Complete Works of Lewis Carroll (212 page)
Read Complete Works of Lewis Carroll Online
Authors: Lewis Carroll
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11.
|—-|—-| 12.
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13.
No x' are y.
i.e.
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14.
All y' are x'.
i.e.
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15.
Some y' exist.
i.e.
|—-|-1-|
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| 1 | 0 |
16.
All y are x, and all x are y.
i.e.
|—-|—-|
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17.
No x' exist.
i.e.
|—-|—-|
| 0 | 0 |
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| 0 | 1 |
18.
All x are y'.
i.e.
|—-|—-|
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| 0 | |
19.
No x are y.
i.e.
|—-|—-|
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20.
Some x' are y, and some are y'.
i.e.
|—-|—-|
| 1 | 1 |
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| 0 | 1 |
21.
No y exist, and some x exist.
i.e.
|—-|—-|
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| | 1 |
22.
All x' are y, and all y' are x.
i.e.
|—-|—-|
| 1 | 0 |
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| 1 | |
17.
Some x are y, and some x' are y'.
i.e.
|—-|—-|
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5.
Smaller Diagram.
Symbols interpreted.
__________
1.
Some y are not-x, or, Some not-x are y.
2.
No not-x are not-y, or, No not-y are not-x.
3.
No not-y are x.
4.
No not-x exist.
i.e.
No Things are not-x.
5.
No y exist.
i.e.
No houses are two-storied.
6.
Some x' exist.
i.e.
Some houses are not built of brick.
7.
No x are y'.
Or, no y' are x.
i.e.
No houses, built of brick, are other than two-storied.
Or, no houses, that are not two-storied, are built of brick.
8.
All x' are y'.
i.e.
All houses, that are not built of brick, are not two-storied.
9.
Some x are y, and some are y'.
i.e.
Some fat boys are active, and some are not.
10.
All y' are x'.
i.e.
All lazy boys are thin.
11.
All x are y', and all y' are x.
i.e.
All fat boys are lazy, and all lazy ones are fat.
12.
All y are x, and all x' are y.
i.e.
All active boys are fat, and all thin ones are lazy.
13.
No x exist, and no y' exist.
i.e.
No cats have green eyes, and none have bad tempers.
14.
Some x are y', and some x' are y.
Or some y are x', and some y' are x.
i.e.
Some green-eyed cats are bad-tempered, and some, that have not green eyes, are good-tempered.
Or, some good-tempered cats have not green eyes, and some bad-tempered ones have green eyes.
15.
Some x are y, and no x' are y'.
Or, some y are x, and no y' are x'.
i.e.
Some green-eyed cats are good-tempered, and none, that are not green-eyed, are bad-tempered.
Or, some good-tempered cats have green eyes, and none, that are bad-tempered, have not green eyes.
16.
All x are y', and all x' are y.
Or, all y are x', and all y' are x.
i.e.
All green-eyed cats are bad-tempered and all, that have not green eyes, are good-tempered.
Or, all good-tempered ones have eyes that are not green, and all bad-tempered ones have green eyes.
6.
Larger Diagram.
Propositions represented.
__________
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| | | | | |
| —-|—- | | —-|—- |
| | 0 | 0 | | | | | | |
1.
|—-|—-|—-|—-| 2.
|-1-|—-|—-|—-|
| | | | | | | | | |
| —-|—- | | —-|—- |
| | | | | |
———————- ———————-
———————- ———————-
| | | | | 0 |
| —-|—- | | —-|—- |
| | 0 | 0 | | | | | | |
3.
|—-|—-|—-|—-| 4.
|—-|—-|—-|—-|
| | - | | | | | | |
| —-|—- | | —-|—- |
| | | | | 0 |
———————- ———————-
———————- ———————-
| 0 | | | | |
| —-|—- | | —-|—- |
| | 0 | 0 | | | | 0 | 1 | |
5.
|—-|—-|—-|—-| 6.
|—-|—-|—-|—-|
| | 1 | | | | | 0 | | |
| —-|—- | | —-|—- |
| 0 | | | | |
———————- ———————-
———————- ———————-
| | | | | 0 |
| —-|—- | | —-|—- |
| | 0 | 0 | | | | | | |
7.
|—-|—-|—-|—-| 8.
|—-|—-|—-|—-|
| | 0 | 1 | | | | 0 | 0 | |
| —-|—- | | —-|—- |
| | | | | 0 |
———————- ———————-
———————-
| | |
| —-|—- |
| | 0 | 0 | |
9.
No x are m.
i.e.
|—-|—-|—-|—-|
| | 0 | | |
| —-|—- |
| | |
———————-
———————-
| | |
| —-|—- |
| | | | |
10.
Some m' are y.
i.e.
|-1-|—-|—-|—-|
| | | | |
| —-|—- |
| | |
———————-
———————-
| | |
| —-|—- |
| | | 0 | |
11.
All y' are m'.
i.e.
|—-|—-|—-|-1-|
| | | 0 | |
| —-|—- |
| | |
———————-
———————-
| | |
| —-|—- |
| | 0 | 0 | |
12.
All m are x'.
i.e.
|—-|—-|—-|—-|
| | 1 | |
| —-|—- |
| | |
———————-
———————-
| 0 | |
| —-|—- |
| | 0 | 0 | |
13.
No x are m; i.e.
|—-|—-|—-|—-|
All y are m.
| | 1 | | |
| —-|—- |
| 0 | |
———————-
———————-
| 0 | 0 |
| —-|—- |
| | | | |
14.
All m' are y; i.e.
|—-|—-|—-|—-|
No x are m'.
| | | | |
| —-|—- |
| 1 | 0 |
———————-
———————-
| 0 | 0 |
| —-|—- |
| | 1 | 0 | |
15.
All x are m; i.e.
|—-|—-|—-|—-|
No m are y'.
| | | 0 | |
| —-|—- |
| | |
———————-
———————-
| 0 | 0 |
| —-|—- |
| | | | |
16.
All m' are y'; i.e.
|—-|—-|—-|—-|
No x are m'.
| | | | |
| —-|—- |
| 0 | 1 |
———————-
———————-
| 0 | 0 |
| —-|—- |
| | 1 | 0 | |
17.
All x are m; i.e.
|—-|—-|—-|—-|
All m are y.
| | | 0 | |
| —-|—- |
[See remarks on No.
7, p.
60.] | | |
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———————-
| 0 | |
| —-|—- |
| | | | |
18.
No x' are m; i.e.
|—-|—-|—-|—-|
No m' are y.
| | 0 | 0 | |
| —-|—- |
| 0 | |
———————-
———————-
| | |
| —-|—- |
| | 1 | 0 | |
19.
All m are x; i.e.
|—-|—-|—-|—-|
All m are y.
| | 0 | 0 | |
| —-|—- |
| | |
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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-who-sent-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
———————- | | | | —-|—- | | | 1 | 0 | | |—-|—-|—-|—-| | | 0 | 0 | | | —-|—- | | | | ———————-
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'.