Academic Journal
Mathematics - an Imagined Tool for Rational Cognition. Part I
| Title: | Mathematics - an Imagined Tool for Rational Cognition. Part I |
|---|---|
| Authors: | Čulina, Boris |
| Source: | Annals of mathematics and philosophy. 2(1):185-213 |
| Publisher Information: | 2024. |
| Publication Year: | 2024 |
| Subject Terms: | applicability of mathematics, mathematical intuition, mathematical models, mathematical objects, mathematical truths |
| Description: | By 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. |
| Document Type: | Article |
| ISSN: | 3038-6381 |
| Access URL: | https://mxphi.com/wp-content/uploads/2025/02/BC.pdf |
| Accession Number: | edsair.dris...01492..3d7be8c667d0796f7daf05c203a4f482 |
| Database: | OpenAIRE |
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