Complete Works of Lewis Carroll (213 page)
Read Complete Works of Lewis Carroll Online
Authors: Lewis Carroll
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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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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.
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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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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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14.
|—-|—-|—-|—-| ———-
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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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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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16.
|—-|—-|—-|—-| ———-
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| —-|—- | |—-|—-|
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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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17.
|—-|—-|—-|—-| ———-
| | 1 | 0 | | | | |
| —-|—- | |—-|—-|
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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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18.
|—-|—-|—-|—-| ———-
| | | | | | 0 | |
| —-|—- | |—-|—-|
| 0 | | | | |
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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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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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20.
|—-|—-|—-|—-| ———-
| | 0 | 0 | | | 1 | |
| —-|—- | |—-|—-|
| 0 | | | 0 | |
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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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21.
|-1-|—-|—-|—-| ———-
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| —-|—- | |—-|—-|
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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 | | | | |
| —-|—- | |—-|—-|
| 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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23.
|-1-|—-|—-|—-| ———-
| | 0 | | | | | |
| —-|—- | |—-|—-|
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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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24.
|—-|—-|—-|—-| ———-
| | 1 | | | | | |
| —-|—- | |—-|—-|
| | | | 1 | |
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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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26.
|—-|—-|—-|—-| ———-
| | 0 | | | | 0 | 1 |
| —-|—- | |—-|—-|
| 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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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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28.
|—-|—-|—-|—-| ———-
| | | | | | 0 | |
| —-|—- | |—-|—-|
| 0 | | | | |
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