Lewis Carroll, The Game Of Logic â WordPress.com - literature save 2

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At last we have found out how to represent the first Proposition of this Section. If youhave not CLEARLY understood all I have said, go no further, but read it over and overagain, till you DO understand it. After that is once mastered, you will find all the restquite easy.It will save a little trouble, in doing the other Propositions, if we agree to leave out theword "Cakes" altogether. I find it convenient to call the whole class of Things, for whichthe cupboard is intended, the 'UNIVERSE.' Thus we might have begun this business bysaying "Let us take a Universe of Cakes." (Sounds nice, doesn't it?)Of course any other Things would have done just as well as Cakes. We might makePropositions about "a Universe of Lizards", or even "a Universe of Hornets". (Wouldn'tTHAT be a charming Universe to live in?)So far, then, we have learned that—————-| | || 1 | || | |—————-means "some x and y," i.e. "some new are nice."I think you will see without further explanation, that—————-| | || | 1 || | |—————-means "some x are y'," i.e. "some new are not-nice."Now let us put a GREY counter into No. 5, and ask ourselves the meaning of—————-| | || 0 | || | |—————-
This tells us that the x y-compartment is EMPTY, which we may express by "no x are y",or, "no new Cakes are nice". This is the second of the three Propositions at the head ofthis Section.In the same way,—————-| | || | 0 || | |—————-would mean "no x are y'," or, "no new Cakes are not-nice."What would you make of this, I wonder?—————-| | || 1 | 1 || | |—————-I hope you will not have much trouble in making out that this represents a DOUBLEProposition: namely, "some x are y, AND some are y'," i.e. "some new are nice, andsome are not-nice."The following is a little harder, perhaps:—————-| | || 0 | 0 || | |—————-This means "no x are y, AND none are y'," i.e. "no new are nice, AND none are notnice":which leads to the rather curious result that "no new exist," i.e. "no Cakes arenew." This is because "nice" and "not-nice" make what we call an 'EXHAUSTIVE'division of the class "new Cakes": i.e. between them, they EXHAUST the whole class, sothat all the new Cakes, that exist, must be found in one or the other of them.
Page 1 and 2: Lewis Carroll, The Game of LogicTHE
Page 3 and 4: epresented . . . . . . . 593. Do. S
Page 5: It is part of the upper half, you s
Page 9 and 10: "All new Cakes are nice"consists of
Page 11 and 12: You will find it a good plan to exa
Page 13 and 14: —————————-| 0 | 0
Page 15 and 16: we should transfer it to the smalle
Page 17 and 18: We have now to express the other Pr
Page 19 and 20: "All Dragon-Animals are uncanny (An
Page 21 and 22: secondly, by taking y as Subject, w
Page 23 and 24: "All soldiers are brave;Some Englis
Page 25 and 26: CROSS QUESTIONS."The Man in the Wil
Page 27 and 28: 2. Half of Smaller Diagram.Proposit
Page 29 and 30: 15. No diligent students are unsucc
Page 31 and 32: |||—y'-|||x'|||——-Taking y="h
Page 33 and 34: 12. All x are y, and all not-y are
Page 35 and 36: ——-__________———- ——
Page 37 and 38: —m—y'-|| | || | |—x'-| | ||
Page 39 and 40: —————- | | | ————
Page 41 and 42: 32. All passionate people are unrea
Page 43 and 44: 21. The Things, in each compartment
Page 45 and 46: ———-| | |9. Some x are y'. i.
Page 47 and 48: 10. No x are y. i.e. No lobsters ar
Page 49 and 50: ———-| 0 | 1 |18. All x are y'
Page 51 and 52: Propositions represented.__________
Page 53 and 54: All y are m. | | 1 | | || —-|—-
Page 55 and 56: 7. Both Diagrams employed.———
Page 57 and 58:
No m are x; &there4 No y' are x.All
Page 59 and 60:
No x are m; &there4 No x are y.No y
Page 61 and 62:
———————-| | || —-|
Page 63 and 64:
———————-| 0 | || —-
Page 65 and 66:
[See remarks on No. 7, p. 60.]CHAPT
Page 67 and 68:
38. Some mountains are insurmountab
Page 69 and 70:
83. Some lessons are difficult; Wha
Page 71 and 72:
99. "What are you talking about ger
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