On the formalisation of indirect discourse
R. L. Goodstein · Journal of Symbolic Logic · 1958
Mr. L. J. Cohen's interesting example of a logical truth of indirect discourse appears to be capable of a simple formalisation and proof in a variant of first order predicate calculus. His example has the form: If A says that anything which B says is false, and B says that something which A says is true, then something which A says is false and something which B says is true. Let ‘A says x’ be formalised by ‘A(x)’ and let assertions of truth and falsehood be formalised as in the following table. We treat both variables x and predicates A (x) as sentences and add to the familiar axioms and inference rules of predicate logic a rule permitting the inference of A(p) from (x)A(x), where p is a closed sentence. We have to prove that from