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Authors: Lewis Carroll

Complete Works of Lewis Carroll (212 page)

BOOK: Complete Works of Lewis Carroll

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———- ———-

| 1 | | | 1 | 0 |

11.
|—-|—-| 12.
|—-|—-|

| 1 | | | | 1 |

———- ———-

———-

| | |

13.
No x' are y.
i.e.
|—-|—-|

| 0 | |

———-

| | 0 |

14.
All y' are x'.
i.e.
|—-|—-|

| | 1 |

———-

| | |

15.
Some y' exist.
i.e.
|—-|-1-|

| | |

———-

| 1 | 0 |

16.
All y are x, and all x are y.
i.e.
|—-|—-|

| 0 | |

———-

| | |

17.
No x' exist.
i.e.
|—-|—-|

| 0 | 0 |

———-

| 0 | 1 |

18.
All x are y'.
i.e.
|—-|—-|

| | |

———-

| 0 | |

19.
No x are y.
i.e.
|—-|—-|

| | |

———-

| | |

20.
Some x' are y, and some are y'.
i.e.
|—-|—-|

| 1 | 1 |

———-

| 0 | 1 |

21.
No y exist, and some x exist.
i.e.
|—-|—-|

| 0 | |

———-

| | 1 |

22.
All x' are y, and all y' are x.
i.e.
|—-|—-|

| 1 | 0 |

———-

| 1 | |

17.
Some x are y, and some x' are y'.
i.e.
|—-|—-|

| | 1 |

———-

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.

__________

———————- ———————-

| | | | | |

| —-|—- | | —-|—- |

| | 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.
|—-|—-|—-|—-|

| —-|—- |

| 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.
|—-|—-|—-|—-|

| —-|—- |

| 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.] | | |

———————-

| 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 | |

| —-|—- |

| | |

———————-

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.

| | |