Antinomies and paradoxes and their solutions

Almost every paper in the area of philosophy or logic can start with the statement that the formulation of the problem in question has different meanings or different aspects. And this is very much the case, too, for a treatment of antinomies and paradoxes. In this paper I shall adopt the following terminology concerning the terms "antinomy" and "paradox." I shall speak of an "antinomy" (or a "logical paradox") if a law of logic is violated, i.e., if logical validity is violated, whereas I shall speak of paradox (perhaps better: pragmatical paradox, in contradistinction to semantical and logical paradox) if no logical law is violated but some prima facie reasonable or even neces sary assumption or some pragmatic rule of thinking, which both go beyond questions of validity of logical laws, are violated. In the case-of a violation of a logical law I shall speak of a fallacy if the application of an invalid mode of inference leads to either a false or a true conclusion. On the other hand, I adopt Quine's terminology1 and speak of a 'falsidical paradox' if the application of an invalid mode of inference leads to a false or inconsistent conclusion.