Symbolic Logic

by Lewis Carroll

Representation of Propositions of Relation in terms of x and m, or of y and m.

Let us take, first, the Pair of Converse Propositions

“Some x are m” = “Some m are x.”

We know that each of these is equivalent to the Proposition of Existence “Some xm exist”, which we already know how to represent.

Similarly for the seven similar Pairs, in terms of x and m, or of y and m.

Let us take, next, the Pair of Converse Propositions

“No x are m” = “No m are x.”

We know that each of these is equivalent to the Proposition of Existence “No xm exist”, which we already know how to represent.