Page:Carroll - Game of Logic.djvu/81

Ch. III. § 5.]
65

§ 5. Smaller Diagram.
Symbols interpreted.

1. Some ${\displaystyle y}$ are not-${\displaystyle x}$,
or, Some not-${\displaystyle x}$ are ${\displaystyle y}$.

2. No not-${\displaystyle x}$ are not-${\displaystyle y}$,
or, No not-${\displaystyle y}$ are not-${\displaystyle x}$.

3. No not-${\displaystyle y}$ are ${\displaystyle x}$.

4. No not-${\displaystyle x}$ exist. i.e. No Things are not-${\displaystyle x}$.

5. No ${\displaystyle y}$ exist. i.e. No houses are two-storied.

6. Some ${\displaystyle x^{\prime }}$ exist. i.e. Some houses are not built of brick.

7. No ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$. Or, no ${\displaystyle y^{\prime }}$ are ${\displaystyle x}$. 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 ${\displaystyle x^{\prime }}$ are ${\displaystyle y^{\prime }}$. i.e. All houses, that are not built of brick, are not two-storied.

9. Some ${\displaystyle x}$ are ${\displaystyle y}$, and some are ${\displaystyle y^{\prime }}$. i.e. Some fat boys are active, and some are not.

10. All ${\displaystyle y^{\prime }}$ are ${\displaystyle x^{\prime }}$. i.e. All lazy boys are thin.

11. All ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$, and all ${\displaystyle y^{\prime }}$ are x. i.e. All fat boys are lazy, and all lazy ones are fat.

[See pp. 46, 7]