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

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Author: Lewis Carroll
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finding the correct Conclusion, and then observing that the Conclusion, offered to us, is neither identical with it nor a part of it.

30. When the offered Conclusion is PART of the correct Conclusion. In this case, we may call it a ‘Defective Conclusion’.

2. Half of Smaller Diagram.

Propositions represented.

__________

––- ––-

| | | | | |

1. | | 1 | 2. | 0 | 1 |

| | | | | |

––- ––-

| | | | | |

3. | 1 | 1 | 4. | 0 | 0 |

| | | | | |

––- ––-

| | | | | |

5. | 1 | 6. | | 0 |

| | | | | |

––- ––-

––-

| | |

7. | 1 | 1 | It might be thought that the proper

| | |

––- ––-

| | |

––-

x exist”: but this is really contained in “some x are y’.” To put a red counter on the division-line would only tell us “ONE OF THE compartments is occupied”, which we know already, in knowing that ONE is occupied.

––-

| | |

8. No x are y. i.e. | 0 | |

| | |

––-

| | |

9. Some x are y’. i.e. | | 1 |

| | |

––-

| | | 10. All x are y. i.e. | 1 | 0 |

| | |

––-

| | | 11. Some x are y. i.e. | 1 | |

| | |

––-

| | | 12. No x are y. i.e. | 0 | |

| | |

––-

| | | 13. Some x are y, and some are y’. i.e. | 1 | 1 |

| | |

––-

| | | 14. All x are y’. i.e. | 0 | 1 |

| | |

––-

–

| | 15. No y are x’. i.e. |–|

| 0 |

–

| 1 | 16. All y are x. i.e. |–|

| 0 |

–

| 0 | 17. No y exist. i.e. |–|

| 0 |

–

| | 18. Some y are x’. i.e. |–|

| 1 |

–

| | 15. Some y exist. i.e. |-1-|

| |

–

3. Half of Smaller Diagram.

Symbols interpreted.

__________

1. No x are y’.

2. No x exist.

3. Some x exist.

4. All x are y’.

5. Some x are y. i.e. Some good riddles are hard.

6. All x are y. i.e. All good riddles are hard.

7. No x exist. i.e. No riddles are good.

8. No x are y. i.e. No good riddles are hard.

9. Some x are y’. i.e. Some lobsters are unselfish.

10. No x are y. i.e. No lobsters are selfish.

11. All x are y’. i.e. All lobsters are unselfish.

12. Some x are y, and some are y’. i.e. Some lobsters are selfish, and some are unselfish.

13. All y’ are x’. i.e. All invalids are unhappy.

14. Some y’ exist. i.e. Some people are unhealthy.

15. Some y’ are x, and some are x’. i.e. Some invalids are happy, and some are unhappy.

16. No y’ exist. i.e. Nobody is unhealthy.

4. Smaller Diagram.

Propositions represented.

__________

––- ––-

| 1 | | | | |

1. |–|–| 2. |–|–|

| 0 | | | 1 | |

––- ––-

| | | | | 1 |

3. |–|–| 4. |–|–|

| | 0 | | | |

––- ––-

| | 1 | | | |

5. |–|–| 6. |–|–|

| | | | 0 | |

––- ––-

| | | | | |

7. |–|–| 8. |–|–|

| | 1 | | 0 | 1 |

––- ––-

| | | | | |

9. |–|-1-| 10. |–|–|

| | | | 0 | 0 |

––- ––-

| 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 | |

| –|– |

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