Frege's Conception of Logic

Abstract

AbstractGoldfarb depicts salient differences between Frege’s and the contemporary philosophical conceptions of logic. On the contemporary conception, logical properties such as validity and consequence are metalinguistic properties of schemata determined by the truth values that result from interpretations of their placeholders. They thus require a truth predicate for their expression, and, moreover, apply only indirectly to actual statements, through the use of Tarskian semantic disquotational facts. On Frege’s universalist conception, in contrast, logical laws are maximally general truths, differing from other truths only in generality. Goldfarb argues that Frege was precluded from adopting the schematic conception by two central aspects of his views. First, Frege doubted that truth is a genuine property, and that the use of a truth predicate expresses genuine claims. Second, logic for Frege constitutes the ultimate standards of justification, and must be applicable to any subject matter without presupposing other truths, in particular independently of semantic facts. The latter point shows that for Frege what counts as a law of logic is not explicable by appeal to any more fundamental facts. Goldfarb argues also that Frege’s conception of the role of logic in justification shows that he is not vulnerable to the type of regress objections against logicism first presented by Poincaré. Finally, Goldfarb argues that although Frege in the end must within his conception of logic take our grasp of inference rules to be non-propositional, deductive justification under the schematic conception involves a regress of assumptions of stronger set theories that Frege’s conception can avoid.