ABSTRACT
Traditional logic places no restriction upon premises which are allowed in deduction unless they are downright contradictions. It is confident that no inconsistency can result in deriving a conclusion in accordance with intuitively certain principles from non-contradictory premises. That is where traditional logic is wrong. Logical paradoxes show inconsistency to be an outcome of certain unrestricted formulations, even when these are seemingly tautological or analytic definitions, i.e. explications of the connotation of some given term. Consistency alone, without regard for the conditions of formation of the premises, is insufficient to insure discourse from contradiction. Modern logic is superior to its traditional predecessor primarily because it has realized the necessity for restrictive conditions of formation, a requirement for the consideration of significance. Of course, there has always been an instinctive rejection of certain formations of terms as insignificant; for example, in denouncing “Justice is triangular” as an expression which is neither true nor false but meaningless. Yet this sense for discrimination of significance did not find explicit recognition as a principle among traditional logicians; hence they were helpless in facing logical paradoxes. Russell’s 48theory of types, as the first systematic treatment of the paradoxes, was a break with tradition and an introduction to logical restrictions of significance.
