ABSTRACT
Although primarily a mathematician in both training and employment, German thinker Gottlob Frege’s writings are thoroughly philosophical in their outlook, style and signi…cance. He despaired at what he saw as the average working mathematician’s inattention to the fundamental questions of their discipline: what the nature of a number is, how our knowledge of them and their properties is possible, what conditions a mathematical argument must meet in order to constitute a legitimate proof, and so on. At least with regard to the proper understanding of arithmetic, he also found the views popular among philosophers of his day severely wanting. Attempting to redress these de…ciencies, Frege produced works that, in time, profoundly changed the practices of logicians, philosophers and mathematicians, though his in¶uence was slow in gaining ground. Most of Frege’s intellectual endeavors grew out of the attempt to get clear about the nature of arithmetical truth. Frege endorsed a position now known as logicism, the thesis that arithmetical truths, when properly analyzed and demonstrated, reveal themselves to be logical or analytical truths. In pursuing this project, Frege developed important and lasting criticisms of rival theories, and innovated a new approach to logic itself so profoundly different from what was prevalent at the time that it is now often described as the fundamental point of departure between contemporary approaches to logic and the Aristotelian tradition which had dominated for over two millennia. In thinking about the proper analysis of mathematical propositions, he also developed views about the logical segmentation of language, the distinction between the sense and reference of linguistic expressions, and the nature of truth, which have been profoundly in¶uential in more recent (especially analytic) philosophy of language and metaphysics.
