The Nature of Mathematical Objects

Carlo Cellucci ()
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Carlo Cellucci: Sapienza University of Rome

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 35-61 from Springer

Abstract: Abstract A traditional question in the philosophy of mathematics is to give an answer to the question: What is the nature of mathematical objects? This chapter considers the main answers that have been given to this question, specifically those according to which mathematical objects are independently existing entities, or abstractions, or logical objects, or simplifications, or mental constructions, or structures, or fictions, or idealizations of sensible things, or idealizations of operations. The chapter also shows the shortcomings of these answers, and considers an alternative answer, according to which mathematical objects are hypotheses introduced to solve mathematical problems by the analytic method.

Keywords: Objects in Platonism; Logicism; Formalism; Intuitionism; Structuralism; Fictionalism; Heuristic view (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_20

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DOI: 10.1007/978-3-031-40846-5_20

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