From Lagrange to Frege: Functions and Expressions

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

Gabriel Sandu
University of Helsinki
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

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.
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 G. Heck - 2007 - Grazer Philosophische Studien 75 (1):27-63.

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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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