Logic as science
pp. 113-160
in: Annalisa Coliva, Paolo Leonardi, Sebastiano Moruzzi (eds), Eva Picardi on language, analysis and history, Berlin, Springer, 2018Abstract
Frege's logicist program is a program of scientific unification of arithmetic and logic via the reduction of arithmetic to logic. Logic on this view is the prior science, indeed, the most fundamental of all sciences. The coherence of this picture has been questioned, based on the claim that the Basic Laws of logic are not justifiable as judgements. That Frege's conception of logic suffers from this fatal flaw is incorrect, and in this paper I explore why. The discussion has three primary parts. The first explores Frege's view of logic, distinguishing pure from applied logic. The second delves into Frege's conception of science as applications of logic, and how arithmetic is understood as such an application. The third concerns Frege's account of judgement, and how it carefully distinguishes a judgement from judging, the cognitive act of recognizing truths. The final section turns to how on Frege's account of judgement, the Basic Laws of logic are in fact justified as judgements, and accordingly can serve as the axioms of the science of arithmetic. The paper concludes with reflections on Frege's understanding of scientific unification and reduction, and its relation to his logical realism.
