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Appears in Collections:Law and Philosophy Journal Articles
Peer Review Status: Refereed
Title: Frege's Recipe (Forthcoming)
Authors: Ebert, Philip
Cook, Roy T
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Issue Date: 2016
Citation: Ebert P & Cook RT (2016) Frege's Recipe (Forthcoming), Journal of Philosophy.
Abstract: First paragraph: This paper has three aims: first, we present a formal recipe that Frege followed in his magnum opus Grundgesetze der Arithmetik when formulating definitions. This generalized recipe, as we will call it, is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied the recipe in developing the formal material of Grundgesetze. Second, we will show that a version of Basic Law V plays a fundamental role in the generalized recipe. We will explicate exactly what this role is and how it differs from the role played by extensions in Die Grundlagen der Arithmetik. Third, and finally, 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.
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