{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_4763/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_4763","id":"gutenberg_4763","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/4763","summary":null,"tags":["Category: Mathematics","Logic -- Juvenile literature","Logic, Symbolic and mathematical","Philosophy"],"text":"Produced by Gregory D. Weeks, L. Lynn Smith, Reina Hosier,\nBrett Fishburne\n\n\n\n\n\n\n\n\n\n\nTHE GAME OF LOGIC\n\nBy Lewis Carroll\n\n\n ---------------------\n |9 | 10|\n | | |\n | -----x------ |\n | |11 | 12| |\n | | | | |\n |---y-----m------y'---|\n | | | | |\n | |13 | 14| |\n | -----x'----- |\n | | |\n |15 | 16|\n ---------------------\n\n COLOURS FOR -------------\n COUNTERS |5 | 6|\n ___ | x |\n | | |\n See the Sun is overhead, |--y-------y'-|\n Shining on us, FULL and | | |\n RED! | x' |\n |7 | 8|\n Now the Sun is gone away, -------------\n And the EMPTY sky is\n GREY!\n ___\n\n\n\nTHE GAME OF LOGIC\n\nBy Lewis Carrol\n\n\n\n To my Child-friend.\n\n I charm in vain; for never again,\n All keenly as my glance I bend,\n Will Memory, goddess coy,\n Embody for my joy\n Departed days, nor let me gaze\n On thee, my fairy friend!\n\n Yet could thy face, in mystic grace,\n A moment smile on me, 'twould send\n Far-darting rays of light\n From Heaven athwart the night,\n By which to read in very deed\n Thy spirit, sweetest friend!\n\n So may the stream of Life's long dream\n Flow gently onward to its end,\n With many a floweret gay,\n Adown its willowy way:\n May no sigh vex, no care perplex,\n My loving little friend!\n\n\n\nNOTA BENE.\n\nWith each copy of this Book is given an Envelope, containing a\nDiagram (similar to the frontispiece) on card, and nine Counters,\nfour red and five grey.\n\nThe Envelope, &c. can be had separately, at 3d. each.\n\nThe Author will be very grateful for suggestions, especially from\nbeginners in Logic, of any alterations, or further explanations,\nthat may seem desirable. Letters should be addressed to him at\n\"29, Bedford Street, Covent Garden, London.\"\n\n\n\nPREFACE\n\n\n\n\"There foam'd rebellious Logic, gagg'd and bound.\"\n\n\nThis Game requires nine Counters--four of one colour and five of\nanother: say four red and five grey.\n\nBesides the nine Counters, it also requires one Player, AT LEAST.\nI am not aware of any Game that can be played with LESS than this\nnumber: while there are several that require MORE: take Cricket,\nfor instance, which requires twenty-two. How much easier it is,\nwhen you want to play a Game, to find ONE Player than twenty-two.\nAt the same time, though one Player is enough, a good deal more\namusement may be got by two working at it together, and correcting\neach other's mistakes.\n\nA second advantage, possessed by this Game, is that, besides being\nan endless source of amusement (the number of arguments, that may\nbe worked by it, being infinite), it will give the Players a little\ninstruction as well. But is there any great harm in THAT, so long\nas you get plenty of amusement?\n\n\n\nCONTENTS.\n\n\nCHAPTER PAGE\n\n I. NEW LAMPS FOR OLD.\n 1. Propositions . . . . . . . 1\n 2. Syllogisms . . . . . . . . 20\n 3. Fallacies . . . . . . . . 32\n\n II. CROSS QUESTIONS.\n 1. Elementary . . . . . . . . 37\n 2. Half of Smaller Diagram. Propositions\n to be represented . . . . . 40\n 3. Do. Symbols to be interpreted. . 42\n 4. Smaller Diagram. Propositions to be\n represented . . . . . . . 44\n 5. Do. Symbols to be interpreted. . 46\n 6. Larger Diagram. Propositions to be\n represented . . . . . . . 48\n 7. Both Diagrams to be employed . . 51\n\n III. CROOKED ANSWERS.\n 1. Elementary . . . . . . . . 55\n 2. Half of Smaller Diagram. Propositions\n represented . . . . . . . 59\n 3. Do. Symbols interpreted . . . 61\n 4. Smaller Diagram. Propositions represented. 62\n 5. Do. Symbols interpreted . . . 65\n 6. Larger Diagram. Propositions represented. 67\n 7. Both Diagrams employed . . . . 72\n\n IV. HIT OR MISS . . . . . . . . . 85\n\n\n\n\nCHAPTER I.\n\nNEW LAMPS FOR OLD.\n\n\n\n\n\n \"Light come, light go.\"\n _________\n\n 1. Propositions.\n\n \"Some new Cakes are nice.\"\n \"No new Cakes are nice.\"\n \"All new cakes are nice.\"\n\nThere are three 'PROPOSITIONS' for you--the only three kinds we\nare going to use in this Game: and the first thing to be done is\nto learn how to express them on the Board.\n\nLet us begin with\n\n\"Some new Cakes are nice.\"\n\nBut before doing so, a remark has to be made--one that is rather\nimportant, and by no means easy to understand all in a moment: so\nplease to read this VERY carefully.\n\nThe world contains many THINGS (such as \"Buns\", \"Babies\", \"Beetles\".\n\"Battledores\". &c.); and these Things possess many ATTRIBUTES\n(such as \"baked\", \"beautiful\", \"black\", \"broken\", &c.: in fact,\nwhatever can be \"attributed to\", that is \"said to belong to\", any\nThing, is an Attribute). Whenever we wish to mention a Thing, we\nuse a SUBSTANTIVE: when we wish to mention an Attribute, we use\nan ADJECTIVE. People have asked the question \"Can a Thing exist\nwithout any Attributes belonging to it?\" It is a very puzzling\nquestion, and I'm not going to try to answer it: let us turn up\nour noses, and treat it with contemptuous silence, as if it really\nwasn't worth noticing. But, if they put it the other way, and ask\n\"Can an Attribute exist without any Thing for it to belong to?\", we\nmay say at once \"No: no more than a Baby could go a railway-journey\nwith no one to take care of it!\" You never saw \"beautiful\" floating\nabout in the air, or littered about on the floor, without any Thing\nto BE beautiful, now did you?\n\nAnd now what am I driving at, in all this long rigmarole? It is\nthis. You may put \"is\" or \"are\" between names of two THINGS (for\nexample, \"some Pigs are fat Animals\"), or between the names of two\nATTRIBUTES (for example, \"pink is light-red\"), and in each case it\nwill make good sense. But, if you put \"is\" or \"are\" between the\nname of a THING and the name of an ATTRIBUTE (for example, \"some\nPigs are pink\"), you do NOT make good sense (for how can a Thing\nBE an Attribute?) unless you have an understanding with the person\nto whom you are speaking. And the simplest understanding would, I\nthink, be this--that the Substantive shall be supposed to be repeated\nat the end of the sentence, so that the sentence, if written out\nin full, would be \"some Pigs are pink (Pigs)\". And now the word\n\"are\" makes quite good sense.\n\nThus, in order to make good sense of the Proposition \"some new Cakes\nare nice\", we must suppose it to be written out in full, in the\nform \"some new Cakes are nice (Cakes)\". Now this contains two\n'TERMS'--\"new Cakes\" being one of them, and \"nice (Cakes)\" the\nother. \"New Cakes,\" being the one we are talking about, is called\nthe 'SUBJECT' of the Proposition, and \"nice (Cakes)\" the 'PREDICATE'.\nAlso this Proposition is said to be a 'PARTICULAR' one, since it\ndoes not speak of the WHOLE of its Subject, but only of a PART of\nit. The other two kinds are said to be 'UNIVERSAL', because they\nspeak of the WHOLE of their Subjects--the one denying niceness, and\nthe other asserting it, of the WHOLE class of \"new Cakes\". Lastly,\nif you would like to have a definition of the word 'PROPOSITION'\nitself, you may take this:--\"a sentence stating that some, or\nnone, or all, of the Things belonging to a certain class, called\nits 'Subject', are also Things belonging to a certain other class,\ncalled its 'Predicate'\".\n\nYou will find these seven words--PROPOSITION, ATTRIBUTE, TERM,\nSUBJECT, PREDICATE, PARTICULAR, UNIVERSAL--charmingly useful, if\nany friend should happen to ask if you have ever studied Logic.\nMind you bring all seven words into your answer, and you friend\nwill go away deeply impressed--'a sadder and a wiser man'.\n\nNow please to look at the smaller Diagram on the Board, and suppose\nit to be a cupboard, intended for all the Cakes in the world (it\nwould have to be a good large one, of course). And let us suppose\nall the new ones to be put into the upper half (marked 'x'), and all\nthe rest (that is, the NOT-new ones) into the lower half (marked\n'x''). Thus the lower half would contain ELDERLY Cakes, AGED\nCakes, ANTE-DILUVIAN Cakes--if there are any: I haven't seen many,\nmyself--and so on. Let us also suppose all the nice Cakes to be\nput into the left-hand half (marked 'y'), and all the rest (that\nis, the not-nice ones) into the right-hand half (marked 'y''). At\npresent, then, we must understand x to mean \"new\", x' \"not-new\",\ny \"nice\", and y' \"not-nice.\"\n\nAnd now what kind of Cakes would you expect to find in compartment\nNo. 5?\n\nIt is part of the upper half, you see; so that, if it has any Cakes\nin it, they must be NEW: and it is part of the left-hand half;\nso that they must be NICE. Hence if there are any Cakes in this\ncompartment, they must have the double 'ATTRIBUTE' \"new and nice\":\nor, if we use letters, the must be \"x y.\"\n\nObserve that the letters x, y are written on two of the edges of\nthis compartment. This you will find a very convenient rule for\nknowing what Attributes belong to the Things in any compartment.\nTake No. 7, for instance. If there are any Cakes there, they must\nbe \"x' y\", that is, they must be \"not-new and nice.\"\n\nNow let us make another agreement--that a red counter in a\ncompartment shall mean that it is 'OCCUPIED', that is, that there\nare SOME Cakes in it. (The word 'some,' in Logic, means 'one or\nmore' so that a single Cake in a compartment would be quite enough\nreason for saying \"there are SOME Cakes here\"). Also let us agree\nthat a grey counter in a compartment shall mean that it is 'EMPTY',\nthat is that there are NO Cakes in it. In the following Diagrams,\nI shall put '1' (meaning 'one or more') where you are to put a RED\ncounter, and '0' (meaning 'none') where you are to put a GREY one.\n\nAs the Subject of our Proposition is to be \"new Cakes\", we are only\nconcerned, at present, with the UPPER half of the cupboard, where\nall the Cakes have the attribute x, that is, \"new.\"\n\nNow, fixing our attention on this upper half, suppose we found it\nmarked like this,\n\n\n -----------\n | | |\n | 1 | |\n | | |\n -----------\n\n\nthat is, with a red counter in No. 5. What would this tell us,\nwith regard to the class of \"new Cakes\"?\n\nWould it not tell us that there are SOME of them in the x y-compartment?\nThat is, that some of them (besides having the Attribute x, which\nbelongs to both compartments) have the Attribute y (that is, \"nice\").\nThis we might express by saying \"some x-Cakes are y-(Cakes)\", or,\nputting words instead of letters,\n\n\n\"Some new Cakes are nice (Cakes)\",\n\n\nor, in a shorter form,\n\n\n\"Some new Cakes are nice\".\n\n\nAt last we have found out how to represent the first Proposition\nof this Section. If you have not CLEARLY understood all I have\nsaid, go no further, but read it over and over again, till you DO\nunderstand it. After that is once mastered, you will find all the\nrest quite easy.\n\nIt will save a little trouble, in doing the other Propositions,\nif we agree to leave out the word \"Cakes\" altogether. I find it\nconvenient to call the whole class of Things, for which the cupboard\nis intended, the 'UNIVERSE.' Thus we might have begun this business\nby saying \"Let us take a Universe of Cakes.\" (Sounds nice, doesn't\nit?)\n\nOf course any other Things would have done just as well as Cakes.\nWe might make Propositions about \"a Universe of Lizards\", or even\n\"a Universe of Hornets\". (Wouldn't THAT be a charming Universe to\nlive in?)\n\nSo far, then, we have learned that\n\n\n -----------\n | | |\n | 1 | |\n | | |\n -----------\n\n\nmeans \"some x and y,\" i.e. \"some new are nice.\"\n\nI think you will see without further explanation, that\n\n\n -----------\n | | |\n | | 1 |\n | | |\n -----------\n\n\nmeans \"some x are y',\" i.e. \"some new are not-nice.\"\n\nNow let us put a GREY counter into No. 5, and ask ourselves the\nmeaning of\n\n\n -----------\n | | |\n | 0 | |\n | | |\n -----------\n\n\nThis tells us that the x y-compartment is EMPTY, which we may express\nby \"no x are y\", or, \"no new Cakes are nice\". This is the second\nof the three Propositions at the head of this Section.\n\nIn the same way,\n\n\n -----------\n | | |\n | | 0 |\n | | |\n -----------\n\n\nwould mean \"no x are y',\" or, \"no new Cakes are not-nice.\"\n\nWhat would you make of this, I wonder?\n\n\n -----------\n | | |\n | 1 | 1 |\n | | |\n -----------\n\n\nI hope you will not have much trouble in making out that this\nrepresents a DOUBLE Proposition: namely, \"some x are y, AND some\nare y',\" i.e. \"some new are nice, and some are not-nice.\"\n\nThe following is a little harder, perhaps:\n\n\n -----------\n | | |\n | 0 | 0 |\n | | |\n -----------\n\n\nThis means \"no x are y, AND none are y',\" i.e. \"no new are nice,\nAND none are not-nice\": which leads to the rather curious result\nthat \"no new exist,\" i.e. \"no Cakes are new.\" This is because\n\"nice\" and \"not-nice\" make what we call an 'EXHAUSTIVE' division\nof the class \"new Cakes\": i.e. between them, they EXHAUST the whole\nclass, so that all the new Cakes, that exist, must be found in one\nor the other of them.\n\nAnd now suppose you had to represent, with counters the contradictory\nto \"no Cakes are new\", which would be \"some Cakes are new\", or,\nputting letters for words, \"some Cakes are x\", how would you do\nit?\n\nThis will puzzle you a little, I expect. Evidently you must put\na red counter SOMEWHERE in the x-half of the cupboard, since you\nknow there are SOME new Cakes. But you must not put it into the\nLEFT-HAND compartment, since you do not know them to be NICE: nor\nmay you put it into the RIGHT-HAND one, since you do not know them\nto be NOT-NICE.\n\nWhat, then, are you to do? I think the best way out of the\ndifficulty is to place the red counter ON THE DIVISION-LINE between\nthe xy-compartment and the xy'-compartment. This I shall represent\n(as I always put '1' where you are to put a red counter) by the\ndiagram\n\n\n -----------\n | | |\n | -1- |\n | | |\n -----------\n\n\nOur ingenious American cousins have invented a phrase to express\nthe position of a man who wants to join one or the other of two\nparties--such as their two parties 'Democrats' and 'Republicans'--but\ncan't make up his mind WHICH. Such a man is said to be \"sitting\non the fence.\" Now that is exactly the position of the red counter\nyou have just placed on the division-line. He likes the look of\nNo. 5, and he likes the look of No. 6, and he doesn't know WHICH to\njump down into. So there he sits astride, silly fellow, dangling\nhis legs, one on each side of the fence!\n\nNow I am going to give you a much harder one to make out. What\ndoes this mean?\n\n\n -----------\n | | |\n | 1 | 0 |\n | | |\n -----------\n\n\nThis is clearly a DOUBLE Proposition. It tells us not only that\n\"some x are y,\" but also the \"no x are NOT y.\" Hence the result\nis \"ALL x are y,\" i.e. \"all new Cakes are nice\", which is the last\nof the three Propositions at the head of this Section.\n\nWe see, then, that the Universal Proposition\n\n\n\"All new Cakes are nice\"\n\n\nconsists of TWO Propositions taken together, namely,\n\n\n \"Some new Cakes are nice,\"\n and \"No new Cakes are not-nice.\"\n\n\nIn the same way\n\n\n -----------\n | | |\n | 0 | 1 |\n | | |\n -----------\n\n\nwould mean \"all x are y' \", that is,\n\n\n\"All new Cakes are not-nice.\"\n\n\nNow what would you make of such a Proposition as \"The Cake you have\ngiven me is nice\"? Is it Particular or Universal?\n\n\n\"Particular, of course,\" you readily reply. \"One single Cake is\nhardly worth calling 'some,' even.\"\n\n\nNo, my dear impulsive Reader, it is 'Universal'. Remember that,\nfew as they are (and I grant you they couldn't well be fewer),\nthey are (or rather 'it is') ALL that you have given me! Thus, if\n(leaving 'red' out of the question) I divide my Universe of Cakes\ninto two classes--the Cakes you have given me (to which I assign\nthe upper half of the cupboard), and those you HAVEN'T given me\n(which are to go below)--I find the lower half fairly full, and the\nupper one as nearly as possible empty. And then, when I am told\nto put an upright division into each half, keeping the NICE Cakes\nto the left, and the NOT-NICE ones to the right, I begin by carefully\ncollecting ALL the Cakes you have given me (saying to myself, from\ntime to time, \"Generous creature! How shall I ever repay such\nkindness?\"), and piling them up in the left-hand compartment. AND\nIT DOESN'T TAKE LONG TO DO IT!\n\nHere is another Universal Proposition for you. \"Barzillai Beckalegg\nis an honest man.\" That means \"ALL the Barzillai Beckaleggs, that\nI am now considering, are honest men.\" (You think I invented that\nname, now don't you? But I didn't. It's on a carrier's cart,\nsomewhere down in Cornwall.)\n\nThis kind of Universal Proposition (where the Subject is a single\nThing) is called an 'INDIVIDUAL' Proposition.\n\nNow let us take \"NICE Cakes\" as the Subject of Proposition: that\nis, let us fix our thoughts on the LEFT-HAND half of the cupboard,\nwhere all the Cakes have attribute y, that is, \"nice.\"\n\n\n -----\n Suppose we find it marked like this:-- | |\n | 1 |\n What would that tell us? | |\n -----\n | |\n | |\n | |\n -----\n\n\nI hope that it is not necessary, after explaining the HORIZONTAL\noblong so fully, to spend much time over the UPRIGHT one. I hope\nyou will see, for yourself, that this means \"some y are x\", that\nis,\n\n\n\"Some nice Cakes are new.\"\n\n\n\"But,\" you will say, \"we have had this case before. You put a red\ncounter into No. 5, and you told us it meant 'some new Cakes are\nnice'; and NOW you tell us that it means 'some NICE Cakes are NEW'!\nCan it mean BOTH?\"\n\nThe question is a very thoughtful one, and does you GREAT credit,\ndear Reader! It DOES mean both. If you choose to take x (that\nis, \"new Cakes\") as your Subject, and to regard No. 5 as part of a\nHORIZONTAL oblong, you may read it \"some x are y\", that is, \"some\nnew Cakes are nice\": but, if you choose to take y (that is, \"nice\nCake\") as your Subject, and to regard No. 5 as part of an UPRIGHT\noblong, THEN you may read it \"some y are x\", that is, \"some nice\nCakes are new\". They are merely two different ways of expressing\nthe very same truth.\n\nWithout more words, I will simply set down the other ways in which\nthis upright oblong might be marked, adding the meaning in each\ncase. By comparing them with the various cases of the horizontal\noblong, you will, I hope, be able to understand them clearly.\n\nYou will find it a good plan to examine yourself on this table,\nby covering up first one column and then the other, and 'dodging\nabout', as the children say.\n\nAlso you will do well to write out for yourself two other tables--one\nfor the LOWER half of the cupboard, and the other for its RIGHT-HAND\nhalf.\n\nAnd now I think we have said all we need to say about the smaller\nDiagram, and may go on to the larger one.\n\n _________________________________________________\n |\n Symbols. | Meanings.\n _______________|_________________________________\n ----- |\n | | |\n | | | Some y are x';\n | | | i.e. Some nice are not-new.\n ----- |\n | | |\n | 1 | |\n | | |\n ----- |\n |\n ----- |\n | | | No y are x;\n | 0 | | i.e. No nice are new.\n | | |\n ----- | [Observe that this is merely another way of\n | | | expressing \"No new are nice.\"]\n | | |\n | | |\n ----- |\n |\n ----- |\n | | |\n | | | No y are x';\n | | | i.e. No nice are not-new.\n ----- |\n | | |\n | 0 | |\n | | |\n ----- |\n |\n ----- |\n | | |\n | 1 | | Some y are x, and some are x';\n | | | i.e. Some nice are new, and some are\n ----- | not-new.\n | | |\n | 1 | |\n | | |\n ----- |\n |\n ----- |\n | | |\n | 0 | | No y are x, and none are x'; i.e. No y\n | | | exist;\n ----- | i.e. No Cakes are nice.\n | | |\n | 0 | |\n | | |\n ----- |\n |\n ----- |\n | | |\n | 1 | | All y are x;\n | | | i.e. All nice are new.\n ----- |\n | | |\n | 0 | |\n | | |\n ----- |\n |\n ----- |\n | | |\n | 0 | | All y are x';\n | | | i.e. All nice are not-new.\n ----- |\n | | |\n | 1 | |\n | | |\n ----- |\n _______________|_________________________________\n\n\nThis may be taken to be a cupboard divided in the same way as the\nlast, but ALSO divided into two portions, for the Attribute m. Let\nus give to m the meaning \"wholesome\": and let us suppose that all\nWHOLESOME Cakes are placed INSIDE the central Square, and all the\nUNWHOLESOME ones OUTSIDE it, that is, in one or other of the four\nqueer-shaped OUTER compartments.\n\nWe see that, just as, in the smaller Diagram, the Cakes in each\ncompartment had TWO Attributes, so, here, the Cakes in each compartment\nhave THREE Attributes: and, just as the letters, representing the\nTWO Attributes, were written on the EDGES of the compartment, so,\nhere, they are written at the CORNERS. (Observe that m' is supposed\nto be written at each of the four outer corners.) So that we can\ntell in a moment, by looking at a compartment, what three Attributes\nbelong to the Things in it. For instance, take No. 12. Here we\nfind x, y', m, at the corners: so we know that the Cakes in it, if\nthere are any, have the triple Attribute, 'xy'm', that is, \"new,\nnot-nice, and wholesome.\" Again, take No. 16. Here we find, at\nthe corners, x', y', m': so the Cakes in it are \"not-new, not-nice,\nand unwholesome.\" (Remarkably untempting Cakes!)\n\nIt would take far too long to go through all the Propositions,\ncontaining x and y, x and m, and y and m which can be represented\non this diagram (there are ninety-six altogether, so I am sure you\nwill excuse me!) and I must content myself with doing two or three,\nas specimens. You will do well to work out a lot more for yourself.\n\nTaking the upper half by itself, so that our Subject is \"new Cakes\",\nhow are we to represent \"no new Cakes are wholesome\"?\n\nThis is, writing letters for words, \"no x are m.\" Now this tells us\nthat none of the Cakes, belonging to the upper half of the cupboard,\nare to be found INSIDE the central Square: that is, the two\ncompartments, No. 11 and No. 12, are EMPTY. And this, of course,\nis represented by\n\n\n -------------------\n | | |\n | _____|_____ |\n | | | | |\n | | 0 | 0 | |\n | | | | |\n -------------------\n\n\nAnd now how are we to represent the contradictory Proposition \"SOME x\nare m\"? This is a difficulty I have already considered. I think\nthe best way is to place a red counter ON THE DIVISION-LINE between\nNo. 11 and No. 12, and to understand this to mean that ONE of the\ntwo compartments is 'occupied,' but that we do not at present know WHICH.\nThis I shall represent thus:--\n\n\n -------------------\n | | |\n | _____|_____ |\n | | | | |\n | | -1- | |\n | | | | |\n -------------------\n\nNow let us express \"all x are m.\"\n\nThis consists, we know, of TWO Propositions,\n\n\n \"Some x are m,\"\n and \"No x are m'.\"\n\nLet us express the negative part first. This tells us that none\nof the Cakes, belonging to the upper half of the cupboard, are to\nbe found OUTSIDE the central Square: that is, the two compartments,\nNo. 9 and No. 10, are EMPTY. This, of course, is represented by\n\n\n -------------------\n | 0 | 0 |\n | _____|_____ |\n | | | | |\n | | | | |\n | | | | |\n -------------------\n\nBut we have yet to represent \"Some x are m.\" This tells us that\nthere are SOME Cakes in the oblong consisting of No. 11 and No.\n12: so we place our red counter, as in the previous example, on\nthe division-line between No. 11 and No. 12, and the result is\n\n\n -------------------\n | 0 | 0 |\n | _____|_____ |\n | | | | |\n | | -1- | |\n | | | | |\n -------------------\n\n\nNow let us try one or two interpretations.\n\nWhat are we to make of this, with regard to x and y?\n\n\n -------------------\n | | 0 |\n | _____|_____ |\n | | | | |\n | | 1 | 0 | |\n | | | | |\n -------------------\n\n\nThis tells us, with regard to the xy'-Square, that it is wholly\n'empty', since BOTH compartments are so marked. With regard to\nthe xy-Square, it tells us that it is 'occupied'. True, it is only\nONE compartment of it that is so marked; but that is quite enough,\nwhether the other be 'occupied' or 'empty', to settle the fact that\nthere is SOMETHING in the Square.\n\nIf, then, we transfer our marks to the smaller Diagram, so as to\nget rid of the m-subdivisions, we have a right to mark it\n\n\n -----------\n | | |\n | 1 | 0 |\n | | |\n -----------\n\n\nwhich means, you know, \"all x are y.\"\n\nThe result would have been exactly the same, if the given oblong\nhad been marked thus:--\n\n\n -------------------\n | 1 | 0 |\n | _____|_____ |\n | | | | |\n | | | 0 | |\n | | | | |\n -------------------\n\n\nOnce more: how shall we interpret this, with regard to x and y?\n\n\n -------------------\n | 0 | 1 |\n | _____|_____ |\n | | | | |\n | | | | |\n | | | | |\n -------------------\n\n\nThis tells us, as to the xy-Square, that ONE of its compartments\nis 'empty'. But this information is quite useless, as there is no\nmark in the OTHER compartment. If the other compartment happened\nto be 'empty' too, the Square would be 'empty': and, if it happened\nto be 'occupied', the Square would be 'occupied'. So, as we do\nnot know WHICH is the case, we can say nothing about THIS Square.\n\nThe other Square, the xy'-Square, we know (as in the previous\nexample) to be 'occupied'.\n\nIf, then, we transfer our marks to the smaller Diagram, we get\nmerely this:--\n\n\n -----------\n | | |\n | | 1 |\n | | |\n -----------\n\n\nwhich means, you know, \"some x are y'.\"\n\nThese principles may be applied to all the other\noblongs. For instance, to represent\n\"all y' are m'\" we should mark the -------\nRIGHT-HAND UPRIGHT OBLONG (the one | |\nthat has the attribute y') thus:-- |--- |\n | 0 | |\n |---|-1-|\n | 0 | |\n |--- |\n | |\n -------\n\nand, if we were told to interpret the lower half of the cupboard,\nmarked as follows, with regard to x and y,\n\n\n -------------------\n | | | | |\n | | | 0 | |\n | | | | |\n | -----|----- |\n | 1 | 0 |\n -------------------\n\n\nwe should transfer it to the smaller Diagram thus,\n\n\n -----------\n | | |\n | 1 | 0 |\n | | |\n -----------\n\n\nand read it \"all x' are y.\"\n\nTwo more remarks about Propositions need to be made.\n\nOne is that, in every Proposition beginning with \"some\" or \"all\",\nthe ACTUAL EXISTENCE of the 'Subject' is asserted. If, for instance,\nI say \"all misers are selfish,\" I mean that misers ACTUALLY EXIST.\nIf I wished to avoid making this assertion, and merely to state\nthe LAW that miserliness necessarily involves selfishness, I should\nsay \"no misers are unselfish\" which does not assert that any misers\nexist at all, but merely that, if any DID exist, they WOULD be\nselfish.\n\nThe other is that, when a Proposition begins with \"some\" or \"no\",\nand contains more that two Attributes, these Attributes may be\nre-arranged, and shifted from one Term to the other, \"ad libitum.\"\nFor example, \"some abc are def\" may be re-arranged as \"some bf are\nacde,\" each being equivalent to \"some Things are abcdef\". Again \"No\nwise old men are rash and reckless gamblers\" may be re-arranged as\n\"No rash old gamblers are wise and reckless,\" each being equivalent\nto \"No men are wise old rash reckless gamblers.\"\n\n\n\n2. Syllogisms\n\n\nNow suppose we divide our Universe of Things in three ways, with regard\nto three different Attributes. Out of these three Attributes, we\nmay make up three different couples (for instance, if they were a,\nb, c, we might make up the three couples ab, ac, bc). Also suppose\nwe have two Propositions given us, containing two of these three\ncouples, and that from them we can prove a third Proposition containing\nthe third couple. (For example, if we divide our Universe for m,\nx, and y; and if we have the two Propositions given us, \"no m are\nx'\" and \"all m' are y\", containing the two couples mx and my, it\nmight be possible to prove from them a third Proposition, containing\nx and y.)\n\nIn such a case we call the given Propositions 'THE PREMISSES', the\nthird one 'THE CONCLUSION' and the whole set 'A SYLLOGISM'.\n\nEvidently, ONE of the Attributes must occur in both Premisses; or\nelse one must occur in ONE Premiss, and its CONTRADICTORY in the\nother.\n\nIn the first case (when, for example, the Premisses are \"some m\nare x\" and \"no m are y'\") the Term, which occurs twice, is called\n'THE MIDDLE TERM', because it serves as a sort of link between the\nother two Terms.\n\nIn the second case (when, for example, the Premisses are \"no\nm are x'\" and \"all m' are y\") the two Terms, which contain these\ncontradictory Attributes, may be called 'THE MIDDLE TERMS'.\n\nThus, in the first case, the class of \"m-Things\" is the Middle\nTerm; and, in the second case, the two classes of \"m-Things\" and\n\"m'-Things\" are the Middle Terms.\n\nThe Attribute, which occurs in the Middle Term or Terms, disappears\nin the Conclusion, and is said to be \"eliminated\", which literally\nmeans \"turned out of doors\".\n\nNow let us try to draw a Conclusion from the two Premisses--\n\n \"Some new Cakes are unwholesome;\n No nice Cakes are unwholesome.\"\n\nIn order to express them with counters, we need to divide Cakes in\nTHREE different ways, with regard to newness, to niceness, and to\nwholesomeness. For this we must use the larger Diagram, making x\nmean \"new\", y \"nice\", and m \"wholesome\". (Everything INSIDE the\ncentral Square is supposed to have the attribute m, and everything\nOUTSIDE it the attribute m', i.e. \"not-m\".)\n\nYou had better adopt the rule to make m mean the Attribute which\noccurs in the MIDDLE Term or Terms. (I have chosen m as the symbol,\nbecause 'middle' begins with 'm'.)\n\nNow, in representing the two Premisses, I prefer to begin with the\nNEGATIVE one (the one beginning with \"no\"), because GREY counters\ncan always be placed with CERTAINTY, and will then help to fix the\nposition of the red counters, which are sometimes a little uncertain\nwhere they will be most welcome.\n\nLet us express, the \"no nice Cakes are unwholesome (Cakes)\", i.e.\n\"no y-Cakes are m'-(Cakes)\". This tells us that none of the Cakes\nbelonging to the y-half of the cupboard are in its m'-compartments\n(i.e. the ones outside the central Square). Hence the two compartments,\nNo. 9 and No. 15, are both 'EMPTY'; and we must place a grey counter\nin EACH of them, thus:--\n\n\n -----------\n |0 | |\n | --|-- |\n | | | | |\n |--|-----|--|\n | | | | |\n | --|-- |\n |0 | |\n -----------\n\n\nWe have now to express the other Premiss, namely, \"some new Cakes\nare unwholesome (Cakes)\", i.e. \"some x-Cakes are m'-(Cakes)\". This\ntells us that some of the Cakes in the x-half of the cupboard are\nin its m'-compartments. Hence ONE of the two compartments, No.\n9 and No. 10, is 'occupied': and, as we are not told in WHICH of\nthese two compartments to place the red counter, the usual rule\nwould be to lay it on the division-line between them: but, in this\ncase, the other Premiss has settled the matter for us, by declaring\nNo. 9 to be EMPTY. Hence the red counter has no choice, and MUST\ngo into No. 10, thus:--\n\n\n -----------\n |0 | 1|\n | --|-- |\n | | | | |\n |--|-----|--|\n | | | | |\n | --|-- |\n |0 | |\n -----------\n\n\nAnd now what counters will this information enable us to place in\nthe SMALLER Diagram, so as to get some Proposition involving x and\ny only, leaving out m? Let us take its four compartments, one by\none.\n\nFirst, No. 5. All we know about THIS is that its OUTER portion\nis empty: but we know nothing about its inner portion. Thus the\nSquare MAY be empty, or it MAY have something in it. Who can tell?\nSo we dare not place ANY counter in this Square.\n\nSecondly, what of No. 6? Here we are a little better off. We\nknow that there is SOMETHING in it, for there is a red counter in\nits outer portion. It is true we do not know whether its inner\nportion is empty or occupied: but what does THAT matter? One solitary\nCake, in one corner of the Square, is quite sufficient excuse for\nsaying \"THIS SQUARE IS OCCUPIED\", and for marking it with a red\ncounter.\n\nAs to No. 7, we are in the same condition as with No. 5--we find\nit PARTLY 'empty', but we do not know whether the other part is\nempty or occupied: so we dare not mark this Square.\n\nAnd as to No. 8, we have simply no information at all.\n\nThe result is\n\n -------\n | | 1 |\n |---|---|\n | | |\n -------\n\n\nOur 'Conclusion', then, must be got out of the rather meager piece\nof information that there is a red counter in the xy'-Square.\nHence our Conclusion is \"some x are y' \", i.e. \"some new Cakes are\nnot-nice (Cakes)\": or, if you prefer to take y' as your Subject,\n\"some not-nice Cakes are new (Cakes)\"; but the other looks neatest.\n\nWe will now write out the whole Syllogism, putting the symbol\n&there4[*] for \"therefore\", and omitting \"Cakes\", for the sake of\nbrevity, at the end of each Proposition.\n\n[*][NOTE from Brett: The use of \"&there4\" is a rather arbitrary\nselection. There is no font available in general practice\nwhich renders the \"therefore\" symbol correction (three dots in a\ntriangular formation). This can be done, however, in HTML, so if\nthis document is read in a browser, then the symbol will be properly\nrecognized. This is a poor man's excuse.]\n\n \"Some new Cakes are unwholesome;\n No nice Cakes are unwholesome\n &there4 Some new Cakes are not-nice.\"\n\nAnd you have now worked out, successfully, your first 'SYLLOGISM'.\nPermit me to congratulate you, and to express the hope that it is\nbut the beginning of a long and glorious series of similar victories!\n\nWe will work out one other Syllogism--a rather harder one than the\nlast--and then, I think, you may be safely left to play the Game\nby yourself, or (better) with any friend whom you can find, that\nis able and willing to take a share in the sport.\n\nLet us see what we can make of the two Premisses--\n\n\n \"All Dragons are uncanny;\n All Scotchmen are canny.\"\n\n\nRemember, I don't guarantee the Premisses to be FACTS. In the\nfirst place, I never even saw a Dragon: and, in the second place,\nit isn't of the slightest consequence to us, as LOGICIANS, whether\nour Premisses are true or false: all WE have to do is to make out\nwhether they LEAD LOGICALLY TO THE CONCLUSION, so that, if THEY\nwere true, IT would be true also.\n\nYou see, we must give up the \"Cakes\" now, or our cupboard will\nbe of no use to us. We must take, as our 'Universe', some class\nof things which will include Dragons and Scotchmen: shall we say\n'Animals'? And, as \"canny\" is evidently the Attribute belonging\nto the 'Middle Terms', we will let m stand for \"canny\", x for\n\"Dragons\", and y for \"Scotchmen\". So that our two Premisses are,\nin full,\n\n\n \"All Dragon-Animals are uncanny (Animals);\n All Scotchman-Animals are canny (Animals).\"\n\n\nAnd these may be expressed, using letters for words, thus:--\n\n\n \"All x are m';\n All y are m.\"\n\n\nThe first Premiss consists, as you already know, of two parts:--\n\n\n \"Some x are m',\"\n and \"No x are m.\"\n\n\nAnd the second also consists of two parts:--\n\n\n \"Some y are m,\"\n and \"No y are m'.\"\n\n\nLet us take the negative portions first.\n\nWe have, then, to mark, on the larger Diagram, first, \"no x are\nm\", and secondly, \"no y are m'\". I think you will see, without\nfurther explanation, that the two results, separately, are\n\n\n ----------- -----------\n | | | |0 | |\n | --|-- | | --|-- |\n | |0 | 0| | | | | | |\n |--|--|--|--| |--|--|--|--|\n | | | | | | | | | |\n | --|-- | | --|-- |\n | | | |0 | |\n ----------- -----------\n\n\n\nand that these two, when combined, give us\n\n\n -----------\n |0 | |\n | --|-- |\n | |0 | 0| |\n |--|--|--|--|\n | | | | |\n | --|-- |\n |0 | |\n -----------\n\n\nWe have now to mark the two positive portions, \"some x are m'\"\nand \"some y are m\".\n\nThe only two compartments, available for Things which are xm', are\nNo. 9 and No. 10. Of these, No. 9 is already marked as 'empty';\nso our red counter must go into No. 10.\n\nSimilarly, the only two, available for ym, are No. 11 and No. 13.\nOf these, No. 11 is already marked as 'empty'; so our red counter\nMUST go into No. 13.\n\nThe final result is\n\n\n -----------\n |0 | 1|\n | --|-- |\n | |0 | 0| |\n |--|--|--|--|\n | |1 | | |\n | --|-- |\n |0 | |\n -----------\n\n\n\nAnd now how much of this information can usefully be transferred\nto the smaller Diagram?\n\nLet us take its four compartments, one by one.\n\nAs to No. 5? This, we see, is wholly 'empty'. (So mark it with a\ngrey counter.)\n\nAs to No. 6? This, we see, is 'occupied'. (So mark it with a red\ncounter.)\n\nAs to No. 7? Ditto, ditto.\n\nAs to No. 8? No information.\n\nThe smaller Diagram is now pretty liberally marked:--\n\n\n -------\n | 0 | 1 |\n |---|---|\n | 1 | |\n -------\n\n\nAnd now what Conclusion can we read off from this? Well, it is\nimpossible to pack such abundant information into ONE Proposition:\nwe shall have to indulge in TWO, this time.\n\nFirst, by taking x as Subject, we get \"all x are y'\", that is,\n\n\n\"All Dragons are not-Scotchmen\":\n\n\nsecondly, by taking y as Subject, we get \"all y are x'\", that is,\n\n\n\"All Scotchmen are not-Dragons\".\n\n\nLet us now write out, all together, our two Premisses and our brace\nof Conclusions.\n\n\n \"All Dragons are uncanny;\n All Scotchmen are canny.\n &there4 All Dragons are not-Scotchmen;\n All Scotchmen are not-Dragons.\"\n\n\nLet me mention, in conclusion, that you may perhaps meet with\nlogical treatises in which it is not assumed that any Thing EXISTS\nat all, by \"some x are y\" is understood to mean \"the Attributes x,\ny are COMPATIBLE, so that a Thing can have both at once\", and \"no\nx are y\" to mean \"the Attributes x, y are INCOMPATIBLE, so that\nnothing can have both at once\".\n\nIn such treatises, Propositions have quite different meanings\nfrom what they have in our 'Game of Logic', and it will be well to\nunderstand exactly what the difference is.\n\nFirst take \"some x are y\". Here WE understand \"are\" to mean \"are,\nas an actual FACT\"--which of course implies that some x-Things EXIST.\nBut THEY (the writers of these other treatises) only understand\n\"are\" to mean \"CAN be\", which does not at all imply that any EXIST.\nSo they mean LESS than we do: our meaning includes theirs (for of\ncourse \"some x ARE y\" includes \"some x CAN BE y\"), but theirs does\nNOT include ours. For example, \"some Welsh hippopotami are heavy\"\nwould be TRUE, according to these writers (since the Attributes\n\"Welsh\" and \"heavy\" are quite COMPATIBLE in a hippopotamus), but\nit would be FALSE in our Game (since there are no Welsh hippopotami\nto BE heavy).\n\nSecondly, take \"no x are y\". Here WE only understand \"are\" to\nmean \"are, as an actual FACT\"--which does not at all imply that no\nx CAN be y. But THEY understand the Proposition to mean, not only\nthat none ARE y, but that none CAN POSSIBLY be y. So they mean\nmore than we do: their meaning includes ours (for of course \"no x\nCAN be y\" includes \"no x ARE y\"), but ours does NOT include theirs.\nFor example, \"no Policemen are eight feet high\" would be TRUE\nin our Game (since, as an actual fact, no such splendid specimens\nare ever found), but it would be FALSE, according to these writers\n(since the Attributes \"belonging to the Police Force\" and \"eight\nfeet high\" are quite COMPATIBLE: there is nothing to PREVENT a\nPoliceman from growing to that height, if sufficiently rubbed with\nRowland's Macassar Oil--which said to make HAIR grow, when rubbed\non hair, and so of course will make a POLICEMAN grow, when rubbed\non a Policeman).\n\nThirdly, take \"all x are y\", which consists of the two partial\nPropositions \"some x are y\" and \"no x are y'\". Here, of course,\nthe treatises mean LESS than we do in the FIRST part, and more than\nwe do in the SECOND. But the two operations don't balance each\nother--any more than you can console a man, for having knocked down\none of his chimneys, by giving him an extra door-step.\n\nIf you meet with Syllogisms of this kind, you may work them, quite\neasily, by the system I have given you: you have only to make\n'are' mean 'are CAPABLE of being', and all will go smoothly. For\n\"some x are y\" will become \"some x are capable of being y\", that\nis, \"the Attributes x, y are COMPATIBLE\". And \"no x are y\" will\nbecome \"no x are capable of being y\", that is, \"the Attributes\nx, y are INCOMPATIBLE\". And, of course, \"all x are y\" will become\n\"some x are capable of being y, and none are capable of being y'\",\nthat is, \"the Attributes x, y are COMPATIBLE, and the Attributes\nx, y' are INCOMPATIBLE.\" In using the Diagrams for this system,\nyou must understand a red counter to mean \"there may POSSIBLY be\nsomething in this compartment,\" and a grey one to mean \"there cannot\nPOSSIBLY be anything in this compartment.\"\n\n\n\n3. Fallacies.\n\n\nAnd so you think, do you, that the chief use of Logic, in real life,\nis to deduce Conclusions from workable Premisses, and to satisfy\nyourself that the Conclusions, deduced by other people, are correct?\nI only wish it were! Society would be much less liable to panics\nand other delusions, and POLITICAL life, especially, would be a\ntotally different thing, if even a majority of the arguments, that\nscattered broadcast over the world, were correct! But it is all\nthe other way, I fear. For ONE workable Pair of Premisses (I mean\na Pair that lead to a logical Conclusion) that you meet with in\nreading your newspaper or magazine, you will probably find FIVE\nthat lead to no Conclusion at all: and, even when the Premisses\nARE workable, for ONE instance, where the writer draws a correct\nConclusion, there are probably TEN where he draws an incorrect one.\n\nIn the first case, you may say \"the PREMISSES are fallacious\": in\nthe second, \"the CONCLUSION is fallacious.\"\n\nThe chief use you will find, in such Logical skill as this Game\nmay teach you, will be in detecting 'FALLACIES' of these two kinds.\n\nThe first kind of Fallacy--'Fallacious Premisses'--you will detect\nwhen, after marking them on the larger Diagram, you try to transfer\nthe marks to the smaller. You will take its four compartments, one\nby one, and ask, for each in turn, \"What mark can I place HERE?\";\nand in EVERY one the answer will be \"No information!\", showing that\nthere is NO CONCLUSION AT ALL. For instance,\n\n\n \"All soldiers are brave;\n Some Englishmen are brave.\n &there4 Some Englishmen are soldiers.\"\n\n\nlooks uncommonly LIKE a Syllogism, and might easily take in a\nless experienced Logician. But YOU are not to be caught by such\na trick! You would simply set out the Premisses, and would then\ncalmly remark \"Fallacious PREMISSES!\": you wouldn't condescend to\nask what CONCLUSION the writer professed to draw--knowing that,\nWHATEVER it is, it MUST be wrong. You would be just as safe as\nthat wise mother was, who said \"Mary, just go up to the nursery,\nand see what Baby's doing, AND TELL HIM NOT TO DO IT!\"\n\nThe other kind of Fallacy--'Fallacious Conclusion'--you will not\ndetect till you have marked BOTH Diagrams, and have read off the\ncorrect Conclusion, and have compared it with the Conclusion which\nthe writer has drawn.\n\nBut mind, you mustn't say \"FALLACIOUS Conclusion,\" simply because\nit is not IDENTICAL with the correct one: it may be a PART of the\ncorrect Conclusion, and so be quite correct, AS FAR AS IT GOES. In\nthis case you would merely remark, with a pitying smile, \"DEFECTIVE\nConclusion!\" Suppose, of example, you were to meet with this\nSyllogism:--\n\n\n \"All unselfish people are generous;\n No misers are generous.\n &there4 No misers are unselfish.\"\n\n\nthe Premisses of which might be thus expressed in letters:--\n\n\n \"All x' are m;\n No y are m.\"\n\n\nHere the correct Conclusion would be \"All x' are y'\" (that is,\n\"All unselfish people are not misers\"), while the Conclusion, drawn\nby the writer, is \"No y are x',\" (which is the same as \"No x' are\ny,\" and so is PART of \"All x' are y'.\") Here you would simply say\n\"DEFECTIVE Conclusion!\" The same thing would happen, if you were\nin a confectioner's shop, and if a little boy were to come in, put\ndown twopence, and march off triumphantly with a single penny-bun.\nYou would shake your head mournfully, and would remark \"Defective\nConclusion! Poor little chap!\" And perhaps you would ask the\nyoung lady behind the counter whether she would let YOU eat the\nbun, which the little boy had paid for and left behind him: and\nperhaps SHE would reply \"Sha'n't!\"\n\nBut if, in the above example, the writer had drawn the Conclusion\n\"All misers are selfish\" (that is, \"All y are x\"), this would\nbe going BEYOND his legitimate rights (since it would assert the\nEXISTENCE of y, which is not contained in the Premisses), and you\nwould very properly say \"Fallacious Conclusion!\"\n\nNow, when you read other treatises on Logic, you will meet with\nvarious kinds of (so-called) 'Fallacies' which are by no means\nALWAYS so. For example, if you were to put before one of these\nLogicians the Pair of Premisses\n\n\n \"No honest men cheat;\n No dishonest men are trustworthy.\"\n\n\nand were to ask him what Conclusion followed, he would probably say\n\"None at all! Your Premisses offend against TWO distinct Rules, and\nare as fallacious as they can well be!\" Then suppose you were bold\nenough to say \"The Conclusion is 'No men who cheat are trustworthy',\"\nI fear your Logical friend would turn away hastily--perhaps angry,\nperhaps only scornful: in any case, the result would be unpleasant.\nI ADVISE YOU NOT TO TRY THE EXPERIMENT!\n\n\"But why is this?\" you will say. \"Do you mean to tell us that all\nthese Logicians are wrong?\" Far from it, dear Reader! From THEIR\npoint of view, they are perfectly right. But they do not include,\nin their system, anything like ALL the possible forms of Syllogisms.\n\nThey have a sort of nervous dread of Attributes beginning with a\nnegative particle. For example, such Propositions as \"All not-x\nare y,\" \"No x are not-y,\" are quite outside their system. And\nthus, having (from sheer nervousness) excluded a quantity of very\nuseful forms, they have made rules which, though quite applicable\nto the few forms which they allow of, are no use at all when you\nconsider all possible forms.\n\nLet us not quarrel with them, dear Reader! There is room enough in\nthe world for both of us. Let us quietly take our broader system:\nand, if they choose to shut their eyes to all these useful forms,\nand to say \"They are not Syllogisms at all!\" we can but stand aside,\nand let them Rush upon their Fate! There is scarcely anything of\nyours, upon which it is so dangerous to Rush, as your Fate. You\nmay Rush upon your Potato-beds, or your Strawberry-beds, without\ndoing much harm: you may even Rush upon your Balcony (unless it\nis a new house, built by contract, and with no clerk of the works)\nand may survive the foolhardy enterprise: but if you once Rush upon\nyour FATE--why, you must take the consequences!\n\n\n\n\n\nCHAPTER II.\n\nCROSS QUESTIONS.\n\n \"The Man in the Wilderness asked of me\n 'How many strawberries grow in the sea?'\"\n __________\n\n\n\n\n\n1. Elementary.\n\n1. What is an 'Attribute'? Give examples.\n\n2. When is it good sense to put \"is\" or \"are\" between two names?\nGive examples.\n\n3. When is it NOT good sense? Give examples.\n\n4. When it is NOT good sense, what is the simplest agreement to\nmake, in order to make good sense?\n\n5. Explain 'Proposition', 'Term', 'Subject', and 'Predicate'.\nGive examples.\n\n6. What are 'Particular' and 'Universal' Propositions? Give\nexamples.\n\n7. Give a rule for knowing, when we look at the smaller Diagram,\nwhat Attributes belong to the things in each compartment.\n\n8. What does \"some\" mean in Logic? [See pp. 55, 6]\n\n9. In what sense do we use the word 'Universe' in this Game?\n\n10. What is a 'Double' Proposition? Give examples.\n\n11. When is a class of Things said to be 'exhaustively' divided?\nGive examples.\n\n12. Explain the phrase \"sitting on the fence.\"\n\n13. What two partial Propositions make up, when taken together,\n\"all x are y\"?\n\n14. What are 'Individual' Propositions? Give examples.\n\n15. What kinds of Propositions imply, in this Game, the EXISTENCE\nof their Subjects?\n\n16. When a Proposition contains more than two Attributes, these\nAttributes may in some cases be re-arranged, and shifted from one\nTerm to the other. In what cases may this be done? Give examples.\n\n__________\n\n\nBreak up each of the following into two partial\nPropositions:\n\n17. All tigers are fierce.\n\n18. All hard-boiled eggs are unwholesome.\n\n19. I am happy.\n\n20. John is not at home.\n\n__________\n\n[See pp. 56, 7]\n\n21. Give a rule for knowing, when we look at the larger Diagram,\nwhat Attributes belong to the Things contained in each compartment.\n\n22. Explain 'Premisses', 'Conclusion', and 'Syllogism'. Give\nexamples.\n\n23. Explain the phrases 'Middle Term' and 'Middle Terms'.\n\n24. In marking a pair of Premisses on the larger Diagram, why is\nit best to mark NEGATIVE Propositions before AFFIRMATIVE ones?\n\n25. Why is it of no consequence to us, as Logicians, whether the\nPremisses are true or false?\n\n26. How can we work Syllogisms in which we are told that \"some x\nare y\" is to be understood to mean \"the Attribute x, y are COMPATIBLE\",\nand \"no x are y\" to mean \"the Attributes x, y are INCOMPATIBLE\"?\n\n27. What are the two kinds of 'Fallacies'?\n\n28. How may we detect 'Fallacious Premisses'?\n\n29. How may we detect a 'Fallacious Conclusion'?\n\n30. Sometimes the Conclusion, offered to us, is not identical with\nthe correct Conclusion, and yet cannot be fairly called 'Fallacious'.\nWhen does this happen? And what name may we give to such a\nConclusion?\n\n[See pp. 57-59]\n\n\n\n\n2. Half of Smaller Diagram.\n\n\nPropositions to be represented.\n\n\n -----------\n | | |\n | x |\n | | |\n --y-----y'-\n\n__________\n\n1. Some x are not-y.\n\n2. All x are not-y.\n\n3. Some x are y, and some are not-y.\n\n4. No x exist.\n\n5. Some x exist.\n\n6. No x are not-y.\n\n7. Some x are not-y, and some x exist.\n\n__________\n\nTaking x=\"judges\"; y=\"just\";\n\n8. No judges are just.\n\n9. Some judges are unjust.\n\n10. All judges are just.\n\n__________\n\nTaking x=\"plums\"; y=\"wholesome\";\n\n11. Some plums are wholesome.\n\n12. There are no wholesome plums.\n\n13. Plums are some of them wholesome, and some not.\n\n14. All plums are unwholesome.\n\n[See pp. 59, 60]\n\n -----\n | |\n | x\n | |\n |--y--|\n | |\n | x'\n | |\n -----\n\n__________\n\nTaking y=\"diligent students\"; x=\"successful\";\n\n15. No diligent students are unsuccessful.\n\n16. All diligent students are successful.\n\n17. No students are diligent.\n\n18. There are some diligent, but unsuccessful, students.\n\n19. Some students are diligent.\n\n[See pp. 60, 1]\n\n\n\n\n3. Half of Smaller Diagram.\n\n\n\nSymbols to be interpreted.\n\n__________\n\n\n -----------\n | | |\n | x |\n | | |\n --y-----y'-\n\n__________\n\n\n ------- -------\n | | | | | |\n 1. | | 0 | 2. | 0 | 0 |\n | | | | | |\n ------- -------\n\n\n ------- -------\n | | | | | |\n 3. | - | 4. | 0 | 1 |\n | | | | | |\n ------- -------\n\n__________\n\nTaking x=\"good riddles\"; y=\"hard\";\n\n\n ------- -------\n | | | | | |\n 5. | 1 | | 6. | 1 | 0 |\n | | | | | |\n ------- -------\n\n ------- -------\n | | | | | |\n 7. | 0 | 0 | 8. | 0 | |\n | | | | | |\n ------- -------\n\n__________\n\n[See pp. 61, 2]\n\nTaking x=\"lobster\"; y=\"selfish\";\n\n ------- -------\n | | | | | |\n 9. | | 1 | 10. | 0 | |\n | | | | | |\n ------- -------\n\n ------- -------\n | | | | | |\n 11. | 0 | 1 | 12. | 1 | 1 |\n | | | | | |\n ------- -------\n\n__________\n\n\n -----\n | |\n x |\n | |\n |--y'-|\n | |\n x' |\n | |\n -----\n\nTaking y=\"healthy people\"; x=\"happy\";\n\n --- --- --- ---\n | 0 | | | | 1 | | 0 |\n 13. |---| 14. |-1-| 15. |---| 16. |---|\n | 1 | | | | 1 | | |\n --- --- --- ---\n\n[See p. 62]\n\n\n\n\n4. Smaller Diagram.\n\n\n\nPropositions to be represented.\n\n -----------\n | | |\n | x |\n |--y--|--y'-|\n | x' |\n | | |\n -----------\n\n__________\n\n\n1. All y are x.\n\n2. Some y are not-x.\n\n3. No not-x are not-y.\n\n4. Some x are not-y.\n\n5. Some not-y are x.\n\n6. No not-x are y.\n\n7. Some not-x are not-y.\n\n8. All not-x are not-y.\n\n9. Some not-y exist.\n\n10. No not-x exist.\n\n11. Some y are x, and some are not-x.\n\n12. All x are y, and all not-y are not-x.\n\n\n[See pp. 62, 3]\n\nTaking \"nations\" as Universe; x=\"civilised\";\ny=\"warlike\";\n\n13. No uncivilised nation is warlike.\n\n14. All unwarlike nations are uncivilised.\n\n15. Some nations are unwarlike.\n\n16. All warlike nations are civilised, and all civilised nations\nare warlike.\n\n17. No nation is uncivilised.\n\n__________\n\nTaking \"crocodiles\" as Universe; x=\"hungry\"; and\ny=\"amiable\";\n\n18. All hungry crocodiles are unamiable.\n\n19. No crocodiles are amiable when hungry.\n\n20. Some crocodiles, when not hungry, are amiable; but some\nare not.\n\n21. No crocodiles are amiable, and some are hungry.\n\n22. All crocodiles, when not hungry, are amiable; and all\nunamiable crocodiles are hungry.\n\n23. Some hungry crocodiles are amiable, and some that are\nnot hungry are unamiable.\n\n[See pp. 63, 4]\n\n\n\n\n5. Smaller Diagram.\n\n\n\nSymbols to be interpreted.\n\n__________\n\n\n -----------\n | | |\n | x |\n |--y--|--y'-|\n | x' |\n | | |\n -----------\n\n __________\n\n\n ------- -------\n | | | | | |\n 1. |---|---| 2. |---|---|\n | 1 | | | | 0 |\n ------- -------\n\n ------- -------\n | | 1 | | | |\n 3. |---|---| 4. |---|---|\n | | 0 | | 0 | 0 |\n ------- -------\n\n__________\n\nTaking \"houses\" as Universe; x=\"built of brick\"; and\ny=\"two-storied\"; interpret\n\n ------- -------\n | 0 | | | | |\n 5. |---|---| 6. |---|---|\n | 0 | | | - |\n ------- ---|---\n\n ------- -------\n | | 0 | | | |\n 7. |---|---| 8. |---|---|\n | | | | 0 | 1 |\n ------- -------\n\n[See p. 65]\n\nTaking \"boys\" as Universe; x=\"fat\"; and y=\"active\";\ninterpret\n\n ------- -------\n | 1 | 1 | | | 0 |\n 9. |---|---| 10. |---|---|\n | | | | | 1 |\n ------- -------\n\n ------- -------\n | 0 | 1 | | 1 | |\n 11. |---|---| 12. |---|---|\n | | 0 | | 0 | 1 |\n ------- -------\n\n__________\n\nTaking \"cats\" as Universe; x=\"green-eyed\"; and\ny=\"good-tempered\"; interpret\n\n ------- -------\n | 0 | 0 | | | 1 |\n 13. |---|---| 14. |---|---|\n | | 0 | | 1 | |\n ------- -------\n\n ------- -------\n | 1 | | | 0 | 1 |\n 15. |---|---| 16. |---|---|\n | | 0 | | 1 | 0 |\n ------- -------\n\n[See pp. 65, 6]\n\n\n\n\n6. Larger Diagram.\n\n\n\nPropositions to be represented.\n\n__________\n\n\n -----------\n | | |\n | --x-- |\n | | | | |\n |--y--m--y'-|\n | | | | |\n | --x'- |\n | | |\n -----------\n\n__________\n\n\n1. No x are m.\n\n2. Some y are m'.\n\n3. All m are x'.\n\n4. No m' are y'.\n\n5. No m are x; All y are m.\n\n6. Some x are m; No y are m.\n\n7. All m are x'; No m are y.\n\n8. No x' are m; No y' are m'.\n\n[See pp. 67,8]\n\nTaking \"rabbits\" as Universe; m=\"greedy\"; x=\"old\"; and\ny=\"black\"; represent\n\n9. No old rabbits are greedy.\n\n10. Some not-greedy rabbits are black.\n\n11. All white rabbits are free from greediness.\n\n12. All greedy rabbits are young.\n\n13. No old rabbits are greedy; All black rabbits are greedy.\n\n14. All rabbits, that are not greedy, are black; No old\nrabbits are free from greediness.\n\n__________\n\nTaking \"birds\" as Universe; m=\"that sing loud\"; x=\"well-fed\";\nand y=\"happy\"; represent\n\n15. All well-fed birds sing loud; No birds, that sing loud,\nare unhappy.\n\n16. All birds, that do not sing loud, are unhappy; No well-fed\nbirds fail to sing loud.\n\n__________\n\nTaking \"persons\" as Universe; m=\"in the house\"; x=\"John\";\nand y=\"having a tooth-ache\"; represent\n\n17. John is in the house; Everybody in the house is suffering\nfrom tooth-ache.\n\n18. There is no one in the house but John; Nobody, out of\nthe house, has a tooth-ache.\n\n__________\n\n[See pp. 68-70]\n\nTaking \"persons\" as Universe; m=\"I\"; x=\"that has taken a\nwalk\"; y=\"that feels better\"; represent\n\n19. I have been out for a walk; I feel much better.\n\n__________\n\nChoosing your own 'Universe' &c., represent\n\n20. I sent him to bring me a kitten; He brought me a kettle\nby mistake.\n\n\n[See pp. 70, 1]\n\n\n\n\n7. Both Diagrams to be employed.\n\n__________\n\n\n -----------\n | | | -----------\n | --x-- | | | |\n | | | | | | x |\n |--y--m--y'-| |--y--|--y'-|\n | | | | | | x' |\n | --x'- | | | |\n | | | -----------\n -----------\n\n__________\n\n\nN.B. In each Question, a small Diagram should be drawn, for x and\ny only, and marked in accordance with the given large Diagram: and\nthen as many Propositions as possible, for x and y, should be read\noff from this small Diagram.\n\n\n ----------- -----------\n |0 | | | | |\n | --|-- | | --|-- |\n | |0 | 0| | | |0 | 1| |\n 1. |--|--|--|--| 2. |--|--|--|--|\n | |1 | | | | |0 | | |\n | --|-- | | --|-- |\n |0 | | | | |\n ----------- -----------\n\n[See p. 72]\n\n ----------- -----------\n | | | | | 0|\n | --|-- | | --|-- |\n | |0 | 0| | | | | | |\n 3. |--|--|--|--| 4. |--|--|--|--|\n | |1 | 0| | | |0 | | |\n | --|-- | | --|-- |\n | | | | | 0|\n ----------- -----------\n\n__________\n\n\nMark, in a large Diagram, the following pairs of Propositions from\nthe preceding Section: then mark a small Diagram in accordance with\nit, &c.\n\n 5. No. 13. [see p. 49] 9. No. 17.\n 6. No. 14. 10. No. 18.\n 7. No. 15. 11. No. 19. [see p. 50]\n 8. No. 16. 12. No. 20.\n\n__________\n\nMark, on a large Diagram, the following Pairs of Propositions: then\nmark a small Diagram, &c. These are, in fact, Pairs of PREMISSES\nfor Syllogisms: and the results, read off from the small Diagram,\nare the CONCLUSIONS.\n\n13. No exciting books suit feverish patients; Unexciting\nbooks make one drowsy.\n\n14. Some, who deserve the fair, get their deserts; None\nbut the brave deserve the fair.\n\n15. No children are patient; No impatient person can sit\nstill.\n\n[See pp. 72-5]\n\n16. All pigs are fat; No skeletons are fat.\n\n17. No monkeys are soldiers; All monkeys are mischievous.\n\n18. None of my cousins are just; No judges are unjust.\n\n19. Some days are rainy; Rainy days are tiresome.\n\n20. All medicine is nasty; Senna is a medicine.\n\n21. Some Jews are rich; All Patagonians are Gentiles.\n\n22. All teetotalers like sugar; No nightingale drinks wine.\n\n23. No muffins are wholesome; All buns are unwholesome.\n\n24. No fat creatures run well; Some greyhounds run well.\n\n25. All soldiers march; Some youths are not soldiers.\n\n26. Sugar is sweet; Salt is not sweet.\n\n27. Some eggs are hard-boiled; No eggs are uncrackable.\n\n28. There are no Jews in the house; There are no Gentiles\nin the garden.\n\n[See pp. 75-82]\n\n29. All battles are noisy; What makes no noise may escape\nnotice.\n\n30. No Jews are mad; All Rabbis are Jews.\n\n31. There are no fish that cannot swim; Some skates are\nfish.\n\n32. All passionate people are unreasonable; Some orators\nare passionate.\n\n\n\n\n[See pp. 82-84]\n\n\n\n\n\nCHAPTER III.\n\nCROOKED ANSWERS.\n\n \"I answered him, as I thought good,\n 'As many as red-herrings grow in the wood'.\"\n\n__________\n\n\n\n\n\n\n1. Elementary.\n\n\n\n1. Whatever can be \"attributed to\", that is \"said to belong to\",\na Thing, is called an 'Attribute'. For example, \"baked\", which\ncan (frequently) be attributed to \"Buns\", and \"beautiful\", which\ncan (seldom) be attributed to \"Babies\".\n\n2. When they are the Names of two Things (for example, \"these\nPigs are fat Animals\"), or of two Attributes (for example, \"pink\nis light red\").\n\n3. When one is the Name of a Thing, and the other the Name of an\nAttribute (for example, \"these Pigs are pink\"), since a Thing cannot\nactually BE an Attribute.\n\n4. That the Substantive shall be supposed to be repeated at the\nend of the sentence (for example, \"these Pigs are pink (Pigs)\").\n\n5. A 'Proposition' is a sentence stating that some, or none, or all,\nof the Things belonging to a certain class, called the 'Subject',\nare also Things belonging to a certain other class, called the\n'Predicate'. For example, \"some new Cakes are not nice\", that is\n(written in full) \"some new Cakes are not nice Cakes\"; where the\nclass \"new Cakes\" is the Subject, and the class \"not-nice Cakes\"\nis the Predicate.\n\n6. A Proposition, stating that SOME of the Things belonging to\nits Subject are so-and-so, is called 'Particular'. For example,\n\"some new Cakes are nice\", \"some new Cakes are not nice.\"\n\nA Proposition, stating that NONE of the Things belonging to its\nSubject, or that ALL of them, are so-and-so, is called 'Universal'.\nFor example, \"no new Cakes are nice\", \"all new Cakes are not nice\".\n\n7. The Things in each compartment possess TWO Attributes, whose\nsymbols will be found written on two of the EDGES of that compartment.\n\n8. \"One or more.\"\n\n9. As a name of the class of Things to which the whole Diagram is\nassigned.\n\n10. A Proposition containing two statements. For example, \"some\nnew Cakes are nice and some are not-nice.\"\n\n11. When the whole class, thus divided, is \"exhausted\" among the\nsets into which it is divided, there being no member of it which\ndoes not belong to some one of them. For example, the class \"new\nCakes\" is \"exhaustively\" divided into \"nice\" and \"not-nice\" since\nEVERY new Cake must be one or the other.\n\n12. When a man cannot make up his mind which of two parties he\nwill join, he is said to be \"sitting on the fence\"--not being able\nto decide on which side he will jump down.\n\n13. \"Some x are y\" and \"no x are y'\".\n\n14. A Proposition, whose Subject is a single Thing, is called\n'Individual'. For example, \"I am happy\", \"John is not at home\".\nThese are Universal Propositions, being the same as \"all the I's\nthat exist are happy\", \"ALL the Johns, that I am now considering,\nare not at home\".\n\n15. Propositions beginning with \"some\" or \"all\".\n\n16. When they begin with \"some\" or \"no\". For example, \"some\nabc are def\" may be re-arranged as \"some bf are acde\", each being\nequivalent to \"some abcdef exist\".\n\n17. Some tigers are fierce, No tigers are not-fierce.\n\n18. Some hard-boiled eggs are unwholesome, No hard-boiled\neggs are wholesome.\n\n19. Some I's are happy, No I's are unhappy.\n\n20. Some Johns are not at home, No Johns are at home.\n\n21. The Things, in each compartment of the larger Diagram, possess\nTHREE Attributes, whose symbols will be found written at three of\nthe CORNERS of the compartment (except in the case of m', which is\nnot actually inserted in the Diagram, but is SUPPOSED to stand at\neach of its four outer corners).\n\n22. If the Universe of Things be divided with regard to three\ndifferent Attributes; and if two Propositions be given, containing\ntwo different couples of these Attributes; and if from these we\ncan prove a third Proposition, containing the two Attributes that\nhave not yet occurred together; the given Propositions are called\n'the Premisses', the third one 'the Conclusion', and the whole set\n'a Syllogism'. For example, the Premisses might be \"no m are x'\"\nand \"all m' are y\"; and it might be possible to prove from them\na Conclusion containing x and y.\n\n23. If an Attribute occurs in both Premisses, the Term containing\nit is called 'the Middle Term'. For example, if the Premisses are\n\"some m are x\" and \"no m are y'\", the class of \"m-Things\" is 'the\nMiddle Term.'\n\nIf an Attribute occurs in one Premiss, and its contradictory in the\nother, the Terms containing them may be called 'the Middle Terms'.\nFor example, if the Premisses are \"no m are x'\" and \"all m' are\ny\", the two classes of \"m-Things\" and \"m'-Things\" may be called\n'the Middle Terms'.\n\n24. Because they can be marked with CERTAINTY: whereas AFFIRMATIVE\nPropositions (that is, those that begin with \"some\" or \"all\")\nsometimes require us to place a red counter 'sitting on a fence'.\n\n25. Because the only question we are concerned with is whether the\nConclusion FOLLOWS LOGICALLY from the Premisses, so that, if THEY\nwere true, IT also would be true.\n\n26. By understanding a red counter to mean \"this compartment CAN\nbe occupied\", and a grey one to mean \"this compartment CANNOT be\noccupied\" or \"this compartment MUST be empty\".\n\n27. 'Fallacious Premisses' and 'Fallacious Conclusion'.\n\n28. By finding, when we try to transfer marks from the larger\nDiagram to the smaller, that there is 'no information' for any of\nits four compartments.\n\n29. By finding the correct Conclusion, and then observing that\nthe Conclusion, offered to us, is neither identical with it nor a\npart of it.\n\n30. When the offered Conclusion is PART of the correct Conclusion.\nIn this case, we may call it a 'Defective Conclusion'.\n\n\n\n\n2. Half of Smaller Diagram.\n\n\n\nPropositions represented.\n\n__________\n\n\n ------- -------\n | | | | | |\n 1. | | 1 | 2. | 0 | 1 |\n | | | | | |\n ------- -------\n\n\n ------- -------\n | | | | | |\n 3. | 1 | 1 | 4. | 0 | 0 |\n | | | | | |\n ------- -------\n\n ------- -------\n | | | | | |\n 5. | 1 | 6. | | 0 |\n | | | | | |\n ------- -------\n\n -------\n | | |\n 7. | 1 | 1 | It might be thought that the proper\n | | |\n ------- -------\n | | |\nDiagram would be | 1 1 |, in order to express \"some\n | | |\n -------\nx exist\": but this is really contained in \"some x are y'.\"\nTo put a red counter on the division-line would only tell\nus \"ONE OF THE compartments is occupied\", which we\nknow already, in knowing that ONE is occupied.\n -------\n | | |\n 8. No x are y. i.e. | 0 | |\n | | |\n -------\n\n -------\n | | |\n 9. Some x are y'. i.e. | | 1 |\n | | |\n -------\n\n -------\n | | |\n 10. All x are y. i.e. | 1 | 0 |\n | | |\n -------\n\n -------\n | | |\n 11. Some x are y. i.e. | 1 | |\n | | |\n -------\n\n -------\n | | |\n 12. No x are y. i.e. | 0 | |\n | | |\n -------\n\n -------\n | | |\n 13. Some x are y, and some are y'. i.e. | 1 | 1 |\n | | |\n -------\n\n -------\n | | |\n 14. All x are y'. i.e. | 0 | 1 |\n | | |\n -------\n ---\n | |\n 15. No y are x'. i.e. |---|\n | 0 |\n ---\n\n ---\n | 1 |\n 16. All y are x. i.e. |---|\n | 0 |\n ---\n\n ---\n | 0 |\n 17. No y exist. i.e. |---|\n | 0 |\n ---\n\n ---\n | |\n 18. Some y are x'. i.e. |---|\n | 1 |\n ---\n\n ---\n | |\n 15. Some y exist. i.e. |-1-|\n | |\n ---\n\n\n\n\n3. Half of Smaller Diagram.\n\n\n\nSymbols interpreted.\n\n__________\n\n1. No x are y'.\n\n2. No x exist.\n\n3. Some x exist.\n\n4. All x are y'.\n\n5. Some x are y. i.e. Some good riddles are hard.\n\n6. All x are y. i.e. All good riddles are hard.\n\n7. No x exist. i.e. No riddles are good.\n\n8. No x are y. i.e. No good riddles are hard.\n\n9. Some x are y'. i.e. Some lobsters are unselfish.\n\n10. No x are y. i.e. No lobsters are selfish.\n\n11. All x are y'. i.e. All lobsters are unselfish.\n\n12. Some x are y, and some are y'. i.e. Some lobsters are\nselfish, and some are unselfish.\n\n13. All y' are x'. i.e. All invalids are unhappy.\n\n14. Some y' exist. i.e. Some people are unhealthy.\n\n15. Some y' are x, and some are x'. i.e. Some invalids are\nhappy, and some are unhappy.\n\n16. No y' exist. i.e. Nobody is unhealthy.\n\n\n\n\n\n4. Smaller Diagram.\n\n\n\nPropositions represented.\n\n__________\n\n ------- -------\n | 1 | | | | |\n 1. |---|---| 2. |---|---|\n | 0 | | | 1 | |\n ------- -------\n\n ------- -------\n | | | | | 1 |\n 3. |---|---| 4. |---|---|\n | | 0 | | | |\n ------- -------\n\n ------- -------\n | | 1 | | | |\n 5. |---|---| 6. |---|---|\n | | | | 0 | |\n ------- -------\n\n ------- -------\n | | | | | |\n 7. |---|---| 8. |---|---|\n | | 1 | | 0 | 1 |\n ------- -------\n\n ------- -------\n | | | | | |\n 9. |---|-1-| 10. |---|---|\n | | | | 0 | 0 |\n ------- -------\n\n ------- -------\n | 1 | | | 1 | 0 |\n 11. |---|---| 12. |---|---|\n | 1 | | | | 1 |\n ------- -------\n\n\n -------\n | | |\n 13. No x' are y. i.e. |---|---|\n | 0 | |\n -------\n\n -------\n | | 0 |\n 14. All y' are x'. i.e. |---|---|\n | | 1 |\n -------\n\n\n -------\n | | |\n 15. Some y' exist. i.e. |---|-1-|\n | | |\n -------\n\n -------\n | 1 | 0 |\n 16. All y are x, and all x are y. i.e. |---|---|\n | 0 | |\n -------\n -------\n | | |\n 17. No x' exist. i.e. |---|---|\n | 0 | 0 |\n -------\n\n -------\n | 0 | 1 |\n 18. All x are y'. i.e. |---|---|\n | | |\n -------\n\n -------\n | 0 | |\n 19. No x are y. i.e. |---|---|\n | | |\n -------\n\n\n -------\n | | |\n 20. Some x' are y, and some are y'. i.e. |---|---|\n | 1 | 1 |\n -------\n\n -------\n | 0 | 1 |\n 21. No y exist, and some x exist. i.e. |---|---|\n | 0 | |\n -------\n\n -------\n | | 1 |\n 22. All x' are y, and all y' are x. i.e. |---|---|\n | 1 | 0 |\n -------\n\n -------\n | 1 | |\n 17. Some x are y, and some x' are y'. i.e. |---|---|\n | | 1 |\n -------\n\n\n\n\n\n5. Smaller Diagram.\n\n\n\nSymbols interpreted.\n\n__________\n\n\n1. Some y are not-x, or, Some not-x are y.\n\n2. No not-x are not-y, or, No not-y are not-x.\n\n3. No not-y are x.\n\n4. No not-x exist. i.e. No Things are not-x.\n\n5. No y exist. i.e. No houses are two-storied.\n\n6. Some x' exist. i.e. Some houses are not built of brick.\n\n7. No x are y'. Or, no y' are x. i.e. No houses, built of\nbrick, are other than two-storied. Or, no houses, that\nare not two-storied, are built of brick.\n\n8. All x' are y'. i.e. All houses, that are not built of\nbrick, are not two-storied.\n\n9. Some x are y, and some are y'. i.e. Some fat boys are\nactive, and some are not.\n\n10. All y' are x'. i.e. All lazy boys are thin.\n\n11. All x are y', and all y' are x. i.e. All fat boys\nare lazy, and all lazy ones are fat.\n\n12. All y are x, and all x' are y. i.e. All active boys\nare fat, and all thin ones are lazy.\n\n13. No x exist, and no y' exist. i.e. No cats have green eyes,\nand none have bad tempers.\n\n14. Some x are y', and some x' are y. Or some y are x', and\nsome y' are x. i.e. Some green-eyed cats are bad-tempered,\nand some, that have not green eyes, are good-tempered.\nOr, some good-tempered cats have not green eyes, and some\nbad-tempered ones have green eyes.\n\n15. Some x are y, and no x' are y'. Or, some y are x, and\nno y' are x'. i.e. Some green-eyed cats are good-tempered, and\nnone, that are not green-eyed, are bad-tempered. Or, some\ngood-tempered cats have green eyes, and none, that are\nbad-tempered, have not green eyes.\n\n16. All x are y', and all x' are y. Or, all y are x', and all\ny' are x. i.e. All green-eyed cats are bad-tempered and\nall, that have not green eyes, are good-tempered. Or, all\ngood-tempered ones have eyes that are not green, and all\nbad-tempered ones have green eyes.\n\n\n\n\n6. Larger Diagram.\n\n\n\nPropositions represented.\n\n__________\n\n --------------- ---------------\n | | | | | |\n | ---|--- | | ---|--- |\n | | 0 | 0 | | | | | | |\n 1. |---|---|---|---| 2. |-1-|---|---|---|\n | | | | | | | | | |\n | ---|--- | | ---|--- |\n | | | | | |\n --------------- ---------------\n\n\n --------------- ---------------\n | | | | | 0 |\n | ---|--- | | ---|--- |\n | | 0 | 0 | | | | | | |\n 3. |---|---|---|---| 4. |---|---|---|---|\n | | - | | | | | | |\n | ---|--- | | ---|--- |\n | | | | | 0 |\n --------------- ---------------\n\n\n --------------- ---------------\n | 0 | | | | |\n | ---|--- | | ---|--- |\n | | 0 | 0 | | | | 0 | 1 | |\n 5. |---|---|---|---| 6. |---|---|---|---|\n | | 1 | | | | | 0 | | |\n | ---|--- | | ---|--- |\n | 0 | | | | |\n --------------- ---------------\n\n\n --------------- ---------------\n | | | | | 0 |\n | ---|--- | | ---|--- |\n | | 0 | 0 | | | | | | |\n 7. |---|---|---|---| 8. |---|---|---|---|\n | | 0 | 1 | | | | 0 | 0 | |\n | ---|--- | | ---|--- |\n | | | | | 0 |\n --------------- ---------------\n\n\n ---------------\n | | |\n | ---|--- |\n | | 0 | 0 | |\n 9. No x are m. i.e. |---|---|---|---|\n | | 0 | | |\n | ---|--- |\n | | |\n ---------------\n\n\n ---------------\n | | |\n | ---|--- |\n | | | | |\n 10. Some m' are y. i.e. |-1-|---|---|---|\n | | | | |\n | ---|--- |\n | | |\n ---------------\n\n\n ---------------\n | | |\n | ---|--- |\n | | | 0 | |\n 11. All y' are m'. i.e. |---|---|---|-1-|\n | | | 0 | |\n | ---|--- |\n | | |\n ---------------\n\n ---------------\n | | |\n | ---|--- |\n | | 0 | 0 | |\n 12. All m are x'. i.e. |---|---|---|---|\n | | 1 | |\n | ---|--- |\n | | |\n ---------------\n\n ---------------\n | 0 | |\n | ---|--- |\n | | 0 | 0 | |\n 13. No x are m; i.e. |---|---|---|---|\n All y are m. | | 1 | | |\n | ---|--- |\n | 0 | |\n ---------------\n\n ---------------\n | 0 | 0 |\n | ---|--- |\n | | | | |\n 14. All m' are y; i.e. |---|---|---|---|\n No x are m'. | | | | |\n | ---|--- |\n | 1 | 0 |\n ---------------\n\n\n ---------------\n | 0 | 0 |\n | ---|--- |\n | | 1 | 0 | |\n 15. All x are m; i.e. |---|---|---|---|\n No m are y'. | | | 0 | |\n | ---|--- |\n | | |\n ---------------\n\n ---------------\n | 0 | 0 |\n | ---|--- |\n | | | | |\n 16. All m' are y'; i.e. |---|---|---|---|\n No x are m'. | | | | |\n | ---|--- |\n | 0 | 1 |\n ---------------\n\n ---------------\n | 0 | 0 |\n | ---|--- |\n | | 1 | 0 | |\n 17. All x are m; i.e. |---|---|---|---|\n All m are y. | | | 0 | |\n | ---|--- |\n[See remarks on No. 7, p. 60.] | | |\n ---------------\n\n ---------------\n | 0 | |\n | ---|--- |\n | | | | |\n 18. No x' are m; i.e. |---|---|---|---|\n No m' are y. | | 0 | 0 | |\n | ---|--- |\n | 0 | |\n ---------------\n\n ---------------\n | | |\n | ---|--- |\n | | 1 | 0 | |\n 19. All m are x; i.e. |---|---|---|---|\n All m are y. | | 0 | 0 | |\n | ---|--- |\n | | |\n ---------------\n\n 20. We had better take \"persons\" as Universe. We\nmay choose \"myself\" as 'Middle Term', in which case\nthe Premisses will take the form\n\n I am a-person-who-sent-him-to-bring-a-kitten;\n I am a-person-to-whom-he-brought-a-kettle-by-mistake.\n\nOr we may choose \"he\" as 'Middle Term', in which case the Premisses\nwill take the form\n\n He is a-person-whom-I-sent-to-bring-me-a-kitten;\n He is a-person-who-brought-me-a-kettle-by-mistake.\n\nThe latter form seems best, as the interest of the anecdote clearly\ndepends on HIS stupidity--not on what happened to ME. Let us then\nmake m = \"he\"; x = \"persons whom I sent, &c.\"; and y = \"persons\nwho brought, &c.\"\n\n Hence, All m are x;\n All m are y. and the required Diagram is\n\n\n ---------------\n | | |\n | ---|--- |\n | | 1 | 0 | |\n |---|---|---|---|\n | | 0 | 0 | |\n | ---|--- |\n | | |\n ---------------\n\n\n\n\n7. Both Diagrams employed.\n\n -------\n | 0 | |\n 1. |---|---| i.e. All y are x'.\n | 1 | |\n -------\n\n -------\n | | 1 |\n 2. |---|---| i.e. Some x are y'; or, Some y' are x.\n | | |\n -------\n\n -------\n | | |\n 3. |---|---| i.e. Some y are x'; or, Some x' are y.\n | 1 | |\n -------\n\n -------\n | | |\n 4. |---|---| i.e. No x' are y'; or, No y' are x'.\n | | 0 |\n -------\n\n -------\n | 0 | |\n 5. |---|---| i.e. All y are x'. i.e. All black rabbits\n | 1 | | are young.\n -------\n\n -------\n | | |\n 6. |---|---| i.e. Some y are x'. i.e. Some black\n | 1 | | rabbits are young.\n -------\n\n -------\n | 1 | 0 |\n 7. |---|---| i.e. All x are y. i.e. All well-fed birds\n | | | are happy.\n -------\n\n\n -------\n | | | i.e. Some x' are y'. i.e. Some birds,\n 8. |---|---| that are not well-fed, are unhappy;\n | | 1 | or, Some unhappy birds are not\n ------- well-fed.\n\n\n -------\n | 1 | 0 |\n 9. |---|---| i.e. All x are y. i.e. John has got a\n | | | tooth-ache.\n -------\n\n\n -------\n | | |\n 10. |---|---| i.e. No x' are y. i.e. No one, but John,\n | 0 | | has got a tooth-ache.\n -------\n\n\n -------\n | 1 | |\n 11. |---|---| i.e. Some x are y. i.e. Some one, who\n | | | has taken a walk, feels better.\n -------\n\n\n -------\n | 1 | | i.e. Some x are y. i.e. Some one,\n 12. |---|---| whom I sent to bring me a kitten,\n | | | brought me a kettle by mistake.\n -------\n\n ---------------\n | | 0 |\n | ---|--- |\n | | 0 | 0 | |\n13. |-1-|---|---|---| -------\n | | | | | | | 0 |\n | ---|--- | |---|---|\n | | 0 | | | |\n --------------- -------\n\n\n Let \"books\" be Universe; m=\"exciting\",\n x=\"that suit feverish patients\"; y=\"that make\n one drowsy\".\n\n No m are x; &there4 No y' are x.\n All m' are y.\n\n i.e. No books suit feverish patients, except such as make\n one drowsy.\n\n ---------------\n | | |\n | ---|--- |\n | | 1 | 0 | |\n14. |---|---|---|---| -------\n | | | 0 | | | 1 | |\n | ---|--- | |---|---|\n | | | | | |\n --------------- -------\n\n\nLet \"persons\" be Universe; m=\"that deserve the fair\";\n x=\"that get their deserts\"; y=\"brave\".\n\n Some m are x; &there4 Some y are x.\n No y' are m.\n\n i.e. Some brave persons get their deserts.\n\n ---------------\n | 0 | |\n | ---|--- |\n | | 0 | 0 | |\n15. |---|---|---|---| -------\n | | | | | | 0 | |\n | ---|--- | |---|---|\n | 0 | | | | |\n --------------- -------\n\n Let \"persons\" be Universe; m=\"patient\";\n x=\"children\"; y=\"that can sit still\".\n\n No x are m; &there4 No x are y.\n No m' are y.\n\n i.e. No children can sit still.\n\n\n ---------------\n | 0 | 0 |\n | ---|--- |\n | | 0 | 1 | |\n16. |---|---|---|---| -------\n | | 0 | | | | 0 | 1 |\n | ---|--- | |---|---|\n | | | | | |\n --------------- -------\n\n\n Let \"things\" be Universe; m=\"fat\"; x=\"pigs\";\n y=\"skeletons\".\n\n All x are m; &there4 All x are y'.\n No y are m.\n\n i.e. All pigs are not-skeletons.\n\n ---------------\n | | |\n | ---|--- |\n | | 0 | 0 | |\n17. |---|---|---|---| -------\n | | 1 | 0 | | | | |\n | ---|--- | |---|---|\n | | | | 1 | |\n --------------- -------\n\n Let \"creatures\" be Universe; m=\"monkeys\";\n x=\"soldiers\"; y=\"mischievous\".\n\n No m are x; &there4 Some y are x'.\n All m are y.\n\n i.e. Some mischievous creatures are not soldiers.\n\n\n ---------------\n | 0 | |\n | ---|--- |\n | | 0 | 0 | |\n18. |---|---|---|---| -------\n | | | | | | 0 | |\n | ---|--- | |---|---|\n | 0 | | | | |\n --------------- -------\n\n Let \"persons\" be Universe; m=\"just\";\n x=\"my cousins\"; y=\"judges\".\n\n No x are m; &there4 No x are y.\n No y are m'.\n\n i.e. None of my cousins are judges.\n\n ---------------\n | | |\n | ---|--- |\n | | 1 | 0 | |\n19. |---|---|---|---| -------\n | | | | | | 1 | |\n | ---|--- | |---|---|\n | | | | | |\n --------------- -------\n\n Let \"periods\" be Universe; m=\"days\";\n x=\"rainy\"; y=\"tiresome\".\n\n Some m are x; &there4 Some x are y.\n All xm are y.\n\n i.e. Some rainy periods are tiresome.\n\nN.B. These are not legitimate Premisses, since the\nConclusion is really part of the second Premiss, so that the\nfirst Premiss is superfluous. This may be shown, in letters,\nthus:--\n\n\"All xm are y\" contains \"Some xm are y\", which\ncontains \"Some x are y\". Or, in words, \"All rainy days\nare tiresome\" contains \"Some rainy days are tiresome\",\nwhich contains \"Some rainy periods are tiresome\".\n\nMoreover, the first Premiss, besides being superfluous, is\nactually contained in the second; since it is equivalent to\n\"Some rainy days exist\", which, as we know, is implied in\nthe Proposition \"All rainy days are tiresome\".\n\nAltogether, a most unsatisfactory Pair of Premisses!\n\n ---------------\n | 0 | |\n | ---|--- |\n | | 1 | | |\n20. |---|---|---|---| -------\n | | 0 | 0 | | | 1 | |\n | ---|--- | |---|---|\n | 0 | | | 0 | |\n --------------- -------\n\n Let \"things\" be Universe; m=\"medicine\";\n x=\"nasty\"; y=\"senna\".\n\n All m are x; &there4 All y are x.\n All y are m.\n\n i.e. Senna is nasty.\n\n [See remarks on No. 7, p 60.]\n\n ---------------\n | | |\n | ---|--- |\n | | 0 | 1 | |\n21. |-1-|---|---|---| -------\n | | 0 | | | | | 1 |\n | ---|--- | |---|---|\n | | | | | |\n --------------- -------\n\n Let \"persons\" be Universe; m=\"Jews\";\n x=\"rich\"; y=\"Patagonians\".\n\n Some m are x; &there4 Some x are y'.\n All y are m'.\n\n i.e. Some rich persons are not Patagonians.\n\n ---------------\n | 0 | |\n | ---|--- |\n | | - | |\n22. |---|---|---|---| -------\n | | 0 | 0 | | | | |\n | ---|--- | |---|---|\n | 0 | | | 0 | |\n --------------- -------\n\n Let \"creatures\" be Universe; m=\"teetotalers\";\n x=\"that like sugar\"; y=\"nightingales\".\n\n All m are x; &there4 No y are x'.\n No y are m'.\n\n i.e. No nightingales dislike sugar.\n\n ---------------\n | | |\n | ---|--- |\n | | 0 | 0 | |\n23. |-1-|---|---|---| -------\n | | 0 | | | | | |\n | ---|--- | |---|---|\n | | | | | |\n --------------- -------\n\n Let \"food\" be Universe; m=\"wholesome\";\n x=\"muffins\"; y=\"buns\".\n\n No x are m;\n All y are m.\n\n There is 'no information' for the smaller Diagram; so\nno Conclusion can be drawn.\n\n ---------------\n | | |\n | ---|--- |\n | | 0 | 0 | |\n24. |---|---|---|---| -------\n | | 1 | | | | | |\n | ---|--- | |---|---|\n | | | | 1 | |\n --------------- -------\n\n Let \"creatures\" be Universe; m=\"that run well\";\n x=\"fat\"; y=\"greyhounds\".\n\n No x are m; &there4 Some y are x'.\n Some y are m.\n\n i.e. Some greyhounds are not fat.\n\n\n ---------------\n | | |\n | ---|--- |\n | | - | |\n25. |-1-|---|---|---| -------\n | | 0 | 0 | | | | |\n | ---|--- | |---|---|\n | | | | | |\n --------------- -------\n\n Let \"persons\" be Universe; m=\"soldiers\";\n x=\"that march\"; y=\"youths\".\n\n All m are x;\n Some y are m'.\n\n There is 'no information' for the smaller Diagram; so\nno Conclusion can be drawn.\n\n ---------------\n | 0 | 0 |\n | ---|--- |\n | | 0 | 1 | |\n26. |---|---|---|---| -------\n | | 0 | | | | 0 | 1 |\n | ---|--- | |---|---|\n | 1 | | | 1 | |\n --------------- -------\n\n\n Let \"food\" be Universe; m=\"sweet\";\n x=\"sugar\"; y=\"salt\".\n\n All x are m; &there4 All x are y'.\n All y are m'. All y are x'.\n\n\n i.e. Sugar is not salt.\n Salt is not sugar.\n\n ---------------\n | | |\n | ---|--- |\n | | 1 | 0 | |\n27. |---|---|---|---| -------\n | | | 0 | | | 1 | |\n | ---|--- | |---|---|\n | | | | | |\n --------------- -------\n\n Let \"Things\" be Universe; m=\"eggs\";\n x=\"hard-boiled\"; y=\"crackable\".\n\n Some m are x; &there4 Some x are y.\n No m are y'.\n\n i.e. Some hard-boiled things can be cracked.\n\n ---------------\n | 0 | |\n | ---|--- |\n | | 0 | 0 | |\n28. |---|---|---|---| -------\n | | | | | | 0 | |\n | ---|--- | |---|---|\n | 0 | | | | |\n --------------- -------\n\nLet \"persons\" be Universe; m=\"Jews\"; x=\"that\n are in the house\"; y=\"that are in the garden\".\n\n No m are x; &there4 No x are y.\n No m' are y.\n\n i.e. No persons, that are in the house, are also in\n the garden.\n\n\n ---------------\n | 0 | 0 |\n | ---|--- |\n | | - | |\n29. |---|---|---|---| -------\n | | | | | | | |\n | ---|--- | |---|---|\n | 1 | 0 | | 1 | |\n --------------- -------\n\n\n Let \"Things\" be Universe; m=\"noisy\";\n x=\"battles\"; y=\"that may escape notice\".\n\n All x are m; &there4 Some x' are y.\n All m' are y.\n\n i.e. Some things, that are not battles, may escape notice.\n\n ---------------\n | 0 | |\n | ---|--- |\n | | 0 | 0 | |\n30. |---|---|---|---| -------\n | | 1 | | | | 0 | |\n | ---|--- | |---|---|\n | 0 | | | 1 | |\n --------------- -------\n\n Let \"persons\" be Universe; m=\"Jews\";\n x=\"mad\"; y=\"Rabbis\".\n\n No m are x; &there4 All y are x'.\n All y are m.\n\n i.e. All Rabbis are sane.\n\n ---------------\n | | |\n | ---|--- |\n | | 1 | | |\n31. |---|---|---|---| -------\n | | 0 | 0 | | | 1 | |\n | ---|--- | |---|---|\n | | | | | |\n --------------- -------\n\n Let \"Things\" be Universe; m=\"fish\";\n x=\"that can swim\"; y=\"skates\".\n\n No m are x'; &there4 Some y are x.\n Some y are m.\n\n i.e. Some skates can swim.\n\n ---------------\n | | |\n | ---|--- |\n | | 0 | 0 | |\n32. |---|---|---|---| -------\n | | 1 | | | | | |\n | ---|--- | |---|---|\n | | | | 1 | |\n --------------- -------\n\n Let \"people\" be Universe; m=\"passionate\";\n x=\"reasonable\"; y=\"orators\".\n\n All m are x'; &there4 Some y are x'.\n Some y are m.\n\n i.e. Some orators are unreasonable.\n\n [See remarks on No. 7, p. 60.]\n\n\n\n\n\n\n\nCHAPTER IV.\n\nHIT OR MISS.\n\n\n \"Thou canst not hit it, hit it, hit it,\n Thou canst not hit it, my good man.\"\n\n__________\n\n\n1. Pain is wearisome; No pain is eagerly wished for.\n\n2. No bald person needs a hair-brush; No lizards have hair.\n\n3. All thoughtless people do mischief; No thoughtful person\nforgets a promise.\n\n4. I do not like John; Some of my friends like John.\n\n5. No potatoes are pine-apples; All pine-apples are nice.\n\n6. No pins are ambitious; No needles are pins.\n\n7. All my friends have colds; No one can sing who has a cold.\n\n8. All these dishes are well-cooked; Some dishes are unwholesome\nif not well-cooked.\n\n9. No medicine is nice; Senna is a medicine.\n\n10. Some oysters are silent; No silent creatures are amusing.\n\n11. All wise men walk on their feet; All unwise men walk on\ntheir hands.\n\n12. \"Mind your own business; This quarrel is no business of\nyours.\"\n\n13. No bridges are made of sugar; Some bridges are picturesque.\n\n14. No riddles interest me that can be solved; All these\nriddles are insoluble.\n\n15. John is industrious; All industrious people are happy.\n\n16. No frogs write books; Some people use ink in writing\nbooks.\n\n17. No pokers are soft; All pillows are soft.\n\n18. No antelope is ungraceful; Graceful animals delight the\neye.\n\n19. Some uncles are ungenerous; All merchants are generous.\n\n20. No unhappy people chuckle; No happy people groan.\n\n21. Audible music causes vibration in the air; Inaudible\nmusic is not worth paying for.\n\n22. He gave me five pounds; I was delighted.\n\n23. No old Jews are fat millers; All my friends are old\nmillers.\n\n24. Flour is good for food; Oatmeal is a kind of flour.\n\n25. Some dreams are terrible; No lambs are terrible.\n\n26. No rich man begs in the street; All who are not rich\nshould keep accounts.\n\n27. No thieves are honest; Some dishonest people are found\nout.\n\n28. All wasps are unfriendly; All puppies are friendly.\n\n29. All improbable stories are doubted; None of these\nstories are probable.\n\n30. \"He told me you had gone away.\" \"He never says one word\nof truth.\"\n\n31. His songs never last an hour; A song, that lasts an\nhour, is tedious.\n\n32. No bride-cakes are wholesome; Unwholesome food should\nbe avoided.\n\n33. No old misers are cheerful; Some old misers are thin.\n\n34. All ducks waddle; Nothing that waddles is graceful.\n\n35. No Professors are ignorant; Some ignorant people are\nconceited.\n\n36. Toothache is never pleasant; Warmth is never unpleasant.\n\n37. Bores are terrible; You are a bore.\n\n38. Some mountains are insurmountable; All stiles can be\nsurmounted.\n\n39. No Frenchmen like plumpudding; All Englishmen like\nplumpudding.\n\n40. No idlers win fame; Some painters are not idle.\n\n41. No lobsters are unreasonable; No reasonable creatures\nexpect impossibilities.\n\n42. No kind deed is unlawful; What is lawful may be done\nwithout fear.\n\n43. No fossils can be crossed in love; Any oyster may be\ncrossed in love.\n\n44. \"This is beyond endurance!\" \"Well, nothing beyond\nendurance has ever happened to me.\"\n\n45. All uneducated men are shallow; All these students are\neducated.\n\n46. All my cousins are unjust; No judges are unjust.\n\n47. No country, that has been explored, is infested\nby dragons; Unexplored countries are fascinating.\n\n48. No misers are generous; Some old men are not generous.\n\n49. A prudent man shuns hyaenas; No banker is imprudent.\n\n50. Some poetry is original; No original work is producible\nat will.\n\n51. No misers are unselfish; None but misers save egg-shells.\n\n52. All pale people are phlegmatic; No one, who is not\npale, looks poetical.\n\n53. All spiders spin webs; Some creatures, that do not spin\nwebs, are savage.\n\n54. None of my cousins are just; All judges are just.\n\n55. John is industrious; No industrious people are unhappy.\n\n56. Umbrellas are useful on a journey; What is useless on\na journey should be left behind.\n\n57. Some pillows are soft; No pokers are soft.\n\n58. I am old and lame; No old merchant is a lame gambler.\n\n59. No eventful journey is ever forgotten; Uneventful\njourneys are not worth writing a book about.\n\n60. Sugar is sweet; Some sweet things are liked by children.\n\n61. Richard is out of temper; No one but Richard can ride\nthat horse.\n\n62. All jokes are meant to amuse; No Act of Parliament is\na joke.\n\n63. \"I saw it in a newspaper.\" \"All newspapers tell lies.\"\n\n64. No nightmare is pleasant; Unpleasant experiences are\nnot anxiously desired.\n\n65. Prudent travellers carry plenty of small change; Imprudent\ntravellers lose their luggage.\n\n66. All wasps are unfriendly; No puppies are unfriendly.\n\n67. He called here yesterday; He is no friend of mine.\n\n68. No quadrupeds can whistle; Some cats are quadrupeds.\n\n69. No cooked meat is sold by butchers; No uncooked meat\nis served at dinner.\n\n70. Gold is heavy; Nothing but gold will silence him.\n\n71. Some pigs are wild; There are no pigs that are not fat.\n\n72. No emperors are dentists; All dentists are dreaded by\nchildren.\n\n73. All, who are not old, like walking; Neither you nor I\nare old.\n\n74. All blades are sharp; Some grasses are blades.\n\n75. No dictatorial person is popular; She is dictatorial.\n\n76. Some sweet things are unwholesome; No muffins are sweet.\n\n77. No military men write poetry; No generals are civilians.\n\n78. Bores are dreaded; A bore is never begged to prolong\nhis visit.\n\n79. All owls are satisfactory; Some excuses are unsatisfactory.\n\n80. All my cousins are unjust; All judges are just.\n\n81. Some buns are rich; All buns are nice.\n\n82. No medicine is nice; No pills are unmedicinal.\n\n83. Some lessons are difficult; What is difficult needs\nattention.\n\n84. No unexpected pleasure annoys me; Your visit is an\nunexpected pleasure.\n\n85. Caterpillars are not eloquent; Jones is eloquent.\n\n86. Some bald people wear wigs; All your children have\nhair.\n\n87. All wasps are unfriendly; Unfriendly creatures are\nalways unwelcome.\n\n88. No bankrupts are rich; Some merchants are not bankrupts.\n\n89. Weasels sometimes sleep; All animals sometimes sleep.\n\n90. Ill-managed concerns are unprofitable; Railways are\nnever ill-managed.\n\n91. Everybody has seen a pig; Nobody admires a pig.\n\n______________\n\n\nExtract a Pair of Premisses out of each of the following: and\ndeduce the Conclusion, if there is one:--\n\n92. \"The Lion, as any one can tell you who has been chased by them\nas often as I have, is a very savage animal: and there are certain\nindividuals among them, though I will not guarantee it as a general\nlaw, who do not drink coffee.\"\n\n93. \"It was most absurd of you to offer it! You might have known,\nif you had had any sense, that no old sailors ever like gruel!\"\n\n\"But I thought, as he was an uncle of yours--\"\n\n\"An uncle of mine, indeed! Stuff!\"\n\n\"You may call it stuff, if you like. All I know is, MY uncles are\nall old men: and they like gruel like anything!\"\n\n\"Well, then YOUR uncles are--\"\n\n94. \"Do come away! I can't stand this squeezing any more. No\ncrowded shops are comfortable, you know very well.\"\n\n\"Well, who expects to be comfortable, out shopping?\"\n\n\"Why, I do, of course! And I'm sure there are some shops, further\ndown the street, that are not crowded. So--\"\n\n95. \"They say no doctors are metaphysical organists: and that lets\nme into a little fact about YOU, you know.\"\n\n\"Why, how do you make THAT out? You never heard me play the organ.\"\n\n\"No, doctor, but I've heard you talk about Browning's poetry: and\nthat showed me that you're METAPHYSICAL, at any rate. So--\"\n\n___________________\n\nExtract a Syllogism out of each of the following: and\ntest its correctness:--\n\n96. \"Don't talk to me! I've known more rich merchants than you\nhave: and I can tell you not ONE of them was ever an old miser\nsince the world began!\"\n\n\"And what has that got to do with old Mr. Brown?\"\n\n\"Why, isn't he very rich?\"\n\n\"Yes, of course he is. And what then?\"\n\n\"Why, don't you see that it's absurd to call him a miserly merchant?\nEither he's not a merchant, or he's not a miser!\"\n\n97. \"It IS so kind of you to enquire! I'm really feeling a great\ndeal better to-day.\"\n\n\"And is it Nature, or Art, that is to have the credit of this happy\nchange?\"\n\n\"Art, I think. The Doctor has given me some of that patent medicine\nof his.\"\n\n\"Well, I'll never call him a humbug again. There's SOMEBODY, at\nany rate, that feels better after taking his medicine!\"\n\n98. \"No, I don't like you one bit. And I'll go and play with my\ndoll. DOLLS are never unkind.\"\n\n\"So you like a doll better than a cousin? Oh you little silly!\"\n\n\"Of course I do! COUSINS are never kind--at least no cousins I've\never seen.\"\n\n\"Well, and what does THAT prove, I'd like to know! If you mean\nthat cousins aren't dolls, who ever said they were?\"\n\n99. \"What are you talking about geraniums for? You can't tell\none flower from another, at this distance! I grant you they're\nall RED flowers: it doesn't need a telescope to know THAT.\"\n\n\"Well, some geraniums are red, aren't they?\"\n\n\"I don't deny it. And what then? I suppose you'll be telling me\nsome of those flowers are geraniums!\"\n\n\"Of course that's what I should tell you, if you'd the sense to\nfollow an argument! But what's the good of proving anything to\nYOU, I should like to know?\"\n\n100. \"Boys, you've passed a fairly good examination, all things\nconsidered. Now let me give you a word of advice before I go.\nRemember that all, who are really anxious to learn, work HARD.\"\n\n\"I thank you, Sir, in the name of my scholars! And proud am I to\nthink there are SOME of them, at least, that are really ANXIOUS to\nlearn.\"\n\n\"Very glad to hear it: and how do you make it out to be so?\"\n\n\"Why, Sir, I know how hard they work--some of them, that is. Who\nshould know better?\"\n\n___________________\n\nExtract from the following speech a series of Syllogisms, or\narguments having the form of Syllogisms: and test their correctness.\n\nIt is supposed to be spoken by a fond mother, in answer to a friend's\ncautious suggestion that she is perhaps a LITTLE overdoing it, in\nthe way of lessons, with her children.\n\n101. \"Well, they've got their own way to make in the world. WE\ncan't leave them a fortune apiece. And money's not to be had, as\nYOU know, without money's worth: they must WORK if they want to\nlive. And how are they to work, if they don't know anything? Take\nmy word for it, there's no place for ignorance in THESE times! And\nall authorities agree that the time to learn is when you're young.\nOne's got no memory afterwards, worth speaking of. A child will\nlearn more in an hour than a grown man in five. So those, that\nhave to learn, must learn when they're young, if ever they're to\nlearn at all. Of course that doesn't do unless children are HEALTHY:\nI quite allow THAT. Well, the doctor tells me no children are\nhealthy unless they've got a good colour in their cheeks. And only\njust look at my darlings! Why, their cheeks bloom like peonies!\nWell, now, they tell me that, to keep children in health, you\nshould never give them more than six hours altogether at lessons\nin the day, and at least two half-holidays in the week. And that's\nEXACTLY our plan I can assure you! We never go beyond six hours,\nand every Wednesday and Saturday, as ever is, not one syllable of\nlessons do they do after their one o'clock dinner! So how you can\nimagine I'm running any risk in the education of my precious pets\nis more than I can understand, I promise you!\"\n\n\n\n\nTHE END.","title":"The Game of Logic","tradition":"philosophy-ethics","translated_text":null,"word_count":17471}