.
2. From the contrary opposition between A and
E it follows, that the validity of the one excludes
that of the other ; the invalidity of the one, on the
contrary, does not involve the validity of the other.
We conclude therefore ad contrariam from + A to
E, and from + E to A ; but not from A to
+ E, or from E to + A.
3. Between A and O and E and I there is contra
dictory opposition. For if A is not valid, it is obvious
that there necessarily occur some cases, in which the
opposite is valid. So then the invalidity of a general
judgment involves the validity of the opposite particu
lar judgment ; and we conclude ad contradictoriam
from A to +O, from E to +1. In the same
1 The sign -j- stands for the validity, and for the invalidity, of a judg
SUBCONTRARY OPPOSITION. 51
way it is self-evident, that when a particular judg
ment is not valid, that is, when there are no
individual instances in which it is valid, then its
opposite is universally valid. We therefore likewise
conclude ad contradictoriam from O to + A,
from I to + E. Finally, it also is self-evident
that the validity of a universal proposition involves
the invalidity of opposite particular ones ; as well as
that the validity of a particular judgment involves
the invalidity of the opposite general judgment.
Therefore we also conclude ad contradictoriam
from +1 to E and conversely, and from + O to
A and conversely.
4. The subcontrary opposition between I and O,
if one of the two is valid, allows no conclusion to be
drawn. For if one particular judgment is correct,
it is possible that the opposite particular is also
valid ; but it is likewise possible that it is not valid,
and that the original proposition is only expressed
in particular form but is really universally valid. If,
on the contrary, a particular judgment is denied, then
the opposite general judgment is hereby affirmed ad
contradictoriam, and as a consequence we have ad
subalternatam the validity of the subordinated (of
the previous opposite) particular judgment. We there
fore conclude ad subcontrariam from I to + O
and conversely, but not from +1 to O or conversely.
52 OUTLINES OF LOGIC.
36. A judgment undergoes conversion (conversio}
when subject and predicate are exchanged. The natu
ral interest of thought in this operation consists in this :
If a proposition S is P gives to the S a predicate,
then we may desire to know whether this is an essen
tial mark of S, whether therefore everywhere, where
P occurs, the subject with which it occurs is an S or
a species of S. That is, we wish essentially to know
whether the converted judgment, P is S, is univer
sally valid, or not.
Pure conversion (conversio pura) is the name given
to that in which the original and the converted prop
osition have the same quantity. Impure (impura or
per accidens) conversion is that in which this is not
37. We may therefore have
a) A universal affirmative judgment: All S are
P. Three cases are here possible :
Fig. i. Fig. 2. Fig. 3.
CONVERSION OF JUDGMENTS. 53
In Fig. i, S is subordinated to P: All metals are
bodies ; in Fig. 2, S is subsumed under P: All
gold is yellow. In both cases it is self-evident that
the whole extension of P is not covered by S ; that
there are consequently many Ps which are not S ;
and that, accordingly, the conversion can only be
imperfect (impura) and give nothing but the particu
lar judgment: Some P are S ( Some bodies are
metals, Some yellow bodies are gold ). Fig. 3 is
therefore to be conceived of in such way, that two
equal circles S and P completely cover each other ;
from which it follows that the conversion is pure
and gives the universal proposition : All P are S.
Such judgments are called reciprocable. But what
judgments belong to this class cannot be known on
logical grounds, but only from knowledge of actual
facts. To it, for example, belong all accurate defini
tions, all correct equations, and many propositions
like this : All equilateral triangles are equiangular.
The violation of this rule of conversion is one of
the most frequent of logical errors.
Fig. 4 .
54 OUTLINES OF LOGIC.
b) The universal negative judgment, No S is P,
obviously (Fig. 4) separates S and P completely, so
that it is self-evident that no P is an S ; that is, uni
versal negative judgments by pure conversion give
universal negative judgments again.
c) The particular affirmative judgment, Some S
are P, if S is subsumed under P, for example,
* Some flowers are yellow (still more, like the analo
gous universal judgment, according to Fig. 2) admits
only of the particular conversion, Some yellow ob
jects are flowers ; if, on the other hand, P is subor
dinated to S, and S is therefore the higher generic
notion, as for instance, Some dogs are pugs,
then conversion gives the universal judgment, All
P are S. This case also we can know only from
knowledge of real things.
d) The particular negative judgment, Some S are
not P/ can in no rational way whatever be converted
into the negative Some P are not S ; for example,
from the statement that some monkeys have no tails
it does not follow that some things without tails are
not monkeys. For the tail might possibly occur only
in the case of monkeys, although they might not
all have it. Or in more general terms ; the negation
of a predicate to any subject does not justify any
affirmation as to what of such predicate otherwise
occurs or does not occur. All that can be done here
CONTRAPOSITION OF JUDGMENTS. 55
is to join the negation to the predicate and convert it
into the particular affirmative. Therefore, Some S
are not P/ gives Some non-P are S.
38. Furthermore, inquiry may be made as to the
relations which take place between a subject S which
has a predicate P, and another subject which has not
this P, that is, a non-P. This leads to what is
called contraposition. According to this form, the
affirmative judgment is changed into a negative, in
which at the same time non-P is substituted for P,
the negative attaches its negation to the predicate,
and thereby becomes affirmative. Both then become
converted according to the customary rules. The
contraposited judgment has the opposite quality
from the original judgment. The quantity in the
particular judgment remains the same ; the universal
affirmative becomes universal negative, and the uni
versal negative becomes particular affirmative.
All S are P.
No S is non-P.
No non-P is S.
No S is P.
All S are non-P.
Some non-P are S.
The conclusions arrived at in this way are not
worthless ; but they can all be reached more con
veniently and clearly without this apparatus of logi
A. The Aristotelian Figures.
39. Before we further prosecute the problem
which the disjunctive judgment propounded as that
of the form of the conclusion, we have first to allude
to certain other forms of conclusion, which do not
indeed solve this problem, but only express as devel
oped what was already contained in the form of the
In the former case a P was attributed to an S, in
so far as this S falls under the concept M. Such a
content is separable into two judgments, one of
which expresses a relation of M to P, and the other
a relation of S to M ; whereupon the proposition it
self asserts as a consequence a relation of S and P.
These are the elements of the ordinary conclusion :
M is the medius terminus, or middle concept, by
means of which a relation is established between S
and P ; the propositions which express the relation,
in part of M to S, and in part of M to P, are the
premises ; the third proposition, which always com
bines S and P, and in which M does not appear, is
THE ARISTOTELIAN FIGURES.
the conclusion (Conclusio). According to the differ
ent possible combinations of the three concepts in
the premises, the three so-called Aristotelian figures
of the conclusion are distinuished :
I. Figure: M-P II. Figure: P M III. Figure: M P
S -M S -31 M- S
S -P S -P S -P
It is only a matter of agreement, and yet one
universally accepted, that in the concluding proposi
tion the concept shall always be the subject which
is combined with M in the second premise ; and the
other one, which stands in the first premise, the
predicate. Accordingly, the first premise may be
in general designated as the ( major premise (Propo-
sitio major}, the second as the minor premise (Pro-
positio minor] ; although, according to the nature of
the thing, no inducement to this is found in the
second and third figures, since their premises are
constructed in a manner quite homogeneous.
For all three figures the universally valid condition
of the cogency of the conclusion consists in the com
plete identity of the middle term in both premises. For
S and P would obviously not be connected together
through M, if the M with which P is connected were
another M from that with which S is connected.
40. If we consider the position of the premises
58 OUTLINES OF LOGIC.
in the First Figure, we discover that, according to
the very nature of the case, the same concept M can
be at one time subject and at another predicate, only
when it is a generic concept for which the major
premise furnishes a predicate, and under which the
minor premise subordinates some subject as a special
instance or example.
The force of the conclusion, therefore, depends
upon the subsumption of the particular under the uni
versal. It will, accordingly, take place only when
1) the major premise is universal (for the S in
the minor premise, which is an M, is with perfect
certainty subsumed under the M of the major pre
mise, only in case this latter includes all M) ; and
2) the minor premise is affirmative (for since the
conclusion depends upon subsumption, a negative
minor premise, which would deny any such subsump
tion, would cut the nerve of the sequence). On the
3) the quality of the major premise is not essential
(for the same relation which it expresses between M
and P, whether it be affirmation or negation, should
and can be carried over in the conclusion to S and P).
4) the quantity of the minor premise is not essen
tial (for it is just this relation of M and P that is not
THE SECOND FIGURE. 59
altered by the number of the subjects to which it
applies). From this it follows, finally,
5) that the conclusion always has the quality of
the major premise and the quantity of the minor
premise (for it borrows from the first the positive or
negative relation which it carries over ; and from the
second, the particular or universal subject to which
it carries the relation over).
If the vowels of the following words of three
syllables (following the mnemonic couplet of 35)
designate, respectively, the quantity and quality of the
propositio major, of the propositio minor, and of the
conclusion of the syllogism, then there are four valid
so-called Modi of the first figure : Barbara, Cela-
rent, Darii, Ferio.
41. In the Second Figure, the premises estab
lish a relation between two subjects P and S, and the
same predicate M.
If now, in the first place, we conceive of both as
possessing the M, then obviously nothing whatever
follows with reference to their reciprocal relation.
And the case would be exactly the same as if they
both did not have the M. Both premises, therefore,
should not be affirmative, nor both negative. If, on
the other hand, the one subject A particular or
universal either does or does not have the M, and
6O OUTLINES OF LOGIC.
the other, B, is in the opposite relation with reference
to M, not particular but universal, and therefore
uniformly has not or has M ; then A cannot be a
species of B.
From this it would follow that one premise must
be affirmative, the other negative ; and that one must
be universal, and the other may be particular as well.
Still, since the A, which is to be the subject in
the conclusion, is always, according to conventional
usage, the subject of the minor premise (S), the
universal premise must be the first or major ; and its
rules are, accordingly, the following :
1) The major premise in the second figure is uni
formly universal, but its quality is either affirmative
2) The minor premise is in quality uniformly the
opposite of the major premise ; but its quantity, on
the contrary, may be either universal or particular.
3) The conclusion is uniformly negative, and fol
lows in quantity that of the minor premise.
The four modes (Modi) are : Camestres, Bartfco,
42. In the Third Figure, the premises establish
a relation between one and the same subject and two
Now if the subject has both predicates, that is,
THE THIRD FIGURE. 6l
if both predicates are affirmative, then there fol
lows, from this given example of an actual combina
tion of S and P, the possibility of such combination
(the fact that S and P are unitable ) ; and, therefore,
the conclusion is : What is S may be P. This con
clusion is customarily (and yet, strictly speaking, not
perfectly correctly) expressed in the particular form :
Some S are P. In order that the medius terminus
may both times signify exactly the same thing, and
therefore the M of the one premise may be certainly
contained in the M of the other also, one premise
it makes no difference which must be universal.
This gives three modes : Darapti, Datisi, Disamis.
If, on the other hand, the M has one predicate, but
not the other, that is, if one premise is affirmative
and the other negative, then it follows from this
that the two predicates are separable. Or (to express
the same thing more accurately) the predicate which
occurs is separable from that which does not occur
in this example (that is, is denied). But it does not
follow that the predicate here denied could occur
separate from that affirmed. From
All animals are living,
Some animals are not rational,
it does not follow that being rational could occur
without being alive (although the latter could very
62 OUTLINES OF LOGIC.
well occur without the former). Now, since ( 39,
last paragraph but one) the subject of the conclu
sion must appear in the minor premise, it must be
affirmed ; and, besides, as in the previous figure, in
case of two affirmative premises, one must be uni
versal. Strictly speaking, the conclusion merely
asserts : What S is, P need not be ; but this again,
expressed as a particular judgment (though strictly
speaking, not with accuracy) becomes : Some S are
not P. This gives us the following three modes :
Felapton, Ferison, Bocardo.
Finally, if both premises are negative, then it is
customary to assert in treatises on logic that no con
clusion is possible ex mere negativis nihil sequi-
tur. This is absolutely groundless and false. If
the same M is neither P nor S, then it follows from
this that P and S are not contradictorily opposed to
each other ; and that, consequently, what is not S
need not, on that account, be P. For example : The
just man is not recognized The just man is not
unhappy ; conclusion : Whoever is not recognized
is not on that account unhappy. Conclusions of this
kind are by no means to be esteemed as of small
value and importance ; since they assert, from affirm
ative or mixed premises, the unitability or (respec
tively) the separability of S and P. And they, in
fact, are occurring every day, in order to refute some
THE FIGURE OF GALEN. 63
false conclusion which has been drawn from the de
ficiency of one predicate : " Because thou art not
that, thou needest not to be the other also."
43. A Fourth Figure, that of Galen, in which
the position of the premises is P M, M S, and
from which the conclusion S P should follow, is
superfluous and faulty ; for example,
All roses are plants.
All plants need air.
Some things needing air are roses.
The natural process of thought always draws from
the foregoing premises, when it converts them, the
following conclusion in accordance with the first
figure: All P are S All roses need air/ The
conclusion of Galen, Some S are P on the
contrary is not merely unnatural, but expresses less
than the other. For if it is converted, then we have
only the particular proposition : Some P are S
Some roses are things that need air. But undoubt
edly it is a logical fault, from given premises to con
clude less than really follows from them.
And in similar manner, the conclusions possible
according to the fourth figure always admit of being
obtained more naturally and better by transposition
and transformation of the premises in accordance
with one of the first three, or Aristotelian figures.
64 OUTLINES OF LOGIC.
The modes of the fourth figure are as follows :
Bamalip, Calemes, Dimatis, Fesapo, Fresiso.
44. Only the first figure appeared to the older
logic to be evidently conclusive and perfect. The
conclusions drawn according to the other figures, on
the contrary, were considered to be completely justi
fied only when they could be referred ( reduced ) by
transformation, conversion, transposition, of the pre
mises, etc., to the first figure ; and then the previous
conclusion drawn from them in accordance with this
figure. The operations necessary for this are signi
fied by the consonants s p m c in the names of the
modes of the second, third, and fourth figures, in
accordance with the couplet,
s vult simpliciter verti, p verti per accid. [accidens],
m vult transponi, c per impossibile duci.
That is to say, if m (metathesis) requires transposi
tion of the premises (that the major premise be
made the minor premise, the minor premise the
major) ; s and p call for Conversio (more particularly,
s for pure conversion, simpliciter, p for impure, per
accidens) of that proposition behind whose character
istic vowel they stand in the name of the modes.
For example ; in order to reduce Disamis to the first
figure, the major premise (on account of the s which
follows its vowel) must undergo pure conversion,
TRANSFORMATION OF PREMISES. 65
that is, in this case, conversion into a particular prop
osition ; it is then to have its position exchanged (on
account of the ni after the a) with the minor pre
mise. Now from these transformed premises a con
clusion is drawn according to the first figure, which
is then in turn converted (on account of the last s) ;
and in that way, finally, the previous conclusion ac
cording to Disamis is derived again.
Original in Disamis :
Some metals are magnetic.
All metals are fusible.
Some things fusible are magnetic.
Reduction to Darii of the first figure :
All metals are fusible.
Some magnetic substances are metals.
Some magnetic substances are fusible.
This conclusion converted :
Some things fusible are magnetic.
Finally, the letter c indicates a more circumstan
tial operation (the Duetto per impossibile s per con-
tradictoriam propositionem), which amounts to the same
thing as that, for example, in Bocardo the conclusion
S0P 1 denies ; accordingly the proposition S#P affirms
1 SaP, S/P, S^P Se>P, are meant to designate, respectively, a universal
affirmative, particular affirmative, universal negative and particular nega
tive judgment, with the subject S and the predicate P. Corresponding to
these, on the other hand, PaS would be a universal affirmative judgment
with the subject P and the predicate S, etc.
66 OUTLINES OF LOGIC.
1 ad contraclictoriam, and (the c stands in the name
of the modus behind the vowel which designates
the major premise) this contradictory opposite of
the conclusion is put in the place of the major pre
mise of Bocardo. From it as major premise, and
from the second premise of Bocardo as minor pre
mise, a conclusion then follows according to Barbara,
which is the contradictory opposite of the premise
given in fact as the first of Bocardo (and accordingly
is just as certainly false as that is correct) ; from
all of which it is clear that the negation of the
original conclusion in Bocardo is not permissible,
and that this other is therefore correct.
45. The distinguishing peculiarities of the three
Aristotelian figures are therefore the following :
1) Only the second figure can draw a conclusion
from a negative minor premise ; only the third
figure from a particular major premise.
2) Only the first figure can lead to a universal
affirmative conclusion. Only it has concluding
propositions of every kind : A, E, I, O ; on the
contrary, the second is only negative : E, O ; the
third is only particular: I, O.
This law holds good in the case of connected
series of syllogisms (syllogismi concatenati, catenae
syllogismorum) which originate from the fact that
NATURE OF THE SORITES.
the conclusion of one syllogism which is then
called prosyllogismus is employed as a premise
for another, which then receives the name of epi-
syllogismus. If the conclusion of the last epi-
syllogism, and therefore of the entire chain of
reasoning, is to be universal affirmative, then the
entire chain must be constructed according to the
mode Barbara of the first figure. If a particular
proposition at any place enters into it, then the
final conclusion can be only particular ; and only
negative, as soon as a negative conclusion has any
where entered into it.
Finally, Sorites (Kettenschluss] is the name for
certain chains of conclusions that are abbreviated
and simplified in expression (abbreviated and simpli
fied by suppressing the concluding propositions of all
the prosyllogisms). It is customary to distinguish
the sorites of Aristotle and the sorites of Goclenius. 1
The structure and difference of the two are as follows :
Sorites of Aristotle. Sorites of Goclenius.
S-MO) MO) -P
MO) -MO) M(-M()
MO) -P S-MO)
1 So called from Rudolph Goclenius (1547-1628), professor in Marburg,
68 OUTLINES OF LOGIC.
46. Strictly speaking, all syllogisms simply carry
over unchanged (as their form of expression makes
perfectly clear in case we conceive of those which
follow the other figures as reduced to the first
figure, 44) that relation which the major premise
states as between P and M, and apply it to the
subject S, which the minor premise somehow obvi
ously includes in the conception of M. Accordingly,
the nature of the judgment which forms the major
premise, as well as of that which forms the minor pre
mise, is unimportant for the form of the conclusion.
If the premises, therefore, are not categorical
judgments (as we have hitherto exclusively assumed
them to be), but if they are furnished to us in
hypothetical or disjunctive form, then these differ
ences (which are, of course, important for the
judgments as such) require consideration ; but they
do not require any alteration of the rules for draw
ing conclusions which are primarily established for
categorical premises. Nevertheless, in some sorts
of conclusions with hypothetical or disjunctive pre
mises, the matter-of-fact interest has led to certain
artificial expressions to which allusion may be made.
author of the Lexicon philosophicum, Francof. 1613, who in his Isagoge
in Organum Aristotelis, Francof. 1598, was the first to require for the
sorites this (in the series of the traditional syllogistic-norms, comp. supra,
p. 57) transformation of the schema of the schools, which is, of course,
NATURE OF THE SORITES. 69
In the first place, there is a series of cases in
which a hypothetical major premise, as a general
rule, attaches a sequence F in the following prop
osition to a reason G that forms the content of
its preceding proposition ; but a categorical minor
premise either affirms or denies the validity either of
G or of F.
a] Now if the major premise asserts positively :
If G is true, then F also is always true ; and the
minor premise just as positively: In all or some
cases of S, G is true ; then the conclusion is : In
all or some cases of S, F is also true. This is called
the Modus ponendo ponens, because by positing
the reason the consequent is established ; and it
corresponds to the modes Barbara and Darii.
b] If the major premise were the same, and the
minor premise, on the other hand, negative and also
assertory : F does not exist ; then the conclusion
would be: Consequently, G also does not exist.
This is a modus tollendo tollens that, by abolishing
the result, abolishes the reason which it would have
necessarily established in case it had been valid; as
for the rest, it is in appearance a type of Camestres
c] If the major premise were negative : In case G
is true, F is never true ; and the minor premise
asserted positively : Now, however, F is true ; then
7O OUTLINES OF LOGIC.
the conclusion would be : Therefore G is not true,
which would make F impossible, if it were/ etc.
This is a Modus ponendo tollens (corresponding to
Cesare and Festino), which by positing a result
denies the reason which would have made it im
And so forth : we see that these consequences
admit of being referred without difficulty to the
course of thought in the Aristotelian figures.
Finally, Dilemma, Trilemma . . . Polylemma,
are the names given to those conclusions with a
disjunctive major premise (having two, three ... or
many members, respectively) and with several minor
premises, whose number is the same as the number
of the disjoined members in the major premise ; and
which assert conjointly for each of these members
one and the same result T, or one and the same predi
cate T. The name dilemma (and corresponding to
it, trilemma, etc.) is by preference originally given to
a conclusion of the form :
If Z is to be true, either U or W must be true,
Now neither U nor W is true,
Therefore Z is not true.
47. The Aristotelian figures admit of being
apprehended in yet another way. If we conclude
according to the first figure in Darii :
DESIGN OF THE CONCLUSION. J I
All men are mortal,
Caius is a man,
Therefore Caius is mortal;
it is indeed the design of the conclusion to deduce
the truth of the final proposition as something in
itself still questionable, from the truth of premises
regarded as already established. But our attention
is soon called to the fact, that aW men are mortal
only in case Caius is, too ; and that Caius also is a
* man only in case he has all the essential properties
of a man, and consequently that of being mortal.
That is to say, the conclusion suffers from a so-called
double circle : major as well as minor premise, in
order themselves to be valid, presuppose the validity
of the conclusion which they ought to demonstrate.
Such a mode of drawing conclusions, therefore,
cannot be of direct service for the expansion of our
knowledge, but only for the purpose of bringing
truths already established into a relation of subordi
nation that corresponds to the actual way things go.
1) It can expand knowledge only in case we are
warranted in asserting universal judgments, in order
to have independent major premises, before the
validity of every special instance subordinated to
them is proved ; and in case we
2) are warranted in subordinating a subject to a
general concept on account of certain marks, in order
72 OUTLINES OF LOGIC.
to have independent minor premises, before we know
whether it has all of its predicates.
48. Now the major premises can be constructed
in the second figure, if we expand them somewhat.
Its premises are formed quite alike: P M, S M.
In experience it often happens that several of them :
Q M, B M, T M . . . are given. But from the
premises given just as many conclusions must be
drawn as follow from them.
If, therefore, the premises P M, S M, Q M,
B M . . . are given, that is to say, if many other
wise different subjects have the same predicate,
then we conclude that not every single one of them
has M through some special accident, but that one
and the same common reason makes it necessary for
them all at the same time.
This reason is put forward in the form of a generic
concept, of which all the aforesaid subjects are
species ; and now the assertion is made that the M
belongs to this concept 2 as a rule, and that those
subjects possess the M only by means of their sub
ordination under S. The concluding proposition
therefore is : * Every S is M, and this is the
simple conclusion of Induction, which has its position
in the system of thought at this place.
KINDS OF INDUCTION. 73
Perfect and imperfect induction are distin
guished. The first takes place if it is known that
the subjects enumerated in the premises, taken
together, exhaust all the species of 2. But then,
although the universal proposition, All 2 are M,
taken strictly, can be asserted, since the same has
already been asserted in the premises of every single
species of 2, yet, on the other hand, this concluding
proposition is a bare summing-up, and not a real
expansion of our previous knowledge. For its
change into a general judgment Every 2 is M
is not, fundamentally considered, permissible ; since
from the mere fact that all species of 2 have one
predicate, it neither follows that they have it as
species of 2, nor that all species of 2 which are
perhaps still to be discovered will have it.
This last conclusion, if it is made, is nothing more
than the imperfect induction, which concludes from
the fact, that some species of 2 have a predicate,
to the appearance of the same predicate in all
species ; and which does this, indeed, in consequence
of its common generic concept. But such induction,
although not strictly conclusive as a consequence ad
subalternantem, does expand our knowledge ; in
applied logic, however, it requires certain rules to
74 OUTLINES OF LOGIC.
49. In a similar way, the third figure can lead
to the formation of the minor premises required above.
If its premises that have a like construction are
increased, M - S, M P, M - Q, M R . . ., they
present the frequently recurring case of manifold
properties being attached to the same subject. Here
also the conclusion is drawn that each one is not
present through some special accident, but that all
come from one and the same reason, and this on
account of the fact that M is a species of the genus
S, in which the combination of the marks S P Q K
. . . is prescribed. The conclusion therefore is: M
is a S/ which is the simplest form of conclusion
This, too, would be perfect only in case it could
be shown that S P Q R . . . are, taken together, the
entire collection of predicates which 2 requires. For,
of course, whatever has all the properties of a 2,
appears itself necessarily to be a S. And yet this
consequence also is not quite strictly drawn. In
reality, we can only sum up the premises, and say
in the concluding proposition, that in fact all the
predicates are found in M which belong to a S.
That they are so, however, not merely in fact, but
by virtue of the truth that M is a S, is never in per
fect strictness a matter of demonstration ; but such
a conclusion stands on an equality with the so-called
FORMS OF CALCULATION. 75
imperfect analogy, which draws a conclusion from
certain observed marks in M to the assumption that
M will also have the other marks which, together
with the foregoing, make out a S ; and that M will
therefore be a S.
B. The Forms of Calculation.
50. The doctrine of judgment concluded with
the disjunctive form, which asserted that the one
or the other special modification of the general pred
icate P must belong to the S, which predicate
belongs to the higher generic concept of S, namely,
to the M. In order that this choice may be decided,
it was necessary that S be taken into consideration,
not merely as a species of M in general, but also with
reference to its specific nature, by which it is distin
guished from other species of M.
The first Aristotelian figure, which depends upon
this relation of subsumption, does not do this. In
the minor premise it only subordinates the S in gen
eral, as a species of M ; and can, therefore, also only
ascribe to it, in the conclusion, the universal P with
out closer definition. This result is, in part, not cor
rect, since the P in such indefiniteness cannot be a
predicate of S ; and, in part, it does not satisfy our
necessities. For in real life it is seldom enough to
conclude : All metals are fusible iron is a metal
76 OUTLINES OF LOGIC.
therefore iron is fusible ; but we wish to know
how iron as iron, in distinction, for example, from
lead as lead (that is, perhaps, at what degree of tem
perature), is fusible.
51. Still another consideration leads to the same
demand. Fixed and changeable (historical) predi
cates of a subject may be distinguished. The man
ner of drawing conclusions hitherto described referred
only to the former. For such properties as belong
to a subject by virtue of its subordination under its
higher genus, of course belong to it always and are
But in real life constantly, and very often in sci--
ence, we are far more interested in the changeable
predicates ; that is to say, in those which designate
some affection, some activity, some state, in brief,
something or other which happens to the S only so
far as certain conditions act on S, but which would
never flow from the mere fact that S is a species of
M (only so much is self-evident, however, that sub
ordination of S under M must establish such a pred
This necessity, too, which occurs for example
in the calculation of all future events, and in the
employment of means for our conduct, requires that
we should discover for S some quite definite predi-
ARGUMENT FROM ANALOGY. 77
cate which does not originate from the subsumption
of S under a general concept, but from one way of
regarding the special nature of the S and of all the
conditions acting upon it.
52. The conclusion of analogy, too, in case it is
to be of any use, requires that, from certain marks
which we observe in a subject, we should draw a con
clusion directly to the presence of other marks also ;
and then from the sum of these marks form a con
clusion secundo loco to the fact that the subject is one
species of a genus. The previous mode of procedure
was the reverse of this : in the first place, a subject
was subsumed as a species of a genus, and then se
cundo loco a conclusion drawn from this to its pred
The question now arises whether that which such
analogy could not strictly accomplish admits of being
thus strictly accomplished at all ; that is to say,
whether we can draw a conclusion from the pres
ence of certain marks or conditions in a subject S,
directly and without taking our way around through
any general generic concept, to the necessary pres
ence or absence, and to the definite value of other
marks of the S.
78 OUTLINES OF LOGIC.
53. The foregoing necessities would be satisfied
by any mode of conclusion, the major premise of which
breaks up a general concept, M, into the collective
number of its parts ; and substitutes for it, as hold
ing equally valid, the developed combination of these
parts ; such a form, therefore, is
M a + bx+cx*^ ----- ,
in which all the mathematical signs are supposed
merely to represent the variety of the possible ways
of combining the marks. The minor premise would
assert of S, not merely that it is a species of M in
general, but that it is the definite species of M which
we get in case we let some further determining con
dition act upon the universal M. This gives to the
minor premise (designated again by a mathematical
symbol) the form, -
And now the concluding proposition has to ex
press with complete dcfiniteness what predicate must
belong to S ; because the combination of marks sub
stituted for M in the major premise has, in the con
clusion, experienced the special influence of the
conditions designated by <|> in the minor premise.
One needs no reminder to comprehend that this
way of drawing a conclusion is directly and strictly
applicable only in mathematics. In the case of other
objects of thought, for example, concepts of nat-
MATHEMATICAL ARGUMENT. 79
ural species and genera, we cannot carry out the
substitution in the major premise ; because we never
perfectly know all the marks of any genus, and still
less accurately all its modes of combination. Fur
ther : we can never perfectly show in the minor prem
ise by what determination, <j>, the genus M passes
over into the species S. If we should be satisfied,
however, with making prominent some single mark
(as x) by which S is distinguished from other spe
cies of M (without positively learning from x the
entire nature of S), then we should not be able in
the conclusion to demonstrate what transforming
influence this x must exercise upon all, or upon any
one, of the marks qualitatively different from it (to
which allusion is made in the major premise) or
upon the combination of such marks.
All this is possible only in the domain of mathe
matics. Since every magnitude is comparable with
the rest, and all are resolvable into the same units,
and producible from them by different combinations ;
and, finally, since they are perfectly defined in their
content, that is, in their value, and since there
are rules of calculation which determine accurately
the Facit that results in case a definite operation
is applied to a definite combination of magnitudes ;
it is, therefore, possible in this domain actually to
carry out the concluding proposition, and to fill out
8O OUTLINES OF LOGIC.
in it the schema <J> (M) by assigning it a definite
value. For example :
M = a +
S -M 2
This limitation to mathematics, nevertheless, does
not rob such a conclusion of its place in Logic.
For calculation, too, is a process of thought, and
that not the most unimportant. On the other hand,
it is to be considered that we succeed in an abso
lutely certain expansion of knowledge only in so
far as we can refer the objects of our reflection to
relations of magnitude, and can make calculations
54. But if such an application of calculation to
concepts of qualitatively different content is to take
place, and if we are to be able to conclude from the
existence and value of one mark to the existence
and value of another, then the connection of the
two and the dependence of one on the other, al
though it does not admit of being placed upon a
strictly logical basis, must be presupposed as a mat
ter of fact ; and nothing further can be done than by
calculating according to a general law which holds
good for such a condition of dependency, to assign
to every given value of the one mark the value of
EXPRESSION OF A PROPORTION. 8 1
the other belonging to it. This is done in the form
of a proportion :
:E = /:T.
The proportion does not refer the content of the
one mark back to the qualitatively different con
tent of the other mark, but allows both to be what
they are. It also makes, in general, no comparison
whatever between the absolute magnitudes of the
changes which the two correspondingly experience.
For these two, since they are measured by quite
different standards, are frequently not comparable.
Strictly speaking, it only compares the number of
the units of change which both marks undergo (the
change in each one as measured according to its
own standard), and from the given number for the
one mark determines the corresponding number for
It is self-evident that almost all application of
mathematics to real objects depends upon this man
ner of drawing conclusions ; further, that propor
tions are possible exactly only where the marks of
the real object are determinable quantitatively; but
that they run into inexact comparisons with refer
ence to other objects of thought.
55. The above-mentioned expression for a pro
portion contains one further inaccuracy. If E be
82 OUTLINES OF LOGIC.
the expansion and T the temperature, then the afore
said expression leads to the idea that there are two
marks which, absolutely and without reference to
the subject in which they occur, stand in an unalter
able relation to each other. But how mtich the ex
pansion increases for every additional degree of
temperature, depends on the nature of the body
heated, and is different in the case of different
bodies. Indeed, the necessity that one mark should
exercise any influence on the other depends simply
on the fact that they are marks of one and the same
subject. This is true for every pair of marks. And
we are on this account obliged to apprehend the
nature of the subject as a law such that from it
flow the proportions of all its single pairs of marks.
Mathematics, and that in Analytical Geometry,
has, indeed, approximately discovered a formal ex
pression for this logical demand in the comparison,
for example, of the different curves, in which it
defines the entire nature of a curved line, its shape
and its direction, etc., by means of a proportion
between the corresponding increments of the ab
scissas and ordinates.
Such comparison also depends, of course, on the
fact that all the properties which can belong to a
spatial figure for example, its curvature and the
like after all depend simply upon different mag-
CONCEPTS AND IDEAS. 83
nitudes of the same species ; and no qualitatively
incomparable properties occur. An extension of
this logical form to the treatment of real objects
for example, the attempt to discover a formula for
the nature of man similar to that which we possess
for the nature of the ellipse is a problem of in
finite complexity and quite impracticable with any
exactness. But approximately the attempt has al
ways been made to solve it, since there has been
an effort to discover a so-called constitutive con
cept for every object.
That is to say : a merely distinguishing con
cept, such as barely suffices to render its object dis
tinct from other objects but does not positively and
exhaustively tell in what it consists, is held to be
different from a descriptive concept, which as far as
possible specifies completely the content of its object,
but makes no essential distinction in order of rank
between marks that are more original and Maw-
giving (as it were) and such as are derived and
dependent. Finally, there are distinguished those
constitutive or * speculative concepts (or the Ideas )
which are limited to designating a certain primitive
content (Ur-In/ialt) of the object, from which all its
individual marks and their combinations are then
derived as its necessary consequences.
84 OUTLINES OF LOGIC.
C. The Systematic Forms.
56. For the discovery of such a constitutive
concept, we remind ourselves as we have already
done in the doctrine of the concept, of the fact,
that the isolated consideration of an object in itself
does not teach us how to distinguish the essential
and law-giving marks in it from the unessential
and dependent. That in it which gives it its law
we find in the universal which is common to it with
others of its species. By this means we are con
ducted to the path of Classification ; and we suppose
that we know the essence of an object just as soon
as we are able to assign to it its position in a Sys
tem, which begins with some most general concept,
subordinates to this many general concepts as spe
cies, and finally, to the latter a variety of partic
57. It is not quite this problem, but a more
superficial one, which is fulfilled by the so-called
artificial classification ; such as either develops all
its species or single instances from one general con
cept M, or one general case M, or else subordi
nates these particulars to M as though they were
already well recognized. The following operations
are distinguished :
MODES OF CLASSIFICATION. 85
1) The Partition of M into its different marks,
a, b, c . . .
2) The Disjunction of each of these marks into
its species ; of a into a x a 2 . . . , of b into 0i /3 2 . . .
3) The Combination of every single species of
each predicate with every species of every other
4) The Arrangement of the species of M thus
deduced, either according to well-known lexical prin
ciples, or according to some other that answers the
ends of use.
5) A Correction by which the non-valid or impos
sible species are again removed ; species which,
accordingly, originated from the fact that we have
had regard only to the presence and not to the mode
of the combination of the marks a b c in M. It is
possible that some modifications of these marks, for
instance, a^ 2 y 2 , do not admit of being combined
in this way at all (example : M = triangle, a = angle,
b = side, ! = right, a 2 = obtuse, angle, & = equal,
/3 2 = unequal, sides. Hence a^ is impossible).
This whole mode of procedure is seldom used for
deducing its species from a concept M ; for the most
part, the species are previously known, and are only
arranged under the M. Much oftener it is of service
86 OUTLINES OF LOGIC.
in developing, from a general case M (some judg
ment), the special instances conceivable ; and, here,
just that which excites our interest is to know, which
of them are possible or impossible, and what standard
for instance is of real use, what absurd.
58. Artificial classifications, strictly speaking,
systematize the way which we must take for a survey
of the content, rather than this content itself. The
single species stand side by side, excluding each
other, without any knowledge of their nature origi
nating from such knowledge of their arrangement.
This particular problem of classification, to wit,
the determining of the essence of each species by
its position in the system, accordingly leads to the
fresh attempt to arrange the species of a concept M
in the so-called natural classification, in a single
series or in series of series, in such manner that
they form a steady advance from the most imperfect
to the most perfect.
That two species may more or less adequately cor
respond to their general concept, the marks of which
they must both possess collectively, is possible on
account of the fact that the marks combine in very
different magnitudes, and the relations between them
may be thought of in a variety of special forms and
different degrees of strictness. For example ; from
MEANING OF THE UNIVERSAL. 8/
general logical pre-judgments, that species is held to
be perfect which has all the marks uniformly elab
orated ; and that to be imperfect in which some
marks disappear and others occur in excess. But
such pre-judgment constantly needs correction or
supplementing from a knowledge of the real thing ;
and only in the particular case does it admit of being
determined from this knowledge of the thing, whether
the aforesaid uniformity, rather than a definite ine
quality of the marks, agrees more adequately with
the meaning of the universal.
But in order to be able to speak of any such mean
ing/ it is further presupposed that the general con
cept M is itself also a member of a higher series, and
has its position in this series side by side with N, O,
P, ... as other species of a yet higher universal ; so
that, by virtue of this position, a definite problem is
proposed to it, according to which it may be esti
mated, which of its own species is the more perfect,
since it best answers this problem.
And so the series of these presuppositions pro
ceeds. For a place in a series that is still higher,
and, finally, in the comprehensive series of the entire
coherent system of the universe, must be discovered
for the series M N O P, a place which it assumes,
and from which some light is thrown upon the direc
tion of that forward movement from the lower to the
OUTLINES OF LOGIC.
higher which goes on in itself. Without such a com
plete demonstration as matter of fact for the basis
of these valuations, all natural classifications, which
are limited to a single domain of objects, events, or
even concepts, remain incapable of logical proof.
Since they only lay at the foundation some general
concept, the direction of whose development they
suppose to be known, they are productive of asser
tions that, although suggestive and not untrue, are
not so exclusively true as would be demanded in such
a case as this, where that constitutive concept is
required for every single concept, from which its
entire mode of behavior shall be deducible.
59. Besides these avoidable deficiencies, the nat
ural classification has yet one other that is universal
and unavoidable. The constitutive concept, for
which we are in search, ought above all to explain to
us, how its content must behave, react, or alter, in
case certain conditions act upon it. Of all this, clas
sification teaches us nothing whatever. It simply
furnishes an indication of the meaning which the
content of the concept thought of as unchangeable
has in the series of species, in connection with
which it expresses the nature of a general concept.
But it does not explain how it can originate, exist,
maintain itself, alter, or perish.
EXPLANATORY SCIENCE. 89
It may be left undecided, which of two logical
forms satisfies a higher necessity. Certain it is that
the aforesaid indication alone is not enough ; that
it absolutely cannot be substituted in the place of
explanation ; and, finally, that the latter belongs to
those problems of life which are practically most
60. Explanatory science, which undertakes the
latter problem, is distinguished from classification,
by its form, as follows :
It does not, like the latter, take its point of depart
ure from a single concept ; and it does not develop
its conceivable species as though it were self-evident
that all which such concept postulates for its complete
manifestation is, on this account alone, also possible
or already actual. But rather since, as concerns this
latter point, and as concerns the manner in which
the content of the concept behaves under any given
conditions, it is of course, not the concept alone,
but only some rule which holds good for it and like
wise for such external condition that can decide ;
explanatory science begins with one or more judg
ments which are propounded as general laius. They
are therefore of such a kind that both their subject
and their predicate (or their major premise and their
minor premise) are universal and comprise under
OUTLINES OF LOGIC.
them many particular instances; but it is the con
tent of the judgment which determines the rule, ac
cording to which one of the instances of the minor
premise depends on one of the instances of the major
Now since nothing results from general laws in
themselves, the second necessary element is a series
of facts, expressed either singly or collectively, which
themselves then take the place of general cases, and
by which in each single case that definite modification
of the content contained in the major premise or in
the subject of the general law is designated, in
reference to which a determination of its minor prem
ise or its consequent is sought.
Now new knowledge originates from the subordi
nation of the fact under the law, on account of the
fact needing to be known only partially, perhaps
on one of its sides, in order to be capable of sub-
sumption under the law ; but, in consequence of such
subsumption, some one of its sides, previously not
recognized, becomes defined and recognized. The
most essential problem of explanatory theory, never
theless, does not consist in this simple sequence of
the conclusion, but in demonstrating the reciprocal
influence which very many conditions, that are inde
pendent of each other, exercise upon each other in
case they act on one and the same subject ; and in
setting forth the entire nature of the subject as the
collective resultant of the complete circle of its con
ditions (comp. the Applied Logic ).
61. The spirit of explanatory theory is at vari
ance with that of classifications.
The latter think not merely to explain the indi
vidual by the general concept, as a species of which
they apprehend it, or by its position in the series of
other species ; but also to legitimate it. That is to
say, only by means of the fact that it is a species of
a general concept which has its well-known place in
the total order of the world, does a justifiable exist
ence, as it were, belong to the individual. It would
be untrue or obscure, if we could not answer the
question, What is it ? by pointing out its gen
Explanatory science surrenders the thought above-
mentioned. It attaches no value, for example, to the
statement whether any particular object lying before
us is a plant or an < animal/ It bids us inves
tigate, out of what elements, in what proportion and
form of combination, the object consists ; and what
forces, according to what laws, are active between
these elements, and between them and the outside
world. If we are certain of this, then we know the
whole object and its whole present and future mode
92 OUTLINES OF LOGIC.
of behavior. But the answer to the question, whether
it is an * animal or a plant, adds nothing whatever
to such knowledge. Complete cognition consists
therefore in this; in apprehending every object as
the final resultant which proceeds from the action
and reaction of different conditions or forces ; which
forces not only act collectively for laying the basis
of this individual object, but also everywhere else act
according to general laws, and only produced this
object because they found themselves in this rather
than in some other one of many forms of combination
possible to them.
62. It is evident that explanatory science does
not furnish perfect satisfaction to our desires for
knowledge. It treats every phenomenon, every event,
only as an unimportant example of general laws,
and as a result of many conditions co-operative in
fact, but which it was not necessary should co-operate
at all, or in precisely such a manner. The objects
are, accordingly, deprived, by the very manner of
considering them, as well of their inner unity as of
the necessary character of their existence. It can
only be said hypothetically that, in case such or such
conditions prevail, then the object must be so or
otherwise. But it remains undecided what conditions
actually do prevail.
THE IDEAL OF COGNITION. 93
Against the foregoing mode of apprehending the
truth, the fundamental thought of classification cer
tainly presents a just consideration. It is necessary
to suppose that not merely do general laws hold good
in the world, while the arrangement of the facts on
account of which a definite form of actuality flows
from the laws is, on the contrary, given over to
chance, uncontrolled by any principle ; but rather
that in the arrangement of the aforesaid facts also,
a principle (that is to say, an Idea ) is effective, and
that this principle fixes beforehand the whole ar
rangement of the final result, the whole system of
the future phenomena which are to be actualized by
means of the aforesaid facts in conformity to the
The Ideal of Cognition would therefore consist in
finding for the Things such constitutive concepts
or Ideas as not only determine their meaning and
significance, but also show how this meaning itself
reaches its own actualization, by bringing together
the necessary conditions and forces. This problem
leads us wholly beyond the limits of Logic, and can
only be taken up again in so-called real Philosophy
(comp. the Encyclopaedia of Philosophy ).
SECOND PRINCIPAL DIVISION.
SECOND PRINCIPAL DIVISION.
APPLICATION OF THE FORMS OF THE CONCEPT.
63. All communication of an inner state, whether
it be feeling or thought, is an attempt so to direct
the inner activities peculiar to another as that this
other must himself have a vital experience of the
very content which is to be communicated. No
content can ever be carried over ready-made, as it
were, from one mind to another.
Now, much admits of being communicated only by
physically transposing the other person into the
state in which he must experience the matter in
question. We turn him toward the light or strike
him, in order that he may know what brightness
or suffering is. In other cases, as in art, we pro
duce a mental mood, since we indirectly, by means
of a series of changing ideas, conduct the mind
through a series of individual feelings.
98 OUTLINES OF LOGIC.
Thoughts, on the contrary, are assumed to be capa
ble of a logical communication, which consists in
this, that an accurately defined series of combina
tions and separations of individual ideas, supposed
to be well known, is prescribed to the other person ;
and then exactly the conception which is to be com
municated remains with him as their logical result
ant. There are two opposite methods of doing this :
the explanation of a concept by abstraction, and its
explanation by construction.
64. We explain by abstraction in case we ab
stract from single examples of the concept to be
explained that are better known to us than is the
concept itself, everything which is so special as not
to belong to it ; so that it alone remains for us to
contemplate. Necessarily, however, this occurs only
in the case of all such simple concepts as, for ex
ample, Being, Becoming/ Unity, etc., whose
content does not consist of a conjunction of other
The second way, that of * construction, which en
deavors to build up the concept from its constituent
parts, must, at least, be attempted in the case of all
composite concepts. For abstraction makes the
content of the concept intuitable only as a whole ;
but teaches us nothing concerning its interior struc-
CONSTRUCTION AND DEFINITION.
ture. Construction is perfectly practicable only in
affairs of mathematics ; because here the meaning of
the individual ideas which are to be combined, and
of the forms in which they are to be combined, can
be fixed unequivocally. In the case of other con
cepts, which combine marks qualitatively different
in manifold relations, neither of these things is pos
sible. And on this account, wherever it is possible,
the intuitive image is included in the explanation.
Now, Definition is that kind of construction which
endeavors to build a concept up by means of merely
logical operations. Fundamentally considered, it
uniformly regards the greatest part of the work as
already achieved since it itself refers to some
higher general concept which is known, and which
already contains that entire mode of combining all the
marks which is so difficult of elucidation. To this,
definition adds a specific mark, which suffices to dis
tinguish the concept in question from other species
of the same universal ; but it entrusts to the imagi
nation, along with this, the task of conceiving the
other corresponding specific marks, which here take
the place of what is universal in the general concept,
and in connection with it form the entire nature of
the thing to be defined. Nevertheless, where the
attempt is made to enumerate them all, the defini
tion becomes a description which, on account of its
100 OUTLINES OF LOGIC.
imperfectibility, is not valid as a proper logical
65. It is essential for definition that the con
cept of genus applied by it should be the one next
higher the Genus proximum.
Definitions that are too wide, and adapted not
merely to what is to be defined, but also to some
thing else which we wish to distinguish from it, arise
in case we choose instead of this genus proximum,
some far higher general notion as our point of depar
ture ; for in that case the Xota specifica does not
always admit of being included in such a way that
nothing else, too, falls under this definition. This
mistake is frequently met with in the practical
domain, in that it is customary to use a very high
and pre-eminent general concept for better recom
mending some proposition.
Too narrow definitions adduce marks that are not
necessary to what is to be defined, and therefore
exclude some of its kinds. They easily originate
from the limited nature of our circle of experience,
which accustoms us to only a few of the more nearly
allied species of the universal.
Definition perpetrates a Circle? in case it assumes
in the explanation that which is to be explained,
although under another form. This mistake always
TASK OF DEFINITION. IOI
originates, in case we aim to -define constructively
simple concepts like Being, Becoming/ and
others similar which are to be made clear only
by means of abstraction.
Finally, the custom of apprehending substantively
all things that are to be defined, even when they are
by nature verbal or adjective, although not itself a
mistake, is one inducement to mistakes. It is more
natural and conformable to our purposes to define
thus : " A body is elastic, in case it, etc." ; or, " An
organism is alive (or is diseased), in case it, etc.," than
to define thus: "Elasticity is" ... or, "Life (disease)
is, etc." The latter modes of expression are indeed
often quite harmless ; but they are also often produc
tive of the habit of treating states, properties, and
events as though they were substantial and inde
66. The task of definition, which is not merely
to specify the content of the concept, but also to
limit it with respect to other concepts, can often be
accomplished only by arbitrarily fixing the usage of
In the first place, there are certain concepts which
have no secure point of departure for their validity,
like the collective ones, throng, heap, bald-
headed ; then there are others contradictory to
102 OUTLINES OF LOGIC.
each other, between which a point of indifference
exists, such as cold and warm, and the like.
In all the former cases a limit is wanting, at which
the concept begins to be valid ; in the latter, the
limit is also wanting at which they pass over into
the contradictory concept. We do not know where
warm ceases and cold begins; we only know in
what direction of the series the cold diminishes and
the warmth increases, and the reverse.
Another great multitude of concepts has originated
in the living formation of speech, in such manner
that, when comparing what is particular, we, at one
and the same time hold to several points of view that
are independent of each other. Accordingly, those
species which fall under the concept attained, agree
ably to all these points of view at once, indubitably
belong there ; on the contrary, other species, although
they appear to fall under it as judged in one respect,
in other respects, on the other hand, appear to be
excluded from it. In such a case nothing remains
to be done but to fix, for the exact use of science,
the extent of the concept, and accordingly the sig
nificance of its name, in a way that agrees with
our purpose but is somewhat arbitrary ; and not to
take too much pains simply to remain in accord
with the usage of speech. The concept of dis
ease, for example, comprehends, on the one hand,
LIMITATION OF CONCEPTS. IC>3
every deviation from the normal condition ; on the
other, it signifies a condition which has a variable
course ; in the third place, it signifies such an one
as is fraught with danger. Just so the conception
of crime has respect, simultaneously, to the bad
will, to the execution of the deed, to the magnitude
of the harm done, etc.
67. With reference to the value which we ascribe
to the fixed limitation of concepts as set over against
each other, our ordinary process of thought controls,
sometimes by means of a principle of logical pedantry,
and sometimes by means of one of logical frivolity.
The former holds every distinction in concepts
insurmountable (the well-known mode of speaking :
" that is something quite different ") ; the other
regards every distinction as fluid, and teaches how
to change every concept by intermediate stages into
any other that is in any degree allied to it. This
change is accomplished by altering at pleasure the
magnitude of individual marks, many (such as are
necessary to the new general concept, but wanting
in the given concept) being considered as present
but of no value, and others (such as are present but
do not belong to the new general concept) being
regarded as such that they must be inserted in these
examples also, and that they are wont to occur only
in certain of its kinds without being of any value.
IO4 OUTLINES OF LOGIC.
All these logical transformations have their correct
use in art, where they are the servants of wit ; and in
ordinary life they are most frequently employed in
excuses, in cases where the intent is to deceive con
cerning the real worth of some action by means of
approximating its content, piecemeal, as it were, as
much as possible toward something innocent. Even
in science they are of the greatest value in the right
place. But proof is always to be demanded that in
the nature of the realities with whose concepts we
are dealing, there lies the possibility or the actual
custom and the effort, of making such transitions.
68. Of every object a variety of concepts is pos
sible, since it can be subordinated to each of its own
marks and to every possible combination of them.
Among these concepts one may be preferred,
namely, that constitutive concept, which we previously
sought for, but found only approximately and in a
few domains, such as in the concepts of species be
longing to the creations of nature.
Nevertheless, the interests of our thinking seldom
require this concept ; and every process of investiga
tion is accustomed only to consider certain single
sides of an object from which it deduces conse
quences in accordance with general laws. Accord
ingly, it is for Jthe most part only a prolixity, and
SOURCES OF SOPHISTRY.
often a source of inaccuracy as well, when we forci
bly aim to have an exhaustive speculative conception
for an object which we are treating ; and then, when
after all we cannot for the most part attain it, pursue
an inaccurate approximation thereto. It is more use
ful to take our point of departure from partial defi
nition, which unites into one general concept only
the properties important for the shifting investigation ;
and then, of course, modifies the consequences that
flow from the subordination of the object under tJiis
general concept, by having regard to the other peculi
arities of the object. Thus, for example, medicine has
to bring man under the concept of a mechanism
consisting of physical elements ; while national econ
omy has to bring him under the concept of capital to
be produced. But both must limit the consequences
drawn therefrom by the reflection, that this mechan
ism and this capital possesses likewise reason and
One of the principal sources of sophistry will be
such partial definitions, in cases where we draw con
sequences from them but neglect to introduce into
them the modifications which are requisite on ac
count of the rest of the nature of the object, although
this is not included in the definition. Little as this
mode of procedure is scientifically permissible, yet
its application is justified in poetry and rhetoric.
CONCERNING THE ADDUCING OF PROOF.
69. In a judgment, what interests us practically
is its truth. Now the simpler case is this, that a
proposition with a definite content is given and its
proof is required ; the more difficult case is this, that
the discovery of a proposition still unknown is de
All adducing of proof to which we now turn our
attention must begin with the demonstration of
the validity in fact of the given proposition. That is
to say, if it is discovered by means of a test which is
made of it either by experience or by single examples,
that it has no such validity whatever, then all pains
taken with adducing proof is wasted. This rule is
not always sufficiently observed, and numberless pro
lixities arise in science as well as in ordinary life from
the attempt to explain facts that is, to demonstrate
them as necessary which have no existence at all.
Only after the validity of the proposition is estab
lished, does the adducing of proof for its justification
begin, that is, the demonstration that it has a right
to be held valid as a consequence of other truths and
NATURE OF AXIOMS.
70. The fact needs no explanation, that all ad
ducing of proof whatever presupposes a number of
propositions which are not, in their turn, in need of
proof, and which are also not capable of such proof.
These propositions are ordinarily comprehended
under the name of axioms. Fundamentally consid
ered, they fall into two classes : the one comprehends
assertory judgments which express certain actual
facts, and which, taken collectively, are derived from
experience and admit only of the above-mentioned
proof of their validity. The other comprehends the
just as undemonstrable principles of reason and con
sequent, in accordance with which alone, from any
fact or truth a conclusion can be drawn to some
other. The latter, strictly speaking, are hypothetical
general judgments, which do not tell what is, but
merely what must be if something else is.
A criterion for affirming that any proposition is an
axiom of the latter kind lies only in the unconditioned
nature of the evidence with which it announces itself
in consciousness as necessarily valid. Nevertheless,
since erroneous prejudgments also can, from a variety
of reasons, unlawfully attain in our mind such evi
dence, it is necessary to test the truth of any propo
sition in question, not merely on its own evidence
but also on that of the impossibility of its contradic
tory opposite. If the latter is not demonstrable, then
IOS OUTLINES OF LOGIC.
the axiomatic and unconditional validity of the propo
sition in question does not stand beyond doubt.
71. Proofs are distinguished, in accordance with
their proximate aim, as direct, which demonstrate
the given proposition immediately, and indirect ( apa-
gogic ), which primarily demonstrate the impossibil
ity of its opposite. Only the first kind are able to
specify, in explanatory fashion, the grounds in right
for the truth of the proposition ; the second always
prove only its validity in fact. In convincing force,
however, the first is not always unqualifiedly to be
ranked as superior to the second.
The direct, as well as the apagogic, proof is uni
formly either a principio ad principiatum, from rea
sons to consequents (progressive, forward-moving) ;
or else it proceeds a principiato ad principium, from
consequents to reasons (regressive, backward-moving).
The different forms of proof that spring out of the
foregoing fact have a very different value ; partly
in general, and partly different according to the do
mains of the content to which they are applied.
72. The direct proof can be progressively (and
therefore in such a manner that the process of think
ing takes the same course, from reasons to conse
quents, as the nature of the thing) carried on in two
THE DIRECT PROOFS.
i) The proposition in question is considered as the
terminal point of a conclusion ; we therefore take our
start from truths that are more general and already
established, and from them, by subordinating other
general or special sub-propositions, deduce the re
quired thesis as a necessary conclusion. This form
is of all most to be preferred ; because it contains,
or may contain, the complete exposition of the thesis.
2) The thesis may be regarded as a point of start
ing, and since it is considered valid, its consequences
developed. If these are at variance neither with
general truths nor with established facts, then the
validity of the thesis is not indeed certain, but
probable. For since all the consequences can never
be developed, it remains possible that, in case we
were to proceed yet further, some contradiction
would still be revealed. As proof of the truth, ac
cordingly, this form is not perfectly stringent. On
the other hand, it occurs in practical life, for recom
mending certain proposals, as a proof of their con
formity to an end.
Rcgrcssively also, ascending from consequents to
reasons, the direct proof may run its course in two
forms. That is to say
i) The thesis in question serves as a point of starting,
and is, therefore, here regarded as a consequent from
which we ascend to its reasons. Now if the reasons
IIO OUTLINES OF LOGIC.
which must hold good, in case the thesis is to hold
good, are in thorough accord with general truths,
then primarily only the conceivability or possibility
of the thesis is demonstrated thereby ; and only in
domains where (as in mathematics) all that is con
ceivable has eo ipso the truth which appears in the
particular case, does such proof include the truth of
the thesis. In relation to everything actual, acces
sory proof would be necessary, to the effect that the
causes are in existence which must actualize the
thesis, as yet in itself only possible. In practical
life, on the other hand, this form of proof is perfectly
sufficient for example to found or defend a legit
imate claim. Finally
2) The thesis can in turn be regarded as the ter
minal point ; and therefore in this case as a reason.
We then take our start from certain other proposi
tions or facts that are known to be valid, and show
that the sole ground of their possibility is to be found
in the validity of the thesis, which thereby is made
necessary. This proof is therefore conclusive, but
is difficult to adduce ; and it often stands in need
of accessory proofs, in order to show that the thesis
is not merely an adequate reason for the aforesaid
facts, but is the exclusively possible and sole reason
THE INDIRECT PROOFS. Ill
73. Indirect proof cannot, strictly speaking,
immediately demonstrate that the opposite of the
given thesis that is, the antithesis is not valid
in fact ; or, in more general terms, the refutation of
a proposition can never be the immediate conclusion
of a proof. For never do anything but merely posi
tive that is to say valid consequences (such as, for
the rest, can consist in affirmative and negative judg
ments) follow from all such principles as could be
chosen for grounds of proof ; and only on account
of the fact that these consequences exclude the an
tithesis, is the latter explained as not valid.
The first progressive form, which sets out from
general truths and shows the antithesis to be im
possible, accordingly cannot occur. What appears
as this, is invariably a direct progressive proof, which
exhibits the necessity of some proposition by which
the antithesis is excluded.
On the contrary, the second progressive form, that
proceeds from the antithesis, which is assumed as
true, to its consequences, and \hefirst regressive, that
proceeds from the same to its presuppositions, are
both of great value as apagogic proofs ( Deductiones
ad absurdum ). They demonstrate the invalid nature
of the assumed proposition by showing that, either
the consequences which would flow from it, or the
reasons which must validate it if it is to be valid, are
112 OUTLINES OF LOGIC.
not compatible with general truths or existing facts.
Now although they do not contain the grounds for
the validity of the thesis whose antithesis they dem
onstrate to be impossible, still they are often to be
preferred to the tedious and involved direct proofs,
on account of the pictorial way in which they show
the absurdity of every proposition contradictory of
The second regressive form would draw a conclu
sion from facts to the impossibility of explaining
them by the antithesis as their ground ; and this
obviously is practicable only in case the necessary
properties of such a ground are first positively de
fined, and it is then shown that the antithesis is
74. Besides the distinctions already alluded to,
a further one is made which has to do with whether
a universal proposition (for example, one concerning
the triangle) is directly proved in its universality, or
in such manner that the demonstration first applies to
all individual instances (first for the right-angled tri
angle, then for the acute-angled, and finally for the
obtuse-angled) and then the proofs are summarized.
Such collective proof requires that we should be in
a condition to enumerate all possible individual in
stances which the general case can contain ; and
PROOF BY EXCLUSION. 113
even when this is done, it always has the disadvan
tage of simply establishing the validity in fact of the
proposition demonstrated for all examples of the
universal ; but it neither proves nor explains how this
validity follows from the proper nature of the univer
sal. Although it is often quite indispensable, since
the nature of a concept or of some general case is
often not so widely known, that we should be able
to recognize the grounds which it contains for the
universal validity of some assertion concerning it.
Related to the foregoing is the proof by exclusion.
This form, likewise, in case of a complete disjunc
tion, enumerates all the conceivable individual in
stances of a general case, and proves of all the rest,
except one, that they are impossible ; so that in case
it is established at all that some one species of the
universal must occur, then this one left rernaining is
Finally, the limitation of a given value between
two limits for example, the proof that a is neither
greater nor less than b, and accordingly equals b
belongs in this connection.
75. In all the forms of proof alluded to, we
have assumed that the conclusion follows as to the
whole, according to the first figure, that is, by sub-
sumption of one proposition under others. We
1 14 OUTLINES OF LOGIC.
speak of the proofs by analogy and induction fur
This being presupposed, the question may arise,
how proofs are discovered, by which we mean,
the superior propositions on which the validity of
the proposition in question depends ; as well as
how the inferior propositions or auxiliary construc
tions are divined by whose mediation the latter
flow from the former.
On the whole, Logic cannot teach how to dis
cover such proof; but it can only admonish us
that in every science stereotyped methods of proof
for the single groups of related problems are de
veloped, which put every one, who understands how
to bring a problem under its own group, upon the
right way. Besides this only one indication is
possible, namely, that the ground for the truth of
a proposition, which expresses not merely a fact, but
some mode of procedure that is dependent on other
truths, must invariably be contained in the content
of the proposition itself, when the latter is perfectly
thought out. Synthetic judgments cannot be given
in such a way as to add to the subject S a predicate
P, which is neither contained, nor has its ground,
in the complete concept of S. Such a predicate
would be false. All correct judgments are as re
spects their content, analytic ; or rather they are
SERIES -OF PROPOSITIONS.
identical and merely appear synthetic in form,
since one and the same content can be designated
in both subject and predicate, from points of view
that are very different and arbitrarily chosen. Ac
cordingly, in order to find the proof on which the
correctness of a proposition is founded, one must
analyze subject and predicate and the combination
between the two, and add all the latent accessory
thoughts which are meant thereby ; in this way one
will see in this complete content of the proposition,
for the most part, its own proof of itself.
It frequently proves of advantage to consider as
not yet valid the subject of the thesis, or the prem
ise to which this is attached as a consequent ; and
to let it originate from another subject or another
premise whose predicate or conclusion has already
been established. In this way it is more easily
shown how, by the changes of this other subject
into the one in question, the predicate in question
also originates from this other. If the different
instances of a universal proposition constitute a
series, as often happens in mathematics, this
proof takes the form of a proof from n to (n + 1) ;
in such manner that the given thesis is first verified
for some special case or value of n, and then it is
shown that, in the formation of each next case
(n -j- 1) from the case n, the conditions, by virtue
Il6 OUTLINES OF LOGIC.
of which the proposition of n holds good either are
maintained unchanged or are reproduced, or else
equivalent conditions take their place.
76. The Fallacies in proof, which logic, alas !
can only mention and not teach us to shun, are the
Petitio principii, or the circle in proof (Diallele)
is committed, in case what is only some other expres
sion for it, or some consequence of the conclusion
which is first to be demonstrated, is employed as an
Fallacia falsi medii (Quaternio terminorum) con
sists in the fallacy of taking, in one of the conclusions
that constitute the proof, the medius terminus in
both premises, in a different signification. The
inducement to this is not far to seek in the case
of abstract conceptions, whose signification has
equivocal elements ; and also in the case of such
empirical concepts (to which allusion has already
been made) as are likewise formed by abstraction
in accordance with different points of view.
In this connection the Fallacia de dicto simplici-
ter ad dictum secundum quid may be referred to ;
that is to say, the fallacy of applying a proposition,
which in itself holds true universally and absolutely,
to definite circumstances, without limiting and modi-
KINDS OF FALLACY.
fying it in such a manner as these circumstances
require. This fallacy is in ordinary life the princi
ple of Doctrinairism and unpractical Idealism, of
riding principles horseback. Conversely, the Fal-
lacia de dicto secundum quid ad dictum simpliciter
extends a principle, valid in a single instance, to
all instances, even to such as are lacking in those
conditions that give grounds to or recommend its
validity. In practical life this is the principle of
pedantry and philistrosity.
Nimium probare, and therefore nihil probare,
is the fallacy of demonstrating the validity of a
proposition, not merely for the subjects and cases
for which it holds good, but also for others for which
it does not in fact hold good, or should not hold
good. The fallacy comes from the choice of a false
argument, or from an otherwise correct argument
not being limited to those of its sub-species which
alone perfectly contain the ground for the validity
of the proposition. Parum probare is in itself only
a fallacy of method, because that which is proved
is correct. It becomes a logical fallacy only when
the validity of the proposition which is demonstrated
for a number of cases, is at the same time appre
hended as a negation of its validity in the other
cases, in which it in fact also holds good.
Hysteron-proteron (va-repov irporepov), in dis-
Il8 OUTLINES OF LOGIC.
tinction from petitio principii, is the awkwardness
in method which from two propositions A and B,
that may be in turn deduced from each other, makes
that one the ground of the proof which would be
more fitly exhibited as the result of the other.
Finally, Heterozetesis (erepov tyrrjo-is), or Ig-
noratio elenchi, is the complete aberration of the
proof, arriving at a conclusion which was not to
be demonstrated at all.
77. Finally, we distinguish Paralogisms ( erro
neous conclusions ) as undesigned fallacies in proof,
from Sophisms ( fraudulent conclusions ), that
is to say, thoughts designedly so combined that from
them, in a way formally correct, either something
wholly absurd and false originates, or contradictory
assertions flow from them with equal correctness.
The first case, again, always depends upon designedly
committing some one of the customary fallacies in
argument. The others, the so-called Dilemmas
that were specially celebrated under that title in
antiquity (the liar/ the crocodile, etc., comp.
46 at the end) originate in this way ; the content
of a judgment A, which .taken logically by itself
must be either correct or incorrect (without any
regard to the circumstances under which it is ut-
KINDS OF FALLACY.
tered, or to facts not as yet established) is never
theless apprehended as though it were conditioned
in its meaning or in its validity, by just those cir
cumstances ( the liar ) or by these not yet estab
lished facts ( the crocodile ).
THE PROCESS OF THOUGHT IN DISCOVERY.
78. The second problem, to which allusion was
previously made ( 69), namely, to discover some
general proposition divides again into several, the
first of which is the discovery of a universal judg-
ment, that comprises a number of particular facts.
This may take place either in such manner that the
same content which a single fact expresses is demon
strated as valid in general for all instances of its re
currence ; or in such manner that a more general
proposition is sought for, which embraces within
itself as classes all the given facts.
79. The first case only furnishes us the occa
sion to observe that the assertions " Experience
teaches nothing universal"; and "What is correct
in one case need not be so in another," are not
rightly made. Quite the contrary, it follows from
the law of Identity, that a truth which is valid once
cannot fail to be valid a second time ; accordingly,
that every individual experience is once for all valid,
that is to say, the same predicate is again valid
at all times for all cases of the recurrence of the
THE IMPERFECT INDUCTION. 121
The difficult thing is simply to determine in praxi
whether a second instance does actually repeat pre
cisely the subject observed in the first case. For this
the probabilities are different in different domains of
research. For example, it is enough for the chem
ist, if he once knows that he has some element be
fore him in a pure state, to observe its reaction
toward some other element a single time, in order
to establish it forever. The zoologist, on the con
trary, will hold some peculiarity of a new animal,
only one example of which has been discovered, to
be normal, that is, to be valid in general (since
disease and malformation are possible in such a
case), only when the analogies of other classes of
animals justify him in this assumption.
80. The second problem would be to deduce a
general judgment of the form "All S are M"
from individual perceptions, which (as previously
alluded to) bear the form : P is M, Q is M, K is M,
etc. This is the simple conclusion by imperfect In
duction, to which allusion was previously made.
It was shown in the Pure Logic that this induc
tive conclusion serves for the widening of our knowl
edge only in case it is imperfect, that is to say,
it follows, without strict conclusive force, from the
fact that some kinds of S have the predicate M,
122 OUTLINES OF LOGIC.
that all kinds of S possess it. The precautionary
rules, which would be required to make the con
clusion at least as probable as possible, are simply
With the rising number of cases in which M oc
curs among the species of S, the probability that it
belongs to all S increases of itself. Nevertheless,
every circle of human experience is limited, and we
can at least never be sure from that which we learn
to know only by experience, whether we are not
merely getting a view of certain particular species,
nearly allied, which do indeed all possess the predi
cate M, and yet do not possess it by virtue of their
general concept, but on account of their other con
cordant special marks. For this reason it is neces
sary to show that the M, which we wish to ascribe
as universal to the concept S, occurs not merely
in the case of very manifold and very diverse species
of the S, but also occurs specifically in the case of
such pairs of them as are related to each other,
with reference to some mark which can be depended
on for having some influence on the establishment
of M, in the most contrary fashion possible. It can
then be concluded that the reason for M, or for the
subject to which M belongs, can only be some ge
neric concept like S, which is common to all the
MORE COMPLEX PROBLEMS. 123
81. This same problem is much more important
for us in another form. That is to say, it is only
rarely of much use to us to show that a P is united
with a general generic concept S, and belongs to all
species of S. As a rule, we desire still further to
know on what ground P belongs to S. This, ex
pressed in general form, leads to the problem of
searching for the conditions on which the occur
rence of an event depends in all the otherwise di
verse instances of its repetition.
In experience we almost uniformly meet with a
complex of diverse facts, a + b + c + =U, with
which another just as composite complex, a + /3 + 7
+ = W, stands in combination. The problem is
to ascertain whether in general U is the condition of
W, and what particular part of TJ forms the condi
tion of what particular part of W.
The means for such investigation are, either the
facts which observation yields spontaneously, or like
wise such others as we add by experimentation.
Observation, for the most part, shows us effects
which depend on a large number of conditions at
the same time ; many of which, moreover, are wholly
withdrawn from observation. The main end of ex
periment does not consist simply in multiplying facts,
but in permitting only a fixed and accurately known
number of conditions to be in every trial. Experi-
124 OUTLINES OF LOGIC.
ment further consists in separating these conditions,
whenever it is possible, so that in every trial only one
is active, and yields an unmixed result, or, at least, so
that in every trial only a small number of conditions
co-operate, and, accordingly, the part of each single
condition in the collective result admits of being
determined by comparison of the different trials, in
the way of elimination. Finally (a matter concerning
which we shall speak later), experiment especially
seeks to secure the measureableness of the magni
tudes of the conditions and of the results.
82. The following general cases serve simply as
examples of investigation :
1) If W (the effect) uniformly follows upon U (the
cause), then it is possible that the reason for W lies
in U ; and it remains a matter for inquiry whether
the whole of U furnishes the reason for W, and
whether some other condition besides U, that is
uniformly connected with it but unobserved, is not
necessary in addition. But it is just as possible
that U and W are ^-effects of a common cause, Z ;
and also possible, finally, that TJ and W occur to
gether by a merely fictitious coincidence, without
any causal connection whatever.
2) After TJ has occurred, W is sometimes wanting.
Then U either is not the cause of W, or U and W
CAUSES AND EFFECTS. 125
are ^-effects of (Z Y) ; so that W occurs if Y is
positive, and not if it is negative ; or TJ is certainly
the adequate, and perhaps the only reason which can
produce W ; but there is in the cases that occur
some hindrance which prevents U from producing
its uniform result.
3) Suppose that W occurs before, or without, U.
Then there is either no connection between the two,
or the two are again co-effects of (Z Y) ; or, finally,
TJ is not the only, although the quite sufficient,
reason for W, but there are other equivalent rea
4) Suppose that U falls out or is experimentally
removed, and then W does not follow. In this case
it is either a mere coincidence, without real connec
tion (which is, however, extremely improbable, and
is only to be assumed in observation, and not in
experimental treatment) ; or TJ is, or contains, the
condition of W (which is most probable) ; or, finally,
TJ and W are r<?-effects of Z, and the same interfer
ence which hindered Z from producing TJ, hinders
also the production of W.
5) If TJ vanishes or is removed (experimentally),
but W remains, then there is either no nexus be
tween them, or they are again ^-effects of Z ; but
this time in such manner that the interference with
Z, which hinders TJ, permits W to exist ; or else TJ is
126 OUTLINES OF LOGIC.
the cause of the origin of W, although not the cause
of its continuance.
The proposition " Cessante causa cessat effectus "
is false in this general form (indeed, if it were not
so, all our labor and action in the world would be
illusory). In general only those effects vanish with
the vanishing of the cause, which the cause would
further have had in case it had not vanished. Effects
already produced, on the contrary, continue after the
cessation of the cause, in so far as they consist in
states of things which are not in contradiction with
the proper nature of things and with the external
conditions in which they stand. Only in the opposite
case would they need a maintaining cause ; and this
is then, besides, not always the same as the produ
6) Further, in case the part a disappears from TJ =
(a + b + c) and W is not altered, then one condition
of the continuance of W does not lie in a, although
perhaps the condition of its origin may. Conse
quently, we have to investigate, where it is possible,
whether b -$- c alone produces W ; in which case a
would be a superfluous part of TJ.
On the other hand, if the whole of W disappears
with the vanishing of a, then a alone may be the
sufficing condition of W. Such condition, however,
may just as well lie in the entire sum (a + b + c),
CAUSES AND EFFECTS.
so that W always vanishes whatever part of U is
removed, but does not depend on any one of them
alone. This is often overlooked ; for example,
when some one part of the brain, a, after the de
struction of which a function W ceases, is physio
logically considered as the sole organ of W.
7) If two different complexes of causes TJ = (a
+ b + c) and V = (m + n -f c) produce the same
effect W, then W will for the most part undoubtedly
depend on the c common to both. Still it is possible
that c is quite without any direct significance ; and
that, on the contrary, (a + b) and (m + n) furnish two
equivalent pairs of causes, in which one and the same
condition for W is only differently distributed to the
8) Finally : if again (compare what is said under 6)
U = (a + b + c), and W also vanishes with the re
moval of a, then a may be the sole cause of W ; but
it is also possible that such cause lies only in c, but
b is a hindrance to the efficiency of c, which was, on
its side, balanced by a.
The foregoing possibilities might be indefinitely
83. Now tne ascertainment of the fact that any
particular a is the condition of some a or other, does
not give us satisfying knowledge, as long as we are
128 OUTLINES OF LOGIC.
unable to subsume under such a proposition certain
others, not wholly like it but only of similar kind ;
that is to say, as long as we do not know according
to what general law a is changed by a fixed difference,
in case a is also changed by another fixed difference.
Now since determinations of number merely, and
not marks of quality, are deducible from each other
in thought according to general laws, the problem is
as follows ; to seek for the law according to which
the values of the magnitude of the results depend
upon the magnitudes of the conditions belonging to
them. This is a problem which must be solved for
the most part experimentally.
84. If it is found that, when the magnitude of the
condition remains uniformly the same, or increases
uniformly or diminishes uniformly, the results de
pendent on it do not alter their values in a perfectly
parallel way ; but for example when the value of
a increases, that of a for some time increases, and
then while a keeps on always increasing, assumes a
diminishing value : then this is a proof that a alone
does not contain the complete reason of a, but that
still other conditions co-operate ; and that these either
consist in accessory conditions which are independ
ent of a, or in alterations which the object affected
by a experiences through the earlier influence of a,
USE OF HYPOTHESES. I2Q
and which oppose resistance, sometimes uniformly
and sometimes periodically, to the further influence
In all such cases as the foregoing, there is a de
mand for a further preliminary investigation. For
although we can often discover very simple general
laws for the course of such a composite effect, as,
for example, the laws of Kepler show ; yet after all
we can only grasp perfectly the whole of it, in case
it can be demonstrated as the resultant of a combina
tion of single effects, whose laws are such that a
constant increase in the result belonging to it always
corresponds to the constant increase of each single
condition. The place of such a preliminary investi
gation is in part supplied by a further employment
of the previous artifices, and in part by hypotheses.
85. If we have discovered experimentally a series
of corresponding values for the conditions and the
results, then the intricate nature of the thing some
times compels us (for example, in many problems of
statistics), inasmuch as many conditions that are
changing independently of each other always co
operate, to confine ourselves to the collection in tab
ular form of the appropriate material.
On the contrary, where it is possible to make the
transition to a general law which expresses the de-
I3O OUTLINES OF LOGIC.
pendence of every member in the series of results
upon the corresponding member in the series of con
ditions, this transition always remains a kind of logi
cal saltus. For no measuring, since it all invariably
depends upon nothing but the sharpness of our per
ception by the senses, gives us absolutely accurate
numbers. Accordingly, if the series of values dis
covered for the results accords accurately with that
calculated by a general formula from the values of
the conditions, it is only extremely probable but not
certain that such formula is the correct law. If it
does not agree with them, but must be corrected in
order to agree, then it is possible that another cor
rection would make it explicable with equal facility
by another law. Nevertheless, if perfect certainty is
wanting, still a probability, which is to be estimated
as quite equal to it, may be attained for the correct
ness of a law. This is principally done by measuring
the discovered series of values according to different
standards of measurement, and arranging the experi
ments so that the dependence of the results on the
conditions is subject to observation from different
points of view. If the same formula fits in all such
altered expressions of the thing, then it will be the
86. On this account, the discovery of a general
law is frequently called an Hypothesis.
CRITERION OF SIMPLICITY.
We employ this word in a more limited meaning.
Hypotheses are conjectures by which we endeavor
to divine something real that is not given in percep
tion, but of which we make the supposition that it
must be existent in actuality, in order that what is
given in perception may be possible ; that is, may
be comprehensible in the light of those laws of the
connection of Things which are recognized as
Among the rules, by following which we endeavor
to give the greatest possible certainty to hypotheses,
it is incorrect to lay down the general one, that sim
plicity is a criterion of truth. We must rather dis
tinguish the nature of the cases. If we have to do
with establishing by hypothesis a relation which is
very general and which unites almost all that is
actual, then simplicity is most probably the correct
thing. On the other hand, to explain a fact which
manifestly depends on very many co-operating con
ditions, a very simple hypothesis about it only awak
ens the suspicion that all the difficulties of the matter
are not observed, and therefore not explained.
As for the rest, no rules can be given which assist
the intelligent process of discovery in the formation
of hypotheses, but only certain ones which limit it.
It is of use in the first place, to make it perfectly
obvious, what are the demands which some matter of
132 OUTLINES OF LOGIC.
reality, when hypothetically assumed, must necessarily
fulfil, in order to satisfy the phenomenon that is to be
explained. This admits of being established with
a perfect cogency by concluding backwards from the
phenomenon itself. From these abstract but unques
tionable parts of the hypothesis, a further special elab
oration of it is to be distinguished, which endeavors
to divine the concrete matter of fact in which the
aforesaid demands are found to be actually fulfilled.
Very often several such matters of fact are possible.
The hypothesis should not blindly choese the one
which first falls in our way ; but it must previously
survey the entire domain of related phenomena, in
order to ascertain what kind of matter of fact is wont
to occur therein.
Now if a hypothesis has been framed with this ref
erence to a rather large number of related phenom
ena, then it very often happens that the progress of
experience contains new facts, for whose explanation
the previous hypothesis does not suffice. It must,
accordingly, be altered by new additions. This build
ing of hypothesis on hypothesis is not to be avoided
in the course of our scientific labors ; and, on this
account, it is incorrect to forbid it. Only it is cer
tain that the investigation is not to be regarded as
ended until these hypotheses, composed piecemeal,
at last admit of being gathered together again into
FICTIONS IN ARGUMENT. 133
one simple assumption corresponding to the sim
plicity of the thing itself.
Finally, the rule " not to frame any hypothesis
whose content lies beyond the borders of a possible
counter-proof" is indeed an excellent one; but in
many domains of investigation, exactly where we are
most in need of hypotheses, it is not practicable.
87. Hypotheses are conjectures by means of
which we suppose that we are divining an actual
matter of fact. Fictions are assumptions which we
make with the consciousness of their incorrectness.
We are compelled to resort to fictions, when for
example, in practical life judgment must be passed
upon a case which does not exactly fall under any
single known rule ; we are then compelled to indicate
it in such a way that it can be subsumed under that
rule which is recognized as over some content most
nearly related to its own.
We are further compelled to adopt fictions, when
in science there are no modes of experience which
admit of a direct application to the data of some prob
lem before us. In this way, for example, curved lines
are regarded as interrupted straight lines (which they
never are), and reckoned accordingly.
In both cases it is, of course, necessary to correct
the consequences which flow from the general ground
134 OUTLINES OF LOGIC.
of judgment assumed by the fiction, with reference
to the fact, that the case in hand is not exactly sub
ordinated thereto. And on this supposition, fictions
lead for example, in mathematics back again to
exact results and not merely to approximations.
Finally, fictions are very frequently, besides, em
ployed as means of illustration, with the purpose of
bringing intricate relations, that obviously, as frequent
perception shows, belong to some case a, to apply to
a case to which possesses relations that, although not
wholly the same, are essentially similar.
88. Fictions of themselves lead to the procedure
called Analogy, which, although it does not propose
to extend a proposition to a subject that is certainly
not to be subsumed under it, still does transfer a
proposition from one subject to another, on account
of the similarity of the two.
This procedure depends upon the perfectly cogent
principle, that what is like must under like conditions
assume like predicates, and under unlike conditions
unlike predicates ; just as what is unlike must under
like conditions assume unlike predicates.
But the first half of this proposition avails nothing
for the extension of our knowledge; and the other
only slightly, because it yields no positive result, but
only teaches us that the predicates are not like.
REASONING BY ANALOGY. 135
Accordingly, such principles, strictly speaking, are
productive only in mathematics, where it is possi
ble to determine the degree of the unlikeness of the
subjects and that of the conditions, and consequently
also to reduce the unlikeness of the predicates to a
definite measure, and to give them a positive content.
Outside of mathematics, the principle that what
is similar assumes similar predicates under like con
ditions, although always correct in abstracto, is still
a very difficult one to apply ; and after all, every
thing comes to this, that we gather from it what
group of marks (x + y) is present in A as a cause of
the predicate P being attributed to the A. For if
P is to be transferred from A to some B, on account
of the similarity of the two subjects, then B must
be like or similar to A in relation to (x + y) ; that
is to say, must have this group of marks in common
with A; in which case, on the contrary, all other
similarity of A and B is of no avail whatever.
Now that (x + y) is the condition of P can be
demonstrated partially on other grounds ; and, in
case P is ascribed to the subject B, is no longer
a conclusion from analogy, but a direct sequence.
If such proof can not be adduced, then different
subjects must be compared as far as possible : and
it must be shown that all their other similarities
cannot produce the common predicate P, unless
136 OUTLINES OF LOGIC.
(x + y) is a common constituent of all the subjects;
and that, on the other hand, difference of the marks,
otherwise, does not destroy the common character
of P, as long as (x + y) remains common to all the
subjects. From this, finally, the conclusion is drawn
with a satisfactory degree of probability, that the
predicate P will belong to all subjects in which
(x + y) is found.
89. The other kind of problem ( 78) is this,
to demonstrate the reality of a single fact.
Three different points of starting may be discov
ered for this purpose. That is to say, we have be
fore us given facts which we can apprehend either
as causes, or as results, or as accompanying signs
of the fact in question.
In none of these ways is a strict demonstration
possible. For even if what is given always contains
the complete cause of what is to be proved, yet this
cause after all since we are here not dealing with
valid truths, but with actual occurrences may be
hindered by counter-forces from the production of
its effect. But if what is given can be explained
from what is to be proved, as its result, still it is
never demonstrable with such perfect cogency that
other equivalent causes could not also be assigned
for the same given fact. Finally, that the mere
PROOF BY INDICIAE. 137
reciprocal companionship of two facts, because it
ordinarily occurs, does not establish any certain con
clusion from one to the other, is self-evident.
90. The general principles, in pursuance of which
we try to give as much of probability as possible to
this proof from indiciae, depend upon the follow
ing general views.
In reality a multitude of different causal nexuses,
which do not issue from one principle, constantly
run on side by side. Now it is not probable that
any one of them will, escaping all disturbance from
the others, produce the effect, abstractly belonging
to it, in its entirety and without abatement. On
this account, finely spun plans, which do not have
regard to accidents, appear to us in practical life
convicted of folly ; and in art and history all repre
sentations appear improbable which make an intrigue
succeed in all its results, or an important factor ac
complish all its theoretically correct results for hun
dreds of years together.
But, on the other hand, it is just as improbable
that an extraordinarily great multitude of causal
nexuses, independent of each other, should have in
tersected each other in such a manner as to pro
duce exactly one special matter of fact that, in the
form in which it exists, is comprehensible from some
138 OUTLINES OF LOGIC.
single other cause. Accordingly, we do not believe
in the efficiency of a thousand minute causes for the
production for example, in history of a result
which flows of itself from some one direction of
the Zeitgeist, so-called. Nor in medicine do we
credit the view, that every symptom of a patient
has its separate harmless cause, as soon as the sum
of all the symptoms exhibit the unity of a disease/
as arising from which they are all comprehensible.
Just so in jurisprudence we do believe in such a
diabolical concatenation of a thousand minutiae that
from them the appearance of single coherent crime
91. The importance of the single indiciae is
estimated according to the same rules as in cases
of inductive proof ; consequently, the probability of
the instance to be proved is referred back to internal
grounds of actual fact.
Now there are instances enough where the proba
bility of the occurrence of an event cannot be judged
at all from grounds of mere fact ; either because, as
in the case of future events, we do not by any means
know them all, or because it would take us into
details too much to estimate actually even the part of
them that is known. Here, however, it may not be
necessary to have an opinion about the occurrence
GROUNDS OF PROBABILITY. 139
or non-occurrence of the event, in order to base upon
it some practical procedure. Nothing remains for
us in such a case but first to enumerate together,
as precisely alike possible, all the possible instances
for the occurrence of which wholly like reasons tes
tify ; and then to ascribe to each of them a like
probability of its occurrence, or else (in case of prob
lems where we are dealing with a manifold repeti
tion of analogous events) the same frequency of ap
pearance. Its probability is therefore measured by
a magnitude which divides the certainty that some
one case must occur (which is here put at unity)
by the number of all the cases alike possible with it.
This probability is distinguished from that pre
viously discussed, which rested on grounds lying in
the very nature of the single case, as one which
occurs precisely where no such grounds exist. It is
in no respect a theoretical assertion about what will
actually occur in the future. For nothing prevents,
in spite of the calculation, the one case from always
occurring, and all the rest of the equally possible
cases, from not occurring. Such probability is rather,
in reality, a practical standard by which we endeavor
to determine the measure of the future confidence
that ought still to be cherished in the occurrence of
a definite single event among many that are alike
I4O OUTLINES OF LOGIC.
92. The purely logical interest taken in choices,
votes, etc., does not consist merely in the attaining
of some result, but also in this, that each of the
single judgments from which it is to be attained
(that is, in this case, each opinioii] should find oppor
tunity for a complete and direct expression. Prac
tical interests, on the contrary, and the considera
tions which are had besides in both cases, are
opposed to this in many ways.
The logical interest is perfectly satisfied only when
a choice is direct, that is, when it relates only to
one object of choice, is followed by aye and no,
and accordingly makes it possible to give an unmixed
expression to the negation. All other choices, which
are directed to several objects of choice at the same
time, which are followed merely with positive votes,
and therefore permit the negation of the one ob
ject to be made only by affirmation of some other,
are logically deficient. They do indeed furnish a
result by means of the majority. But it remains pos
sible that some other result would have satisfied in
like manner the collective will of those voting ; since,
although the result actually reached is somewhat
preferable to the majority, it is on the contrary de
cidedly disagreeable to the minority ; while the other
result would have been scarcely less agreeable to the
majority and the only one agreeable to the minority.
THE LOGIC OF VOTES.
It depends upon the nature of the relation which the
choice induces, whether the more decided satisfaction
of the majority, or one less perfect but more equal
ized among the entire collection of choices, is to be
As a purely logical question it is taken for granted
that the constituency of voters all vote together on a
certain matter (that is, as united into one collection),
and form only a single decisive majority. On prac
tical grounds, however, they are frequently divided
into a multitude of groups to be treated separately,
and the establishment of the definite result of the
choice follows on the ground of the majorities which
appear in the single groups ; so that, if the vote for
a candidate should be taken by aye and no, he
would be chosen as soon as in case the whole were
divided into nine groups he had for him five of
these groups (each one, according to its majority).
It can easily be understood that in this way the
decision may be reached by a minority of those
entitled to vote at all in the matter on hand. If
we divide 100 votes into 10 groups of 10 each, or
into 20 groups of 5 each ; then we have, in the first
case, 6 X 6 = 36, in the other 11X3 = 33, as the
number of votes necessary for a decision, instead
of 51, which without this partition into groups, in
case the 100 voters gave their vote together, would
142 OUTLINES OF LOGIC.
be required for a majority. It can be calculated that,
under such circumstances, the number of votes nec
essary to a decision may perhaps fall as low as a
quarter of the whole number. And a still smaller
number is sufficient, in case the number of the votes
is not placed as equal (as we have done hitherto),
but different, in the single groups.
93. In voting on proposals for laws, which seek
to satisfy one and the same necessity by formulating
it in ways different and exclusive of each other, the
usage employed accords, strictly speaking, at only
one point with the logical interest. That is to say,
if the voting assembly wishes not to recognize in
principle the general thought which underlies all
these ways of formulating it, or the necessity itself ;
then this cannot be satisfactorily done by successive
negations of the single proposals, but only by a
1 motion to fix the order of the day/ which must
always be established as soon as such a vote of the
whole body is expected.
From this point on, however, the logical procedure
must either be such that a decision must be reached
by an aye-and-no vote upon every proposal of the
kind, and that one of them all retained which gets
the majority of affirmative votes ; or else, at least,
one of the proposals must first be selected by merely
THE LOGIC OF VOTES. 143
the votes in favor of it, without any further issue,
so as to make obvious what is the condition of opin
The actual procedure is frequently much more
speculative as to its want of obvious significance, or
at least admits the existence of such speculation.
For whatever the order of questions may be, yet
custom hinders, by the affirmative of any question
of all those that follow being excluded from the
vote, as well the free expression of opinions as also
the attainment of a result that is wholly accommo
dated to them. For every aye or no has in this
case a double significance ; either it means a choice
(or non-choice) of the individual proposal in itself
considered, or an affirmative (or negative) for it from
fear (or hope) of defeating (or carrying) by this
means some subsequent less (or more) agreeable
measure. Accordingly, the procedure passes out of
the purely logical domain into that of practical politi
cal calculation and trickery.
ENCYCLOPEDIA OF PHILOSOPHY.
1. Philosophy should not be considered as an
employment of the thinking faculty, which attempts
to solve problems of its own, that are otherwise wholly
unknown, by means and methods just as peculiar and
otherwise unheard of ; and which, therefore, makes
its appearance as a kind of luxury superfluous to
our real life. The rather is it nothing else than the
strenuous effort of the human spirit, by a coherent
investigation, to find a solution, that is universally
valid and free from contradictions, for those riddles
by which our mind is oppressed in life, and about
which we are perforce compelled to hold some view
or other, in order to be able really to live at all.
Life itself involves, in that which we are wont to
call education, numerous attempts at such a solu
tion. As well concerning the nature of things and
their connection under law, as concerning the grounds
of beauty in phenomena, and, finally, concerning the
146 ENCYCLOPAEDIA OF PHILOSOPHY.
rules obligatory for human conduct, education is
accustomed to establish a number of trains of thought
that excite a great interest on account of the liveli
ness and warmth which they possess as witnesses,
not for unprejudiced reflection but for life s immedi
ate experience. Their disadvantage, however, con
sists in this, that they are not connected systemati
cally together, are often contradictory of each other,
and are as a rule interrupted before they have at
tained the ultimate ground of certainty. Aroused
by certain events, which happen to one man in one
way and to another in a different way, all these reflec
tions retreat in a lively manner some steps backward,
in order to" discover the reasons that will explain such
experiences. They then ordinarily come to a halt,
and regard as sufficiently ultimate principles certain
points of view, which themselves include what is yet
more of a riddle. It is natural that many such trains
of thought, setting out as they do from different
points of view, should not coincide in one whole but
leave gaps and contradictions between them.
The same relation maintains itself with the indi
vidual sciences. They attach themselves to single
domains of actuality, and are satisfied when they
discover principles which are constantly valid within
such a domain, but which at once become doubtful
in their application on being carried over to any other
EXISTENCE OF TRUTH. 147
domain. Thus the conception of a cause that acts
according to law is undoubtedly valid in physics.
But the consideration of organic life, as well as ethi
cal speculations, frequently oppose to it the concep
tion of a cause that is determined only by its ends
and not by laws, or of one that acts with a complete
freedom. It is the problem of philosophy to deter
mine the claims of these different principles and the
circuit within which they are valid. Accordingly it
admits, for the present, of being defined as the en
deavor, by means of an investigation which has for
its object that which is the principle of investigation
in education and in the particular sciences, to estab
lish a view of the world that is certain, coherent, and
of universal validity.
2. To this entire undertaking two presupposi
tions are necessary.
The first is this, that there exists in the world at
large a truth which affords a sure object for cog
nition. This assumption has seldom been called in
doubt. To its denial there stands opposed, princi
pally, the moral conviction that without such truth
the world would be absurd ; and that the world can
not after all be this.
The other presupposition is, that we are in a con
dition to apprehend this truth, although by no
148 ENCYCLOPEDIA OF PHILOSOPHY.
means necessarily the whole of it ; and yet some
part which shall serve us as a firm basis for an in
vestigation that is not perfectible in particulars.
In opposition to this assumption, doubt arises in
three forms :
a) A Scepticism that is without motif raises the
question whether, at last, all may not be quite dif
ferent from what we are necessarily compelled to
think it. This doubt we pass by. For since it does
not arise out of the content of what is necessary to
thought, but only demands in a general way some
pledge for the truth of our thinking, that lies out
side of all our thought, no satisfaction can ever be
given it, but it can only be overcome by a conviction
of the absurdity of its own content.
b) A second kind of Scepticism, with a motif,
endeavors to show that the thoughts which we are
compelled to think according to the necessary rules
of our cognition are frequently impossible according
to rules just as necessary; and, therefore, that what
is a necessity to our thought does not lead us to any
true knowledge. Such doubts are not to be refuted
or confirmed, without investigation. We derive from
them simply the rule of circumspection, accurately
to test the most general conceptions and principles
which appear to us as necessities of thought ; to sep
arate what they in truth mean and prescribe from
SCEPTICISM AND CRITICISM. 149
the more special and not necessary adjunct thoughts,
such as have attached themselves to the former dur
ing their application to limited circles of objects ;
and then to see whether, in this way, the contradic
tions are made to vanish.
c) As related to scepticism and derived from it,
Criticism endeavors to establish cognition more
securely, since it premises an investigation of the
nature of the faculty of cognition, and thereby seeks
to determine the limits of the validity of our forms
of cognition, previous to their application to their
objects. Nevertheless, although a preliminary ori
entating of ourselves concerning the origin and
connection of our knowledge may guard us against
many vain undertakings, yet we cannot regard the
undertaking of criticism as anything more than a
petitio principii. That is to say, previous to the
application of knowledge to things, we cannot do
anything but become conscious of those grounds
of judgment which our reason contributes to the
consideration of things as necessities of its thought.
Whether these principles are applicable to things
themselves, does not admit of being decided in a
preliminary way from the history of the genesis of
our cognition ; because, in order to have such a his
tory at all, one must necessarily already have taken
one s point of departure from actual presuppositions
150 ENCYCLOPEDIA OF PHILOSOPHY.
concerning the nature of things cognizable, concern
ing the nature of the cognizing spirit, and concern
ing the kind of reciprocal action that takes place
3. We therefore enter upon our philosophizing
with the confidence which reason has toward itself,
that is to say, with the principle that all propositions
which remain, after the correction of all accidental
and changeable errors, as always and universally
necessary to thought, are put by us at the founda
tion of everything as confessedly true ; and that
according to them must our views concerning the
nature of things be determined, and from them alone
must a theory of our cognition be obtained.
But as concerns the way which we are to take
in our philosophizing, two views are distinguished.
Both are at one so far as this, that the world itself
must be a unity ; and consequently the perfected
cognition of it mus-t be, as it were, a closed system,
which can contain no parts that are not united, or
that stand toward each other without any ordering
One view, however, believes that it is both able
and obligated to divine at the beginning the One
Real Principle, on which the world actually depends,
and from it to deduce or construe the entire actuality
INVESTIGATION OF TRUTH.
as the sum of its consequences. Such a beginning
for cognition would be the best if we were gods.
On the contrary, as finite beings, we do not ourselves
stand in the creative centre of the world, but eccen
trically in the hurly-burly of its individual sequences.
It is not at all probable and is never certain, that we
should perfectly divine the one true Principle of the
world in any one fundamental thought, however
noble and important, to which some sudden intui
tion might lead us ; still more uncertain that we
should formally apprehend it so accurately that the
series of its true consequences should obviously pro
ceed from it. It is rather altogether probable that
the first expression of the principle will be defective,
and that mistakes will always multiply in the course
of the deduction ; since one has regard to no inde
pendent point of view from which they might be
The second view of which we fully approve
distinguishes the investigation from the exhibition
of truth. The mere search for the truth is by no
means under the necessity of taking its point of
departure from one principle, but is justified in set
ting forth from many points of attachment that lie
near each other. It is only bound to the laws of
thought, beyond that, to no so-called method
whatever. All direct and indirect means of getting
152 ENCYCLOPEDIA OF PHILOSOPHY.
behind the truth must be applied by it in the freest
manner possible. The latter, however, the exhibi
tion of truths already gained has only to satisfy
the need for unity and systematic coherency. But
for it, too, this is a problem of which we do not
know beforehand in how far it is solvable.
4. A preliminary division of Philosophy may be
attempted simply with the design of separating the
different groups of the problems, each one of which
appears to be self-coherent and to require an inves
tigation of a specific kind. We attribute little value
to the reciprocal arrangement of these single groups
under each other. In the history of science, too,
names for these single groups are customary before
any definite usage as to their systematic arrange
Two domains are now, in the first place, distin
guished. We require, on the one hand, certain in
vestigations concerning that which exists ; and, on
the other hand, concerning the value which we attach
to what is actual or to what ought to be. We now
see that nothing in relation to its value follows im
mediately from insight into the origin and continued
existence of anything actual whatever ; and nothing
in relation to the possibility of its being actual fol
lows from insight into its value. Accordingly, al-
DIVISIONS OF PHILOSOPHY. 153
though we assume that at the end of the investiga
tion a close connection will be shown between that
which exists and that which is of some value, still,
at the beginning we separate the two investigations,
the one concerning the actuality and the one con
cerning the value of things.
5. Of the further organization of the subject,
what " follows may be presupposed :
Inducements to questions that concern the expla
nation of actuality come to us in part from external
nature and in part from the life of the soul. The two
domains do not immediately exhibit the appearance
of complete similarity ; but the consideration of both
leads to a series of quite similar inquiries, for ex
ample, concerning the possibility of the alteration of
one and the same Being, concerning the possibility
of the influence of one Thing upon another, etc.
Such inquiries may be separated from others and
combined into a universal preliminary investigation,
Metaphysic, upon which the Philosophy of Nature
and Psychology should then follow, as applications of
the results reached in it to special cases.
The second main division finds two obviously re
lated subjects in the kinds of value which we ascribe
to the existent, and in those which we ascribe to
such actions or sentiments as ougJit to be ; these are,
154 ENCYCLOPAEDIA OF PHILOSOPHY.
however, primarily distinguished by the fact that
only the latter directly include an obligation. On
this account, the investigation of the two divides
into ^Esthetics and Ethics ; and for these two inves
tigations a third, common to both, may be conceived,
but has hitherto never been carried out, namely,
an investigation concerning the nature of all deter
minations of value (corresponding to Metaphysic).
6. In life and in the particular sciences we are
constantly employed with the explanation of phenom
ena which, in the form in which they are presented
to us, are full of riddles through their contradictions,
gaps, and lack of coherence, a fact to which allu
sion has already been made. In doing this we nec
essarily start from certain general presuppositions
to which nature and the coherency of things must
correspond in order to be true. These presupposi
tions are ordinarily employed only in an uncritical
way and without any clear consciousness of their
meaning ; but Metaphysic endeavors to make a col
lection of them, to explain their true meaning, and
to remove the prejudgments which have become at
tached to them from being accustomed to a limited
circle of experience. Three great groups of inves
tigations appear at this point :
1) one, concerning the most general conceptions
and propositions which we apply in judging of every
2) a second, concerning the most general forms
156 ENCYCLOPEDIA OF PHILOSOPHY.
in which this actuality appears in the existences of
nature (Space, Time, Motion) ;
3) a third, concerning the possibility of the recip
rocal being (Filreinanderseiii) of things/ by which the
one becomes a perceivable object, and the other a
These three groups appear under different titles, with
somewhat of deviating limitations and, of course, very
differently treated, in most systems of Metaphysic.
In the Metaphysic of the older school the first
part appears as Ontology ; the second as Cosmology,
having the problem of showing how the individual
things are connected together into an orderly world-
whole, a problem which, although it is related to
the second of those mentioned above, is still not
identical with it. Rational Psychology corresponds
to the third group. On the contrary, the fourth
part of such Metaphysic, rational theology, must be
distinguished as a constituent of a foreign kind and
not strictly belonging to Metaphysic.
Just so in Herbart s Metaphysic, if we count out
the first part, the Methodology , then the others
correspond perfectly to the above-mentioned divis
ion : Ontology, Synechology, as the doctrine of
what is permanent, and Eidolology, or the doctrine
of images (etSwXa), which arise in one being as com
ing from the others.
QUESTIONS OF ONTOLOGY. 157
In the same way does Hegel s Logic/ by its par
tition into the doctrines of Being, of Phenomenon
(from which, of course, though to its disadvantage,
space and time remain excluded), and of Idea, ex
hibit the plainest analogies to the foregoing division
of such problems.
7. Ontology, from its being employed with expe
rience, is led to the following principal inquiries :
1) What, exactly, is the absolute Subject, which
is not a predicate of another ; that is to say, in what
does that consist which is the truly existent in all
Things/ whose nature we ordinarily believe our
selves able to specify by a number of so-called prop
erties ; and which is the support (Trdger) of these
properties and not itself in turn a property of any
2) How is the possibility of a variety of simulta
neous and successive properties belonging to one
and the same subject to be comprehended ?
3) How can such a unity exist among a variety of
Things that the states of one become causes for alter
ations in the states of another ?
8. Before we consider the different answers
which have been given to these inquiries, we make
prominent some very general kinds of error.
158 ENCYCLOPEDIA OF PHILOSOPHY.
The first is the confounding of the logical analysis
\ of our mental representations and the metaphysical
explanation of the things to which the mental repre
sentations relate. It is in general quite obvious that
there cannot be, in the matter of fact itself and as
developments of its own nature, as many movements
and turnings as would correspond to the various
steps, the separations and combinations, and in gen
eral to all the turnings which we must make in
thought, in order from our point of view to appre
hend the nature of such matters of fact. This is
perfectly clear to every one, in case one has to do,
for example, with the more intricate artifices of inves
tigation through which we endeavor to discover any
secret fact. Here the whole expenditure of the oper
ations of thought is quite obviously nothing but our
subjective exertion, as it were, to get behind the in
itself simple thing. On the contrary, all this be
comes obscure, in case one has to do with the simplest
logical operations. And at this point we very gen
erally fall into the error of regarding our logical sep
arations and combinations of the mental images and
their parts as events which happen also in the nature
of the things themselves.
For example ; in definition we premise for the
individual a general conception, and elaborate this
by added modifications up to the point of likeness
JUDGMENT AND REALITY. 159
with the individual in question. Hence the frequent
error, as though in reality some primitive animal/
some primitive matter/ some primitive substance/
must precede as a substratum in fact, from which, as
something secondary, the individual subordinate spe
cies might originate through the influence of modify
ing conditions. The logical dependence of the sepa
rate members of a classification is, therefore, con
founded with a real, matter-of-fact derivation of one
from the other.
In judgment we divide the object of a perception
into a subject, from which we as yet exclude a pred
icate ; then into such predicate ; and, finally, into the
third mental representation, that of the copula by
which the predicate is united again with the subject.
These operations are necessary in order to secure
clearness to the process of thinking. But it is an
error to assume that, in general, any like transaction
corresponds to them as a matter of fact, so that
there can really be, in the last analysis, a somewhat
that is without all predicates, and only just a some
what, but not any definite somewhat ; and, further,
that there can be predicates which were somewhat
previous to their being actualized in some subject ;
and, finally, that there is in rerum natura some
cement/ as it were, similar to the logical copula
by means of which the predicates are brought to
I6O ENCYCLOPAEDIA OF PHILOSOPHY.
inhere - as the customary expression goes in
One of the most frequent inducements to such
errors as the foregoing lies in the comparisons
which we are able at will to establish in the pro
cess of thinking between the contents of any
two ideas we please. We are very much inclined
to regard the .predicates for example, greater,
smaller, different, opposed, and the like which
belong to the content compared, only after the com
parison is made, as essential, integrating properties
of the content itself.
From these mistakes there originate, in part, a
multitude of artificial difficulties, inasmuch as we
begin to seek for an explanation of matter-of-fact
properties of things which we have previously cre
ated for them (as, for example, when the question
is raised, how an x can be at the same time greater
and f smaller, that is, greater than y and smaller
than z) : and, in part, many actual difficulties are
met with and no solution for them found, because
we imagine that we have succeeded in exhibiting
the development of a matter of fact, when we -have
in truth merely depicted the development of our
conceptions of the matter of fact. To this latter
case belongs, for example, the application of the
conceptions of potentia and actus, or of dynamis
EXPLANATION OF PRINCIPLES. l6l
and entelechy, or of power and expression,
faults of a kind which is especially frequent in
ancient philosophy (compare Microcosmus, vol. II,
pp. 321 ff.).
9. A second very general mistake, the exact
opposite of the previous one, consists in the effort to
make clear the supreme principles by explanations
that have no meaning except in the case of individual
phenomena dependent on the principles ; and that
even here have their meaning only in virtue of the
principles themselves. The simplest way of making
this obvious is, in brief, the following.
Our cognition is accustomed to the investigation
of individual events. These have their definite con
ditions, under which they are produced and main
tained. On this account, we can often show step
by step in a pictorial manner, how the phenomenon
arises from the co-operation of its conditions ; that
is to say, we know the mechanism of its coming
to be, the way in which it is produced. Now this
same inquiry may also very easily be raised with
reference to the general principles, which are the
very foundation of the possibility of the aforesaid
mechanism, or of every way in which any thing
whatever can be produced. For example, the ques
tion is asked, how does it happen that in all
1 62 ENCYCLOPAEDIA OF PHILOSOPHY.
becoming one state follows upon the others ; or
how does a cause begin to produce its appropriate
effect. This is as though one should wish to inves
tigate some internal mechanism, by which the points
of relation existing between these two most general
conceptions were held together; although just the
other way every possible mechanism presupposes
the validity of these two conceptions.
It is just so in many other cases. This fault is the
opposite of the foregoing, inasmuch as in the case of
objects of thought that are absolutely incomprehen
sible except in the form of abstract concepts and are
definable only as to their essential meaning, it is not
satisfied with such apprehension as belongs to the
concept, but demands for them a kind of intuitive
knowledge such as in this case is quite impossible.
10. The difference in different treatises on Met-
aphysic admits of being referred to two antithetic
principles which are dependent on fundamental pre
suppositions that are together introduced to consid
One view, which is realistic, finds the inducement
to investigation exclusively in the contradictions
of experience. If there were none of these, then
Realism would take no offence at letting the world
pass in the form in which it exists as bare matter
METAPHYSIC OF REALISM. 163
of fact ; and would raise no further inquiries. Ac
cordingly, if it succeeds in placing underneath this
world of experience, a world of what is existent truly
and devoid of contradictions, out of which the former
becomes comprehensible ; then it regards its problems
The other and idealistic view sees in every fact,
even although it include no contradiction, some rid
dle ; and it believes that we ought to recognize as
truly existent only such matter-of-fact as, by virtue
of its meaning and significance, admits of being
demonstrated to be an essential member of the
11. The Metaphysic of Realism is more inclined
to the pursuit of special investigations which are at
tached to single groups of problems ; and it is only
afterward that it endeavors to combine the results it
has attained into one whole. The Metaphysic of
Idealism, on the contrary, prefers to apprehend as
its single main problem the meaning of the world
as a whole ; and it believes that the solution of this
problem includes that of all the special problems,
and that thereby a coherent, uninterrupted develop
ment can best be obtained. The methods of both
partake of this distinction.
Realism takes its point of departure from the abso-
164 ENCYCLOPEDIA OF PHILOSOPHY.
lute certainty of the law of identity. Accordingly,
it sees so-called contradictions everywhere that
ordinary experience shows us a unity of the one
and the many (for example, the many properties
of a Thing and their alteration ). It further
tries to find a general solution for the contradiction
in the assertion that the unity is here only appar
ent ; and that what corresponds as subject to the
many properties (whether simultaneous or succes
sive) is not one Being that remains the same with
itself and yet undergoes change, but is a complex
of many beings which, in themselves always simple
and always self-identical, only appear to us as one
Thing through their relations to each other and
through their changes as one Thing with many
properties, as one changeable thing.
12. The Metaphysic of Idealism sets itself a
single main problem, which is as follows ; to dis
cover the nature of the truly Existent, against the
recognition of which as absolute, independent, and
supreme Ground of actuality, none of those presup
positions which our reason is compelled to make
concerning such a principle, any longer protests.
Such a problem leads to a method of its own.
That is to say, the aforesaid truly Existent/ which
we wish to discover, hovers before us, at the begin-
METAPHYSIC OF IDEALISM. 165
ning of philosophy, in the form of a very obscure
although very lifelike presentiment. Positively, we
are not able exhaustively to express what we mean
by it. But yet, in case some thought not identical
with it is mentioned to us, we are able very definitely
to deny that it is this which we mean. If we there
fore assume that we have first established for this
obscure content X some definition a, which contains
those features of X that are relatively most clear to
us ; then we can next compare a with X, and there
upon observe not merely in general that a does not
perfectly represent what we mean by X, but also
why or wherein a is unlike X, and consequently
stands in need of improvement. Thus there origi
nates a second definition a = X, with which the
same procedure is instituted as with a : and so on,
until we finally discover a definition A. = X in which
we see all that we obscurely meant under X trans
formed into clear conceptions.
Thus regarded, this method is nothing but a series
of subjective operations of thought by which we in
tend to transform a knowledge of our object which
is at first unsatisfactory into one more adequate ;
that is, of operations executed, with an altogether defi
nite purpose in view, by us as interpreting subjects.
If the object X still remains as obscure as are those
high-flying thoughts called the truly Existent, the
166 ENCYCLOPEDIA OF PHILOSOPHY.
Absolute, etc., then, as a rule, it becomes very diffi
cult to get any altogether accurate consciousness of
the precise reasons why a first definition a is not sat
isfactory. We indeed feel its unsatisfactoriness in a
general way, and this of itself urges us toward a sec
ond definition a which much better corresponds to
the X. But the logical motives for this transition
remain obscure. It merely follows with a certain
poetic justice ; and now it appears to us, since we
have lost hold of the reins that are to guide the
process of thought, as an inner development pecu
liar to X itself, of which we as thinking subjects
are simply spectators.
On the other hand, Idealism took its point of
departure from the matter-of-fact supposition of a
single Ground of the world, of an Absolute/ which
* develops into the variety of phenomena. If it
had been known what this Absolute is, then we
should have been able to deduce from its nature a
mode of development corresponding to it. But this
was not known ; on the contrary, the name Abso
lute merely designated the value of a Supreme Prin
ciple to which a content as yet unknown was, so to
speak, to be elevated. No definite mode of devel
opment could therefore be divined, but it could sim
ply be asserted what mode may possibly be attrib
uted to the Absolute ; and so in any case it must
BEING IN ITSELF. l6/
at least correspond to the general conception of
Now the following thoughts are involved in the
foregoing conception, namely, that the self-devel
oping being is not yet that which it is to become,
but that at the same time the possibility of its be
coming this lies in it alone. It therefore appears
as a * germ which is not yet fully unfolded, but
which is in itself what it will later become. Fur
ther, the germ must not remain germ, but must
develop into a variety of actual phenomena ; none
of which, although they all correspond perfectly to
its essence, is exclusively correspondent thereto, with
out having others beside itself. Therefore that which
is in itself (das An Sick) is at the same time realized
and brought to an end in this development, which is
the being other than itself ; since it assumes a defi
nite form, and thus excludes other possible forms
which it might have assumed. This incongruity
between that which the Being is in itself and the
being other than itself of the phenomenon must
be in turn removed : and it is a further step neces
sary to the development, by which the one-sidedness
of the phenomenon is negated and the Being re
turns into its own infiniteness ; although since it
has this definite development behind it, it does
not return to the simplicity of Being in itself,
l68 ENCYCLOPEDIA OF PHILOSOPHY.
but to the higher state of Being for self (Fur-
These three steps deduced from the conception of
development in abstracto have been established, be
sides, by many significant examples taken from expe
rience, as, for example, from vegetable, animal, and
spiritual life ; and so it came about that the afore
said primary and subjective method of explaining
obscure conceptions blended with this objective
rhythmus of development ; and philosophy came
to believe that it possesses herein a method at once
subjective and objective, according to which things
have unfolded themselves before our consciousness
(compare Geschichte der Aesthetik in Deutschlandj
Munchen, 1868, pp. 176-183).
13. It is obvious that, from the foregoing method,
there is to be expected only a development in which
a certain poetic justice more or less clearly rules ;
but not such an one as that every step in it can
be made good by definite proofs as necessary or as
alone possible to the exclusion of others.
In fact, the use of the same method by different
philosophers of this school has led to wholly diver
Only the fundamental thought of their Ontology
remains ; and it is this, that Being is never simple,
RESULTS OF REALISM. 169
unchangeable Position, but is constant movement
through the three Moments above alluded to,
namely, Being-in-itself, Being-other-than-self, and
Being-for-self. It is further agreed that there is
only one Existent/ whose finite and limited mani
festation is the individual things ; and, finally (a fact
which may be observed here in a preliminary way),
that this one Absolute does not remain a wholly
empty name for an obscure point, but has essen
tially the nature of the Spirit, and its development
is the advance from the * being-in-itself of uncon
scious existence to the being-f or-self of self-con
14. The results of Realism are different. Di
rected primarily toward the explanation of the pos
sibility of phenomena, it naturally required, in oppo
sition to the change which would include a contra
diction, that Being should be considered as a simple,
irremovable position. It further required, that the
primary elements, from whose changeable combina
tion the phenomena proceed, should be seen in a
variety of ultimate subjects or real beings. The
original nature of these beings it believed cannot
be recognized ; but it simply concluded, from the
facts that * appear] back to relations which must
take place between them in order to make this
I/O ENCYCLOPAEDIA OF PHILOSOPHY.
Both views, Idealism and Realism, come from dif
ferent sides on one and the same difficulty. The
former can perchance develop, in a general way,
from the one Idea which it presupposes, those prob
lems which reality must solve in order to correspond
to this Idea. Only it is not able to explain the spe
cial actions and reactions which take place between
the individual examples of those species of Being that
are derived from it ; but for this it needs the plural
istic assumption that the aforesaid Idea, in a manner
that requires additional demonstration, has previously
divided into a variety of elements which are in the
future to act independently.
Realism, on the contrary, in order to comprehend
an action and reaction between its many elements,
must assume a unity of general laws to which they
are all subjected. The explanation of how this sub
ordination of the many under this unity is possible,
is the counterpart of the before-mentioned problem
of Idealism. We may therefore consider as the final
problem of Ontology a problem not yet satisfac
torily solved this inquiry after the connection
between the necessary unity and the alike neces
sary manifoldness of the Existent.
15. After Ontology has established certain gen
eral conceptions of Being, of the Existent, of Hap-
COSMOLOGICAL PROBLEMS. I/I
pening and Acting, cosmological investigations raise
the inquiry after the relation of this Being and Act
ing to Space and Time. Under this head the prin
cipal problems are the following three :
1) The problem whether space exists in itself,
and things are in it, so that the latter are partially
distinguished by their place in space ; or whether
space is in things only as a form of intuiting them,
and the latter are accordingly distinguished only
qualitatively, and appear at different points in one
space intuited of them, in consequence of their
qualitative differences toward each other.
Connected with this inquiry after the reality or
ideal character of space stands
2) The inquiry after the nature of matter,
although the two do not coincide. The question
is : Should the spatial volume of any body of matter
be held to be a continuous volume full of what is
real ? Or is it only a space-volume within which
many active elements exist that are distinguished by
their place but are in themselves unextended ? This
is the question in dispute between the dynamic filling
of space and Atomism, the meaning of which, how
ever, it appears must be apprehended in a way the
very reverse of what customarily happens. The
conception of matter as continuous asserts that what
is real accomplishes an actual achievement by filling
ENCYCLOPAEDIA OF PHILOSOPHY.
up space ; and, indeed, by filling it up with its pres
ence. The other view allows space to be simply
controlled and not crammed full, as it were, by
real existence. It alone, besides, would be compati
ble with the correct view concerning the ideal char
acter of space.
3) A third question in dispute arises from the
consideration of what happens in the physical realm.
On the one hand, we are necessitated to recognize
the origin of phenomena from the co-operation of
many previously unconnected elements, and at the
same time the validity of general laws according
to which these elements act in every case ; so that
they are dependent for their effect only upon these
laws, upon their own permanent nature, and upon
the momentary disposition of circumstances, and
not at all upon a result which, according to hypoth
esis, has not as yet been attained. Over against this
so-called mechanical view of forces working blindly
according to general laws, there stands the idealistic
view, which regards only active Ideas as truly effec
tive in the world of things. Such Ideas are ever
striving to realize themselves, and on this account
are not bound to constantly uniform laws of their
action, but modify their mode of behavior at every
moment with a teleological reference to the result
for which they strive. Now it needs no explanation
VALIDITY OF COGNITION. 1/3
to see that, as long as the Ideas use means for their
actualization, this actualization cannot follow without
certain general laws being valid, in accordance with
which these means act. But just so, on the other
hand, would the world be absurd if there existed in
it mere mechanism without any power of Ideas or
final purposes. The ultimate object of Cosmology
will therefore be the inquiry, how Ideas and final
purposes can be effective within a world whose
events are subject to the laws of a mechanism.
16. After we have, in Ontology and Cosmology,
formed a view concerning the nature of Things and
their reciprocal actions, we should in the last part of
Metaphysic investigate Cognition itself as a single but
important case of the reciprocal action between two
elements, to wit, the case in which the one being
is capable of apprehending as conscious ideas the
impressions which it receives from the others.
In the first place, we should in realistic fashion
discover from the consideration of this reciprocal
action, that the image of the one being A cannot
be formed like A within the other being B ; be
cause, although it always on the one side depends
upon the impression from A, it likewise on the
other side depends on the nature of B. This,
therefore, is the same as saying that, by virtue of
174 ENCYCLOPAEDIA OF PHILOSOPHY.
this unavoidable subjectivity of all ideation/ cog
nition cannot be true in the sense that it copies
the essence of objects in form similar to the objects
themselves ; but at most in the sense that it repeats
the relations between things in the form of relations
of their mental images.
The foregoing result, however, causes us to raise
the inquiry of Idealism after the significance of this
entire mode of procedure. The Realism of common
opinion is wont to regard the world, apart from cog
nition, as a ready-made matter-of-fact that subsists
entirely complete in itself ; and cognition as only a
kind of appendage by means of which this subsist
ing fnatter-of-fact is simply recapitulated for the
best good of the cognizing being, but without in
this way experiencing any increment of reality.
Now Idealism establishes the truth that the pro
cess of ideation itself is one of the most essen
tial constituents of the world s ongoing course ;
that objectivity is not a goal the attainment and
further shaping of which is a task set before idea
tion ; but that ideation or, rather, the whole spir
itual life is a goal, to the attainment of which is
summoned the entire world of objects that do not
share in the process, and the entire ordering of
relations between them.
PHILOSOPHY OF NATURE. -- 175
17. The design in dividing theoretical Philoso
phy into Metaphysic and its applications, the Phi
losophy of Nature and Psychology, is that the first
shall answer the question : How must all that be
which is really to be at all ? or, If anything what
ever really is, to what necessary laws of all thought
is it subjected ? Over against this abstract science
are the two other concrete ones. That is to say,
they must consider the actuality which, although it
obeys the laws of Metaphysic, still does so in a spe
cial form that might be otherwise, and that therefore
is provisionally regarded as only an example, empi
rically given, of the aforesaid necessary laws of
thought. But the design of this distinction is neither
accurately carried out, nor does it possess any great
The problem of the Philosophy of Nature would
accordingly be the following ; not so much to describe
the elements which are in existence, as rather to
show what general habitudes of action and reaction
occur in this definite Nature so-called ; and, there
fore, what ones among the different forces conceivable
in abstracto actually occur and what ones among the
many possible dispositions of them actually subsist
from the beginning and maintain themselves amid
manifold forms of change. For example, that the
mass of matter in the world is separated into indi-
176 ENCYCLOPAEDIA OF PHILOSOPHY.
vidual material bodies ; that these are distinguished
among themselves into cohering and reciprocally
exclusive systems ; that on our planet the three dif
ferent forms of inorganic, vegetable, and animal
existence occur ; that what exists in these three
kingdoms is or how far it is divided into spe
cies, kinds, etc. ; that a systematic action and reac
tion, which is necessary for their continued exist
ence, takes place between everything living and the
inorganic material, all this constitutes the prob
lems of the concrete Philosophy of Nature. From
the realistic point of view, we take an interest in
investigating the effective conditions upon which
all these facts concerning the ordering of nature de
pend ; from the idealistic, in showing that it is an
ordering in which, if one knows it once for all, the
striving after the fulfilment of those universal prob
lems that are unavoidable in every conceivable rational
world may be recognized again and again. But Ideal
ism claims far too much when it, as in Schelling s
philosophy of nature, aims to deduce all these con
crete forms of existence, as consequences necessary
to thought, from one Supreme Idea.
18. In Psychology, too, the same principal views
stand in contrast with one other. The realistic aims
by investigations in causality to discover the condi-
PROBLEMS OF PSYCHOLOGY. 177
tions under which every single phenomenon of the
life of the Soul occurs, endures, or changes, and by
reciprocal action with other phenomena lays the
foundation for new states. Such investigations
may either be founded, in a manner quite like that
of natural science, upon experience and experiment,
or philosophically upon metaphysical presuppositions.
The larger gain with reference to the explanation of
the individual comes in the former way ; but a more
secure apprehension for the whole of a theory is only
to be gained in the second way. But the entire real
istic investigation is indispensable, because it is only
the knowledge of the working forces in the life of the
Soul which admits of practical applications, in Paed-
agogics, Psychiatry, etc.
Idealism also upon this point investigates, in the
first place, the constitutive conception of the Soul,
that is to say, the special Idea for the realization
of which the Soul is summoned to a definite place
in the whole coherent system of the world ; and it
then aims at demonstrating the individual activities
of the Soul as a cohering series of steps of develop
ment, which gradually construct for this conception an
ever more adequate realization. The previous attempts
(Schelling, Hegel, etc.) suffer, in part, from inaccu
racies to which the previous article alludes, and, in
part, from an over-estimate (that is without sufficient
ENCYCLOPEDIA OF PHILOSOPHY.
motif} of mere intelligence in comparison with the
whole spiritual life. They look upon mere self-knowl
edge, the most perfect self-consciousness, as the final
goal of the Soul and of the World ; while in our view
all intelligence is only the conditio sine qua non, under
which alone the final purposes that are really supreme
personal love and hate, the moral culture of char
acter and, in general, the whole content of life so
far as it has value appears possible at all.
19. Realism takes up those claims, of the con
science that obligates us to a definite form of con
duct, which urge themselves upon our interior life,
as though they were mere problems of fact, -
problems on this account because, in spite of the
clearness with which the claims of conscience fol
low in many individual cases, still in other cases
we feel ourselves obligated in a contradictory fash
ion to irreconcilable modes of conduct.
Investigation, accordingly, proceeds in the first
place to the confirming of the matter of fact,
that is to say, to establishing certain fundamental
moral principles in which, since they refer to the
most simple relations of several personal wills
toward one another, a uniformly similar and un
changeable judgment of approbation or disappro
bation is expressed concerning a definite mode of
the will s behavior. Whence these judgments of
conscience originate within us ; in what connection
they stand with the laws that govern what happens
in reality ; whether, finally, they admit of being de-
l8O ENCYCLOPAEDIA OF PHILOSOPHY.
duced from one supreme command or not, all
these are allied questions, the answer to which,
however it may turn out, neither heightens nor
diminishes the obligatory force of the aforesaid
Realism pronounces it to be a capital fault to sur
render this independence of the moral principles, and
to be willing to deduce the supreme rules, according
to which our conduct has to be directed, from any
theoretical insight whatever into the nature of real
ity. In Being alone no significance with respect
to what ought to be is involved. From that which
is and happens, prudential maxims for conduct
which will shun the dangers of this reality admit
of being developed ; but not the obligations which,
apart from any consequences, make any kind of
conduct appear in itself valuable, honorable, and
The investigations of Idealism have, for the most
part, justified these observations. Since it takes its
point of starting from a supreme fact, to wit, the
development of the absolute Ground of the world,
it has not discovered, strictly speaking, any place
for the conception of such an obligatory ought ;
but it substitutes for the conceptions of the morally
Good, and the morally Bad/ simply certain theo
retical conceptions of the harmonizing or not-har-
ETHICS AND PRACTICAL PHILOSOPHY. l8l
monizing of any mode of conduct with the tendency
of the self-development of the Absolute.
20. The formal distinction between the two
modes of treatment consists in this, that the realis
tic proceeds from general laws of conduct, from
which the special maxims of conduct that are
necessary in consideration of the circumstances
can be deduced for each particular case of an oc
casion for conduct ; and from which, besides, since
it brings into consideration the empirical nature of
man and the ever recurring social relations, science
is also able to develop a series of permanent life-
aims that hold good both for the individual and for
society. This last problem may be called that of
Practical Philosophy in special ; while the doctrine
of the culture of character according to general ethi
cal principles is called Moral Science or Ethics.
Idealism, as a rule, does not reach any special dis
tinction in these two forms of discipline. To it the
* Good appears, not as that which merely ought to
be, but likewise as that which eternally is. As well
the individual man as society and the history of soci
ety are, in its view, factors in the development of
the Absolute. To it that appears as good/ which
adapts itself to the meaning of this development.
PHILOSOPHY OF RELIGION.
21. A common conclusion for both theoretical
and practical investigations in philosophy is sought
for in the Philosophy of Religion.
We designate this part of philosophy by this name,
because the human mind has uniformly sought in
religion for such a conclusion to its view of the world ;
that is to say, for certainty concerning the final and
supreme Cause of that reality, of which every indi
vidual investigation, since it proceeds from limited
points of view, gives only a one-sided explanation.
More particularly, however, this certainty has refer
ence to the inquiry, how it is that what appears in
our conscience as the only thing that has real value,
- how the Good and the Beautiful possess a validity
corresponding to their value in the totality of the
world. Finally, we employ the term, because the
human mind has sought for a supplement to our
experience of the world, that shall follow from the
results of such painstaking endeavors, by means of
some intuition of a supersensible extension of the
world into realms withdrawn from experience.
PHILOSOPHY OF RELIGION. 183
It is in * Religion that the human mind has either
solved all these problems by a lively phantasy, or
some revelation has furnished the solution. In the
first case, philosophy has to explain, to test, and to
correct, the impulses by which the phantasy would
be directed. In the second case, it has to demon
strate, to what demands of the mind, that are in
themselves justifiable, the revelation vouchsafes a
satisfaction which is not discoverable by the reason,
but which is intelligible as soon as it exists.
But even apart from this relation to religion as a
fact actually met with, philosophy carries within
itself the very greatest demand for reflection upon
the connection between its theoretical and its ethi
cal view of the world.
22. Should the before-mentioned problem be
completely solved, then the Philosophy of Relig
ion would be in a position to make the transition
from the way of investigation to the way of a con
tinuous, systematic exhibition of philosophical truth ;
since it would indeed have fused all the results of
investigation into a single unity.
But at this point philosophy concludes with an
unattainable ideal : that is to say, with the con
viction that the universal and necessary laws of
thought, in accordance with which we judge of all
184 ENCYCLOPEDIA OF PHILOSOPHY.
reality ; second, that the primitive facts of this
reality; third, that the supreme Ideas of the Good
and the Beautiful, which hover before us as the
final purposes of the world, are all perfectly
coherent factors of one and the same Supreme
Principle, of the nature of God, although we are
unable strictly to demonstrate this fact of their
coherency. From the fact that such general laws
hold good in mathematics, it does not follow that
this system of nature which is empirically given
is necessary, and any other is impossible. Both
the laws and the facts appear to us possible and
valid, even although no Idea of the Good were
ruling the world. In brief, laws, facts, and final
purposes (Ideas) are for us three principles, dis
tinct from each other, and not deducible from each
For this reason Philosophy can never be such an
unchanging science, as to be able to deduce from
one Supreme Principle all its results in uniform
sequence ; but its investigations will always be sep
arated into (i) those of Metaphysic, which con
cern the possibility of the world s course ; (2) into
those of the Philosophy of Nature, which concern
the connection, in fact, of its reality; and (3) into
those of the Philosophy of Religion, which concern
its ideal significance and final purposes.
Absolute, as supreme principle in philosophy, i66f., 184; self-development
of, 166 f.
Abstraction, formation of concepts by, 23 ; in definition, 98.
Esthetics, nature of, 154.
Analogy, conclusion by, 74 f., 77, 134 f.
Aristotle, figures of, 57 f., 67 f. ; sorites of, 67.
Axioms, nature of, 107.
Being, in itself, 167, 169 ; for self, 167 f., 169.
Calculation, forms of, 75 f. ; application of, 80 f. ; the mathematical, 81 f.
Cause, nature of a, 42 f. ; investigation of, 124 f., 136.
Classification, nature of, 84 ; kinds of, 85 f. ; the artificial, 86 ; the natural,
88 ; spirit of, 91 f.
Cognition, ideal of, 93 ; theory of, 173 f.
Concepts, formation of, 9 f., 17 f. ; nature of, 13 f., 19 f. ; content and extent
of, 16 f., 20 f. ; kinds of, 19 f. ; subordination of, 21 f.; subsumption of,
22 f. ; the distinguishing, 83 ; the descriptive, 83 ; the constitutive, 83,
84, 88, 104 f. ; application of the forms of, 97 f. ; limitation of, 100 f., 103.
Conclusion, form of, 56 f., 69 f. ; design of, 71 f. ; by analogy, 74 f., 77 ; by
imperfect induction, 121 f.
Content, of concepts, i f., 21 f. ; number of marks in, 16 f., 20 f.
Contraposition, nature of, 55 f.
Copula, significance of, 24 f.
Cosmology, questions of, 170 f.
Criticism, nature of the philosophical, 149 f.
Definition, by abstraction, 98 f. ; by construction, 98 f. ; method of, 100 f. ;
too wide, 100; too narrow, 100; circle in, loof. ; task of, 101 f. ; a source
of sophistry, 105, 158 f.
Dilemmas, nature of. 118 f.
Discovery, method of, 120 f.
Ethics, nature of, 154, 181.
Excluded Middle, principle of, 47 f.
Fallacies, forms of, 116 f.
Fictions, logical nature of, 133 f.
Figures, of the Syllogism, 56 f.; the Aristotelian, 57 f., 66 f., 70 f.; First,
58 f., 64 ; Second, 59 f. ; Third, 60 f. ; Fourth, 63 f.
Galen, figure of, 63.
Genus, in definition, 100 f.
Goclenius, sorites of, 67.
God, as supreme Ideal of philosophy, 184.
Hegel, the logic of, 157.
Herbart, metaphysic of, 156.
Hypotheses, nature of, 130 ; discovery of, 130 f., 132 f.
Idealism, the metaphysic of, 164 ; results of, 169 f. ; its theory of cognition,
173 f. ; of practical philosophy, 179 f.
Ideas, distinguished from thoughts, 2 f., 17 f. ; logical form of, 12 f., 17 f. ;
association of, in judgment, 25 f.
Identity, principle of, 34 f.
Indiciae, kinds of, 137 ; importance of, 138 f.
Induction, nature of, 72; perfect and imperfect, 73 f., 121 f. ; method of,
Inferences, the immediate, 48 f. ; kinds of, 49 f. ; by conversion of judg
ments, 52 f.
Judgments, nature of, 24 f. ; formation of, 25 f. ; classification of, 27 f. ; of
quantity, 28 ; of quality, 28 f. ; of relation, 30; of modality, 30 f. ; forms
of, in system, 31 f. ; the impersonal, 31 f . ; the analytic, 33, 114; the
synthetic, 33 f. ; the categorical, 35 f., 37 f. ; the historical, 38 f. ; the
hypothetical, 39 f. ; the general, 44 f . ; the disjunctive, 45 f. ; subalterna-
tion of, 49 f. ; opposition of, 50 f. ; conversion of, 52 f.
Kant, classification of judgments, 27 f.
Language, relation of, to thought, 10 f.
Logic, pure, 9-93; principal laws of, 34 f., 40 f. ; applied, 97-143; no help
to discover proof, 114.
Marks, relation of, to concept, 14 f. ; similar and dissimilar, 15 f. ; univer
sal, 17 f.
Mathematics, inferences of, 78 f., 82 f., 135.
Matter, nature of, 171 f.
Metaphysic, nature of, 153 f., 155 f. ; divisions of, 155 f.; of Realism, 163 f.;
of Idealism, 164 f.
Middle Term, nature of, 56 f.
Name, as applied to concept, 14 f., 19 f.
Ontology, questions of, 157 ; its concept of Being, 168 f.
Opposition, of judgments, kinds of, 50.
Paralogisms, nature of, 118.
Philosophy, nature of, 145, 150 f. ; relation to the sciences, 146 f. ; method
of, 150 f., 157 f., 161 f. ; divisions of, 152 f. ; the theoretical, 155 f. ; the
practical, 179 f. ; of religion, 182.
Philosophy of Nature, the problem of, 175 f.
Predicates, of judgments, 24 f. ; compatible and incompatible, 36 ; fixed
and changeable, 76 f.
Premises, of syllogisms, 56 f. ; major, 57 ; minor, 51 ; position of, 57 f.
Proof, the adducing of, 106 f. ; direct, 108 f. ; indirect or apagogic, 108,
in f. ; progressive, 108 f., in f. ; regressive, 109 f., 112; by exclusion,
113 f . ; reduction of, to first figure, 113 f. ; by indiciae, 137 f.
Psychology, place of, in a philosophical system, 153 f. ; the rational, 156;
views of Realism, 176 f. ; and of Idealism, 177 f.
Realism, views of, 162 f., 168 f. ; metaphysic of, 163 f. ; results of, 169 f. ; its
theory of cognition, 173 f. ; of practical philosophy, 179 f.
Reasoning, nature of, 56 f. ; kinds of, 58 f. ; the mathematical, 78 f.
Eeligion, philosophy of, 182 f. ; nature of, 183 f.
Scepticism, kinds of, 148.
Science, the explanatory, 89 f., 91 f. ; spirit of, 91.
Sorites, nature of, 67.
Space, the problem of, 171 f.
Species, in classification, 86 f., 88.
Subalternation, of judgments, 49 f.
Subject, of judgments, 24 f. ; changes of, in conversion, 52 f.
Subordination, of concepts, 21 f.
Subsumption, of concepts, 22 f.
Sufficient Eeason, principle of, 40 f. ; distinguished from cause, 42 f.
Syllogism, nature of, 56 f. ; figures in, 57 f.; position of premises in, 57 f. ;
hypothetical and disjunctive, 68 f.
Things, relation of, to thought, 5 f. ; realistic view of, 164.
Thought, nature of, i f., 5 f., 9 f., 98 ; process of, 4 f., 120 ; metaphysical
principles underlying, 5 f. ; first work of, 10 f. ; relation to language, 10,
ii f. ; second work of, II f. ; communication of, 98 ; in discovery, 120 f.
Truth, criterion of, 131 f. ; existence of, assumed by philosophy, 147.
TJniversals, kinds of, 16 f. ; meaning of, 87 f. ; relation to experience, 120 f.
Votes, logic of, 140 ; majority of, 141 f.
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