The Game of Logic - Lewis Carroll (red queen free ebook TXT) 📗

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20. We had better take “persons” as Universe. We may choose “myself” as ‘Middle Term’, in which case the Premisses will take the form

 

I am a-person-whosent-him-to-bring-a-kitten;

I am a-person-to-whom-he-brought-a-kettle-by-mistake.

Or we may choose “he” as ‘Middle Term’, in which case the Premisses will take the form

 

He is a-person-whom-I-sent-to-bring-me-a-kitten;

He is a-person-who-brought-me-a-kettle-by-mistake.

The latter form seems best, as the interest of the anecdote clearly depends on HIS stupidity—not on what happened to ME. Let us then make m = “he”; x = “persons whom I sent, &c.”; and y = “persons who brought, &c.”

 

Hence, All m are x;

All m are y. and the required Diagram is

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7. Both Diagrams employed.

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1. |–|–| i.e. All y are x’.

| 1 | |

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2. |–|–| i.e. Some x are y’; or, Some y’ are x.

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3. |–|–| i.e. Some y are x’; or, Some x’ are y.

| 1 | |

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4. |–|–| i.e. No x’ are y’; or, No y’ are x’.

| | 0 |

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5. |–|–| i.e. All y are x’. i.e. All black rabbits

| 1 | | are young.

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6. |–|–| i.e. Some y are x’. i.e. Some black

| 1 | | rabbits are young.

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| 1 | 0 |

7. |–|–| i.e. All x are y. i.e. All well-fed birds

| | | are happy.

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| | | i.e. Some x’ are y’. i.e. Some birds,

8. |–|–| that are not well-fed, are unhappy;

| | 1 | or, Some unhappy birds are not

––- well-fed.

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9. |–|–| i.e. All x are y. i.e. John has got a

| | | tooth-ache.

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| | | 10. |–|–| i.e. No x’ are y. i.e. No one, but John,

| 0 | | has got a tooth-ache.

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| 1 | | 11. |–|–| i.e. Some x are y. i.e. Some one, who

| | | has taken a walk, feels better.

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| 1 | | i.e. Some x are y. i.e. Some one, 12. |–|–| whom I sent to bring me a kitten,

| | | brought me a kettle by mistake.

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| | 0 | 0 | | 13. |-1-|–|–|–| ––-

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Let “books” be Universe; m=“exciting”,

x=“that suit feverish patients”; y=“that make

one drowsy”.

 

No m are x; &there4 No y’ are x.

All m’ are y.

 

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

one drowsy.

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| | 1 | 0 | | 14. |–|–|–|–| ––-

 

| | | 0 | | | 1 | |

| –|– | |–|–|

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Let “persons” be Universe; m=“that deserve the fair”;

x=“that get their deserts”; y=“brave”.

 

Some m are x; &there4 Some y are x.

No y’ are m.

 

i.e. Some brave persons get their deserts.

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| | 0 | 0 | | 15. |–|–|–|–| ––-

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Let “persons” be Universe; m=“patient”;

x=“children”; y=“that can sit still”.

 

No x are m; &there4 No x are y.

No m’ are y.

 

i.e. No children can sit still.

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| | 0 | 1 | | 16. |–|–|–|–| ––-

| | 0 | | | | 0 | 1 |

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Let “things” be Universe; m=“fat”; x=“pigs”;

y=“skeletons”.

 

All x are m; &there4 All x are y’.

No y are m.

 

i.e. All pigs are not-skeletons.

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| | 0 | 0 | | 17. |–|–|–|–| ––-

| | 1 | 0 | | | | |

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| | | | 1 | |

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Let “creatures” be Universe; m=“monkeys”;

x=“soldiers”; y=“mischievous”.

 

No m are x; &there4 Some y are x’.

All m are y.

 

i.e. Some mischievous creatures are not soldiers.

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| | 0 | 0 | | 18. |–|–|–|–| ––-

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Let “persons” be Universe; m=“just”;

x=“my cousins”; y=“judges”.

 

No x are m; &there4 No x are y.

No y are m’.

 

i.e. None of my cousins are judges.

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| | 1 | 0 | | 19. |–|–|–|–| ––-

| | | | | | 1 | |

| –|– | |–|–|

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Let “periods” be Universe; m=“days”;

x=“rainy”; y=“tiresome”.

 

Some m are x; &there4 Some x are y.

All xm are y.

 

i.e. Some rainy periods are tiresome.

N.B. These are not legitimate Premisses, since the Conclusion is really part of the second Premiss, so that the first Premiss is superfluous. This may be shown, in letters, thus:—

“All xm are y” contains “Some xm are y”, which contains “Some x are y”. Or, in words, “All rainy days are tiresome” contains “Some rainy days are tiresome”, which contains “Some rainy periods are tiresome”.

Moreover, the first Premiss, besides being superfluous, is actually contained in the second; since it is equivalent to “Some rainy days exist”, which, as we know, is implied in the Proposition “All rainy days are tiresome”.

Altogether, a most unsatisfactory Pair of Premisses!

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| | 1 | | | 20. |–|–|–|–| ––-

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Let “things” be Universe; m=“medicine”;

x=“nasty”; y=“senna”.

 

All m are x; &there4 All y are x.

All y are m.

 

i.e. Senna is nasty.

 

[See remarks on No. 7, p 60.]

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Let “persons” be Universe; m=“Jews”;

x=“rich”; y=“Patagonians”.

 

Some m are x; &there4 Some x are y’.

All y are m’.

 

i.e. Some rich persons are not Patagonians.

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| | - | | 22. |–|–|–|–| ––-

| | 0 | 0 | | | | |

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Let “creatures” be Universe; m=“teetotalers”;

x=“that like sugar”; y=“nightingales”.

 

All m are x; &there4 No y are x’.

No y are m’.

 

i.e. No nightingales dislike sugar.

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| | 0 | 0 | | 23. |-1-|–|–|–| ––-

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Let “food” be Universe; m=“wholesome”;

x=“muffins”; y=“buns”.

 

No x are m;

All y are m.

 

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

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| | 0 | 0 | | 24. |–|–|–|–| ––-

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Let “creatures” be Universe; m=“that run well”;

x=“fat”; y=“greyhounds”.

 

No x are m; &there4 Some y are x’.

Some y are m.

 

i.e. Some greyhounds are not fat.

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| | - | | 25. |-1-|–|–|–| ––-

| | 0 | 0 | | | | |

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Let “persons” be Universe; m=“soldiers”;

x=“that march”; y=“youths”.

 

All m are x;

Some y are m’.

 

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

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| | 0 | 1 | | 26. |–|–|–|–| ––-

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| 1 | | | 1 | |

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Let “food” be Universe; m=“sweet”;

x=“sugar”; y=“salt”.

 

All x are m; &there4 All x are y’.

All y are m’. All y are x’.

 

i.e. Sugar is not salt.

Salt is not sugar.

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| | 1 | 0 | | 27. |–|–|–|–| ––-

| | | 0 | | | 1 | |

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Let “Things” be Universe; m=“eggs”;

x=“hard-boiled”; y=“crackable”.

 

Some m are x; &there4 Some x are y.

No m are y’.

 

i.e. Some hard-boiled things can be cracked.

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| | 0 | 0 | | 28. |–|–|–|–| ––-

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| 0 | | | | |

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Let “persons” be Universe; m=“Jews”; x=“that

are in the house”; y=“that are in the garden”.

 

No m are x; &there4 No x are y.

No m’ are y.

 

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

the garden.

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| | - | | 29. |–|–|–|–| ––-

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| 1 | 0 | | 1 | |

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Let “Things” be Universe; m=“noisy”;

x=“battles”; y=“that may escape notice”.

 

All x are m; &there4 Some x’ are y.

All m’ are y.

 

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

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| | 0 | 0 | | 30. |–|–|–|–| ––-

| | 1 | | | | 0 | |

| –|– | |–|–|

| 0 | | | 1 | |

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Let “persons” be Universe; m=“Jews”;

x=“mad”; y=“Rabbis”.

 

No m are x; &there4 All y are x’.

All y are m.

 

i.e. All Rabbis are sane.

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| | 1 | | | 31. |–|–|–|–| ––-

| | 0 | 0 | | | 1 | |

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Let “Things” be Universe; m=“fish”;

x=“that can swim”; y=“skates”.

 

No m are x’; &there4 Some y are x.

Some y are m.

 

i.e. Some skates can swim.

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| | 0 | 0 | | 32. |–|–|–|–| ––-

| | 1 | | | | | |

| –|– | |–|–|

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Let “people” be Universe; m=“passionate”;

x=“reasonable”; y=“orators”.

 

All m are x’; &there4 Some y are x’.

Some