Symbolic Logic

by Lewis Carroll

15. xm₀ † m′y₀ ¶ xy₀ [Fig. I.
i.e. “No x are y.”

16. x₁m₀ † y₁m′₀ ¶ (x₁y₀ † y₁x₀) [Fig. I (β).
i.e. “All x are y′ and all y are x′.”

17. xm₀ † m′₁y′₀ ¶ xy′₀ [Fig. I.
i.e. “No x are y′.”

18. xm′₀ † my₀ ¶ xy₀ [Fig. I.
i.e. “No x are y.”

19. m₁x′₀ † m₁y₀ ¶ xy′₁ [Fig. III.
i.e. “Some x are y′.”

20. mx₀ † m′₁y′₀ ¶ xy′₀ [Fig. I.
i.e. “No x are y′.”

21. x₁m′₀ † m′y₁ ¶ x′y₁ [Fig. II.
i.e. “Some x′ are y.”

22. xm₁ † y₁m′₀ ¶ nothing.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]

23. m₁x′₀ † ym₁ ¶ xy₁ [Fig. II.
i.e. “Some x are y.”

24. xm₀ † y₁m′₀ ¶ y₁x₀ [Fig. I (α).
i.e. “All y are x′.”