From Lagrange to Frege: Functions and Expressions

In Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur (eds.), Functions and Generality of Logic. Springer Verlag (2015)

Authors
Gabriel Sandu
University of Helsinki
Hourya Benis Sinaceur
Centre National de la Recherche Scientifique
Marco Panza
Centre National de la Recherche Scientifique
Abstract
Both Frege's Grundgesetze, and Lagrange's treatises on analytical functions pursue a foundational purpose. Still, the former's program is not only crucially different from the latter's. It also depends on a different idea of what foundation of mathematics should be like . Despite this contrast, the notion of function plays similar roles in their respective programs. The purpose of my paper is emphasising this similarity. In doing it, I hope to contribute to a better understanding of Frege's logicism, especially in relation to its crucial differences with a set-theoretic foundational perspective. This should also spread some light on a question arisen by J. Hintikka and G. Sandu in a widely discussed paper, namely whether Frege should or should not be credited with the notion of arbitrary function underlying our standard interpretation of second-order logic. In section 1, I account for Lagrange's notion of function. In section 2, I advance some remarks on connected historical matters. This will provide an appropriate framework for discussing the role played by the notion of function in Frege's Grundgesetze. Section 3 is devoted to this. Some concluding remarks will close the paper
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References found in this work BETA

Elucidation and Nonsense in Frege and Early Wittgenstein.James Conant - 2000 - In Alice Crary & Rupert J. Read (eds.), The New Wittgenstein. Routledge. pp. 174--217.
Frege and Semantics.Richard Heck - 2007 - Grazer Philosophische Studien 75 (1):27-63.
Objectivity and Objecthood: Frege's Metaphysics of Judgment.Thomas Ricketts - 1986 - In Hintikka J. & Haaparanta L. (eds.), Frege Synthesized. Kluwer Academic Publishers. pp. 65--95.

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Citations of this work BETA

The Epistemological Question of the Applicability of Mathematics.Paola Cantù - 2018 - Journal for the History of Analytical Philosophy 6 (3).

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