ABSTRACT
This comes from Lewis Carroll’s (C. L. Dodgson’s) Symbolic Logic. We can abbreviate the argument as follows:
(1) If C, then if A then not-B. (2) If A then B.
So (3) not-C.
It seems that, if (2) is true, then the consequent, or main ‘then’ clause, of (1) is false: doesn’t if A then not-B contradict if A then B? But then the antecedent, or principal ‘if ’ clause, of (1), namely C, will be false too. (For, if it is true that if p then q but false that q, then it must be false that p.) Hence (3).
