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Full text of "The game of logic"

VMM'' 



University of California • Berkeley 

Gift of 
Mrs. Robert Bruce Porter 



THE GAME 



LOGIC 



BY 



LEWIS CARROLL 



PRICE THREE SHILLINGS 

3Lon5on 

MACMILLAN AND CO. 

AND NEW YORK 

1886 

\All Rights reserved \ 



THE GAME OF "LOGIC 1 




COLOURS FOR 
COUNTERS. 

See, the Sun is overhead, 
Shining on ns, full and 
RED ! 

Now the Sun is gone away, 
And the empty sky is 
GREY ! 



X 



THE GAME 



LOGIC 



BY 

LEWIS CARROLL 



PRICE THREE SHILLINGS 

Hottton 

MACMILLAN AND CO. 

AND NEW YOBK 

1886 
[ All Rights reserved] 



§0 mg <ptld-<$rim(L 

| t|rcrm in train : far nefrer again, 
{pi fceenlg as mg glance 1 benb, 

Mill Pcmorg, gobbess cog, 

(Smbobg for mg jog 
^eparteb bags, nor let me ga§e 

©n %e, mg Jairg d rienb I 

§Jet conlb t|jg fare, in mgstic grace, 
% moment smile on me, 'tfoonlb senb 
Jfar-barting rags of liglrt 
^rom geaoen at^bart % nigjjt, 
§)g fajjiclj to reab in oerg beeb 

spirit, sfaeetest <f rienb I 



So mag % stream of JRfe's long bream 
^lofo gentlg onfoarb to its enb, 
SKitlr mang a flofoeret gag, 
gibotonits foillofog feag : 
no siglj ires, no care perplex 
Slg looing little ^rienb ( 



PREFACE. 

* There foam'd rebellious Logic, gagg'd and bound." 



TPHIS 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 FOE OLD. 

§ 1. Propositions 1 

§ 2. Syllogisms 20 

§ 3. Fallacies 32 

II. CEOSS QUESTIONS. 

§ 1. Elementary 37 

§ 2. Half of Smaller Diagram, Propo- 
sitions 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. CEOOKED ANSWEES. 

§ 1. Elementary % 55 

§ 2. Half of Smaller Diagram. Propo- 
sitions represented . . . 59 

§ 3. Do. Symbols interpreted . • • 61 

§ 4. Smaller Diagram. Propositions re- 
presented 62 

§ 5. Do. Symbols interpreted 65 

§ 6. Larger Diagram. Propositions re- 
presented ..... 67 

§ 7. Both Diagrams employed ... 72 

IV. HIT OE MISS 85 



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. 



CHAPTER I. 
NEW LAMPS FOR OLD. 

" Light come, light go." 



§ 1. Propositions. 

u Some red Apples are ripe." 
" No red Apples are ripe." 
" All red Apples are ripe." 

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 red Apples are ripe." 

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. [Ch. 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 



§ 1.] 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 red Apples are ripe'', we must suppose it to 
be written out in full, in the form "some red Apples 

are ripe (Apples)". Now this contains two * Terms' 

" red Apples " being one of them, and " ripe (Apples) " 
the other. " Red Apples," being the one we are talking 
about, is called the 'Subject' of the Proposition, and 
"ripe (Apples)" the 'Predicate 9 . 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 ripeness, and the other asserting it, of the 
whole class of "red Apples". 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 \" 

b2 



4 NEW LAMPS FOR OLD. [Ch. 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 Apples in the world (it would have to be a 
good large one, of course). And let us suppose all the 
red ones to be put into the upper half (marked '#'), 
and all the rest (that is, the not-xe& ones) into the 
lower half (marked { x"). Thus the lower half would 
contain yellow Apples, blue Apples, mauve-coloured 
Apples if there are any : I haven't seen many, my- 
self and so on. Let us also suppose all the ripe 

Apples to be put into the left-hand half (marked s y'), 
and all the rest (that is, the unripe ones) into the 
right-hand half (marked '#"). At present, then, we 
must understand x to mean "red", x' "not-red", 
y " ripe ", and y' " unripe ". 

And now what kind of Apples would you expect 
to find in compartment No. 5? 

It is part of the upper half, you see; so that, if it 
has any Apples in it, they must be red : and it is part 



§ I*] PROPOSITIONS. 5 

of the left-hand half; so that they must be ripe* 
Hence, if there are any Apples in this compartment, 
they must have the double 'Attribute ' " red and ripe " : 
or, if we use letters, they must be " x y 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 Apples there, 
they must be " x 'y'\ that is, they must be "not-red 
and ripe". 

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 Apples in it. 
(The word ' some,' in Logic, means ' one or more ' : 
so that a single Apple in a compartment would be 
quite enough reason for saying " there are some Apples 
here"). Also let us agree that a grey counter in a 
compartment shall mean that it is ' empty \ that is, 
that there are no Apples in it. In the following 
Diagrams, I shall put 'I 9 (meaning 'one or more')* 
where you are to put a red counter, and ' ' (meaning 
'none') where you are to put a grey one. 

As the Subject of our Proposition is to be "red 
Apples", we are only concerned, at present, with the 
upper half of the cupboard, where all the Apples have 
the attribute x, that is, " red." 



6 NEW LAMPS FOR OLD. [Ch. I. 

Now, fixing our attention on this upper half, sup- 
pose we found it marked like this, 



I 



that is, with a red counter in No. 5. What would 
this tell us, with regard to the class of "red Apples"? 

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 9 which belongs to both 
compartments) have the Attribute y (that is, "ripe"). 
This we might express by saying u some tf-Apples are 
^-(Apples) ", or, putting words instead of letters, 

11 Some red Apples are ripe (Apples) ", 
or, in a shorter form, 

" Some red Apples are ripe ". 

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 
Propositions, if we agree to leave out the word 
"Apples" altogether. I find it convenient to call the 
whole class of Things, for which the cupboard is in- 
tended, the c Universe. 9 Thus we might have begun 
this business by saying "Let us take a Universe of 
Apples." (Sounds nice, doesn't it?) 



§1.] 



PROPOSITIONS. 



Of course any other Things would have done just 
as well as Apples. 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 



1 



means " some x are y," i. e. " some red are ripe." 

I think you will see, without further explanation, that 



1 



means " some x are #'," i. e. " some red are unripe." 

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 red 
are ripe". 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 red are unripe." 



8 NEW LAMPS FOR OLD. [Ch. I. 

What would you make of this, I wonder ? 



1 1 



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 tf 9 n i. e. " some red are 
ripe, and some are unripe." 

The following is a little harder, perhaps : — 










This means u no x are y, and none are y'" i. e. u no 
red are ripe, and none are unripe " : which leads to the 
rather curious result that " no red exist at all." This 
follows from the fact that " ripe " and M not ripe " 
make what we call an * exhaustive ' division of the class 
" red Apples " : i. e., between them, they exhaust the 
whole class, so that all the red Apples, that exist, must 
be found in one or the other of them. 

And now suppose I were to ask you to represent, 
with counters, the contradictory to "no red exist at 
all ", that is, " some red exist ", or, putting letters 
for words, " some x exist ", how would you do it ? 

This will puzzle you a little, I expect. Evidently 
you must put a red counter somewhere in the #-half 
of the cupboard, since you know there are some red 
Apples. But you must not put it into the left-hand 
compartment, since you do not know them to be ripe: 
nor may you put into the right-hand one, since you 
do not know them to be unripe. 



§ 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 ^-compartment and the 
^'-compartment. This I shall represent (as I 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 
M 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 ? 



1 



This is clearly a double Proposition. It tells us, 
not only that "some x are #," but also that "no x 
are not y? Hence the result is " all x are y? i. e. 
" all red are ripe ", which is the last of the three 
Propositions at the head of this Section. 



10 NEW LAMPS FOR OLD. [Ch. I. 

We see, then, that the Universal Proposition 
" All red Apples are ripe " 
consists of two Propositions taken together, namely, 
M Some red Apples are ripe," 
and " No red Apples are unripe." 

In the same way 



1 



would mean "all x are yf ", that is, 

"All red Apples are unripe." 

Now what would you make of such a Proposition 
as "The Apple you have given me is ripe"? Is it 
Particular, or Universal? 

"Particular, of course," you readily reply. "One 
single Apple 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 Apples 

into two classes the Apples 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 ripe Apples to the left, and the unripe ones to 



§ 1.] PROPOSITIONS. 11 

the right, I begin by carefully collecting all the Apples 
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 
compartment. And it doesn't take long to do it I 

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 one single thing) is sometimes called an " Individual " 
Proposition. 

Now let us take "ripe Apples" as the Subject of 
our Proposition : that is, let us fix our thoughts on 
the left-hand half of the cupboard, where all the 
Apples have the attribute y, that is, "ripe". 

Suppose we find 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 u some y are x ", that is, 
" Some ripe Apples are red." 



12 NEW LAMPS FOR OLD. [Ch. I. 

u But," you will say, u we have had this case before. 
You put a red counter into No. 5, and you told us it meant 
1 some red Apples are ripe ' ; and now you tell us that it 
means ' some ripe Apples are red '! Can it mean both ? M 

The question is a very thoughtful one, and does you 
great credit, dear Reader ! It does mean both. If you 
choose to take x (that is, "red Apples") 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 red Apples 
are ripe " : but, if you choose to take y (that is, " ripe 
Apples") 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 ripe Apples are red". 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. 



*!•] 



PROPOSITIONS. 



13 



Symbols. 



Meanings. 



Some y are #'; 

i. e. Some ripe are not-red. 



No y are x ; 

i. e. No ripe are red. 

[Observe that this is merely another way of 
expressing " No red are ripe."] 

No y are x' ; 

i. e. No ripe are not-red. 



Some y are x 9 and some are x' \ 

i.e. Some ripe are red, and some are 
not-red. 

No y are x, and none are a?'; i.e. No y 
exist ; 

i. e. No ripe exist. 

All y are x ; 

i. e. All ripe are red. 



All y are x' ; 

i. e. All ripe are not-red. 



14 NEW LAMPS FOE OLD. [Ch. I. 

You will find it a good plan to examine yourself on 
this table, by covering up first one column and then 
the other, and i 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 rigtit-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. 

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 m. Let us give to m the meaning 
" wholesome " : and let us suppose that all wholesome 
Apples 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 
Apples in each compartment had two Attributes, so, 
here, the Apples 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 m' 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. 



§ 1-3 



PROPOSITIONS. 



15 



Here we find w, y\ ?ra, at the corners : so we know 
that the Apples in it, if there are any, have the triple 
Attribute ' xy'm\ that is, "red, unripe, and wholesome." 
Again, take No. 16. Here we find, at the corners, 
x\ y\ rri : so the Apples in it are " not-red, unripe, 
and unwholesome." (Remarkably untempting Apples !) 

It would take far too long to go through all the 
Propositions, containing x and y, x and m, and y and m, 
which can be represented on this diagram (there are 
ninety-six altogether, so I am sure you will excuse 
me !), 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 "red Apples", how are we to represent "no red 
Apples are wholesome " ? 



This is, writing letters for words, " no x are m." Now 
this tells us that none of the Apples, belonging to the upper 
half of the cupboard, are to be found inside the central 
Square: that is, the two compartments, No. 1 1 and No. 12, 
are empty. And this, of course, is represented by 






















16 



NEW LAMPS FOR OLD. 



[Ch. I. 



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 : — 






Now let us express u all x are ?ra." 

This consists, we know, of two Propositions, 
" Some x are wz," 
and " No x are m'." 

Let us express the negative part first. This tells 
us that none of the Apples, 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 






















But we have yet to represent " Some x are m." This 
tells us that there are some Apples in the oblong con- 
sisting of No. 11 and No. 12: so we place our red 



§ 1.] 



PROPOSITIONS. 



17 



counter, as in the previous example, on the division-line 
between No. 11 and No. 12, and the result is 






















Now let us try one or two interpretations. 

What are we to make of this, with regard to x and y ? 














1 








This tells us, with regard to the a?y'-Square, that 
it is wholly c empty', since both compartments are so 
marked. With regard to the ##-Square, it tells us 
that it is * occupied \ True, it is only one compartment 
of it that is so marked; but that is quite enough, 
whether the other compartment be * occupied ' or 
* empty ', to settle 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 



1 






which means, you know, " all x are y.' 

c 



18 



NEW LAMPS FOR OLD. 



[Ch. I. 



The result would have been exactly the same, if the 
given oblong had been marked thus : — 



1 



















Once more : how shall we interpret this, with regard 
to x and y 1 










1 











This tells us, as to the a?y-Square, that one of its 
compartments is ' empty'. But this information is 
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 ##'-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 : — 



1 



which means, you know, " some x are y'." 



§1.] 



PROPOSITIONS. 



19 



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 










we should transfer it to the smaller Diagram thus, 



1 






and read it " all x are y ". 

One more remark about Propositions should be made. 
When they begin with " some " or fl no ", and contain 
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 u some bf are acde" each being equi- 
valent to " some abcdef exist ". Again, " No wise old 
men are rash and reckless gamblers " may be re-arranged 
as " No rash old gamblers are wise and reckless." 



c2 



20 



§ 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 rri 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 i 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. L] new lamps for old. 21 

In the first case (when, for example, the Premisses 
are "some m are x" and " no m are y'") the Term, 
which occurs twice, is called " the Middle 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 two Terms, 
which contain these contradictory Attributes, may be 
called "the Middle Terms". 

Thus, in the first case, the class of " ^-Things " is 
the Middle Term ; and, in the second case, the two 
classes of " ^-Things " and " wa'-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 red Apples are unwholesome ; | 
No ripe Apples are unwholesome." / 

In order to express them with Counters, we need to 
divide Apples in three different ways, with regard to 
redness, to ripeness, and to wholesomeness. For this 
we must use the larger Diagram, making x mean 
"red", y "ripe", and m "wholesome". (Everything 



22 



NEW LAMPS FOR OLD. 



[Ch. I. 

inside the central Square is supposed to have the at- 
tribute m, and everything outside it the attribute m\ 
i.e. "not-m".) 

You had better adopt the rule of making m mean 

the Attribute which occurs in the Middle Term or 

Terms. (I have chosen m as the symbol, because 
1 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 will be most welcome. 

Let us express, then, " no ripe Apples are unwhole- 
some (Apples)", i.e. "no ^-Apples are m'-( Apples)". 
This tells us that none of the Apples belonging to the 
^-half of the cupboard are in its m'-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 : — 






































§2-3 



SYLLOGISMS. 



23 



We have now to express the other Premiss, namely, 
" some red Apples are unwholesome (Apples) ", i. e. 
"some #-Apples are w'-(Apples) ". This tells us that 
some of the Apples in the a?-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 Compartments to place 
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 de- 
claring No. 9 to be empty. Hence the red Counter has 
no choice, and must go into No. 10, thus:-— 










1 


























And now what Counters will all 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. 



[CH. I. 



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 Apple, in one corner of the Square, is quite 
sufficient excuse for saying "this 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 





1 







Our * Conclusion', then, must be got out of the rather 
meagre piece of information that there is a red Counter 
in the ^'-Square. Hence our Conclusion is "some 
x are y ", i. e. " some red Apples are unripe (Apples) " : 
or, if you prefer to take y as your Subject, " some unripe 
Apples are red (Apples)"; but the other is neatest, 
I think. 

We will now write out the whole Syllogism, putting 
the symbol .'. for " therefore ", and omitting " Apples ", 
for the sake of brevity, at the end of each Proposition. 



§ 2.] SYLLOGISMS. 25 

" Some red Apples are unwholesome ; | 

No ripe Apples are unwholesome, j 

.'• Some red Apples are unripe." 

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 — 
11 All Dragons are uncanny ; \ 
All Scotchmen are canny.") 

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 " Apples " 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 
1 Animals ' ? And, as M canny " is evidently the At- 



26 



NEW LAMPS FOR OLD. 



[CH. I. 



,',} 



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, 

M All Dragon-Animals are uncanny (Animals) ; 

All Scotchman-Animals are canny ( Animals).' 

And these may be expressed, using letters for words, 

thus : — 

11 All x are m ; | 

All y are w." I 

The first Premiss consists, as you already know, of 

two parts : — 

" Some x are wrf? 

and " No x are ?rc." 

And the second also consists of two parts : — 
" Some y are tw," 
and " No y are wV 

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 




































We have now to mark the two positive portions, 
" some x are m " and M 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 9 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 










I 











1 











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 : — 






1 


1 





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, j 

{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 
understood to mean lf the Attributes x, y are compatible, 
so that a Thing can have both at once ", and M no x 
are y M 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 

11 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 be y"), but theirs does not 
include ours. For example, "some Welsh hippopotami 
are heavy " would be true, according to these writers (since 



30 NEW LAMPS FOR OLD. [Ch. I. 

the Attributes " Welsh" and "heavy" are quite com- 
patible 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 they cannot 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 Policemen are eight feet high" would 
be true in our Game (since, as an actual fact, no such 
splendid specimens can be 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 pre- 
vent 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 



§ 2.] SYLLOGISMS. 31 

each other 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 #-Things are capable of 
being ^-(Things) ", that is, " the Attributes x, y are 
compatible". And " no x are y " will become " no 
a?-Things are capable of being ^-(Things)", that is, 
" the Attributes x, y are incompatible ". And, of 
course, " all x are y " will become " some ^-Things 
are capable of being ^-(Things), and none are capable 
of being ^'-(Things) ", that is, " the Attributes x, y 
are compatible, and x y 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 anything in this compartment." 



32 



§ 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. L] 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 



i 



34 NEW LAMPS FOR OLD. [Ch. 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 a?'," 
(which is the same as " No x are «/," 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 confectioner'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 mourn- 
fully, 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 " Sha'n'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 ! M 

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 st The Conclusion is € No men who cheat 
are trustworthy'," I f ear your Logical friend would 
turn away hastily perhaps angry, perhaps only scorn- 
ful : in any case, the result would be unpleasant. 
I advise you not to try the experiment ! 

" But why is this ? " you will say. u 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 Syllogism. 

d2 



86 FALLACIES. [Ch. I. § 3. 

They have a sort of nervous dread of Attributes 
beginning with a negative particle. For example, 
such Propositions as " All not-# are y" " No x are 
not-y," 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 ! 



CHAPTER II. 
CROSS QUESTIONS 



' The Man in the Wilderness asked of me 
4 How many stra wherries 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. 

3. 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 ? 



38 CROSS QUESTIONS. [Ch. 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. 



§ 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 #, 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? 



40 



§ 2. Half of Smaller Diagram. 
Propositions to be represented. 



X 



-y 



tf~ 



1. Some x are not-y. 

2. All x are not-t/. 

3. Some x are y, and some are not-y. 

4. No x exist. 



Taking x = " judges " ; ?/ = "just " ; 

5. No judges are just. 

6. Some judges are unjust. 

7. All judges are just. 



Taking x = " cakes " ; y = " wholesome " ; 

8. Some cakes are wholesome. 

9. There are no wholesome cakes. 

10. Cakes are some of them wholesome, and some not. 

11. All cakes are unwholesome. 



Ch. II.] 



CROSS QUESTIONS. 



41 



y 



X 



Taking y = " diligent students " ; x = " successful " ; 

12. No diligent students are unsuccessful, 

13. All diligent students are successful. 

14. No students are diligent. 

15. There are some diligent, but unsuccessful, students. 

16. Some students are diligent. 



Taking y = " old men " ; x = " strong and active " ; 

17. All old men are strong and active. 

18. Some old men are weak or lazy. 

19. No old men are strong. 

20. All old men are lazy. 



42 



§ 3. Half of Smaller Diagram. 
Symbols to be interpreted. 



x 

-y— y- 



I. 











3. 


" 


i 










4. 1 



Taking x = " good riddles " ; y = " hard " ; 

6. 



5. 


1 










7. 









8. 



Ch. II.] CROSS QUESTIONS. 43 

Taking x = " lobsters " ; y = " selfish and unforgiving "; 

10. 



9. 




1 






1. 





1 







12. 1 1 




Taking y = " healthy people n ; x = " happy "; 



13. 












1 









14. 


-1- 


15. 




16. 






1 








1 








44 



§ 4. Smaller Diagram. 
Propositions to be represented. 




1. All y are a?. 

2. Some y are not-a?. 

3. No not-a? are not-y. 

4. Some x are not-y. 
6. Some not-y are a?. 

6. No not-a? are y. 

7. Some not-a? are not-y. 

8. All not-a? are not-y. 

9. Some not-y exist. 

10. No not-a? exist. 

11. Some y are a?, and some are not-a?. 

12. All a? are y, and all not-y are not-a?. 



Ch. II.] CROSS QUESTIONS. 45 

Taking " nations " as Universe ; x = " civilised " ; and 
y ss " warlike " ; 

13. No uncivilised nation is warlike. 

14. All un warlike nations are uncivilised. 

15. Some nations are unwarlike. 

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. 



46 



§ 5. Smaller Diagram. 
Symbols to be interpreted. 




1 













8. 





1 








4. 














Taking " houses " as Universe ; x == " built of brick " ; 
and y = " two-storied " ; interpret 


































1 



Ch. II.] 



CROSS QUESTIONS. 



47 



Taking " boys " as Universe ; x = " fat "; 
and y as " active " ; interpret 



10. 



11. 



1 


1 











1 








12. 










1 




1 







1 



Taking " cats " as Universe ; x = " green-eyed " ; 
and y = " good-tempered " ; interpret 



13. 



15. 
















1 










14. 



16. 





1 


1 









1 


1 






48 



§ 6. Larger Diagram. 
Propositions to be represented. 




L No f are m. 

2. Some y are n 

3. All m are x. 

4. No m' are y'. 

5. No m are x, 
All y are m. 

6. Some x are m, } 
No y are m. j 

7. All m are a;' } "j 
No m are ?/. J 

8. No as' are m, \ 
No 1/' are m\ ) 



x,\ 



Ch. II.] 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. J 

14. All rabbits, that are not greedy, are black, 1 
No old rabbits are free from greediness. J 



Taking " birds " as Universe ; m = " that sing loud "; 
x ss " 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, 1 
No well-fed birds fail to sing loud. J 



Taking " persons " as Universe ; m = " in the house "; 
x as "John "; and y ss "having a tooth-ache "; represent 

17. John is in the house, 
Every body in the house is suffering from tooth-ache 

18. There is no one in the house but John, 1 
Nobody, out of the house, has a tooth-ache. J 



j 



50 CROSS QUESTIONS. [Ch. II. 

Taking " persons " as Universe ; m = u I"; 
x ss " that has taken a walk " ; y ss " that feels better " ; 
represent 

19. I have been out for a walk, I 
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. 



51 



§ 7. Both Diagrams to be employed. 





N.B. 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 



























1 




















E 2 



52 



CROSS QUESTIONS. 



[Ch. II. 



3. 























1 

















































Mark, on a large Diagram, the following pairs of Pro- 
positions from the preceding Section: then mark a email 
Diagram in accordance with it, &c. 

5. No. 13. 9. No. 17. 

6. No. 14. 10. No. 18. 

7. No. 15. 11. No. 19. 

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 books suit feverish patients ; 
Unexciting books make one drowsy. 

14. Some, who deserve the fair, get their deserts ; 
None but the brave deserve the fair. 

15. No children are patient; 

No impatient person can sit still. 



§ 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. 

18. None of my cousins are just ; 
No judges are unjust. 

19. Some days are rainy; 
Kainy days are tiresome. 

20. All medicine is nasty ; 
Senna is a medicine. 

21. Some Jews are rich ; 

All Kamschatgans are Gentiles. 

22. All teetotalers like sugar ; 
No nightingale drinks wine. 

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. 

28. There are no Jews in the house ; 
There are no Gentiles in the garden. 



54 CROSS QUESTIONS. [Ch. II. 

29. All battles are noisy ; 

What makes do noise may escape notice. 

30. No Jews are mad ; 
All Kabbis are Jews. 

31. There are no fish that cannot swim ; 
Some skates are fish. 

32. All passionate people are unreasonable ; 
Some orators are passionate. 



CHAPTER III. 
CROOKED ANSWERS. 



1 1 answered him, as I thought good, 
4 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)"). 



56 CROOKED ANSWERS. [Ch. III. 

5. A * Proposition * is a sentence stating that some, or 
none, or all, of the Things belonging to a certain class, 
called the * Subject ', are also Things belonging to a certain 
other class, called the ' Predicate '. For example, " some 
red Apples are not ripe ", that is (written in full) " some red 
Apples are not ripe Apples " ; where the class " red Apples " 
is the Subject, and the class "not-ripe Apples" is the 
Predicate. 

6. A Proposition, stating that some of the Things belonging 
to its Subject are so-and-so, is called Particular'. For 
example, "some red Apples are ripe", "some red Apples 
are not ripe." 

A Proposition, stating that none of the Things belonging 
to its Subject, or that all of them, are so-and-so, is called 
1 Universal \ For example, " no red Apples are ripe ", " all 
red Apples are ripe ". 

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. 

1 0. A Proposition containing two statements. For example, 
" some red Apples are ripe and some are unripe." 

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 " red Apples " is " exhaustively " 



§ 1.] ELEMENTARY. 57 

divided into "ripe" and "not ripe", since every red Apple 
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. 






13. " Some x are y " and " no x are y n \ 

14. A Proposition, whose Subject is one 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. * Particular ' and * Universal ' Propositions. 

16. When they begin with " some " or " no ". For example, 
" some abc are def" may be re-arranged as "some bf are acde", 
each being equivalent to " some abcdej 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 
found written at three of the corners of the compartment 



58 CROOKED ANSWERS. [Ch. III. 

(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 
given, 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 may be called ' the 
Middle Terms '. For example, if the Premisses are " no m 
are as' " and " all m' are y ", the two classes of " m-Things " 
and " m'-Things " may be called 4 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 \ 

25. Because the only question we are concerned with is 
whether the Conclusion follows logically from the Premisses, 
so that, if they were true, it also would be true. 



§1.] 



ELEMENTARY. 



59 



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 in- 
formation ' 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, 
ret 





1 




1 


1 



5. No x are y. i. e. 



6. Some x are y\ i. e. 



1 






1 











60 CROOKED ANSWERS. 

7. All x are y. i. e. 







8. Some x are y. i. e. 1 







9. No x are y. i. e. 



1 0. Some x are y, and some are t/\ i. e. 



11. All x are t/\ i.e. 1 



12. No y are a;', i.e. 



1 3. All y are x. i. e. 



14. No y exist, i.e. 



15. Some y are a?', i.e. 



16. Some y exist, i.e. 



-1- 



[Ch. III. 



1 1 



2.] PROPOSITIONS REPRESENTED. 

17. All y are x. i. e. 



61 



18. Some y are x'. i. e. 



19. No y are x. i. e. 



20. All y are a', i. e. 



§ 3. Half of Smaller Diagram. 
Symbols interpreted. 



1. No a? are y'. 

2. No x exist. 

3. Some x exist. 

4. All x are y'. 

5. Some a? are y. 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. 



(>2 CROOKED ANSWERS. [Ch. III. 

8. No x are y. i. e. No good riddles are hard. 

9. Some x are y'. i.e. Some lobsters are unselfish or 

forgiving. 

10. No x are y. i. e. No lobsters are selfish and unforgiving. 

11. All x are %f. i. e. All lobsters are unselfish or for- 

giving. 

12. Some x are y, and some are «/'. i.e. Some lobsters are 

selfish and unforgiving, and some are unselfish or 
forgiving. 

13. All y' are x'. i. e. All invalids are unhappy. 

14. Some %f exist, i. e. Some people are unhealthy. 

15. Some y' are x t and some are of. i. e. Some invalids are 

happy, and some are unhappy. 

16. No y' exist, i.e. Nobody is unhealthy. 



§ 4. Smaller Diagram. 
Propositions represented. 



1 


















2. 



4. 



1 

1 



§ 4.] PROPOSITIONS REPRESENTED. 63 



9. 



11. 





1 










1 






-1- 




1 




1 





10. 



12. 





















1 
















1 







] 



13. No x' are y. i.e. 













14. All xj are x. i. e. 










1 



15. Some y' exist, i. e. 





-1- 



64 



CROOKED ANSWERS. [Ch. III. 



16. All y are x> and all x are y. i. e. 



17. No x 1 exist, i.'e. 



18. All a? are y'. i. e. 



1 


























1 


















19. No x are y. i. e. 



20. Some x' are t/, but some are y'. i.e. 



21. No y exist, and some x exist, i. e. 



22. All x' are y, and all y' are x. i. e. 



23. Some x are y, and some #' are y'. i. e. 



1 1 






1 










1 


1 






1 






1 



65 



§ 5. Smaller Diagram. 
Symbols interpreted. 



1 . Some y are not-rc, 

or, Some not-# are y. 

2. No not-rc are not-y, 

or, No not-?/ are not-#. 

3. All not-y are ar. 

4. No not-a; exist, (i. e. There are no not-#.) 

5. No y exist, i. e. No two-storied houses exist, (i. e. No 

houses are two-storied.) 

6. Some x f exist, i.e. Some houses, not built of brick, 

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. 

8. 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. 

F 



66 CROOKED ANSWERS. [Ch. III. 

12. All y are x, an(l 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 x', 

and some y' are x. 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. 

1 6. All x are t/', 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. 



§ 6. Larger Diagram. 
Propositions represented. 



67 






































-1- 



3. 











4. 








































































6. 























1 







1 






























68 



CROOKED ANSWERS. [Ch. III. 


















1 


















































9. No x are m. i. e. 






































1 0. Some m' are y. i. e. 



-1- 



11. All y are m'. i.e. 


















-1- 


















§6.] 



PROPOSITIONS REPRESENTED. 



69 



12. All m are as', i. e. 



13. No x are m, 
All y are m 



:Kf 



14. All m' are i/, 1 • 

No a; are m'. i 



15. All a; are m, 
No m are y. 



},, 



















1 
1 




























1 


























1 

























1 



















70 



CROOKED ANSWERS. 



[CH. III. 



16. All m are y\\ . e 
No a: are m. 1 



17. All cc are m, 
All m are y 



■} 



i.e. 
























1 


















1 

















18. No x are m, 1 
No m' are i/. • 



i.e. 



19. All m are a; 
All m are ?/ 



:) 



i. e. 




































1 


























§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. J 

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. J 

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 y 
All m are y, 



and the required Diagram is 













1 


























72 



§ 7. Both Diagrams employed. 



2. 



3. 



5. 








1 








1 








1 



















1 






1 





i. e. All y are x'. 



i. e. Some x are y' ; or, Some y' are x. 



i. e. Some y are x' ; or, Some a/ are y. 



i. e. No X* are y' ; or, No i/' are a/. 



i. e. All y are #'. i. e. All black rabbits 
are young. 



i. e. Some y are x'. i. e. Some black 
rabbits are young. 



Ch. III.] BOTH DIAGRAMS EMPLOYED. 



73 



10. 



11. 



12. 



1 

















1 




1 






















1 










1 









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. 



i. e. All x are y. i. e. John has got a 
tooth-ache. 



i. e. No of 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. 



[CH. III. 



13. 












-1- 




































Let " books " be Universe ; m = " exciting "; 

x = " that suit feverish patients " ; y = " that make 

one drowsy ". 



No m are x, \ 
ri are v. J 



No t/' are a?. 



All rri are ?/. J 

i. e. No books suit feverish patients, except such as make 
one drowsy. 



14. 













1 

























1 









Let " persons " be Universe ; m = 44 that deserve the fair " ; 

x = " that get their deserts" ;?/ = ** brave ". 

Some m are x, \ _, 

J* .-. Some y are re. 
No y are m. i 

i. e. Some brave persons get their deserts. 



§7-] 



BOTH DIAGRAMS EMPLOYED. 



75 



15. 


















































Let " persons " be Universe ; m = " patient " ; 

x = " children " ; y = " that can sit still ". 

No x are m, 1 

h .\ No x are v. 
No m are y. J 

i. e. No children can sit still. 



16. 




















1 






















1 











Let " things " be Universe ; m = " fat " ; x =t " pigs " ; 

y = " skeletons ". 

All x are mA ... , 

\ .*. All x are ?/ . 
No y are m. J 

i. e. All pigs are not-skeletons. 



76 



CROOKED JN8WERS. 



[Ch. III. 



17. 























1 




















1 





Let " creatures " be Universe ; m = " monkeys " ; 

x = " soldiers " ; y = " mischievous ". 

No m are x, ) 

. .. \ .*. Some v are x\ 

All m are y. > 

i. e. Some mischievous creatures are not soldiers. 



18. 














































Let •■ persons " be Universe ; m = "just " ; 
x = " my cousins " ; y = "judges ". 

No x are m, } 

_ T , f .-. No x are y. 

No ?/ are m . J 

i. e. None of my cousins are judges. 



§7.] 



BOTH DIAGRAMS EMPLOYED. 



77 



19. 













1 







• 

















1 









Let " things " be Universe ; m = " days " ; 

x = " rainy "; y = " tiresome ". 

Some m are x,\ 

y .\ Some x are w. 
All ##1 are y. j 

i. e. Some rainy things are tiresome. 

N. B. These are not legitimate Premisses, since x and y 
both enter into the second Premiss ; so that the Conclusion 
is really part of the second Premiss, and 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 tire- 
some " contains " Some rainy days are tiresome ", which 
contains " Some rainy things 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 ! 



78 



CROOKED ANSWERS. 



[Ch. III. 



20. 














1 


























1 










Let " things " be Universe ; m = " medicine " ; 

x = " nasty " ; y = " senna ". 

All m are x, \ 

t .-. All y are x. 
All y are m. J 

i. e. Senna is nasty. 



31. - 



1 











1 






















1 







Let " persons " be Universe , m = " Jews " ; 

x = " rich " ; y = " Kamschatgans ". 

Some m are x, \ ^ . 

\ /. Some x are y . 
All y are m'. J 

i. e. Some rich persons are not Kamschatgans. 



§7.] 



BOTH DIAGRAMS EMPLOYED. 



79 



22 














































Let " creatures " be Universe ; m = " teetotalers " ; 
x = " that like sugar "; y =s " nightingales ". 

,\ No y are x'. 

i. e. No nightingales dislike sugar. 



All m are x, \ 

No y are m'. J 



23. 











-1- 


























Let " food " be Universe ; m = " wholesome " ; 
x = ** muffins " ; y = " buns ". 
No x are m, t 
All y are m\ J 

There is * no information * for the smaller Diagram ; so 
no Conclusion can be drawn. 



80 



CROOKED ANSWERS. 



[Ch. III. 



24. 























1 











1 





Let " creatures " be Universe ; m = " that run well " ; 

x ts " fat n ; y = " greyhounds ". 

No x are m, I ^ , 

f .•. Some t/ are a; . 
Some y are m. J 

i. e. Some greyhounds are not fat. 



25. 



1 








— 1 — 











Let " persons " be Universe ; m = " soldiers " ; 
x =* " that march " ; y m " youths ". 
All m are x> \ 
Some t/ are w'.i 

There is ' no information ' for the smaller Diagram ; so 
no Conclusion can be drawn. 



7.] 



BOTH DIAGRAMS EMPLOYED. 



81 



26. 









1 





1 

















1 


1 





Let " food " be Universe ; m = " sweet " ; 

x = " sugar " ; y = " salt ". 
All x are m,| J All x are y'. 
All y are w»'- J I All y are x\ 

( Sugar is not salt. 
i e i 

I Salt is not sugar. 



27. 













1 

























1 







Let " things " be Universe ; m = " eggs " ; 
x = " hard-boiled " ; y sc " crackable ". 
Some m are #, 1 
No m are ?/'. 
i. e. Some hard-boiled things can be cracked. 

G 



f .•. Some a? are y. 



82 



CROOKED ANSWERS. 



[Ch. III. 



38. 










































Let " persons " be Universe ; m = " Jews " ; x = " that 

are in the house " ; y = " that are in the garden ". 

No m are x, i __ 

, I .\ No x are y. 

No m are y. J 

i. e. No persons, that are in the house, are also in 

the garden. 



29. 




Let " things " be Universe ; m = " noisy " ; 

x = " battles " ; y = " that may escape notice ". 

All x are m,\ 

..,•■:••-. I .*. Some # are v. 

All m are y. J 

i. e. Some things, that are not battles, may escape notice. 



§7.] 



BOTH DIAGRAMS EMPLOYED. 



83 



30. 























1 


















1 





Let " persons " be Universe ; m = " Jews " ; 

x = " mad " ; y as « Kabbis ". 

No m are x, \ . ,_ 
.„ L .•. All v are #'. 

All y are m. J ^ 

i. e. All Rabbis are sane. 



81. 













1 

























1 









Let " things " be Universe ; m = " fish " ; 
x = " that can swim "; y = " skates ' 
No m are a;', 
Some y are m. 

i. e. Some skates can swim. 
g2 



}.\ Some y are a?. 



84 



CROOKED ANSWERS. 



[Ch. III. 



32. 























1 



















1 





Let " people " be Universe ; m = " passionate " ; 

x = " reasonable " ; y = " orators ". 

All m are x\ \ 

\ .*. Some y are x. 
Some y are m. J 

i. e. Some orators are unreasonable. 



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. 

4. I do not like John ; 

Some of my friends like John. 

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. 

8. All these dishes are well-cooked ; 

Some dishes are unwholesome if not well-cooked. 



86 HIT OR MISS. [Ch. 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. 

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 ; 

Ail industrious people are happy. 

16. No frogs write books ; 

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 ; 
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.] MT OR MISS. 87 

22. He gave me five pounds ; 
I was delighted. 

23. No old Jews are fat millers ; 
All my friends are old millers. 

24. Flour is good for food ; 
Oatmeal is a kind of flour. 

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. 

34. All ducks waddle ; 

Nothing that waddles is graceful. 



88 HIT OR MISS. [Ch. IV, 

35. No Professors are ignorant ; 

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. 

39. No Frenchmen like plumpudding; 
All Englishmen like plumpudding. 

40. No idlers win fame ; 
Some painters are not idle. 

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 ; 
All these students are educated. 

46. All my cousins are unjust ; 
No judges are unjust. 



Ch. IV.] BIT 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. 

49. A prudent man shuns hyaenas ; 
No banker is imprudent. 

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 ; 
All judges are just. 

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. [CH. IV. 

59. No eventful journey is ever forgotten ; 
Uneventful journeys are not worth writing a book 

about. 

60. Sugar is sweet ; 

Some sweet things are liked by children. 

61. Kichard is out of temper; 

No one but Kichard can ride that horse. 

62. All jokes are meant to amuse ; 
No Act of Parliament is a joke. 

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. 

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. 



Ch. IV.] HIT OR MTSS. 91 

72. No emperors are dentists ; 

All dentists are dreaded by children. 

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. 

77. No military men write poetry ; 
No generals are civilians. 

78. Bores are dreaded ; 

A bore is never begged to prolong his visit. 

79. All owls are satisfactory ; 
Some excuses are unsatisfactory. 

80. All my cousins are unjust ; 
All judges are just. 

81. Some buns are rich ; 
All buns are nice. 

82. No medicine is nice ; 
No pills are unmedicinal. 

83. Some lessons are difficult ; 
What is difficult needs attention. 

84. No unexpected pleasure annoys me ; 
Your visit is an unexpected pleasure. 



92 HIT OB MISS. [Ch. TV. 

85. Some bald people wear wigs; 
All your children have hair. 

86. All wasps are unfriendly ; 

Unfriendly creatures are always unwelcome. 

87. No bankrupts are rich ; 

Some merchants are not bankrupts. 

88. Ill-managed concerns are unprofitable ; 
Kailways are never ill-managed. 

89. Everybody has seen a pig ; 
Nobody admires a pig. 



Extract a Pair of Premisses out of each of the following : 
and deduce the Conclusion, if there is one : — 

90. "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 certainly individuals among them, though 
I will not guarantee it as a general law, who do not drink 
coffee." 

91. " Good morning, dear Mrs. Jones ! I've just seen 
the most extraordinary people you ever met! You never 
saw such bonnets ! " 

" Oh, I know who you mean. They lodge just opposite." 
" Do they ? Well, I do wonder who they are ! " 
'< So do I." 

92. " 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 ! " 

"But I thought, as he was an uncle of yours " 



Ch. IV.] BIT OR MISS. 93 

" An uncle of mine, indeed ! Stuff ! " 
"Well, 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 " 

93. " 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 " 

94. " They say doctors are never enthusiastic 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, but I've heard you talk about Browning's poetry: 
and that showed me that you're enthusiastic, at any rate. 
So " 



Extract a Syllogism out of each of the following : and 
test its correctness : — 

95. " Don't talk to me ! I've known more rich merchants 
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 ? " 

" 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 ! " 



94 HIT OR MISS. [Ch. IV. 

96. "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's 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 ! " 

97. " 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 Tve 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 ? " 

98. "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" 

" 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 ? " 



Ch. IV.] HIT OR MISS. 95 

99. " You're as greedy as a pig ! " 

" That doesn't prove much, unless you mean to say that 
every pig, as ever is, is greedy." 

" Then that's just what I do mean to say." 

"Well, I'll tell you another interesting fact about pigs. 
Not one of them can fly ! " 

" I knew that before, Mister Impertinence ! So something, 
that's greedy, can't fly : and I think its you ! " 

100. " Boys, you've passed a fairly good examination, all 
things considered. Now let me give you a word of advice 
before I go. Eemember 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 
belong to that category ! " 

" What category, might I ask ? " 

" The category, Sir, of them as 1 mean of boys that 

are really anxious to learn." 

"Very glad to hear it: and how do you make it out 
to be so ? " 

" Why, Sir, I 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. 



96 HIT OR MISS. [Ch. IV. 

101. "Well, they've got their own way to make in the 
world. We can't leave them a fortune apiece ! 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 anything? 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 I can 
understand, I promise you ! " 



THE END. 



BAXTER, PRINTER, OXFORD, 



[TURN OVER. 



WORKS BY LEWIS CARROLL. 



PUBLISHED BY 



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ALICES ADVENTURES IN WONDERLAND. 

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l\ 1 to I 



\uO')P 



c/