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A Strict Finite Foundation for Geometric Constructions

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Abstract

Strict finitism is a minority view in the philosophy of mathematics. In this paper, we develop a strict finite axiomatic system for geometric constructions in which only constructions that are executable by simple tools in a small number of steps are permitted. We aim to demonstrate that as far as the applications of synthetic geometry to real-world constructions are concerned, there are viable strict finite alternatives to classical geometry where by one can prove analogs to fundamental results in classical geometry. We consider this as one of many early steps investigating the extent to which strict finite foundations can be developed for the application of mathematics to the real-world.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rhode Island College, 600 Mount Pleasant Ave., Providence, RI, 02908, USA

    John R. Burke

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  1. John R. Burke
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Correspondence to John R. Burke.

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Burke, J.R. A Strict Finite Foundation for Geometric Constructions. Axiomathes 32 (Suppl 2), 499–527 (2022). https://doi.org/10.1007/s10516-022-09616-4

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  • DOI: https://doi.org/10.1007/s10516-022-09616-4

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