The knowing mathematician
type: Item
instance of: scholarly article
title: The knowing mathematician
zbMATH Open document ID: 0543.01006
DOI: 10.1007/BF00485616
author: Nicolas D. Goodman
published in: Synthese
publication date: 1984-01-01T00:00:00Z
review text: The author diagnoses a ''new foundational crisis'' in mathematics, caused by external conditions of today mathematical working as well as by problems of the usual set-theoretic foundation, especially its reductionistic tendency. In analogy to two theories in modern physics, relativity and quantum mechanics, he claims that a ''similar dualistic view on the foundations of mathematics is both possible and desirable''. One essential element of such a view must be the inclusion of the (researching) human subject - the ''knowing mathematician''. The author refers to a formalization of such a view, published in \textit{S. Shapiro} (ed.), Intensional Mathematics, North-Holland Publ. Co. (1984). Besides the concept of ''knowability'', ''properties'', instead of extensionally defined sets, play an important role in this theory. The aim is the ''reintroduction of intensional epistemic notions into mathematical practice''.
Mathematics Subject Classification ID: 01A65
Mathematics Subject Classification ID: 00A30
zbMATH DE Number: 3863153
zbMATH Keywords: foundational crisis
zbMATH Keywords: intensional epistemic notions
MaRDI profile type: Publication
cites work: Q5573965
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full work available at URL: https://doi.org/10.1007/bf00485616
OpenAlex ID: W4245777693
description: scientific article; zbMATH DE number 3863153