DUKE UNIVERSITY 
 LIBRARY 
 
 NEWMAN COLLECTION 
 
 PRESENTED BY 
 
 RUTH GALLERT NEWMAN 
 
 IN MEMORY 
 
 OF 
 
 JAMES R. NEWMAN 
 
PERKINS LIBRARY 
 
 Duke Universitj 
 
 Rare Books 
 
9 
 
 
 
 
 
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 12 
 
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 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 
 
 y 
 
THE GAME 
 
 LOGIC 
 
 CWs.r\t* 'u>1<1 
 
 LEWIS CARROLL 
 
 ae 
 
 PRICE THREE SHILLINGS 
 
 ILontioit 
 
 MACMILLAN AND CO. 
 
 AND NEW YORK 
 
 1887 
 
 IAU Rights reserved.] 
 
Richard Clay and Sons, 
 london and bungay. 
 
c 
 
 C0 mg Cfexlir-J^runtr* 
 
 31 cJjatm in toain ; for neber again, 
 3H keenly as mp dance 3[ fcenti, 
 
 223iII iHemorp, eoUTiess cop, 
 
 (EEmboUp for mp jog 
 Departed tiaps, nor let me <ja$e 
 
 2Dn tfjee, my jFairp JFrienti ! 
 
 ^et couIU x^t face, in mystic grace, 
 2L moment smile on me, 'ttoouiu senti 
 jfar^Uarting rags of Iicf?t 
 jFrom Upeatien atfjtoart tf?e nigf?t, 
 23y lt>&ic|? to reati in toery Ueeti 
 ®fjp spirit, stoeetest JFrienti ! 
 
 &o map ti>e stream of Hife's lone nream 
 JFIoto Gently ontoarti to its enU, 
 
 S2ait|? many a flotoeret cap, 
 
 gUoton its toillotoy toay : 
 fElay no sici) tier, no care perpler, 
 
 iBp losing little JFrienti ! 
 
NOTA BENE. 
 
 With eacli 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 foam'd rebellious Logic, gagg'd and bound." 
 
 rP HIS 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 he 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 80 
 
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 FOB OLD. [Ch. I. 
 
 The world contains many Things (such as "Buns", 
 "Babies", "Beetles", "Battledores", &c.) ; and theC 
 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 
 /Jhing 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 ichole 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 
 ivhole 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. [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 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 ' x'), 
 and all the rest (that is, the not-new ones) into the 
 lower half (marked 'x"). 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 l 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 ", x' " 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 must be new: and it is part 
 
§ 1.] 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 " x 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 " x' 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 * ' (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 FOR OLD. [Ch. I. 
 
 Now, fixing our attention on this upper half, sup- 
 pose we found it marked like this, 
 
 1 
 
 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 
 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 ?) 
 
§ !•] 
 
 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 
 
 1 
 
 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, 
 
 
 j 
 
 would mean " no x are y '," or, " no new Cakes are not-nice/ 
 
NEW LAMPS FOR OLD. [Ch. I. 
 
 What would you make of this, I wonder ? 
 
 i > ' 
 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 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 someivhcrc 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 #2/-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 can'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 ? 
 
 1 
 
 This is clearly a double Proposition. It tells us, 
 not only that "some x are y," but also that "no x 
 are not yT 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. [Ch. 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 
 
 1 
 
 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 
 
§ 1.] 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 Beckaleo-or i s an honest man." That means " All the 
 
 oo 
 
 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 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 " 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 NE IV LAMPS FOR OLD. [Ch. I. 
 
 ' some new Cakes are nice ' ; and now you tell us that it 
 means ' some nice Cakes are new ' ! 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. 
 
§ ij 
 
 PROPOSITIONS. 
 
 13 
 
 Symbols. 
 
 Meanings. 
 
 
 
 
 
 
 
 ■ 
 
 Some y are x' ; 
 
 i. e. Some nice are not-new. 
 
 
 1 
 
 
 
 
 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. 
 
 
 
 
 
 
 
 
 
 1 
 
 
 Some y are x, and some are x' ; 
 
 i. e. Some nice are new, and some are 
 
 
 1 
 
 not-new. 
 
 
 
 
 
 
 
 
 
 
 No y are x, and none are x' \ i.e. Ko j/ 
 exist ; 
 
 i. e. No Cakes are nice. 
 
 
 
 
 
 
 1 
 
 
 
 
 All y are x ; 
 
 i. e. All nice are new. 
 
 
 
 
 
 
 
 
 1 
 
 
 All y are x' ; 
 
 i. e. All nice are not-new. 
 
 
 
 
 
14 NEW LAMPS FOR OLD. [Ch. 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 m. Let us give to m the meaning 
 " wholesome " : and let us supj>ose that all ivholesomc 
 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 comers. (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. 
 Here we find x, y', m, 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\ m : 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 m 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 !) 
 
§ 1.] 
 
 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 
 
 
 
 
 
 
 
 
 
 
 
 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. [Ch. 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 
 
 
 
 
 
 
 I 
 
 
 
 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 
 
 
 
 
 
 
 
 
 - 
 
 Now let us try one or two interpretations. 
 
 What are we to make of this, with regard to x and y ? 
 
 
 
 
 1 
 
 1 
 
§ 1-] 
 
 PROPOSITIONS. 
 
 17 
 
 This tells us, with regard to the # /-Square, that 
 it is wholly ' empty ', since both compartments are so 
 marked. With regard to the ^-Square, it tells us 
 that it is i occupied \ True, it is only one compartment 
 of it that is so marked; but that is quite enough, 
 whether the other 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." 
 
 The result would have been exactly the same, if the 
 given oblong had been marked thus : — 
 
 1 
 
 
 
 1 
 1 
 
 o 1 
 
 Once more : how shall we interpret this, with regard 
 to x and y ? 
 
 
 
 
 
 1 
 
 
 
 
 
 This tells us, as to the ^-Square, that one of its 
 compartments is ' empty '. But this information is 
 
 c 
 
18 
 
 NEW LAMPS FOR OLD. 
 
 [Ch. 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 ^'-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'" 
 
 These principles may be applied to 
 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 
 
 
 
 
 
§ 1.] PROPOSITIONS. 19 
 
 we should transfer it to the smaller Diagram thus, 
 
 1 
 
 ° 
 
 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 
 vjould 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 clef" may be re-arranged as " some bf are aede" 
 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." 
 
& 
 
 § 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 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, 
 
 <k?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 " m-Things " is 
 the Middle Term ; and, in the second case, the two 
 classes of " m-Things " 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. [Ch. 1. 
 
 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 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 will be most welcome. 
 
 Let us express, then, "no nice Cakes are unwhole- 
 some (Cakes) ", i.e. " no ^/-Cakes are ra'-(Cakes) " 
 This tells us that none of the Cakes belonging to the 
 y-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.] 
 
 SYLLOGISMS. 
 
 23 
 
 We have now to express the other Premiss, namely, 
 " some new Cakes are unwholesome (Cakes) ", i.e. 
 " some cc-Cakes are m'-(Cakes) ". This tells us that 
 some of the Cakes in the ^-half of the cupboard are 
 in its ra'-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 declaring 
 No. 9 to be cmjrfy. Hence the red counter has no choice, 
 and must go into No. 10, thus : — 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 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. [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 Cake, 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 
 Ave 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 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 y' 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 °\Lorious 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.' 
 
 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 had 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. 
 
 [Ch. I. 
 
 tribute belonging to the 'Middle Terms', we will let 
 
 m stand for " canny ", x for " Dragons " 3 and y for 
 
 " Scotchmen ". So that our two Premisses are, in full, 
 
 " All Dragon- Animals are uncanny (Animals) ; 
 
 All Scotchman-Animals are canny (Animals).' 1 
 
 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 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 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 
 mvst 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 
 
 
 
 1 
 
 
 
 
 
 1 ' 
 
 
 
 
28 
 
 NEW LAMPS FOR OLD. 
 
 [Oh. 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 tvjo, 
 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 ; 
 I 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 be 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. [Cil. I. 
 
 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 he 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 eigdrt 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 Eowland'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 i 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 
 x 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'" 9 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 five 
 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 a 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 i Fallacious Conclusion ' 
 
 you will not detect till you have marked hoth 
 
 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. [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." 
 
 i 
 
 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 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 : arid 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 x"), this would be going heyond 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." J 
 and were to ask him what Conclusion followed, he would 
 probably say " None at all ! Your Premisses offend 
 against two distinct Eules, 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 V ? I fear your Logical friend would turn away 
 
 hastily perhaps angry, perhaps only scornful : in any 
 
 case, the result would be unpleasant. / advise yon 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 Header ! 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. [Ch. I. § 3. 
 
 They have a sort of nervous dread of Attributes be- 
 ginning 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 ! 
 
27 
 
 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 c 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 ? 
 [See pp. 55, 6] 
 
38 CROSS QUESTIONS. [Ch. II. 
 
 9. In what sense do we use the w r ord ' 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 
 
 CEOSS QUESTIONS. 
 
 [Ch. II. 
 
 § 2. Half of Smaller Diagram. 
 Propositions to be represented. 
 
 x 
 
 y 
 
 -y- 
 
 1. Some x are not-y. 
 
 2. All x are not-;?/. 
 
 3. Some x are y, and some are not-;?/. 
 
 4. No a; exist. 
 
 5. Some x exist. 
 
 6. No a? are not-;?/. 
 
 7. Some a? are not-?/, and some x exist. 
 
 Taking x = "judges " ; y 
 
 8. No judges are just. 
 
 9. Some judges are unjust. 
 10. All judges are just. 
 
 '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.] 
 
 CEOSS QUESTIONS. 
 
 41 
 
 Taking y = " diligent students " ; x = " successful " ; 
 
 15. No diligent students are unsuccessful. 
 
 16. All diligent students are successful. 
 
 17. No students are diligent. 
 
 18. There are some diligent, but unsuccessful, students. 
 
 19. Some students are diligent. 
 
 [See pp. 60, 1] 
 
42 
 
 CROSS QUESTIONS. 
 
 [Ch. II. 
 
 § 3. Half of Smaller Diagram. 
 Symbols to be interpreted. 
 
 i 
 
 x 
 
 y — y'— 
 
 1. 
 
 2. 
 
 3. 
 
 
 
 1 
 
 Taking x = " good riddles " ; y = " hard " 
 
 5. i 
 
 7- I I 
 
 6. 
 
 1 
 
 
 
 
 
 
 8. 
 
 1 o 
 
 1 
 
 
 [See pp. 61, 2] 
 
§ 3.] CROSS QUESTIONS. 
 
 Taking x = " lobsters " ; y = " selfish " ; 
 
 43 
 
 9. 
 
 
 1 
 
 
 11. 
 
 
 
 1 
 
 10. 
 
 12. i 1 1 
 
 x 
 
 x' 
 
 Taking y = " healthy people " ; x = " happy " ; 
 
 13. 
 
 
 
 1 
 
 14. 
 
 -1- 
 
 15. 
 
 1 
 1 
 
 16. 
 
 
 
 
 
 [See p. 62] 
 
44 
 
 CJROSS QUESTIONS. 
 
 [Ch. II. 
 
 § 4. Smaller Diagram. 
 Propositions to be represented. 
 
 9. 
 10. 
 11. 
 12. 
 
 All y are x. 
 
 Some y are not-#. 
 
 No not-# are not-?/. 
 
 Some x are not-?/. 
 
 Some not-?/ are x. 
 
 No not-# are y. 
 
 Some not-# are not-?/. 
 
 All not-# are not-?/. 
 
 Some not-?/ exist. 
 
 No not-# exist. 
 
 Some y are #, and some are not-#. 
 
 All a? are y, and all not-?/ are not-#. 
 
 [See pp. 62, 3] 
 
§ 4.] CEOSS QUESTIONS. 45 
 
 Taking " nations " as Universe ; x = " civilised " ; 
 y = " warlike " ; 
 
 13. No uncivilised nation is warlike. 
 
 14. All unwarlike 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 n ; 
 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. 
 
 I~Ch. II. 
 
 1. 
 
 3. 
 
 § 5. Smaller Diagram. 
 Symbols to be interpreted. 
 
 1 
 
 2. 
 
 — 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 Taking "houses" as Universe; x = " built of brick"; 
 and y = " two-storied " ; interpret 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 [See p. 65 
 
§5-] 
 
 CROSS QUESTIONS. 
 
 47 
 
 Taking " boys " as Universe ; x= " fat " ; 
 and y = " active " ; interpret 
 
 9. 
 
 11. 
 
 1 
 
 1 
 
 
 
 
 1 
 
 
 i 
 
 10. 
 
 12. 
 
 i 
 
 
 
 i 
 
 1 
 
 
 1 
 
 
 
 
 1 
 
 Taking "cats " as Universe ; x = " green-eyed " ; 
 and y = " good-tempered " ; interpret 
 
 13. 
 
 15. 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 14. 
 
 16. 
 
 
 1 
 
 i 
 
 
 
 
 
 1 
 
 1 
 
 
 
 [See pp. 65, 6] 
 
48 
 
 CROSS QUESTIONS. 
 
 [Ch. II. 
 
 § 6. Larger Diagram. 
 Propositions to be represented. 
 
 1. No x are m. 
 
 2. Some y are m' 
 
 3. All m are a?'. 
 
 4. No m' are y'. 
 
 5. No m are a? ; 
 All y are m. 
 
 6. Some x are m ; 
 No y are m. 
 
 7. All m are a?' ; ) 
 No m are ^/. J 
 
 8. No x' are m 
 No y' are m 
 
 ■■:} 
 
 [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 ; 
 All black rabbits are greedy. 
 
 14. All rabbits, that are not greedy, are black ; | 
 No old rabbits are free from greediness. J 
 
 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 CEOSS QUESTIONS. [Oh. II. § 6. 
 
 Taking " persons" as Universe ; ra=" I" ; 
 
 x=" that has taken a walk " ; y = " that feels better " ; 
 
 represent 
 
 19. I have been out for a walk : 
 I feel much better. 
 
 Choosing your own ' Universe ' &c, represent 
 
 20. I sent him to bring me a kitten ; | 
 He brought me a kettle by mistake. J 
 
 [See pp. 70, 1] 
 
Ch. II. § 7.] 
 
 CBOSS QUESTIONS. 
 
 51 
 
 § 7. Both Diagrams to be employed. 
 
 x 
 
 y m — y 
 
 -x 
 
 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. 
 
 [See p. 72] 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 E '1 
 
o-2 
 
 CMOSS QUESTIONS. 
 
 [Ch. II. 
 
 3. 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 4. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 1 
 
 
 
 
 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 books suit feverish patients; ) 
 Unexciting books make one drowsy. J 
 
 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 
 
 .} 
 
 [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. J 
 
 19. Some days are rainy ; 
 Rainy days are tiresome 
 
 20. All medicine is nasty ; ) 
 
 } 
 
 .} 
 } 
 
 ; nasty ; ) 
 Senna is a medicine. J 
 
 21. Some Jews are rich ; 
 All Patagonians 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. J 
 
 26. Sugar is sweet ; ) 
 Salt is not sweet. J 
 
 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. 
 
 [See pp. 75—82] 
 
 } 
 
54 CROSS QUESTIONS. [Oh. II. § 7. 
 
 29. All battles are noisy ; | 
 What makes no noise may escape notice. J 
 
 30. No Jews are mad ; 
 All Rabbis are Jews. 
 
 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. [Ch. 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. 
 
 13. " Some x are y " and " no x are y' ". 
 
 14. A Proposition, whose Subject is a single Thing, is 
 called c 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, u some abc are def " may be re-arranged as " some hf 
 are acde ", each being equivalent to " some abcdef exist ". 
 
 17. Some tigers are fierce, 
 No tigers are not-fierce. 
 
 18. Some hard-boiled eggs are unwholesome, 
 
 DO 
 
 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, [Ch. 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 
 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 
 wJ 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 m' 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] 
 
§!•] 
 
 ELEMENTARY. 
 
 59 
 
 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. 
 
 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 
 
 3. 
 
 [See pp. 39, 40] 
 
 1 
 
 1 
 
 2. 
 
 4. 
 
 
 
 1 
 
 
 
 
 
 
60 
 
 CROOKED ANSWERS 
 
 [Ch. III. 
 
 
 
 
 1 It might be thought that the proper 
 
 Diagram would be 
 
 , 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. 
 
 
 
 
 1 
 
 10. All x are y. i. e. 1 
 
 11. Some x are y. i. e. 1 
 
 12. No x are y. i. e. i 
 
 13. Some x are y, and some are y'. i. e. 
 
 14. All x are y f . i. e. 
 
 1 
 
 1 
 
 1 
 
 15. No y are x'. i. e. 
 
 [See pp. 40, 1] 
 
§ 2.] PROPOSITIONS REPRESENTED. 
 
 1 
 
 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 x are y f . 
 
 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. 
 [See pp. 41, 2] 
 
62 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. 
 
 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. 
 
 3. 
 
 
 
 
 2. 
 
 4. 
 
 
 
 1 
 
 
 
 
 1 
 
 
 
 [See pp. 42—4] 
 
§ 4.] PROPOSITIONS REPRESENTED. 
 
 63 
 
 } o. 
 
 9. 
 
 11. 
 
 
 1 
 
 
 
 
 
 
 
 1 
 
 
 
 -1- 
 
 
 1 
 
 
 1 
 
 
 6. 
 
 10. 
 
 12. 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 1 
 
 13. No x' are y. i.e. 
 
 14. All y' are x'. i.e. 
 
 15. Some y' exist, i.e. 
 
 [See pp. 44, 5] 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 - 1 
 
64 
 
 CROOKED ANSWERS. [Ch. III. § 4. 
 
 16. All y are x, and all x are y. i. e. 
 
 17. No x' exist, i. e. 
 
 18. All x are ?/'. i. e. 
 
 19. No x are y. i. e. 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 20. Some x' are y, and some are y . i. e. 
 
 21. No y exist, and some # exist, i. e. 
 
 22. All x' are y, and all y' are a?, i. e. 
 
 23. Some a? are ^, and some x' are y r . i. e. 
 
 
 
 1 
 
 1 
 
 
 
 1 
 
 
 
 
 
 1 
 
 1 
 
 
 
 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-# are not-?/, 
 
 or, No not-y are not-# f 
 
 3. No not-?/ are #. 
 
 4. No not-£ exist, i. e. No Things are not-a?. 
 
 5. No y exist, i. e. No houses are two-storied. 
 
 fj. Some x' exist, i. e. Some houses are not built of 
 brick. 
 
 7. No x are y' . Or, no if 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 r 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. [Ch. 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 #', 
 
 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 f 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. 
 
 3. 
 
 
 
 
 
 
 
 
 
 1 
 
 1 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 5. 
 
 [See p. 48] 
 
 
 
 
 
 -1- 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 1 
 
 F 2 
 
68 
 
 CROOKED ANSWERS. [Ch. III. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 9. No x are m. i. e. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10. Some m' are v. i. e. 
 
 -1- 
 
 11. All y r are m' . i. e. 
 
 
 
 
 
 
 
 
 
 
 
 
 -1- 
 
 
 
 
 
 
 
 
 [See pp. 48, 9] 
 
§ 6.] PROPOSITIONS REPRESENTED. 
 
 69 
 
 12. All m are x\ i. e. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 13. No x are m: ) . 
 
 An r 1 - 6 - 
 
 All y are m. ) 
 
 14. All m' are v; ) . 
 
 JN o x are m . J 
 
 15. All x are m ; ) . 
 
 No m are y' . 
 
 l. e. 
 
 [See p. 49] 
 
70 
 
 CROOKED ANSWERS. 
 
 [Ch. III. 
 
 16. All m f are y f ; 
 No x are ra'. 
 
 1. e. 
 
 17. All a? are m\ 
 
 All ??i are y, 
 
 ;},. 
 
 [See remarks on No. 7, p. 60.] 
 
 18. No #' are m ; ) . 
 
 No m' are y. 
 
 i. e. 
 
 19. All m are a?; ) . 
 
 All m are ^/. 
 
 i. e. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 [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 w. = " he " ; x = " persons 
 whom I sent, &c." ; and y = " persons who brought, &c." 
 
 All m are x ; 
 
 ,} 
 
 Hence, ~7Z ' \ and the required Diagram is 
 
 All m are y. ' 
 
 
 
 
 1 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 [See p. 50] 
 
72 
 
 CROOKED ANSWERS. [Ch. III. 
 
 § 7. Both Diagrams employed. 
 
 1. 
 
 i. e. All y are x'. 
 
 1 
 
 2. i. e. Some x are y' ; or, Some y' are x. 
 
 3. 
 
 
 
 1 
 
 
 i. e. Some 3/ are *' ; or, Some x are y. 
 
 4. 
 
 o. 
 
 6. 
 
 
 
 
 1 
 
 
 
 
 1 
 
 
 i. e. No x' are y' ; or, No 3/' 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. 
 
 # 
 
 [See pp. 51, 2] 
 
§7-] 
 
 BOTE DIAGRAMS EMPLOYED. 
 
 7. 
 
 1 
 
 
 
 
 
 
 
 
 8. 
 
 
 1 
 
 
 1 
 
 
 
 
 9. 
 
 1 
 
 
 
 
 
 
 
 
 10. 
 
 
 
 
 
 
 
 
 
 11. 
 
 1 
 
 
 
 
 
 
 1 9 
 
 1 
 
 
 l — . 
 
 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 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. 
 
 [See p. 52] 
 
74 
 
 CROOKED ANSWERS. 
 
 [Oh. III. 
 
 13. 
 
 -1- 
 
 
 
 
 
 
 
 
 
 
 
 Oj 
 
 
 
 
 
 
 Let " books " be Universe ; m = " exciting " , 
 a; = " 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. 
 
 .*. No y are x. 
 
 
 
 
 
 
 1 
 
 
 
 
 
 | 
 
 
 
 
 
 
 1 
 
 
 
 
 14. 
 
 Let " persons " be Universe ; m = " that deserve the fair " : 
 
 x = " that get their deserts " ; y = " brave ". 
 
 Some m are a? ; ) 
 
 - T , > .*. Some v are #. 
 
 JN o y are m. J 
 
 i. e. Some brave persons get their deserts. 
 
 [See p. 52] 
 
§7.] 
 
 BOTH DIAGRAMS EMPLOYED. 
 
 75 
 
 15. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Let " persons " be Universe ; m — ■ " patient " ; 
 
 x = " children n ; y = " that can sit still ". 
 
 No x are m ; ) ^ T 
 
 f >\ :. No x 
 No m are y. ) 
 
 i. e. No children can sit still. 
 
 are y. 
 
 16. 
 
 
 
 
 
 
 i ° 
 
 1 
 
 
 o 
 
 
 
 
 
 
 
 
 1 
 
 
 
 Let " things " be Universe ; m = u fat '" ; x = " pigs " ; 
 
 y = " skeletons M . 
 
 All x are m ; , 
 
 .*. All x are y . 
 
 No y are m, 
 
 i. e. All pigs are not-skeletons. 
 [See pp. 52, 3] 
 
76 
 
 CROOKED ANSWERS. 
 
 [Ch. III. 
 
 17. 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 Let " creatures " be Universe ; m = " monkeys " ; 
 x = " soldiers " ; y = " mischievous ". 
 No m are x ; 
 All m are #. 
 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 a? are ??i ; ) _>_ 
 
 __ V ,\ No £ are £/. 
 
 No 3/ are m . J 
 
 i. e. None of my cousins are judges. 
 
 [See p. 53] 
 
§7.] 
 
 BOTH DIAGRAMS EMPLOYED. 
 
 77 
 
 19. 
 
 Let " periods " be Universe ; m = " days " ; 
 
 x = " rainy " ; y = " tiresome ". 
 
 Some 7/i are a? : 1 ^ 
 
 } .'. borne 05 are y. 
 All #m are 7y. J 
 
 i. e. Some rainy periods are tiresome. 
 
 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] 
 
CROOKED ANSWERS. 
 
 [Ch. III. 
 
 20. 
 
 j o 
 
 
 
 
 
 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. ) 
 
 i. e. Senna is nasty. 
 
 LSee remarks on No. 7, p. 60.] 
 
 21. 
 
 
 
 
 
 
 
 1 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 Let " persons " be Universe ; m = " Jews " ; 
 x— u rich " ; y = " Patagonians ". 
 Some m are x ; 
 
 All y are m' . 
 
 ;. Some x are y'. 
 
 i. e. Some rich persons are not Patagonians. 
 
 [See p. 53] 
 
5 7.1 
 
 BOTH DIAGRAMS EMPLOYED. 
 
 7 ( J 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 Let " creatures " be Universe ; m = "teetotalers " ; 
 
 x = " that like sugar " ; y = " nightingales ". 
 
 All m are x ; \ 
 
 XT , \ :. No y are x'. 
 
 -So y are m .) 
 
 i. e. No nightingales dislike sugar. 
 
 23. 
 
 
 
 
 
 
 1 
 
 [ 
 
 
 
 
 
 
 
 
 , 
 
 
 
 
 Let " food v be Universe ; m = " wholesome " ; 
 a? = " muffins " ; y = " buns '\ 
 No a? are m ; 
 All 2/ are m , 
 
 There is 'no information' for the smaller Diagram ; so 
 no Conclusion can be drawn. 
 [See p. 53] 
 
80 
 
 CROOKED ANSWERS. 
 
 [C'H. III. 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 1 
 
 
 24. 
 
 Let " creatures " be Universe ; m = " that run well " ; 
 x = " fat " ; y = " greyhounds ". 
 No x are m ; 
 Some y are m. 
 
 i. e. Some greyhounds are not fat. 
 
 .*. Some y are x' . 
 
 25. - 
 
 -1- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Let " persons " be Universe ; m = " soldiers " ; 
 a? = " that march " ; y = " youths ". 
 All m are a? ; | 
 Some y are m'. i 
 
 There is ' no information ' for the smaller Diagram ; so 
 no Conclusion can be drawn. 
 
 [See p. 53] 
 
7-J 
 
 BOTH DIAGRAMS EMPLOYED. 
 
 81 
 
 26. 
 
 
 
 1 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 1 
 
 1 
 
 Let " food " be Universe ; m = " sweet " ; 
 
 x = " sugar " ; y = " salt ". 
 All x are m ; ) . ( All a? are £/'. 
 All y are m'. J I All y are a?'. 
 
 ( Sugar is not salt. 
 
 i.e. 
 
 I Salt is not sugar. 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 Let " Things " be Universe ; m = " eggs " ; 
 
 x = " hard-boiled " ; y = " crackable ". 
 
 Some m are a? ; ) ^ 
 
 .'. borne a? are y. 
 
 No m are gf. 
 i. e. Some hard-boiled things can be cracked. 
 [See p. 53] 
 
82 
 
 CROOKED ANSWERS. 
 
 [Ch. III. 
 
 28. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Let " persons " be Universe ; m = " Jews " ; x = " that 
 
 are in the house " ; y = " that are in the garden ". 
 
 No m are x; ) _ T 
 
 _ T , V .'. JNo a? are y. 
 
 JN o m' are y. J 
 
 i. e. No persons, that are in the house, are also in 
 
 the garden. 
 
 29. 
 
 
 
 
 
 
 
 
 
 
 — 
 
 
 
 1 
 
 
 
 
 
 1 
 
 Let " Things " be Universe ; m = " noisy " ; 
 
 x = u battles " ; y = " that may escape notice ". 
 
 All x are m:\ ~ 
 ... . > .*. borne x are y. 
 
 All m are y. J 
 
 i. e. Some things, that are not battles, may escape notice. 
 
 [See pp. 53, 54] 
 
§7.] 
 
 BOTH DIAGRAMS EMPLOYED. 
 
 83 
 
 30. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 Let " persons " be Universe ; rrt = " Jews " ; 
 x = " mad " ; y = u Rabbis " 
 No m are x ; 
 All 2/ are m. 
 
 i. e. All Rabbis are sane. 
 
 .\ All y are x. 
 
 31. 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 Let " Things ,J be Universe ; m = " fish " ; 
 x = " that can swim " ; y = " skates ". 
 No m are x' : 
 Some 2/ are m. 
 
 i. e. Some skates can swim. 
 [See p. 54] 
 
 G 2 
 
 ? i .*. Some y are #. 
 
84 
 
 CROOKED ANSWERS. [Ch. III. § 7. 
 
 32. 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 1 
 
 
 Let " people " be Universe ; m = " passionate " ; 
 x =■ " reasonable " ; y = " orators ". 
 
 All m are a;' ; 
 
 Some y are 
 i. e. Some orators are unreasonable. 
 
 I . * Some y are x . 
 3 m. f J 
 
 [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. J 
 
 2. No bald person needs a hair-brush ; j 
 No lizards have hair. J 
 
 3. All thoughtless people do mischief ; | 
 No thoughtful person forgets a promise, i 
 
 4. I do not like John ; ) 
 Some of my friends like John, i 
 
 5. No potatoes are pine-apples ; j 
 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. 
 
$6 HIT OH MISS. [Oh. 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. J 
 
 12. " Mind your own business ; ) 
 This quarrel is no business of yours." i 
 
 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. j 
 
 15. John is industrious ; \ 
 All industrious people are happy, i 
 
 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. J 
 
 21. Audible music causes vibration in the air; | 
 Inaudible music is not worth paying for. i 
 
 i) 
 
Ch. IV.] HIT 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, i 
 
 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 
 Some dishonest people are found out. J 
 
 .} 
 
 27. No thieves are honest ; 
 Some dishonest people 
 
 28. All wasps are unfriendly ; 
 All puppies are friendly. 
 
 29. All improbable stories are doubted ; ) 
 None of these stories are probable. J 
 
 30. " He told me you had gone away." ) 
 " He never says one word of truth." J 
 
 31. His songs never last an hour; } 
 A song, that lasts an hour, is tedious. J 
 
 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. 
 
 } 
 
SS HIT OR MISS. [On. IY^. 
 
 35. No Professors are ignorant ; i 
 Some ignorant people are conceited. ) 
 
 36. Toothache is never pleasant ; j 
 Warmth is never unpleasant, f 
 
 37. Bores are terrible ; ) 
 You are a bore. i 
 
 38. Some mountains are insurmountable ; 
 All stiles can be surmounted. 
 
 39. No Frenchmen like plumpudding ; ) 
 All Englishmen like plumpudding. i 
 
 40. No idlers win fame ; 
 Some painters are not idle. 
 
 '41. No lobsters are unreasonable ; | 
 
 No reasonable creatures expect impossibilities, i 
 
 42. No kind deed is unlawful; | 
 What is lawful may be done without fear. J 
 
 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. J 
 
 46. All my cousins are unjust ; 
 No judges are unjust. 
 
Ch. it.] hit or miss. 89 
 
 47. No country, that has been explored, x 
 
 is infested by dragons ; I 
 
 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. 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, i 
 
 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. 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. J 
 
 57. Some pillows are soft ; | 
 No pokers are soft. J 
 
 58. I am old and lame ; \ 
 No old merchant is a lame gambler. / 
 
90 HIT OR MISS. [Oh. 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. J 
 
 61. Richard is out of temper ; ) 
 No one but Richard can ride that horse. J 
 
 62. All jokes are meant to amuse ; j 
 No Act of Parliament is a joke. ) 
 
 63. "I saw it in a newspaper." 
 
 )er. ) 
 " All newspapers tell lies." J 
 
 ; . . 1 
 
 Unpleasant experiences are not anxiously desired. J 
 
 } 
 
 64. No nightmare is pleasant ; 
 Unpleasant experiences are 
 
 65. Prudent travellers carry plenty of small change 
 Imprudent travellers lose their luggage. 
 
 66. All wasps are unfriendly ; \ 
 No puppies are unfriendly, i 
 
 67. He called here yesterday ; ) 
 He is no friend of mine. J 
 
 68. No quadrupeds can whistle ; | 
 Some cats are quadrupeds, i 
 
 69. No cooked meat is sold by butchers ; \ 
 No uncooked meat is served at dinner, i 
 
 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 MISS. 9 L 
 
 72. No emperors are dentists ; | 
 All dentists are dreaded by children. 1 
 
 73. All, who are not old, like walking ; 
 Neither you nor I are old. 
 
 74. All blades are sharp ; | 
 Some grasses are blades, i 
 
 75. No dictatorial person is popular ; i 
 She is dictatorial. f 
 
 76. Some sweet things are unwholesome ; 
 No muffins are sweet. 
 
 77. No military men write poetry ; i 
 No generals are civilians. 1 
 
 78. Bores are dreaded ; | 
 A bore is never begged to prolong his visit, f 
 
 79. All owls are satisfactory ; \ 
 Some excuses are unsatisfactory. J 
 
 80. All my cousins are unjust ; | 
 All judges are just. i 
 
 81. Some buns are rich ; | 
 All buns are nice. J 
 
 82. No medicine is nice ; \ 
 No pills are unmedicinal. j 
 
 83. Some lessons are difficult ; j 
 What is difficult needs attention, i 
 
 84. No unexpected pleasure annoys me ; | 
 Your visit is an unexpected pleasure. J 
 
92 HIT OB MISS. [Ch. IV. 
 
 85. Caterpillars are not eloquent ; | 
 Jones is eloquent. J 
 
 86. Some bald people wear wigs ; | 
 All your children have hair. J 
 
 87. All wasps are unfriendly ; i 
 Unfriendly creatures are always unwelcome. J 
 
 88. No bankrupts are rich ; 
 Some merchants are not bankrupts. 
 
 89. Weasels sometimes sleep ; } 
 All animals sometimes sleep. J 
 
 90. Ill-managed concerns are unprofitable ; | 
 Railways are never ill-managed. J 
 
 91. 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 : — 
 
 92. " The Lion, as any one can tell you who has been 
 chased by them as often as / 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 ! " 
 
Cii. 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 BIT OR MISS. [Ch. 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 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 ( 
 
 99. " What are you talking about geraniums for ? You 
 cant 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 ycni, 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. 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 
 are 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. [Ch. 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. 
 
[TURX OVER 
 
WORKS BY LEWIS CARROLL. 
 
 PUBLISHED BY 
 
 MACMILLAN AND CO., LONDON 
 
 ALICE'S ADVENTURES IN WONDERLAND. 
 
 With Forty-two Illustrations by Tenniel. (First published in 
 1865.) Crown 8vo, cloth, gilt edges, price 6s. Seventy-ninth 
 Thousand. 
 
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WORKS BY LEWIS CARROLL. 
 
 PUBLISHED BY 
 
 MACMILLAN AND CO., LONDON. 
 
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 taining a card diagram and nine counters — four red and five grey. ) 
 Crown 8vo, cloth, price 35. 
 
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•:. 
 

 THE GAME 
 
 LOGIC 
 
 BY 
 
 LEWIS CARROLL 
 
 PRICE THREE SHILLINGS 
 
 HonBon 
 MACMILLAIST AND CO. 
 
 AND NEW YORK 
 
 1886 
 
 \All Rights reserved I 
 
THE GAME 
 
 LOGIC 
 
 BY 
 
 LEWIS CARROLL 
 
 PRICE THREE SHILLINGS 
 
 lLonUon 
 MACMILLAN AND CO. 
 
 AND NEW YORK 
 
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 [All Rights resetted) 
 
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 THE GAME 
 
 "LOGIC." 
 
 Instructions, for playing 
 this Game, will be found in 
 tlie accompanying Book. 
 
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