Abstract

This thesis is an investigation of the question of the probative force of the syllogism. It examines on what the probative force of propositions constituting an argument depends and some of the cases in which the conclusion of a syllogism is and is not proven by the premises. The investigation begins by looking at certain preliminary notions associated with arguments in general and categorical syllogisms in particular. In each categorical syllogism are found two claims. One is the claim to truth made by each proposition, and another is the claim to validity made by the syllogism. When each of these claims are fulfilled the syllogism is then sound. The question is whether or not every sound syllogism also represents a proof of the conclusion. John Stuart Mill asserted that no deductive argument including the syllogism can be a proof of the truth of the conclusion on the grounds that the premises presuppose the conclusion. In fact each syllogism is an example of the fallacy of petitio principii which it must by its very nature commit. Alexander Pfänder instead claimed that only in certain cases is the conclusion not proven by the premises, while in other cases the truth of the conclusion is actually proven by the truth of the premises. An independent investigation of the question of the probative force of the syllogism is made. Because of a crucial difference between propositions affirming contingent states of fact and essentially necessary propositions affirming necessary states of fact, it is shown that no syllogism containing contingent propositions can be a proof, while a proof is present in the case of a syllogism containing essentially necessary propositions. When the propositions of an argument are contingent their truth follows from the fact each particular existing instance they refer to actually has what is affirmed by the proposition. Therefore, if the syllogism is valid, the conclusion will refer to at least some of the same particular existing instances on which the truth of each of the premises depends. The premises can be true only if the conclusion is true, and any uncertainty about the truth of the conclusion extends also to the premises. The premises cannot prove the truth of the conclusion since their truth presupposes the truth of the conclusion. Propositions which are essentially necessary are true regardless of whether or not any particular instance exists or will ever exist. Because the state of fact is essentially necessary, the predicate is intelligibly grounded necessarily in the subject. If these kinds of propositions are found in a syllogism, their truth will not depend on the truth of a conclusion. Essentially necessary propositions have probative force, and their presence in a valid argument results in an actual proof of the conclusion.