The Methodology and Structure of Gottlob Frege's Logico-philosophical Investigations

Abstract

In this essay I try to give a general outline of the structural and methodological characteristics of Frege's logical-philosophical investigations as a whole.Frege's lifelong enterprise is to establish so-called ‘logicism’, i.e., to show ‘that arithmetic is developed logic.’ This project is, philosophically, an attempt to answer the epistemological question concerning what kind of epistemic status an arithmetical proposition has, and Frege's presumptive reply is that arithmetic is a priori and analytic.In order to verify this claim, however, it is necessary to solve the logical-mathematical problem, that is, it must be shown that any arithmetical concept is definable by means of logical terms alone and that the axiomatic system of arithmetic is actually deducible without any gap in inference from the fundamental laws of logic alone. Nevertheless, in the second half of the 19c. there was no logical system powerful enough to reduce arithmetic as a whole. So in order to realize his own project, Frege himself had to carry out a revolutionary revision of traditional Aristotelian logic and construct a completely new logic.Thus one can divide Frege's logical-philosophical investigations roughly into three parts as follows:I. The invention of a new logic, its axiomatic systematization and the development of the logicist philosophy of arithmetic.II. Philosophy of logic.III. Controversies with his distinguished scholars of his time concerning psychologism, empiricism, physicalism, formalism, etc., though I do not take these up in the present paper.