ABSTRACT
Consider the following argument: “My keys are either in my pocket or on the shelf. Therefore, if my keys are not in my pocket, they are on the shelf ”. This argument sounds extremely compelling, but is it logically valid? For it to be logically valid, we would require that the conclusion (i.e., the conditional) follows necessarily from the premise (i.e., the disjunction) by virtue of its form, regardless of its content. Thus, for any propositions A and C, it cannot be the case that the premise “A or C” is true but the conclusion “if not A then C” is false. Whether or not the inference from a disjunction “A or C” to a corresponding conditional “if not A then C” is logically valid depends on how the conditional is understood.
