Frege's Recipe



Cook RT & Ebert P (2016) Frege's Recipe. Journal of Philosophy, 113 (7), pp. 309-345.

In this paper, we present a formal recipe that Frege followed in his magnum opus “Grundgesetze der Arithmetik” when formulating his definitions. This recipe is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied it in developing the formal material of Grundgesetze. We then show that a version of Basic Law V plays a fundamental role in Frege’s recipe and, in what follows, we will explicate what exactly this role is and explain how it differs from the role played by extensions in his earlier book “Die Grundlagen der Arithmetik”. Lastly, we will demonstrate that this hitherto neglected yet foundational aspect of Frege’s use of Basic Law V helps to resolve a number of important interpretative challenges in recent Frege scholarship, while also shedding light on some important differences between Frege’s logicism and recent neo-logicist approaches to the foundations of mathematics.

Journal of Philosophy: Volume 113, Issue 7

FundersArts and Humanities Research Council, The Royal Society of Edinburgh and Keep Scotland Beautiful
Publication date31/07/2016
Date accepted by journal30/11/2015
PublisherColumbia University

People (1)


Professor Philip Ebert

Professor Philip Ebert

Professor, Philosophy

Projects (2)