The meaning of pure mathematics
type: Item
instance of: scholarly article
title: The meaning of pure mathematics
zbMATH Open document ID: 0677.03002
DOI: 10.1007/BF00274069
author: Jan Mycielski
published in: Journal of Philosophical Logic
publication date: 1989-01-01T00:00:00Z
review text: In contrast to formalism and Platonism, being two classical approaches to the treatment of the meaning of pure mathematics, the author proposes intentionalism as a viewpoint according to which ``pure mathematics is a description of finite structures consisting of finitely many individually imagined objects''. Such an opinion, resulting from a sequence of the author's previous papers [see, e.g., J. Symb. Logic 51, 59-62 (1986; Zbl 0609.03003) and ibid. 46, 625-633 (1981; Zbl 0466.03024)], close to some ideas outlined by D. Hilbert and H. Poincaré, is supported by an interesting proof-theoretic consideration and result.
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 00A35
Mathematics Subject Classification ID: 03B30
zbMATH DE Number: 4108718
zbMATH Keywords: meaning of pure mathematics
zbMATH Keywords: intentionalism
zbMATH Keywords: finite structures
MaRDI profile type: Publication
cites work: Hilbert's program relativized; Proof-theoretical and foundational reductions
cites work: Locally finite theories
cites work: Analysis without actual infinity
cites work: Hilbert's program sixty years later
cites work: Partial realizations of Hilbert's program
cites work: Against intuitionism: Constructive mathematics is part of classical mathematics
description: scientific article; zbMATH DE number 4108718