Mathematics -- an imagined tool for rational cognition

Boris Čulina

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arXiv · 2306.03909

Mathematics -- an imagined tool for rational cognition

Boris Čulina

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Abstract

Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are imagined objects, some of which, at least approximately, exist in our internal world of activities or we can realize or represent them there; (ii) mathematical truths are not truths about the external world but specifications (formulations) of mathematical conceptions; (iii) mathematics is first and foremost our imagined tool by which, with certain assumptions about its applicability, we explore nature and synthesize our rational cognition of it.

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Boris Čulina. 2023-06-06. Mathematics -- an imagined tool for rational cognition. https://arxiv.org/abs/2306.03909

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