On Showing Invalidity

Abstract

In studying logic, one learns how to establish that a conclusion follows from a set of premises. Those arguments that exhibit one of the valid forms of the deductive system under study are valid. There may be questions about what forms are exhibited by various arguments - Is this English conditional (or any other) really truth-functional? Is this disjunction really inclusive? Are the English predicates used with uniform meaning? - but none of these problems undermine the claim that if an argument exhibits a valid form of a system for deductive logic, then that argument is valid.When we move on to study invalidity, however, we find that the situation is not parallel. Every argument is an instance of some invalid argument forms, and we cannot say that every instance of every invalid form is invalid.