Abstract
The paper argues that Frege’s primary foundational purpose concerning arithmetic was neither that of making natural numbers logical objects, nor that of making arithmetic a part of logic, but rather that of assigning to it an appropriate place in the architectonics of mathematics and knowledge, by immersing it in a theory of numbers of concepts and making truths about natural numbers, and/or knowledge of them transparent to reason without the medium of senses and intuition.
The paper originated in a discussion during a conference at Keio Univ. (Tokyo), and preliminary versions of it were presented at the IHPST (Paris), Univ. San Raffaele (Milano), Chapman Univ. (Orange, CA), Univ. de Lorraine (Nancy), and the Czech Acad. of Sci., Dept. of Philophy (Prague). I thank the audience of all these talks for useful objections and suggestions that greatly helped me to improve the paper. Special thanks to J. Bertran-San Millán, F. Boccuni, A. Coliva, G. Heinzmann, R. May, A. Sereni, D. Struppa, G. Sundholm, J. Tappenden and P. Wagner.
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Panza, M. (2018). Was Frege a Logicist for Arithmetic?. In: Coliva, A., Leonardi, P., Moruzzi, S. (eds) Eva Picardi on Language, Analysis and History. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-95777-7_5
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DOI: https://doi.org/10.1007/978-3-319-95777-7_5
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