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20. We had better take β€œpersons” as Universe. We may choose β€œmyself” as β€˜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 β€œhe” as β€˜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 stupidityβ€”not on what happened to ME. Let us then make m = β€œhe”; x = β€œpersons whom I sent, &c.”; and y = β€œpersons who brought, &c.”

 

Hence, All m are x;

All m are y. and the required Diagram is

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| | 1 | 0 | |

|–|–|–|–|

| | 0 | 0 | |

| –|– |

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7. Both Diagrams employed.

––-

| 0 | |

1. |–|–| i.e. All y are x’.

| 1 | |

––-

––-

| | 1 |

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

| | |

––-

––-

| | |

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

| 1 | |

––-

––-

| | |

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

| | 0 |

––-

––-

| 0 | |

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

| 1 | | are young.

––-

––-

| | |

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

| 1 | | rabbits are young.

––-

––-

| 1 | 0 |

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

| | | are happy.

––-

––-

| | | 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.

––-

| 1 | 0 |

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

| | | tooth-ache.

––-

––-

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

| 0 | | has got a tooth-ache.

––-

––-

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

| | | has taken a walk, feels better.

––-

––-

| 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 | 0 | | 13. |-1-|–|–|–| ––-

| | | | | | | 0 |

| –|– | |–|–|

| | 0 | | | |

––––– ––-

Let β€œbooks” be Universe; m=β€œexciting”,

x=β€œthat suit feverish patients”; y=β€œthat 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 | |

| –|– | |–|–|

| | | | | |

––––– ––-

Let β€œpersons” be Universe; m=β€œthat deserve the fair”;

x=β€œthat get their deserts”; y=β€œbrave”.

 

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 | 0 | | 15. |–|–|–|–| ––-

| | | | | | 0 | |

| –|– | |–|–|

| 0 | | | | |

––––– ––-

Let β€œpersons” be Universe; m=β€œpatient”;

x=β€œchildren”; y=β€œthat 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 | 0 |

| –|– |

| | 0 | 1 | | 16. |–|–|–|–| ––-

| | 0 | | | | 0 | 1 |

| –|– | |–|–|

| | | | | |

––––– ––-

Let β€œthings” be Universe; m=β€œfat”; x=β€œpigs”;

y=β€œskeletons”.

 

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 | | | | |

| –|– | |–|–|

| | | | 1 | |

––––– ––-

Let β€œcreatures” be Universe; m=β€œmonkeys”;

x=β€œsoldiers”; y=β€œmischievous”.

 

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 | 0 | | 18. |–|–|–|–| ––-

| | | | | | 0 | |

| –|– | |–|–|

| 0 | | | | |

––––– ––-

Let β€œpersons” be Universe; m=β€œjust”;

x=β€œmy cousins”; y=β€œjudges”.

 

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 | |

| –|– | |–|–|

| | | | | |

––––– ––-

Let β€œperiods” be Universe; m=β€œdays”;

x=β€œrainy”; y=β€œtiresome”.

 

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:β€”

β€œAll xm are y” contains β€œSome xm are y”, which contains β€œSome x are y”. Or, in words, β€œAll rainy days are tiresome” contains β€œSome rainy days are tiresome”, which contains β€œSome rainy periods are tiresome”.

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

Altogether, a most unsatisfactory Pair of Premisses!

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| –|– |

| | 1 | | | 20. |–|–|–|–| ––-

| | 0 | 0 | | | 1 | |

| –|– | |–|–|

| 0 | | | 0 | |

––––– ––-

Let β€œthings” be Universe; m=β€œmedicine”;

x=β€œnasty”; y=β€œsenna”.

 

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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| | |

| –|– |

| | 0 | 1 | | 21. |-1-|–|–|–| ––-

| | 0 | | | | | 1 |

| –|– | |–|–|

| | | | | |

––––– ––-

Let β€œpersons” be Universe; m=β€œJews”;

x=β€œrich”; y=β€œPatagonians”.

 

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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| 0 | |

| –|– |

| | - | | 22. |–|–|–|–| ––-

| | 0 | 0 | | | | |

| –|– | |–|–|

| 0 | | | 0 | |

––––– ––-

Let β€œcreatures” be Universe; m=β€œteetotalers”;

x=β€œthat like sugar”; y=β€œnightingales”.

 

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-|–|–|–| ––-

| | 0 | | | | | |

| –|– | |–|–|

| | | | | |

––––– ––-

Let β€œfood” be Universe; m=β€œwholesome”;

x=β€œmuffins”; y=β€œbuns”.

 

No x are m;

All y are m.

 

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

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| | |

| –|– |

| | 0 | 0 | | 24. |–|–|–|–| ––-

| | 1 | | | | | |

| –|– | |–|–|

| | | | 1 | |

––––– ––-

Let β€œcreatures” be Universe; m=β€œthat run well”;

x=β€œfat”; y=β€œgreyhounds”.

 

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 | | | | |

| –|– | |–|–|

| | | | | |

––––– ––-

Let β€œpersons” be Universe; m=β€œsoldiers”;

x=β€œthat march”; y=β€œyouths”.

 

All m are x;

Some y are m’.

 

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

–––––

| 0 | 0 |

| –|– |

| | 0 | 1 | | 26. |–|–|–|–| ––-

| | 0 | | | | 0 | 1 |

| –|– | |–|–|

| 1 | | | 1 | |

––––– ––-

Let β€œfood” be Universe; m=β€œsweet”;

x=β€œsugar”; y=β€œsalt”.

 

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 | |

| –|– | |–|–|

| | | | | |

––––– ––-

Let β€œThings” be Universe; m=β€œeggs”;

x=β€œhard-boiled”; y=β€œcrackable”.

 

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 | 0 | | 28. |–|–|–|–| ––-

| | | | | | 0 | |

| –|– | |–|–|

| 0 | | | | |

––––– ––-

Let β€œpersons” be Universe; m=β€œJews”; x=β€œthat

are in the house”; y=β€œthat 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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| 0 | 0 |

| –|– |

| | - | | 29. |–|–|–|–| ––-

| | | | | | | |

| –|– | |–|–|

| 1 | 0 | | 1 | |

––––– ––-

Let β€œThings” be Universe; m=β€œnoisy”;

x=β€œbattles”; y=β€œthat 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 | 0 | | 30. |–|–|–|–| ––-

| | 1 | | | | 0 | |

| –|– | |–|–|

| 0 | | | 1 | |

––––– ––-

Let β€œpersons” be Universe; m=β€œJews”;

x=β€œmad”; y=β€œRabbis”.

 

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 | |

| –|– | |–|–|

| | | | | |

––––– ––-

Let β€œThings” be Universe; m=β€œfish”;

x=β€œthat can swim”; y=β€œskates”.

 

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 | | | | | |

| –|– | |–|–|

| | | | 1 | |

––––– ––-

Let β€œpeople” be Universe; m=β€œpassionate”;

x=β€œreasonable”; y=β€œorators”.

 

All m are x’; &there4 Some y are x’.

Some

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