PARADOXES' SOLVED BY SIMPLE RELEVANCE CRITERIA Paul WEINGARTNER and Gerhard SCHURZ ABSTRACT In this paper we show that a number of paradoxes in the areas of deontic and epistemic logic, value theory, explanation, confirmation, lawlikeness and disposition predicates can be solved by applying two simple relevance criteria based on classical logic: the Aristotelean Criterion (A-relevance) and the"Korner-Criterion (K-relevance). They are roughly as follows: An inference (or the corresponding valid implication) is A-relevant iff there is no propositional variable and no predicate which occurs in the conclusion but not in the premises. And an inference (or in general any valid formula) is K-relevant iff it contains no single occurrence of a sub/ormula which can be replaced by its negation salva validitate. The purpose of this paper is to show that a number of paradoxes in quite different areas can be easily solved by applying two very simple relevance criteria. The paradoxes in question are those in the areas of deontic logic, value theory, epistemic logic, explanation, comrrma- tion, lawlikeness, and disposition predicates. C') The paper is divided into two main parts: In the frrst one we apply the relevance criteria to Standard Propositional Logic and to an extension of it by allowing operators to be attached to propositional variables. In this part we describe the criteria and its properties and show how they rule out paradoxa of Standard Propositional Logic and of the usual systems of Deontic Logic, Value Theory, Logic, and Logic of Voli- tions. In the second part we apply the relevance criteria to First Order Predicate Logic. Here we show how they rule out most of the well (1) Notice that we usc the term "paradox" in a wide sense. The kernel ofaparadox is that some logical consequences of plausible and important axioms or definitions are counterintuitive. For our discussion we concentrate only on standard cases which are known as paradoxical from the philosophical and scientific literature.