Synthese 102 (3):319 - 361 (1995)

Authors
Jamie Tappenden
University of Michigan, Ann Arbor
Abstract
This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and geometry and the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer.
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DOI 10.1007/BF01064120
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References found in this work BETA

Critique of Pure Reason.I. Kant - 1787/1998 - Philosophy 59 (230):555-557.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford, England: Oxford University Press.
Kant and the Exact Sciences.Michael Friedman - 1990 - Harvard University Press.

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Citations of this work BETA

Marriages of Mathematics and Physics: A Challenge for Biology.Arezoo Islami & Giuseppe Longo - 2017 - Progress in Biophysics and Molecular Biology 131:179-192.
Frege’s Philosophy of Geometry.Matthias Schirn - 2019 - Synthese 196 (3):929-971.
Frege on the Foundation of Geometry in Intuition.Jeremy Shipley - 2015 - Journal for the History of Analytical Philosophy 3 (6).

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