ABSTRACT
The discussion of material equivalence began with considerations about forms of inference. In this chapter, the authors call any syllogism, at least one of whose premises is an equivalence, an equivalential syllogism. The general forms are the same as for the hypothetical syllogism. We have seen that ‘If and only if p, then q’ has, as it were, two components – ‘if p then q’, and ‘only if p then q’. The first of these asserts that the truth of p is a sufficient condition for the truth of q, while the second asserts that the truth of p is a necessary condition for the truth of q. Inference from the absence of a sufficient condition to absence of result is invalid, since it amounts to Denying the Antecedent in a mixed hypothetical syllogism.
