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On mathematical realism and applicability of hyperreals. (English) Zbl 1436.00032

The article is of an epistemological value and relates to the place of Robinsonian nonstandard analysis in modern science.
The article argues mainly with the position of the paper [K. Easwaran and H. Towsner, “Realism in mathematics: the case of the hyperreals”, 9 February 2019 version, http://u.math.biu.ac.il/~katzmik/easwaran19.pdf]. The authors of the latter paper claim that nonstandard analysis is unsuitable for describing physical phenomenа.
The article under review states that the claim of unsuitability is based on inadequate arguments and illustrates this position with a few convincing examples.

MSC:

00A30 Philosophy of mathematics
03H05 Nonstandard models in mathematics
03A05 Philosophical and critical aspects of logic and foundations
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