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date: 15 May 2021

Abstract and Keywords

This article is organized around logicism's answers to the following questions: What is the basis for our knowledge of the infinity of the numbers? How is arithmetic applicable to reality? Why is reasoning by induction justified? Although there are, as is seen in this article, important differences, the common thread that runs through all three of the authors discussed in this article their opposition to the Kantian thesis that reflection on reasoning with mere concepts (i.e., without attention to intuitions formed a priori) can never succeed in providing satisfactory answers to these three questions. This description of the core of the view differs from more usual formulations which represent the opposition to Kant as an opposition to the contention that mathematics in general, and arithmetic in particular, are synthetic a priori rather than analytic.

Keywords: logicism, infinity of the numbers, arithmetic, Kantian thesis, mathematics, Russell

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