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. 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. For a treatment of logical paradoxes the dependence of the significance of propositions on the significance of functions is of primary importance. This dependence can best be explained by introducing the two ways of transformation of a propositional function into a proposition, evaluation and generalization.
