THE GAME OF "LOGIC."
11
X
12
y
m
18
0/
15
COLOURS FOR
COUNTERS.
See, the Sun is overhead,
Shining on us, FULL and
RED!
Now the Sun is gone away,
And the EMPTY sky is
GREY!
y
X
/-
X
THE GAME
LOGIC
LEWIS CARROLL
PRICE THREE SHILLINGS
ILon&on
MACMILLAN AND CO.
AND NEW YORK
1887
[AH Rights reserved.}
BC
135
RICHARD CLAY AND SONS,
LONDON AND BUNQAY.
31 cjjarm in bain ; for netoer again,
an fceenlg a0 mg glance 3( benB,
Sfflill jfglemorp, goBBe00 cop,
(ZBmboBg for mg jog
Departed Bage, nor let me ca?e
Dn ti)ee, mp Jfairp JFrienti !
Pet couiu ti>2 face, in mgetic grace,
3 moment 0mile on me, 'ttooittti
/Far=Uarting rapa of ltgl>t
/From C^eatoen atijtoart tfje
38g tul)tcl) to reati in berg Been
spirit, 0toeete0t JFrienB !
So ma? tfje stream of Hife'0 long Bream
JFloto gentlg ontnarB to it0 cnB,
22Hit!) manp a flotoeret gag,
2Botnn it0 totllotop toap :
no 0ig|) toejc, no care perpler,
lotting little JFrienB !
NOTA BENE.
With each copy of this Book is
given an Envelope, containing a
Diagram (similar to the frontis-
piece) on card, and nine Counters,
four red and five grey.
The Envelope, &c. can be had
separately, at 3d. each.
The Author will be very grateful
for suggestions, especially from be-
ginners in Logic, of any alterations,
or further explanations, that may
seem desirable. Letters should be
addressed to him at "29, Bedford
Street, Covent Garden, London."
PREFACE
" There foara'd rebellious Logic, gagg'd and bound."
PHIS Game requires nine Counters — four of one
colour and five of another: say four red and five
grey-
Besides the nine Counters, it also requires one Player,
at least. I am not aware of any Game that can be played
with less than this number : while there are several that
require more : take Cricket, for instance, which requires
twenty-two. How much easier it is, when you want to play
a Game, to find one Player than twenty-two. At the
same time, though one Player is enough, a good deal
more amusement may be got by two working at it together,
and correcting each other's mistakes.
A second advantage, possessed by this Game, is that,
besides being an endless source of amusement (the number
of arguments, that may be worked by it, being infinite), it
will give the Players a little instruction as well. But is
there any great harm in that, so long as you get plenty of
amusement ?
CONTENTS.
CHAPTER PAGE
I. NEW LAMPS FOR OLD.
§ 1. Propositions ...... 1
§ 2. Syllogisms 20
§ 3. Fallacies 32
II. CROSS QUESTIONS.
§ 1. Elementary 37
§ 2. Half of Smaller Diagram. Propositions
to be represented ..... 40
§ 3. Do. Symbols to be interpreted ... 42
§ 4. Smaller Diagram. Propositions to be
represented . . ' . . . . 44
§ 5. Do. /Symbols to be interpreted ... 46
§ 6. Larger Diagram. Propositions to be
represented 48
§ 7. Both Diagrams to be employed ... 51
III. CROOKED ANSWERS.
§ 1. Elementary 55
§ 2. Half of Smaller Diagram. Propositions
represented ...... 59
§ 3. Do. Symbols interpreted .... 61
§ 4. Smaller Diagram. Propositions represented. 62
§ 5. Do. Symbols interpreted .... 65
§ 6. Larger Diagram. Propositions represented. 67
§ 7. Both Diagrams employed .... 72
IV. HIT OR MISS 85
CHAPTER I.
NEW LAMPS FOR OLD.
" Light come, light go."
<§ 1. Propositions.
" Some new Cakes are nice."
" No new Cakes are nice."
" All new Cakes are nice."
There are three 'Propositions' for you the only
three kinds we are going to use in this Game : and the
first thing to be done is to learn how to express them
on the Board.
Let us begin with
" Some new Cakes are nice."
But, before doing so, a remark has to be made —
one that is rather important, and by no means easy
to understand all in a moment : so please to read this
very carefully.
2 NEW LAMPS FOR OLD. [On. I.
The world contains many Things (such as "Buns",
" Babies ", " Beetles ", " Battledores ", &c.) ; and these
Things possess many Attributes (such as "baked",
" beautiful ", " black ", " broken ", &c. : in fact, what-
ever can be " attributed to ", that is " said to belong
to", any Thing, is an Attribute). Whenever we wish
to mention a Thing, we use a Substantive : when we
wish to mention an Attribute, we use an Adjective.
People have asked the question "Can a Thing exist
without any Attributes belonging to it ? " It is a very
puzzling question, and I'm not going to try to answer
it : let us turn up our noses, and treat it with con-
temptuous silence, as if it really wasn't worth noticing.
But, if they put it the other way, and ask "Can an
Attribute exist without any Thing for it to belong
to ? ", we may say at once " No : no more than a Baby
could go a railway-journey with no one to take care
of it ! " You never saw " beautiful " floating about in
the air, or littered about on the floor, without any
Thing to be beautiful, now did you ?
And now what am I driving at, in all this long
rigmarole? It is this. You may put "is" or "are"
between the names of two Things (for example, " some
Pigs are fat Animals"), or between the names of two
Attributes (for example, "pink is light-red"), and in
each case it will make good sense. But, if you put
" is " or " are " between the name of a Thing and the
name of an Attribute (for example, "some Pigs are
§ !•] PROPOSITIONS. 3
pink"), you do not make good sense (for how can a
Thing be an Attribute?) unless you have an under-
standing with the person to whom you are speaking.
And the simplest understanding would, I think, be
this that the Substantive shall be supposed to be
repeated at the end of the sentence, so that the sen-
tence, if written out in full, would be "some Pigs
are pink (Pigs)". And now the word "are" makes
quite good sense.
Thus, in order to make good sense of the Proposition
"some new Cakes are nice", we must suppose it to
be written out in full, in the form " some new Cakes
are nice (Cakes) ". Now this contains two ' Terms '
" new Cakes " being one of them, and " nice (Cakes) "
the other. " New Cakes," being the one we are talking
about, is called the ' Subject ' of the Proposition, and
" nice (Cakes) " the ' Predicate '. Also this Proposition
is said to be a ' Particular ' one, since it does not speak
of the whole of its Subject, but only of a part of it.
The other two kinds are said to be ' Universal ', because
they speak of the whole of their Subjects the one
denying niceness, and the other asserting it, of the
whole class of "new Cakes". Lastly, if you would
like to have a definition of the word ' Proposition '
itself, you may take this : — " a sentence stating that
some, or none, or all, of the Things belonging to a
certain class, called its 'Subject', are also Things be-
longing to a certain other class, called its ' Predicate ' ".
B 2
4 NEW LAMPS FOR OLD. [Cn. I.
You will find these seven words — - Proposition,
Attribute, Term, Subject, Predicate, Particular, Universal
—charmingly useful, if any friend should happen to
ask if you have ever studied Logic. Mind you bring
all seven words into your answer, and your friend will
go away deeply impressed 'a sadder and a wiser
man .
Now please to look at the smaller Diagram on the
Board, and suppose it to be a cupboard, intended for
all the Cakes in the world (it would have to be a
good large one, of course). And let us suppose all the
new ones to be put into the upper half (marked '«'),
and all the rest (that is, the not-new ones) into the
lower half (marked '»"). Thus the lower half would
contain elderly Cakes, aged Cakes, ante-diluvian
Cakes if there are any : I haven't seen many, my-
self and so on. Let us also suppose all the nice
Cakes to be put into the left-hand half (marked 'y'},
and all the rest (that is, the not-nice ones) into the
right-hand half (marked 'y"). At present, then, we
must understand x to mean "new", sc' "not-new",
y "nice", and y' "not-nice."
And now what kind of Cakes would you expect to
find in compartment No. 5 ?
It is part of the upper half, you see ; so that, if it
has any Cakes in it, they musr- be new: and it is part
§ !•] PROPOSITIONS. 5
of the left-hand half; so that they must be nice. Hence
if there are any Cakes in this compartment, they must
have the double ' Attribute ' " new and nice " : or, if we use
letters, they must be " sc y."
Observe that the letters x, y are written on two of
the edges of this compartment. This you will find a
very convenient rule for knowing what Attributes
belong to the Things in any compartment. Take
No. 7, for instance. If there are any Cakes there,
they must be " x1 y ", that is, they must be " not-new
and nice."
Now let us make another agreement that a red
counter in a compartment shall mean that it is 'oc-
cupied ', that is, that there are some Cakes in it.
(The word ' some,' in Logic, means ' one or more ' :
so that a single Cake in a compartment would be
quite enough reason for saying " there are some Cakes
here"). Also let us agree that a grey counter in a
compartment shall mean that it is 'empty', that is,
that there are no Cakes in it. In the following
Diagrams, I shall put ' 1 ' (meaning ' one or more ')
where you are to put a red counter, and ' 0 ' (meaning
' none ') where you are to put a grey one.
As the Subject of our Proposition is to be "new
Cakes", we are only concerned, at present, with the
upper half of the cupboard, where all the Cakes have
the attribute x, that is, " new."
6 NEW LAMPS FOB OLD. [Cn. I.
Now, fixing our attention on this upper half, sup-
pose we found it marked like this,
that is, with a red counter in No. 5. What would
this tell us, with regard to the class of " new Cakes " ?
Would it not tell us that there are some of them in
the x ^-compartment ? That is, that some of them
(besides having the Attribute x, which belongs to both
compartments) have the Attribute y (that is, "nice").
This we might express by saying " some £-Cakes are
y- (Cakes) ", or, putting words instead of letters,
" Some new Cakes are nice (Cakes)",
or, in a shorter form,
" Some new Cakes are nice ".
At last we have found out how to represent the
first Proposition of this Section. If you have not
clearly understood all I have said, go no further, but
read it over and over again, till you do understand it.
After that is once mastered, you will find all the rest
quite easy.
It will save a little trouble, in doing the other
O
Propositions, if we agree to leave out the word
"Cakes" altogether. I find it convenient to call the
whole class of Things, for which the cupboard is in-
tended, the ' Universe' Thus we might have begun
this business by saying "Let us take a Universe of
Cakes." (Sounds nice, doesn't it ?)
§ 1.]
PROPOSITIONS.
Of course any other Things would have done just
as well as Cakes. We might make Propositions
about " a Universe of Lizards ", or even " a Universe
of Hornets". (Wouldn't that be a charming Universe
to live in ? )
So far, then, we have learned that
means " some x and y" i. e. " some new are nice."
I think you will see, without further explanation, that
means " some x are y' ," i. e. " some new are not-nice."
Now let us put a grey counter into No. 5, and ask
ourselves the meaning of
This tells us that the x ^-compartment is empty,
which we may express by " no x are y ", or, " no new Cakes
are nice ". This is the second of the three Propositions at
the head of this Section.
In the same way,
would mean " no x are y '," or, " no new Cakes are not-nice."
8 NEW LAMPS FOR OLD.
What would you make of this, I wonder ?
[On. I.
I hope you will not have much trouble in making
out that this represents a double Proposition : namely,
"some x are y, and some are y'" i. e. "some new are
nice, and some are not-nice."
The following is a little harder, perhaps :—
This means " no x are y, and none are ?/," i. e. " no
new are nice, and none are not-nice " : which leads to the
rather curious result that " no new exist," i.e. " no Cakes
are new." This is because " nice " and " not-nice " make
what we call an 'exhaustive' division of the class "new
Cakes " : i. e. between them, they exhaust the whole
class, so that all the new Cakes, that exist, must be
found in one or the other of them.
And now suppose you had to represent, with counters,
the contradictory to " no Cakes are new ", which would be
"some Cakes are new", or, putting letters for words,
" some Cakes are x ", how would you do it ?
This will puzzle you a little, I expect. Evidently
you must put a red counter somewhere in the cc-half
of the cupboard, since you know there are some new
Cakes. But you must not put it into the left-hand
compartment, since you do not know them to be nice :
nor may you put it into the right-hand one, since you
do not know them to be not-nice.
§ 1.] PROPOSITIONS. 9
What, then, are you to do? I think the best way
out of the difficulty is to place the red counter on
the division-line between the o^-compartment and the
^'-compartment. This I shall represent (as / always
put ' 1 ' where you are to put a red counter) by the
diagram
Our ingenious American cousins have invented a
phrase to express the position of a man who wants to
join one or other of two parties such as their two
parties ' Democrats ' and ' Republicans ' but ca'n't
make up his mind which. Such a man is said to be
" sitting on the fence." Now that is exactly the position
of the red counter you have just placed on the division-
line. He likes the look of No. 5, and he likes the
look of No. 6, and he doesn't know which to jump
down into. So there he sits astride, silly fellow,
dangling his legs, one on each side of the fence !
Now I am going to give you a much harder one to
make out. What does this mean ?
This is clearly a double Proposition. It tells us,
not only that "some x are y" but also that "no x
are not y." Hence the result is "all x are y" i. e.
" all new Cakes are nice ", which is the last of the three
Propositions at the head of this Section.
10 NEW LAMPS FOR OLD. [On. I.
We see, then, that the Universal Proposition
" All new Cakes are nice "
consists of two Propositions taken together, namely,
" Some new Cakes are nice,"
and " No new Cakes are not-nice."
In the same way
would mean "all x are y'", that is,
"All new Cakes are not-nice."
Now what would you make of such a Proposition
as " The Cake you have given me is nice " ? Is it
Particular, or Universal?
" Particular, of course," you readily reply. " One
single Cake is hardly worth calling ' some,' even."
No, my dear impulsive Reader, it is ' Universal '.
Remember that, few as they are (and I grant you they
couldn't well be fewer), they are (or rather ' it is ')
all that you have given me ! Thus, if (leaving ' red '
out of the question) I divide my Universe of Cakes
into two classes the Cakes you have given me (to
which I assign the upper half of the cupboard), and
those you haven't given me (which are to go below)
I find the lower half fairly full, and the upper one
as nearly as possible empty. And then, when I am
told to put an upright division into each half, keeping
the nice Cakes to the left, and the not-nice ones to
§ !•] PROPOSITIONS. 11
the right, I begin by carefully collecting all the Cakes
you have given me (saying to myself, from time to
time, " Generous creature ! How shall I ever repay such
kindness ? "), and piling them up in the left-hand com-
partment. And it doesn't take long to do it !
Here is another Universal Proposition for you. " Bar-
zillai Beckalegg is an honest man." That means " All the
Barzillai Beckaleggs, that I am now considering, are
honest men." (You think I invented that name, now
don't you ? But I didn't. It's on a carrier's - cart,
somewhere down in Cornwall.)
This kind of Universal Proposition (where the Subject
is a single Thing) is called an ' Individual ' Proposition.
Now let us take " nice Cakes " as the Subject of our
Proposition: that is, let us fix our thoughts on the left-
hand half of the cupboard, where all the Cakes have the
attribute y, that is, " nice."
Suppose we fird it marked like this : —
What would that tell us ?
I hope that it is not necessary, after explaining the
horizontal oblong so fully, to spend much time over the
upright one. I hope you will see, for yourself, that this
means " some y are x ", that is,
" Some nice Cakes are new."
" But," you will say, " we have had this case before.
You put a red counter into No. 5, and you told us it meant
12 NEW LAMPS FOR OLD. [Cn. I.
' some new Cakes are nice ' ; and now you tell us that it
means ' some nice Cakes are new ' I Can it mean both ? "
The question is a very thoughtful one, and does you
great credit, dear Eeader ! It does mean both. If you
choose to take x (that is, " new Cakes ") as your Subject,
and to regard No, 5 as part of a horizontal oblong, you
may read it " some x are y ", that is, " some new Cakes are
nice " : but, if you choose to take y (that is, " nice Cakes ")
as your Subject, and to regard No. 5 as part of an upright
oblong, then you may read it " some y are x ", that is,
" some nice Cakes are new ". They are merely two
different ways of expressing the very same truth.
Without more words, I will simply set down the other
ways in which this upright oblong might be marked,
adding the meaning in each case. By comparing them
with the various cases of the horizontal oblong, you will,
I hope, be able to understand them clearly.
You will find it a good plan to examine yourself on
this table, by covering up first one column and then
the other, and ' dodging about ', as the children say.
Also you will do well to write out for yourself two
other tables one for the lower half of the cupboard,
and the other for its right-hand half.
And now I think we have said all we need to say
about the smaller Diagram, and may go on to the
larger one.
PROPOSITIONS.
13
Symbols.
Meanings.
Some y are x' ;
i. e. Some nice are not-new.
No y are x ;
i. e. No nice are new.
[Observe that this is merely another way of
expressing "No new are nice."]
No y are x' ;
i. e. No nice are not-new.
Some y are x, and some are x' ;
i. e. Some nice are new, and some are
not-new.
No y are x, and none are x' ; i. e. No y
exist;
i. e. No Cakes are nice.
All y are a>;
i. e. All nice are new.
All y are x' ;
i. e. All nice are not-new.
H NEW LAMPS FOR OLD. [On. I.
This may be taken to be a cupboard divided in the
same way as the last, but also divided into two portions,
for the Attribute TO. Let us give to TO the meaning
" wholesome " : and let us suppose that all wholesome
Cakes are placed inside the central Square, and all
the unwholesome ones outside it, that is, in one or other
of the four queer-shaped outer compartments.
We see that, just as, in the smaller Diagram, the
Cakes in each compartment had two Attributes, so,
here, the Cakes in each compartment have three Attri-
butes: and, just as the letters, representing the two
Attributes, were written on the edges of the compart-
ment, so, here, they are written at the corners. (Observe
that TO' is supposed to be written at each of the four
outer corners.) So that we can tell in a moment, by
looking at a compartment, what three Attributes belong
to the Things in it. For instance, take No. 12.
Here we find x, y', TO, at the corners : so we know
that the Cakes in it, if there are any, have the triple
Attribute, ' xy'm ', that is, " new, not-nice, and wholesome."
Again, take No. 16. Here we find, at the corners,
x', y', TO' : so the Cakes in it are " not-new, not-nice,
and unwholesome." (Remarkably untempting Cakes !)
It would take far too long to go through all the
Propositions, containing x and y, x and TO, and y and TO,
which can be represented on this diagram (there are
ninety-six altogether, so I am sure you will excuse me !)
Mv]
PROPOSITIONS.
15
and I must content myself with doing two or three, as
specimens. You will do well to work out a lot more
for yourself.
Taking the upper half by itself, so that our Subject is
" new Cakes ", how are we to represent " no new Cakes
are wholesome"?
This is, writing letters for words, "no x are m." Now
this tells us that none of the Cakes, belonging to the
upper half of the cupboard, are to be found inside the
central Square: that is, the two compartments, No. 11
and No. 12, are empty. And this, of course, is repre-
sented by
0 0
And now how are we to represent the contradictory
Proposition " some x are m " ? This is a difficulty I
have already considered. I think the best way is to
place a red counter on the division-line between No. 11
and No. 12, and to understand this to mean that one of
the two compartments is ' occupied,' but that we do not
at present know which. This I shall represent thus : —
16 NEW LAMPS FOR OLD. [Cn. I
Now let us express " all x are m."
This consists, we know, of two Propositions,
" Some x are m"
and " No x are m'."
Let us express the negative part first. This tells us
that none of the Cakes, belonging to the upper half of
the cupboard, are to be found outside the central Square :
that is, the two compartments, No. 9 and No. 10, are
empty. This, of course, is represented by
0
But we have yet to represent " Some x are m." This
tells us that there are some Cakes in the oblong con-
sisting--of No. 11 and No. 12 : so we place our red
counter, as in the previous example, on the division-line
between No. 11 and No. 12, and the result is
0
Now let us try one or two interpretations.
What are we to make of this, with regard to x and y ?
S. 1 1
PROPOSITIONS. 17
This tells us, with regard to the ^'-Square, that
i wholly 'empty', since loth compartments are so
marked. With regard to the ,,-Square, it tells us
that it is 'occupied'. True, it is only one compartment
' that is so marked; but that is quite enough
whether the other be 'occupied' or 'empty' to
the fact that there is something in the Square.
If, then, we transfer our marks to the smaller Diagram,
so as to get rid of the m-subdivisions, we have a right
to mark it
which means, you know, « all x are y."
^ The result would have been exactly the same, if the
given oblong had been marked thus :—
Once more : how shall we interpret this, with regard
to x and y ?
This tells us, as to the ^-Square, that one of its
compartments is 'empty'. But this information is
c
18
NEW LAMPS FOR OLD.
[On. I.
quite useless, as there is no mark in the other com-
partment. If the other compartment happened to be
' empty ' too, the Square would be ' empty ' : and, if it
happened to be 'occupied', the Square would be
' occupied '. So, as we do not know which is the case,
we can say nothing about this Square.
The other Square, the ;» y'-Square, we know (as in
the previous example) to be ' occupied '.
If, then, we transfer our marks to the smaller Diagram,
we get merely this : —
which means, you know, " some x are y'"
These principles may be applied to all the other
oblongs. For instance, to represent
" all y' are m' " we should mark the
right -hand upright oblong (the one
that has the attribute y'} thus : —
and, if we were told to interpret the lower half of the
cupboard, marked as follows, with regard to x and y,
§ 1.] PROPOSITIONS. 19
we should transfer it to the smaller Diagram thus,
and read it " all x' are y."
Two more remarks about Propositions need to be
made.
One is that, in every Proposition beginning with
" some " or " all ", the actual existence of the ' Subject ' is
asserted. If, for instance, I say " all misers are selfish," I
mean that misers actually exist. If I wished to avoid
making this assertion, and merely to state the law that
miserliness necessarily involves selfishness, I should say
" no misers are unselfish " which does not assert that any
misers exist at all, but merely that, if any did exist, they
would be selfish.
The other is that, when a Proposition begins with
" some " or " no ", and contains more than two Attributes,
these Attributes may be re-arranged, and shifted from
one Term to the other, ad libitum. For example, " some
abc are def" may be re-arranged as " some If are acde"
each being equivalent to " some Things are abcdef". Again
" No wise old men are rash and reckless gamblers " may-
be re-arranged as " No rash old gamblers are wise and
reckless," each being equivalent to " No men are wise old
rash reckless gamblers."
c 2
§ 2. Syllogisms.
Now suppose we divide our Universe of Things in
three ways, with regard to three different Attributes.
Out of these three Attributes, we may make up three
different couples (for instance, if they were a, b, c, we
might make up the three couples ab, ac, be). Also
suppose we have two Propositions given us, containing
two of these three couples, and that from them we
can prove a third Proposition containing the third
couple. (For example, if we divide our Universe for
m, x, and y ; and if we have the two Propositions
given us, " no m are x' " and " all m' are y ", con-
taining the two couples mx and my, it might be possible
to prove from them a third Proposition, containing
x and y.)
In such a case we call the given Propositions 'the
Premisses ', the third one ' the Conclusion ' and the
whole set ' a Syllogism '.
Evidently, one of the Attributes must occur in both
Premisses; or else one must occur in one Premiss, and
its contradictory in the other.
CH. I. § 2.] NEW LAMES FOR OLD.. 21
In the first case (when, for example, th(e Premisses
are "some m are x" and "no m are yijffY'ilie Term,
which occurs twice, is called 'the Jmadle Term',
because it serves as a sort of link between the other
two Terms.
In the second case (when, for example, the Premisses
are "no m are x'" and "all m' are y"} the Jwo Terms,
which contain these contradictory Attributes, may be
called ' the Middle Terms '.
Thus, in the first case, the class of " m-Things " is
the Middle Term ; and, in the second case, the two
classes of " ?^-Thmgs " and " m'-Things " are the Middle
Terms.
The Attribute, which occurs in the Middle Term
or Terms, disappears in the Conclusion, and is said to
be " eliminated-", which literally means " turned out
of doors ".
Now let us try to draw a Conclusion from the. . two
Premisses —
" Some new Cakes are unwholesome ;
No nice Cakes are unwholesome."
In order to express them with counters, we need to
divide Cakes in three different ways, with regard to
newness, to niceness, and to wholesomeness. For this
we must use the larger Diagram, making x mean
"new", y "nice", and m "wholesome". (Everything
22 NEW LAMPS FOR OLD. [Cn. I.
inside the central Square is supposed to have the at-
tribute ra, and everything outside it the attribute m',
i.e. " not-ra ".)
You had better adopt the rule to make m mean
the Attribute which occurs in the Middle Term or
Terms. (I have chosen m as the symbol, because
' middle ' begins with ' m '.)
Now, in representing the two Premisses, I prefer
to begin with the negative one (the one beginning
with " no "), because grey counters can always be
placed with certainty, and will then help to fix the
position of the red counters, which are sometimes a
little uncertain where they wih1 be most welcome.
Let us express, then, "no nice Cakes are unwhole-
some (Cakes) ", i.e. " no y-Cakes are m'-(Cakes) ".
This tells us that none of the Cakes belonging to the
y-half of the cupboard are in its ??i'-compartments (i.e.
the ones outside the central Square). Hence the two
compartments, No. 9 and No. 15, are both 'empty';
and we must place a grey counter in each of them,
thus : —
§ 2.]
SYLLOGISMS.
23
We have now to express the other Premiss, namely,
" some new Cakes are unwholesome (Cakes) ", i.e.
" some ic-Cakes are m'-(Cakes) ". This tells us that
some of the Cakes in the re-half of the cupboard are
in its m'-compartments. Hence one of the two compart-
ments, No. 9 and No. 10, is 'occupied': and, as we are
not told in which of these two comjoajteiovit'rj to pLtcc-.
the red counter, the usual rule would be to lay it on
the division-line between them : but, in this case, the
other Premiss has settled the matter for us, by declaring
No. 9 to be empty. Hence the red counter has no choice,
and must go into No. 10, thus : —
0
0
And now what counters will this information enable
us to place in the smaller Diagram, so as to get some
Proposition involving x and y only, leaving out m ? Let
us take its four compartments, one by one.
First, No. 5. All we know about this is that its outer
portion is empty : but we know nothing about its inner
portion. Thus the Square may be empty, or it may have
something in it. Who can tell ? So we dare not place
any counter in this Square.
24 NEW LAMPS FOR OLD.
Secondly, what of No. 6 ? Here we are a little better
off. We know that there is something in it, for there is a
red counter in its outer portion. It is true we do not
know whether its inner portion is empty or occupied : but
what does that matter ? One solitary Cake, in one corner
of the Square, is quite sufficient excuse for saying "ttfc
Square is occupied ", and for marking it with a red counter.
As to No. 7, we are in the same condition as with No. 5
we find it partly 'empty', but we do not know
whether the other part is empty or occupied : so we dare
not mark this Square.
And as to No. 8, we have simply no information at all.
The result is
Our ' Conclusion ', then, must be got out of the rather
meagre piece of information that there is a red counter
in the x /-Square. Hence our Conclusion is " some x are
y' ", i.e. " some new Cakes are not-nice (Cakes) " : or, if
you prefer to take i/ as your Subject, "some not-nice
Cakes are new (Cakes) " ; but the other looks neatest.
We will now write out the whole Syllogism, putting
the symbol .'. for "therefore", and omitting "Cakes", for
the sake of brevity, at the end of each Proposition.
§ 2.] SYLLOGISMS. 25
" Some new Cakes are unwholesome ; )
No nice Cakes are unwholesome. J
.'. Some new Cakes are not-nice."
And you have now worked out, successfully, your
first ' Syllogism '. Permit me to congratulate you, and
to express the hope that it is but the beginning of a
long and glorious series of similar victories !
We will work out one other Syllogism a rather
harder one than the last and then, I think, you may
be safely left to play the Game by yourself, or (better)
with any friend whom you can find, that is able and
willing to take a share in the sport.
Let us see what we can make of the two Premisses —
" All Dragons are uncanny ; }
All Scotchmen are canny." J
Remember, I don't guarantee the Premisses to be
facts. In the first place, I never even saw a Dragon :
and, in the second place, it isn't of the slightest con-
sequence to us, as Logicians, whether our Premisses are
true or false : all we have to do is to make out
whether they lead logically to the Conclusion, so that,
if they were true, it would be true also.
You see, we must give up the " Cakes " now, or
our cupboards will be of no use to us. We must
take, as our ' Universe ', some class of things which
will include Dragons and Scotchmen : shall we say
' Animals ' ? And, as " canny " is evidently the At-
26 NEW LAMPS FOR OLD. L°H- L
tribute belonging to the 'Middle Terms', we will let
m stand for "canny", x for "Dragons", and y for
« Scotchmen ". So that our two Premisses are, in full,
" All Dragon- Animals are uncanny (Animals) ;
All Scotchman- Animals are canny (Animals)."
And these may be expressed, using letters for words,
thus : —
" All x are m ;
All y are m."
The first Premiss consists, as you already know, of
two parts : —
" Some x are m',"
and " No x are m."
And the second also consists of two parts : —
" Some y are m,"
and " No y are m'."
Let us take the negative portions first.
We have, then, to mark, on the larger Diagram, first,
" no x are m ", and secondly, " no y are m' ". I think
you will see, without further explanation, that the
two results, separately, are
§ 2.] SYLLOGISMS.
and that these two, when combined, give us
27
0
We have now to mark the two positive portions,
" some x are m' " and " some y are m ".
The only two compartments, available for Things
which are xm', are No. 9 and No. 10. Of these, No. 9
is already marked as ' empty ' ; so our red counter
must go into No. 10.
Similarly, the only two, available for ym, are No. 11
and No. 13. Of these, No. 11 is already marked as
'empty'; so our red counter must go into No. 13.
The final result is
28
NEW LAMPS FOR OLD.
[CH. I.
And now how much of this information can usefully
be transferred to the smaller Diagram ?
Let us take its four compartments, one by one.
As to No. 5? This, we see, is wholly 'empty'.
(So mark it with a grey counter.)
As to No. 6? This, we see, is 'occupied'. (So
mark it with a red counter.)
As to No. 7 ? Ditto, ditto.
As to No. 8? No information.
The smaller Diagram is now pretty liberally marked : —
And now what Conclusion can we read off from this ?
Well, it is impossible to pack such abundant information
into one Proposition : we shall have to indulge in two,
this time.
First, by taking x as Subject, we get " all x are y ",
that is,
" All Dragons are not-Scotchmen " :
secondly, by taking y as Subject, we get " all y are x' ",
that is,
" All Scotchmen are not-Dragons ".
Let us now write out, all together, our two Premisses
and our brace of Conclusions.
§ 2.] SYLLOGISMS. 29
" All Dragons are uncanny ;
All Scotchmen are canny.
( All Dragons are not- Scotchmen ;
' All Scotchmen are not-Dragons."
Let me mention, in conclusion, that you may perhaps
meet with logical treatises in which it is not assumed
that any Thing exists at all, but " some x are y " is under-
stood to mean " the Attributes x, y are compatible, so that
a Thing can have both at once ", and " no x are y " to
mean " the Attributes x, y are incompatible, so that
nothing can have both at once ".
In such treatises, Propositions have quite different
meanings from what they have in our ' Game of Logic ',
and it will be well to understand exactly what the
difference is.
First take " some x are y ". Here we understand
" are " to mean " are, as an actual fact " which of
course implies that some ^-Things exist. But they (the
writers of these other treatises) only understand " are "
to mean " can be ", which does not at all imply that any
exist. So they mean less than we do : our meaning
includes theirs (for of course "some x are y" includes
"some x can le y"}, but theirs does not include ours.
For example, " some Welsh hippopotami are heavy "
would be true, according to these writers (since the
30 NEW LAMPS FOR OLD. [Cn- *•
Attributes "Welsh" and "heavy" are quite compatible
in a hippopotamus), but it would be false in our Game
(since there are no Welsh hippopotami to be heavy).
Secondly, take "no x are y". Here we only under-
stand " are " to mean " are, as an actual fact " - which
does not at all imply that no x can be y. But they
understand the Proposition to mean, not only that none
are y, but that none can possibly be y. So they mean
more than we do : their meaning includes ours (for of
course " no x can be y " includes " no x are y "), but
ours does not include theirs. For example, "no Police-
men are eight feet high" would be true in our Game
(since, as an actual fact, no such splendid specimens are
ever found), but it would be false, according to these
writers (since the Attributes " belonging to the Police
Force " and " eight feet high " are quite compatible : there
is nothing to prevent a Policeman from growing to that
height, if sufficiently rubbed with Rowland's Macassar
Oil— —which is said to make hair grow, when rubbed
on hair, and so of course will make a Policeman grow,
when rubbed on a Policeman).
Thirdly, take "all x are y", which consists of the
two partial Propositions "some x are y" and "no x are
y'". Here, of course, the treatises mean less than we
do in the first part, and more than we do in the second.
But the two operations don't balance each other
§ 2.] SYLLOGISMS. 31
any more than you can console a man, for having
knocked down one of his chimneys, by giving him an
extra door-step.
If you meet with Syllogisms of this kind, you may
work them, quite easily, by the system I have given
you : you have only to make ' are ' mean ' are capable
of being', and all will go smoothly. For "some x
are y " will become " some x are capable of being y ",
that is, " the Attributes x, y are compatible ". And " no
* are y " will become " no x are capable of being y ",
that is, "the Attributes x, y are incompatible". And,
of course, " all x are y " will become " some x are capable
of being y, and none are capable of being y'", that
is, " the Attributes x, y are compatible, and the Attributes
x, y' are incompatible." In using the Diagrams for this
system, you must understand a red counter to mean
"there may possibly be something in this compartment,"
and a grey one to mean " there cannot possibly be any-
thing in this compartment."
§ 3. Fallacies.
And so you think, do you, that the chief use of Logic,
in real life, is to deduce Conclusions from workable
Premisses, and to satisfy yourself that the Conclusions,
deduced by other people, are correct? I only wish it
were ! Society would be much less liable to panics
and other delusions, and political life, especially, would
be a totally different thing, if even a majority of the
arguments, that are scattered broadcast over the world,
were correct ! But it is all the other way, I fear. For
one workable Pair of Premisses (I mean a Pair that lead
to a logical Conclusion) that you meet with in reading
your newspaper or magazine, you will probably find Jive
that lead to no Conclusion at all: and, even when the
Premisses are workable, for one instance, where the writer
draws a correct Conclusion, there are probably ten where
he draws an incorrect one.
In the first case, you may say "the Premisses are
fallacious " : in the second, " the Conclusion is fallacious."
CH. I. § 3.] NEW LAMPS FOR OLD. 33
The chief use you will find, in such Logical skill as this
Game may teach you, will be in detecting ' Fallacies ' of
these two kinds.
The first kind of Fallacy ' Fallacious Premisses '
you will detect when, after marking them on the larger
Diagram, you try to transfer the marks to the smaller.
You will take its four compartments, one by one, and
ask, for each in turn, " What mark can I place here ? " ; and
in every one the answer will be " No information ! ", showing
that there is no Conclusion at all. For instance,
" All soldiers are brave ; \
Some Englishmen are brave. /
.'. Some Englishmen are soldiers."
looks uncommonly like a Syllogism, and might easily take
in a less experienced Logician. But you are not to be
caught by such a trick ! You would simply set out the
Premisses, and would then calmly remark "Fallacious
Premisses ! " : you wouldn't condescend to ask what
Conclusion the writer professed to draw knowing that,
whatever it is, it must be wrong. You would be just as
safe as that wise mother was, who said " Mary, just go up
to the nursery, and see what Baby's doing, and tell him
not to do it ! "
The other kind of Fallacy ' Fallacious Conclusion '
— you will not detect till you have marked both
Diagrams, and have read off the correct Conclusion,
and have compared it with the Conclusion which the
writer has drawn.
D
34 NEW LAMPS FOR OLD. [On. I.
But mind, you mustn't say "Fallacious Conclusion,"
simply because it is not identical with the correct one :
it may be a part of the correct Conclusion, and so be quite
correct, as far as it goes. In this case you would merely
remark, with a pitying smile, " Defective Conclusion ! "
Suppose, for example, you were to meet with this
Syllogism : —
" All unselfish people are generous ; |
No misers are generous.
.'. No misers are unselfish."
the Premisses of which might be thus expressed in
letters : —
" All x are m ; |
No y are m" )
Here the correct Conclusion would be " All x' are y' "
(that is, " All unselfish people are not misers "), while the
Conclusion, drawn by the writer, is " No y are x'" (which
is the same as " No x' are y" and so is part of " All x' are
y'."} Here you would simply say " Defective Conclusion ! "
The same thing would happen, if you were in a confec-
tioner's shop, and if a little boy were to come in, put down
twopence, and march off triumphantly with a single penny-
bun. You would shake your head mournfully, and would
remark " Defective Conclusion ! Poor little chap ! " And
perhaps you would ask the young lady behind the counter
whether she would let you eat the bun, which the little
boy had paid for and left behind him : and perhaps she
would reply " Shan't ! "
§ 3.] FALLACIES. 35
But if, in the above example, the writer had drawn
the Conclusion " All misers are selfish " (that is, " All
y are «"), this would be going beyond his legitimate
rights (since it would assert the existence of y, which is
not contained in the Premisses), and you would very
properly say " Fallacious Conclusion ! "
Now, when you read other treatises on Logic, you
will meet with various kinds of (so-called) ' Fallacies' ,
which are by no means always so. For example, if
you were to put before one of these Logicians the
Pair of Premisses
"No honest men cheat ;
No dishonest men are trustworthy."
and were to ask him what Conclusion followed, he would
probably say " None at all ! Your Premisses offend
against two distinct Rules, and are as fallacious as they
can well be ! " Then suppose you were bold enough to
say "The Conclusion is 'No men who cheat are trust-
worthy '," I fear your Logical friend would turn away
hastily perhaps angry, perhaps only scornful : in any
case, the result would be unpleasant. / advise you not to
try the experiment !
" But why is this ? " you will say. " Do you mean to
tell us that all these Logicians are wrong ? " Far from it,
dear Reader ! From their point of view, they are perfectly
right. But they do not include, in their system, anything
like all the possible forms of Syllogisms.
D 2
36 FALLACIES. [On. I. § 3.
They have a sort of nervous dread of Attributes be-
ginning with a negative particle. For example, such
Propositions as " All not-aj are y" " Wo x are not-?/," are
quite outside their system. And thus, having (from sheer
nervousness) excluded a quantity of very useful forms, they
have made rules which, though quite applicable to the few
forms which they allow of, are no use at all when you
consider all possible forms.
Let us not quarrel with them, dear Reader ! There is
room enough in the world for both of us. Let us quietly
take our broader system : and, if they choose to shut their
eyes to all these useful forms, and to say " They are not
Syllogisms at all ! " we can but stand aside, and let them
Rush upon their Fate ! There is scarcely anything of
yours, upon which it is so dangerous to Rush, as your
Fate. You may Rush upon your Potato-beds, or your
Strawberry-beds, without doing much harm : you may
even Rush upon your Balcony (unless it is a new house,
built by contract, and with no clerk of the works) and
may survive the foolhardy enterprise: but if you
once Rush upon your Fate— why, you must take the
consequences !
37
CHAPTER II.
CROSS QUESTIONS.
" The Man in the Wilderness asked of me
' How many strawberries grow in the sea ? ' "
§ 1. Elementary.
1. What is an ' Attribute ' ? Give examples.
2. When is it good sense to put " is " or " are " between
two names? Give examples.
o. When is it not good sense ? Give examples.
4. When it is not good sense, what is the simplest agree-
ment to make, in order to make good sense ?
5. Explain ' Proposition ', ' Term ', ' Subject ', and ' Pre-
dicate'. Give examples.
6. What are ' Particular ' and ' Universal ' Propositions ?
Give examples.
7. Give a rule for knowing, when we look at the smaller
Diagram, what Attributes belong to the things in each
compartment.
8. What does " some " mean in Logic ?
[See pp. 55, 6]
38 CROSS QUESTIONS. [Cn. II.
9. In what sense do we use the word ' Universe ' in this
Game?
10. What is a ' Double ' Proposition ? Give examples.
11. When is a class of Things said to be 'exhaustively'
divided ? Give examples.
12. Explain the phrase "sitting on the fence."
13. What two partial Propositions make up, when taken
together, " all x are y " ?
14. What are ' Individual ' Propositions ? Give examples.
15. What kinds of Propositions imply, in this Game,
the existence of their Subjects ?
16. When a Proposition contains more than two Attri-
butes, these Attributes may in some cases be re-arranged,
and shifted from one Term to the other. In what cases
may this be done ? Give examples.
Break up each of the following into two partial
Propositions :
17. All tigers are fierce.
18. All hard-boiled eggs are unwholesome.
19. I am happy.
20. John is not at home.
[See pp. 56, 7]
§ 1.] ELEMENTARY. 39
21. Give a rule for knowing, when we look at the
larger Diagram, what Attributes belong to the Things
contained in each compartment.
22. Explain ' Premisses ', ' Conclusion ', and ' Syllogism '.
Give examples.
23. Explain the phrases 'Middle Term' and 'Middle
Terms '.
24. In marking a pair of Premisses on the larger
Diagram, why is it best to mark negative Propositions
before affirmative ones ?
25. Why is it of no consequence to us, as Logicians,
whether the Premisses are true or false ?
26. How can we work Syllogisms in which we are told
that " some x are y " is to be understood to mean " the
Attributes x, y are compatible ", and " no x are y " to mean
" the Attributes x, y are incompatible " ?
27. What are the two kinds of ' Fallacies ' ?
28. How may we detect ' Fallacious Premisses ' ?
29. How may we detect a ' Fallacious Conclusion ' ?
30. Sometimes the Conclusion, offered to us, is not
identical with the correct Conclusion, and yet cannot be
fairly called ' Fallacious '. When does this happen ? And
what name may we give to such a Conclusion ?
[See pp. 57—59]
40 CROSS QUESTIONS.
§ 2. Half of Smaller Diagram.
Propositions to be represented.
[On. II.
x
II
y
1. Some x are not-?/.
2. All x are not-y.
3. Some x are y, and some are not-y.
4. No ic exist.
5. Some x exist.
6. No a? are not-?/.
7. Some # are not-?/, and some x exist.
Taking x = "judges " ; y = "just " ;
8. No judges are just.
9. Some judges are unjust.
10. All judges are just.
Taking x = " plums " ; y = " wholesome " ;
11. Some plums are wholesome.
12. There are no wholesome plums.
13. Plums are some of them wholesome, and some not.
14. All plums are unwholesome.
[See pp. 59, 60]
§2.]
CROSS QUESTIONS.
41
X'
-Taking y 4»" diligent students " ; x = " successful " ;
15. No diligent students /are unsuccessful.-
students.
diligent students are successful.
17. No students are diligent.
18. There are some diligent, but unsuccessful;
19. Some students are diligent.
Ooe
[See pp. 60, 1J
42
CROSS QUESTIONS.
[CH. II.
§ 3. Half of Smaller Diagram.
Symbols to be interpreted.
x
—y — y —
\.
2.
Taking x = " good riddles " ; y = « hard " :
5.
0.
7.
[See pp. 61, 2]
§ 3.] CBOSS QUESTIONS.
Taking x = " lobsters " ; y = " selfish " ;
9.
43
Taking y = " healthy people " ; x = " happy " ;
13.
0
14.
i
15.
1
16.
0
1
1
0
[See p. 62]
44
CBOSS QUESTIONS.
[Cn. II.
§ 4. Smaller Diagram.
Propositions to be represented.
—y
-y-
1. All y are x.
2. Some y are not-z.
3. No not-a; are noi-y.
4. Some x are not-?/.
5. Some not-y are x.
6. No not-£ are y.
7. Some not-a? are not-t/.
8. All not-# are not-y.
9. Some not-y exist.
10. No not-a; exist.
11. Some y are x, and some are not-».
12. All x are y, and all not-y are not-x.
[See pp. 62, 3]
§ 4.] CROSS QUESTIONS. 45
Taking " nations " as Universe ; x = " civilised " ;
y = " warlike " ;
13. No uncivilised nation is warlike.
14. All un warlike nations are uncivilised.
15. Some nations are un warlike.
16. All warlike nations are civilised, and all civilised
nations are warlike.
17. No nation is uncivilised.
Taking " crocodiles " as Universe ; x = " hungry " ;
and y = " amiable " ;
18. All hungry crocodiles are unamiable.
19. No crocodiles are amiable when hungry.
20. Some crocodiles, when not hungry, are amiable ; but
some are not.
21. No crocodiles are amiable, and some are hungry.
22. All crocodiles, when not hungry, are amiable ; and
all unamiable crocodiles are hungry.
23. Some hungry crocodiles are amiable, and some that
are not hungry are unamiable.
[See pp. 63, 4]
46
CROSS QUESTIONS.
. II.
§ 5. Smaller Diagram.
Symbols to be interpreted.
1.
3.
2.
Taking "houses" as Universe; x = " built of brick";
and y = " two-storied " ; interpret
5.
6.
7.
[See p. 65]
§ 5.] CSOSS QUESTIONS.
Taking " boys " as Universe ; x = " fat " ;
and y = " active " ; interpret
47
9.
11.
0
1
0
10.
12.
Taking "cats " as Universe ; x = " green-eyed " ;
and y = " good-tempered " ; interpret
13.
15.
14.
16.
[See pp. 65, 6]
48
CROSS QUESTIONS.
[On. II.
§ 6. Larger Diagram.
Propositions to be represented.
1. No x are m.
2. Some y are m'.
3. All m are as'.
4. No m' are y'.
5. No m are as ;
All y are m.
6. Some x are m
No y are m.
7. All m are as' ;
No m are y.
8. No as' are m ;
No y' are m'.
— y m—y —
— x
[See pp. 67, 8]
§ 6.] CROSS QUESTIONS. 49
Taking " rabbits " as Universe ; m = " greedy " ;
x = " old " ; and y = " black " ; represent
9. No old rabbits are greedy.
10. Some not-greedy rabbits are black.
11. All white rabbits are free from greediness.
12. All greedy rabbits are young.
13. No old rabbits are greedy ; 1
All black rabbits are greedy. /
14. All rabbits, that are not greedy, are black ;
No old rabbits are free from greediness.
Taking " birds " as Universe ; m = " that sing loud " ;
x=" well-fed " ; and y=" happy " ; represent
15. All well-fed birds sing loud ;
No birds, that sing loud, are unhappy.
16. All birds, that do not sing loud, are unhappy ;
No well-fed birds fail to sing loud.
Taking " persons " as Universe ; m = " in the house " ;
x = " John " ; and y = " having a tooth-ache " ; represent
17. John is in the house ;
Everybody in the house is suffering from tooth-ache.
18. There is no one in the house but John ;
Nobody, out of the house, has a tooth-ache
[See pp. 68—70]
.}
50 CROSS QUESTIONS. [On. II. § 6.
Taking " persons " as Universe ; m = " I " ;
x=" that has taken a walk " ; y = " that feels better " ;
represent
19. I have been out for a walk ; \
I feel much better. j
Choosing your own ' Universe ' &c., represent
20. I sent him to bring me a kitten ;
He brought me a kettle by mistake.
[See pp. 70, 1]
CH. II. § 7.]
CROSS QUESTIONS.
51
§ 7. Both Diagrams to be employed.
-x
y m y
x
KB. In each Question, a small Diagram should be
drawn, for x and y only, and marked in accordance with
the given large Diagram : and then as many Propositions
as possible, for x and y, should be read off from this small
Diagram.
1.
[See
0
0
0
0
1
p. 72]
2.
E 2
52
S.
CROSS QUESTIONS.
[On. I]
0
0
0
0
Mark, on a large Diagram, the following pairs of Pro-
positions from the preceding Section : then mark a small
Diagram in accordance with it, &c.
5. No. 13. [seep. 49] 9. No. 17.
6. No. 14. 10. No. 18.
7. No. 15. 11. No. 19. [seep. 50]
8. No. 16. 12. No. 20.
Mark, on a large Diagram, the following Pairs of Pro-
positions : then mark a small Diagram, &c. These are,
in fact, Pairs of Premisses for Syllogisms : and the results,
read off from the small Diagram, are the Conclusions.
13. No exciting hooks suit feverish patients ; )
Unexciting books make one drowsy. /
14. Some, who deserve the fair, get their deserts ; |
None but the brave deserve the fair. j
15.,.No children are patient ; |
No impatient person can sit still. /
[See pp. 72—5]
§ 7.] BOTH DIAGRAMS TO BE EMPLOYED. 53
16. All pigs are fat ; |
No skeletons are fat. /
17. No monkeys are soldiers ; ^
All monkeys are mischievous. J
18. None of my cousins are just ; |
No judges are unjust. /
19. Some days are rainy ;
Rainy days are tiresome.
(3 a
20. All medicine is nasty ; ]
\^) 9 >
Senna is a medicine. J
21. Some Jews are rich ; )
All Pa tagonians are Gentiles. /-ALL ESfraWDO
22. All teetotalers like sugar ; i riue •
No nightingale drinks wine. J
23. No muffins are wholesome ;
All buns are unwholesome.
24. No fat creatures run well ; |
Some greyhounds run well. /
25. All soldiers march ;
Some youths are not soldiers.
26. Sugar is sweet ; )
Salt is not sweet. /
27. Some eggs are hard-boiled ; )
No eggs are uncrackable. J
28. There are no Jews in the house ;
There are no Gentiles in the garden.
[See pp. 75—82]
54 CROSS QUESTIONS. [On. II. § 7.
29. All battles are noisy ; |
What makes no noise may escape notice. J
30. No Jews are mad ; |
All Eabbis are Jews. J
31. There are no fish that cannot swim ;
Some skates are fish.
32. All passionate people are unreasonable ; )
Some orators are passionate. J
[See pp. 82—84]
55
CHAPTER III.
CROOKED ANSWERS.
I answered him, as I thought good,
' As many as red-herrings grow in the wood'
§ 1. Elementary.
1. Whatever can be "attributed to", that is "said to
belong to ", a Thing, is called an ' Attribute '. For example,
" baked ", which can (frequently) be attributed to " Buns ",
and "beautiful", which can (seldom) be attributed to
" Babies ".
2. When they are the Names of two Things (for example,
" these Pigs are fat Animals"), or of two Attributes (for
example, " pink is light red ").
3. When one is the Name of a Thing, and the other
the Name of an Attribute (for example, " these Pigs are
pink "), since a Thing cannot actually be an Attribute.
4. That the Substantive shall be supposed to be repeated
at the end of the sentence (for example, " these Pigs are
pink (Pigs)").
5. A ' Proposition ' is a sentence stating that some, or
none, or all, of the Things belonging to a certain class,
[See p. 37]
56 CROOKED ANSWERS. [On. III.
called the ' Subject ', are also Things belonging to a certain
other class, called the ' Predicate '. For example, " some
new Cakes are not nice ", that is (written in full) " some
new Cakes are not nice Cakes " ; where the class " new
Cakes " is the Subject, and the class " not-nice Cakes " is
the Predicate.
6. A Proposition, stating that some of the Things belong-
ing to its Subject are so-and-so, is called ' Particular '. For
example, " some new Cakes are nice ", " some new Cakes
are not nice."
A Proposition, stating that none of the Things belonging
to its Subject, or that all of them, are so-and-so, is called
' Universal '. For example, " no new Cakes are nice ", " all
new Cakes are not nice ".
7. The Things in each compartment possess two
Attributes, whose symbols will be found written on two
of the edges of that compartment.
8. " One or more."
9. As a name of the class of Things to which the whole
Diagram is assigned.
10. A Proposition containing two statements. For
example, " some new Cakes are nice and some are not-
nice."
11. When the whole class, thus divided, is " exhausted "
among the sets into which it is divided, there being no
member of it which does not belong to some one of them.
For example, the class "new Cakes" is "exhaustively"
[See pp. 37, 8]
§ 1.] ELEMENTARY. 57
divided into " nice " and " not-nice " since every new Cake
must be one or the other.
12. When a man cannot make up his mind which of
two parties he will join, he is said to be " sitting on the
fence "- —not being able to decide on which side he will
jump down.
1 3. " Some x are y " and " no x are y' ".
14. A Proposition, whose Subject is a single Thing, is
called ' Individual '. For example, " I am happy ", " John
is not at home ". These are Universal Propositions, being
the same as " all the I's that exist are happy ", " all the
Johns, that I am now considering, are not at home ".
15. Propositions beginning with " some " or " all ".
16. When they begin with " some " or " no ". For exam-
ple, " some abc are def " may be re-arranged as " some If
are acde ", each being equivalent to " some alcdef exist ".
17. Some tigers are fierce,
No tigers are not-fierce.
18. Some hard-boiled eggs are unwholesome,
No hard-boiled eggs are wholesome.
19. Some I's are happy,
No I's are unhappy.
20. Some Johns are not at home,
No Johns are at home.
21. The Things, in each compartment of the larger
Diagram, possess three Attributes, whose symbols will be
[See pp. 38, 9]
58 CROOKED ANSWERS. [On. III.
found written at three of the corners of. the compartment
(except in the case of m, which is not actually inserted
in the Diagram, but is supposed to stand at each of its
four outer corners).
22. If the Universe of Things be divided with regard
to three different Attributes ; and if two Propositions be
oiven, containing two different couples of these Attributes ;
and if from these we can prove a third Proposition, contain-
ing the two Attributes that have not yet occurred together ;
the given Propositions are called ' the Premisses ', the third
one 'the Conclusion', and the whole set 'a Syllogism'. For
example, the Premisses might be " no m are x " and " all
m' are y " ; and it might be possible to prove from them a
Conclusion containing x and y.
23. If an Attribute occurs in both Premisses, the Term
containing it is called ' the Middle Term '. For example,
if the Premisses are " some m are x " and " no m are y ",
the class of " m-Things " is ' the Middle Term.'
If an Attribute occurs in one Premiss, and its contradictory
in the other, the Terms containing them maybe called 'the
Middle Terms '. For example, if the Premisses are "no m
are x' " and " all mf are y ", the two classes of " m-Things "
and " m'-Things " may be called ' the Middle Terms '.
24. Because they can be marked with certainty : whereas
affirmative Propositions (that is, those that begin with
" some " or " all ") sometimes require us to place a red
counter ' sitting on a fence '.
[See p. 39]
§1-1
ELEMENTARY.
59
25. Because the only question we are concerned with is
whether the Conclusion follows logically fron^the Premisses,
so that, if they were true, it also would be true.
26. By understanding a red counter to mean " this com-
partment can be occupied ", and a grey one to mean " this
compartment cannot be occupied" or "this compartment
must be empty ".
27. ' Fallacious Premisses ' and ' Fallacious Conclusion '.
28. By finding, when we try to transfer marks from the
larger Diagram to the smaller, that there is ' no informa-
tion ' for any of its four compartments.
29. By finding the correct Conclusion, and then observing
that the Conclusion, offered to us, is neither identical with
it nor a part of it.
30. When the offered Conclusion is part of the correct
Conclusion. In this case, we may call it a ' Defective
Conclusion '.
§ 2. Half of Smaller Diagram.
Propositions represented.
1.
2.
4.
[See pp. 39, 40]
KO
5.
CROOKED ANSWERS
6.
[On. III.
It might be thought that the proper
Diagram would be - 1 , in order to express " some
x exist " : but this is really contained in " some x are y'."
To put a red counter on the division-line would only tell
us " one of the two compartments is occupied ", which we
know already, in knowing that one is occupied.
8. No x are y. i.e.
9. Some x are y'. i. e.
10. All x are y. i. e.
11. Some x are y. i. e.
12. No x are y. i. e.
13. Some x are y, and some are y'. i. e.
14. All x are y'. i. e.
15. No y are x'. i.e.
[See pp. 40, 1]
§2.]
PROPOSITIONS REPRESENTED.
61
16. All y are x. i. e.
17. No y exist, i. e.
18. Some y are x'. i. e.
19. Some y exist, i. e.
-1-
§ 3. Half of Smaller Diagram.
Symbols interpreted.
1. No a; are y'.
2. No a? exist.
3. Some x exist.
4. All £ are y'.
5. Some a? are T/. i. e. Some good riddles are hard.
6. All x are y. i. e. All good riddles are hard.
7. No x exist, i. e. No riddles are good.
[See pp. 41, 2]
62 CROOKED ANSWERS. [Cn. III.
8. No x are y. i. e. No good riddles are hard.
9.. Some x are y'. i. e. Some lobsters are unselfish.
10. No x are y. i. e. No lobsters are selfish.
11. All x are y'. i. e. All lobsters are unselfish.
12. Some x are y, and some are y'. i. e. Some lobsters
are selfish, and some are unselfish.
13. All y' are x'. i. e. All invalids are unhappy.
14. Some y' exist, i. e. Some people are unhealthy.
15. Some y' are x, and some are x'. i. e. Some invalids
are happy, and some are unhappy.
16. No y' exist, i. e. Nobody is unhealthy.
§ 4. Smaller Diagram.
Propositions represented.
2.
4.
[See pp. 42—4]
§ 4.] PROPOSITIONS REPRESENTED.
63
5.
7.
9.
11.
6.
8.
10.
12.
13. No x' are y. i. e.
14. All y' are x'. i. e.
15. Some y' exist, i.e.
[See pp. 44, 5]
64
CROOKED ANSWERS. [Ch. III. § 4.
0
0
0
1
0
16. All y are x, and all x are y. i. e.
17. No x' exist, i. e.
18. All x are y'. i. e.
19. No £ are y. i. e.
20. Some x' are £/, and some are y'. i. e.
21. No y exist, and some x exist, i. e.
22. All x' are ^, and all y' are a?, i. e.
23. Some « are y, and some #' are y'. i. e.
1
1
0
1
1
[See p. 45]
CH. III. § 5.] CROOKED ANSWERS. 65
§ 5. Smaller Diagram.
Symbols interpreted.
1. Some y are not-£,
or, Some not-a; are y.
2. No not-a? are not-y,
or, No not-?/ are not-«.
3. No TLQi-y are a?.
4. No not-a? exist, i. e. No Things are not-#.
5. No y exist, i. e. No houses are two-storied.
6. Some x' exist, i. e. Some houses are not built of
brick.
7. No x are y'. Or, no y' are x. i. e. No houses, built
of brick, are other than two-storied. Or, no houses,
that are not two-storied, are built of brick.
S. All x' are y'. i. e. All houses, that are not built of
brick, are not two-storied.
9. Some x are y, and some are y'. i. e. Some fat boys
are active, and some are not.
10. All y' are x'. i. e. All lazy boys are thin.
11. All x are y', and all y' are x. i. e. All fat boys are
lazy, and all lazy ones are fat.
[See pp. 46, 7]
66 CROOKED ANSWERS. [On. III. § 5.
12. All y are x, and all x' are y. i. e.. All active boys are
fat, and all thin ones are lazy.
13. No x exist, and no y' exist, i. e. No cats have green
eyes, and none have bad tempers.
14. Some x are y', and some x' are y. Or, some y are a?',
and some y' are a?, i.e. Some green-eyed cats are
bad-tempered, and some, that have not green eyes,
are good-tempered. Or, some good-tempered cats
have not green eyes, and some bad-tempered ones
have green eyes.
15. Some x are y, and no x' are y'. Or, some y are x, and
no y' are x'. i. e. Some green-eyed cats are good-
tempered, and none, that are not green-eyed, are
bad-tempered. Or, some good-tempered cats have
green eyes, and none, that are bad-tempered, have
not green eyes.
16. All x are y', and all x' are y. Or, all y are x', and all
y' are x. i. e. All green-eyed cats are bad-tempered,
and all, that have not green eyes, are good-tem-
pered. Or, all good-tempered ones have eyes that
are not green, and all bad-tempered ones have
green eyes.
[See p. 47]
CH. III. § 6.] CROOKED ANSWERS.
67
§ 6. Larger Diagram.
Propositions represented.
I.
3.
5.
0
[See p. 48]
2.
1-
4.
6.
F 2
68
CROOKED ANSWERS.
9. No x are m. i. e.
10. Some m' are y. i. e.
11. All y' are m'. i. e.
[See pp. 48, 9]
§6.]
PROPOSITIONS REPRESENTED.
69
12. All m are x'. i. e.
13. No x are w; ) .
All y are
m;\ .
\i.e.
in. )
14. All m' are y; ) .
No x are m'.
i. e.
15. All x are w; ) .
No m are y'.
i e.
[See p. 49]
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
70
CROOKED ANSWERS.
[OH. III.
16. All m' are y' ;\ .
No a; are m'. )
0
0
0
1
17. All a? are m ; ) .
>i. e.
All m are y. J
[See remarks on No. 7, p. 60.]
18. No »' are m ; ) .
XT/ r L a
No m are t/. J
19. All m are x',\.
All m are y. /
0
0
1
0
0
0
0
0
0
1
0
0
0
[See pp. 49; 50]
$6.]
PROPOSITIONS REPRESENTED.
71
20. We had better take "persons" as Universe. We
may choose " myself " as ' Middle Term ', in which case
the Premisses will take the form
I am a-person-who-sent-him-to-bring-a-kitten ;
I am a-person-to-whom-he-brought-a-kettle-by-mistake.
Or we may choose " he " as ' Middle Term ', in which
case the Premisses will take the form
He is a-person-whom-I-sent-to-bring-me-a-kitten ;
He is a-person-who-brought-me-a-kettle-by-mistake.
The latter form seems best, as the interest of the anecdote
clearly depends on his stupidity not on what happened
to me. Let us then make m = " he " ; x = " persons
whom I sent, &c." ; and y = " persons who brought, &c."
Hence,
All m are x ;
All m are y.
\ and the required Diagram is
[See p. 50]
72
CROOKED ANSWERS. [On. III.
§ 7. Both Diagrams employed.
o.
ti.
i. e. All y are
i. e. Some x are ?/' ; or, Some y' are x.
i. e. Some y are x' ; or, Some x are i/.
i. e. No #' are y' ; or, No y' are #'.
i. e. All y are x'. i. e. All black rabbits
are young.
i. e. Some y are x'. i. e. Some black
rabbits are young.
[See pp. 51, 2]
§7-]
BOTH DIAGRAMS EMPLOYED.
73
i. e. All x are y. i. e. All well-fed birds
are happy.
i. e. Some x' are y'. i. e. Some birds,
that are not well-fed, are unhappy ;
or, Some unhappy birds are not
well-fed.
12.
[See p. 52]
i. e. All x are y. i. e. John has got a
tooth-ache.
i. e. No x' are y. i. e. No one, but John,
has got a tooth-ache.
i. e. Some x are y. i. e. Some one, who
has taken a walk, feels better.
i. e. Some x are y. i. e. Some one,
whom I sent to bring me a kitten,
brought me a kettle by mistake.
74
CROOKED ANSWERS.
[On. III.
13.
-1-
0
Let " books " be Universe ; m = " exciting " ,
x=" that suit feverish patients " ; y = " that make
one drowsy ".
No m are x ;
All m' are y.
i. e. No books suit feverish patients, except such as make
one drowsy.
t .'. No y' are x.
I. ) 3
14.
Let " persons " be Universe ; m = " that deserve the fair " :
x = " that get their deserts " ; y •— " brave ".
Some m are x ; )
,.T . } :. Some y are #.
JNo ?/ are m. )
i. e. Some brave persons get their deserts.
[See p. 52 J
§7-]
15.
BOTH DIAGRAMS EMPLOYED,
75
Let " persons " be Universe ; m = " patient " ;
x = " children " ; y = " that can sit still ".
No x are TO ; )
^ , > .'. No x are y.
No TO are y. )
i. e. No children can sit still.
16.
0 1
Let " things " be Universe ; m = " fat " ; x = " pigs " ;
y = " skeletons ".
All x are TO ; )
TVT f .'. All x are 11 .
No % are m. )
i. e. All pigs are not- skeletons.
[See pp. 52, 3]
76
CROOKED ANSWERS.
[On. III.
17.
Let " creatures " be Universe ; m = " monkeys " ;
x- = " soldiers " ; y = " mischievous ".
No m are x ;
. 1T
All m are y.
i. e. Some mischievous creatures are not soldiers.
; )
\ .'.
. )
Some y are x'.
18.
Let " persons " be Universe ; m = "just " ;
x = " my cousins " ; y = " judges ".
No x are m ; )
AT , > .". No x are y.
JMo y are m . )
i. e. None of my cousins are judges.
[See p. 53]
§7.]
BOTH DIAGRAMS EMPLOYED.
77
Let " periods " be Universe ; TO = " days " ;
x = " rainy " ; y = " tiresome ".
Some in are x ;
All xm are y.
i. e. Some rainy periods are tiresome.
' ,(• /. Some x are y.
N.B. These are not legitimate Premisses, since the
Conclusion is really part of the second Premiss, so that the
first Premiss is superfluous. This may be shown, in letters,
thus : —
" All xm are y " contains " Some xm are y ", which
contains " Some x are y". Or, in words, " All rainy days
are tiresome " contains " Some rainy days are tiresome ",
which contains " Some rainy periods are tiresome ".
Moreover, the first Premiss, besides being superfluous, is
actually contained in the second ; since it is equivalent to
" Some rainy days exist ", which, as we know, is implied in
the Proposition " All rainy days are tiresome ".
Altogether, a most unsatisfactory Pair of Premisses !
[See p. 53]
78
CROOKED ANSWERS.
[OH. III.
20.
Let "things" be Universe ; m = " medicine " ;
x = " nasty " ; y = " senna ".
All m are x ; )
> .'. All y are x.
All y are m. >
i. e. Senna is nasty.
[See remarks on No. 7, p. 60. ]
21.
-1-
Let " persons " be Universe ; m = " Jews " ;
x = " rich " ; y = " Patagonians ".
Some m are x ; ]
m , } :. Some x are y'.
All y are m . }
i. e. Some rich persons are not Patagonians.
[See p. 53]
§<•]
BOTH DIAGRAMS EMPLOYED,
79
Let " creatures " be Universe ; m = " teetotalers " ;
x = " that like sugar " ; y = " nightingales ".
All m are x ;
No y are m'
i. e. No nightingales dislike sugar.
•v* • \
, \ .'. No y are x'.
23.
Let " food " be Universe ; m = " wholesome " ;
x = " muffins " ; y = " buns ".
No x are m ;
All y are m
There is 'no information ' for the smaller Diagram ; so
no Conclusion can be drawn.
[See p. 53]
80
CROOKED ANSWERS.
[Cn. III.
24.
Let " creatures " be Universe ; m = " that run well " ;
x = " fat " ; y = " greyhounds ".
No x are mi) „
v .'. Some y are or.
borne T/ are m. J
i. e. Some greyhounds are not fat.
25.
Let " persons " be Universe ; m = " soldiers " ;
x — " that march " ; y = " youths ".
All m are a? ;
Some y are m'.
There is ' no information ' for the smaller Diagram ; so
no Conclusion can be drawn.
[See p. 53]
§7.]
BOTH DIAGRAMS EMPLOYED.
81
26.
Let " food " be Universe ; m = " sweet " ;
x = " sugar " ; y = " salt ".
All x are m ; } . ( All x are y'.
All y are m'. / I All y are a?'.
Sugar is not salt.
i.e.
I Salt is not sugar.
Let " Things " be Universe ; m = "
x = " hard-boiled " ; y = " crackable ".
Some m are x ;
No m are y
i. e. Some hard-boiled things can be cracked.
[See p. 53]
G
3 a;; )
, \ .'.
Some x are
82
CROOKED ANSWERS.
[On. III.
28.
Let " persons " be Universe ; m = " Jews " ; x = " that
are in the house " ; y = " that are in the garden ".
No m are x ;
No m' are y.
i. e. No persons, that are in the house, are also in
the garden.
.'. No x are .
29.
Let " Things " be Universe ; m = " noisy " ;
x = " battles " ; y = " that may escape notice ".
All x are m ; ) „
... . \ .'. borne x are y.
All m are y. }
i. e. Some things, that are not battles, may escape notice.
[See pp. 53, 54]
§7.]
BOTH DIAGRAMS EMPLOYED.
83
30.
Let " persons " be Universe ; TO = " Jews " ;
x — " mad " ; y — " Rabbis ".
No TO are x ;
All y are TO.
i. e. All Rabbis are sane.
• \
'>••,*. All y are x.
31.
Let " Things " be Universe ; TO = " fish " ;
# = " that can swim " ; y = " skates ".
No TO are x' ;
Some y are TO.
i. e. Some skates can swim.
[See p. 54]
G 2
I . '. Some y are x.
i. )
84
CROOKED ANSWERS. [On. III. § 7.
32.
Let " people " be Universe ; TO = " passionate " ;
x — " reasonable " ; y = " orators ".
All m are x ; )
0 > . ' Some y are x .
borne y are m. }
i. e. Some orators are unreasonable.
[See remarks on No. 7, p. 60. ]
[See p. 54]
CHAPTER IV.
HIT OR MISS.
' Thou canst not hit it, hit it, hit it,
Thou canst not hit it, my good man."
1. Pain is wearisome ;
No pain is eagerly wished for.
2. No bald person needs a hair-brush
No lizards have hair.
3. All thoughtless people do mischief ; )
No thoughtful person forgets a promise. J
4. I do not like John ; i
Some of my friends like John. J
5. No potatoes are pine-apples ; |
All pine-apples are nice. /
6. No pins are ambitious ; |
No needles are pins. /
7. All my friends have colds ; )
No one can sing who has a cold. J
8. All these dishes are well-cooked ;
Some dishes are unwholesome if not well-cooked.
86 HIT OR MISS. [On. IV.
9. No medicine is nice ;
Senna is a medicine.
10. Some oysters are silent ;
No silent creatures are amusing.
11. All wise men walk on their feet ;
All unwise men walk on their hands.
)
in. /
12. " Mind your own business ; |
This quarrel is no business of yours." \
13. No bridges are made of sugar;
Some bridges are picturesque.
14. No riddles interest me that can be solved ;
All these riddles are insoluble.
15. John is industrious ; )
All industrious people are happy, j
16. No frogs write books ; j
Some people use ink in writing books. )
17. No pokers are soft ; |
All pillows are soft. /
18. No antelope is ungraceful ;
Graceful animals delight the eye.
19. Some uncles are ungenerous ; j
All merchants are generous. /
20. No unhappy people chuckle; |
No happy people groan. )
21. Audible music causes vibration in the air; |
Inaudible music is not worth paying for. /
CH. IV.] HIT OR MISS. 87
22. He gave me five pounds ; \
I was delighted. J
23. No old Jews are fat millers ; \
All my friends are old millers, j
24. Flour is good for food ; }
Oatmeal is a kind of flour. J
25. Some dreams are terrible ; }
No lambs are terrible. /
26. No rich man begs in the street ;
All who are not rich should keep accounts
27. No thieves are honest :
Some dishonest people are found out.
28. All wasps are unfriendly ;
All puppies are friendly
29. All improbable stories are doubted ;
None of these stories are probable
30. " He told me you had gone away."
" He never says one word of truth."
31. His songs never last an hour;
A song, that lasts an hour, is tedious.
32. No bride-cakes are wholesome ;
Unwholesome food should be avoided.
33. No old misers are cheerful ; |
Some old misers are thin. J
34. All ducks waddle ;
Nothing that waddles is graceful.
:;i
88 HIT OR MISS. [On. IV.
35. No Professors are ignorant ; i
Some ignorant people are conceited. /
36. Toothache is never pleasant ;
Warmth is never unpleasant.
37- Bores are terrible ; )
You are a bore. /
38. Some mountains are insurmountable ; }
All stiles can be surmounted. • /
lot idle. /
39. No Frenchmen like plumpudding ; |
All Englishmen like plumpudding. J
40. No idlers win fame ;
Some painters are not
41. No lobsters are unreasonable;
No reasonable creatures expect impossibilities.
42. No kind deed is unlawful ;
What is lawful may be done without fear.
43. No fossils can be crossed in love ; |
An oyster may be crossed in love. /
44. " This is beyond endurance ! " \
" Well, nothing beyond endurance ^
has ever happened to me."
45. All uneducated men are shallow ; j
All these students are educated. /
46. All my cousins are unjust ; j
No judges are unjust. J
rill. J
CH. IV.] HIT OR MISS. 89
47. No country, that has been explored,
is infested by dragons ;
Unexplored countries are fascinating. )
48. No misers are generous ; )
Some old men are not generous. J
49. A prudent man shuns hyenas ; |
No banker is imprudent. J
50. Some poetry is original ;
No original work is producible at will.
51. No misers are unselfish ; )
None but misers save egg-shells. /
52. All pale people are phlegmatic ;
No one, who is not pale, looks poetical.
53. All spiders spin webs ;
Some creatures, that do not spin webs, are savage.
54. None of my cousins are just ; i
All judges are just. J
55. John is industrious ;
No industrious people are unhappy.
56. Umbrellas are useful on a journey ;
What is useless on a journey should be left behind.
57. Some pillows are soft ;
No pokers are soft.
58. I am old and lame ; ]
No old merchant is a lame gambler. /
90 HIT OR MISS. [On. IY.
59. No eventful journey is ever forgotten ; \
Uneventful journeys are not worth V
writing a book about.
60. Sugar is sweet ; )
Some sweet things are liked by children. /
61. Richard is out of temper ; )
No one but Richard can ride that horse. J
62. All jokes are meant to amuse ; |
No Act of Parliament is a joke, f
63. " I saw it in a newspaper."
" All newspapers tell lies."
64. No nightmare is pleasant ;
Unpleasant experiences are not anxiously desired.
65. Prudent travellers carry plenty of small change ;
Imprudent travellers lose their luggage.
66. All wasps are unfriendly ;
No puppies are unfriendly.
67. He called here yesterday ; )
He is no friend of mine. /
68. No quadrupeds can whistle ; |
Some cats are quadrupeds, j
69. No cooked meat is sold by butchers ;
No uncooked meat is served at dinner.
70. Gold is heavy ;
Nothing but gold will silence him.
71. Some pigs are wild ;
There are no pigs that are not fat.
\
im. j
CH. IV.] HIT OR MISS. 91
72. No emperors are dentists ; |
All dentists are dreaded by children. J
73. All, who are not old, like walking ;
Neither you nor I are old.
74. All blades are sharp ;
Some grasses are blades.
75. No dictatorial person is popular ;
She is dictatorial.
76. Some sweet things are unwholesome ;
)
No muffins are sweet. /
i
No generals are civilians. J
is visit. ;
77. No military men write poetry ;
No generals are cr
78. Bores are dreaded ;
A bore is never begged to prolong his
79. All owls are satisfactory ;
Some excuses are unsatisfactory.
80. All my cousins are unjust ; )
All judges are just. J
81. Some buns are rich ;
All buns are nice.
82. No medicine is nice ; >
No pills are unmedicinal. I
83. Some lessons are difficult ; |
What is difficult needs attention. )
84. No unexpected pleasure annoys me ; )
Your visit is an unexpected pleasure. J
92 HIT OR MISS. [Cn. IV.
85. Caterpillars are not eloquent ; >
Jones is eloquent. /
86. Some bald people wear wigs ; }
All your children have hair. /
87. All wasps are unfriendly ; i
Unfriendly creatures are always unwelcome. J
88. No bankrupts are rich ; }
Some merchants are not bankrupts. J
89. Weasels sometimes sleep ; |
All animals sometimes sleep. /
90. Ill-managed concerns are unprofitable ; )
Railways are never ill-managed. J
91. Everybody has seen a pig; }
Nobody admires a pig. J
Extract a Pair of Premisses out of each of the following :
and deduce the Conclusion, if there is one : —
92. " The Lion, as any one can tell you who has been
chased by them as often as I have, is a very savage animal :
and there are certain individuals among them, though
I will not guarantee it as a general law, who do not drink
coffee."
93. " It was most absurd of you to offer it ! You might
have known, if you had had any sense, that no old sailors
ever like gruel ! "
On. IV.] HIT OR MISS. 93
" But I thought, as he was an uncle of yours
" An uncle of mine, indeed ! Stuff ! "
" You may call it stuff, if you like. All I know is, my
uncles are all old men : and they like gruel like anything ! "
" Well, then your uncles are "
94. " Do come away ! I can't stand this squeezing any
more. No crowded shops are comfortable, you know very
well."
" Well, who expects to be comfortable, out shopping ? "
" Why, I do, of course ! And I'm sure there are some
shops, further down the street, that are not crowded.
So "
95. " They say no doctors are metaphysical organists :
and that lets me into a little fact about you, you know."
" Why, how do you make that out ? You never heard me
play the organ."
" No, doctor, but I've heard you talk about Browning's
poetry : and that showed me that you're metaphysical, at
any rate. So "
Extract a Syllogism out of each of the following : and
test its correctness : —
96. " Don't talk to me ! I've known more rich merch-
ants than you have : and I can tell you not one of them
was ever an old miser since the world began ! "
" And what has that got to do with old Mr. Brown ? "
94 HIT OR MISS. [Cn. IV.
" Why, isn't he very rich ? "
" Yes, of course he is. And what then ? "
" Why, don't you see that it's absurd to call him a miserly
merchant? Either he's not a merchant, or he's not a miser ! "
97. " It is so kind of you to enquire ! I'm really feeling
a great deal better to-day."
" And is it Nature, or Art, that is to have the credit of
this happy change ? "
" Art, I think. The Doctor has given me some of that
patent medicine of his."
"Well, I'll never call him a humbug again. There's
somebody, at any rate, that feels better after taking his
medicine ! "
98. " No, I don't like you one bit. And I'll go and play
with my doll. Dolls are never unkind."
" So you like a doll better than a cousin ? Oh you little
silly ! "
" Of course I do ! Cousins are never kind at least no
cousins I've ever seen."
" Well, and what does that prove, I'd like to know ! If
you mean that cousins aren't dolls, who ever said they
were ? "
99. " What are you talking about geraniums for ? You
can't tell one flower from another, at this distance ! I grant
you they're all red flowers : it doesn't need a telescope to
know that."
CH. IV.] HIT OR MISS. 95
" Well, some geraniums are red, aren't they ? "
" I don't deny it. And what then ? I suppose you'll be
telling me some of those flowers are geraniums ! "
" Of course that's what I should tell you, if you'd the
sense to follow an argument ! But what's the good of
proving anything to you, I should like to know ? "
100. "Boys, you've passed a fairly good examination, all
things considered. Now let me give you a word of advice
before I go. Remember that all, who are really anxious
to learn, work hard."
" I thank you, Sir, in the name of my scholars ! And
proud am I to think there are some of them, at least, that
ire really anxious to learn."
" Very glad to hear it : and how do you make it out
to be so ? "
" Why, Sir, /know how hard they work some of them,
that is. Who should know better ? "
Extract from the following speech a series of Syllogisms,
or arguments having the form of Syllogisms : and test their
correctness.
It is supposed to be spoken by a fond mother, in answer
to a friend's cautious suggestion that she is perhaps a little
overdoing it, in the way of lessons, with her children.
101. " Well, they've got their own way to make in
the world. We can't leave them a fortune apiece !
96 HIT OR MISS. [On. IV.
And money's not to be had, as you know, without
money's worth: they must work if they want to live.
And how are they to work, if they don't know any-
thing ? Take my word for it, there's no place for
ignorance in these times ! And all authorities agree that
the time to learn is when you're young. One's got no
memory afterwards, worth speaking of. A child will
learn more in an hour than a grown man in five. So
those, that have to learn, must learn when they're young,
if ever they're to learn at all. Of course that doesn't do
unless children are healthy : I quite allow that. Well,
the doctor tells me no children are healthy unless
they've got a good colour in their cheeks. And only
just look at my darlings ! Why, their cheeks bloom like
peonies ! Well, now, they tell me that, to keep children
in health, you should never give them more than six
hours altogether at lessons in the day, and at least two
half-holidays in the week. And that's exactly our plan,
I can assure you ! We never go beyond six hours, and
every Wednesday and Saturday, as ever is, not one
syllable of lessons do they do after their one o'clock
dinner ! So how you can imagine I'm running any
risk in the education of my precious pets is more than
/ can understand, I promise you ! "
THE END.
WORKS BY LEWIS CARROLL.
PUBLISHED BY
MACMILLAN AND CO., LONDON.
THE GAME OF LOGIC. (With an Envelope con-
taining a card diagram and nine counters — four red and five grey. )
Crown 8vo, cloth, price 3s.
N.B. — The Envelope, etc., may be had separately at 3d. each.
ALICE'S ADVENTURES UNDER GROUND.
Being a Facsimile of the original MS. Book, afterwards developed
into "Alice's Adventures in "Wonderland." With Thirty-seven
Illustrations by the Author. Crown 8vo, cloth, gilt edges. 4s.
THE NURSERY ALICE. A selection of twenty of
the pictures in "Alice's Adventures in Wonderland," enlarged,
and coloured under the Artist's superintendence, with expla-
nations. [Jn preparation.
N.B. In selling the above-mentioned books to the Trade, Messrs.
Macmillan and Co. will abate 2d. in the shilling (no odd copies), and
allow 5 per cent, discount for payment within six months, and 10 per
cent, for cash. In selling them to the Public (for cash only) they will
allow 10 per cent, discount.
MR. LEWIS CARROLL, having been requested to allow " AN EASTER
GREETING " (a leaflet, addressed to children, and frequently given with
his books) to be sold separately, has arranged with Messrs. Harrison,
of 59, Pall Mall, who will supply a single copy for Id., or 12 for 9d.,
or 100 for 5s.
3C
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-Dodge ory, Char lee--
The game of logic
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