Analysis of various practices of referring in classical or non standard mathematics

Yves Péraire ()
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Yves Péraire: Université Blaise Pascal (Clermont II), Département de Mathématiques

Chapter 3 in The Strength of Nonstandard Analysis, 2007, pp 33-46 from Springer

Abstract: Abstract The thesis underlying this text is that the various approaches of mathematics, both the conventional or the diverse non standard approaches, pure or applied, are characterized primarily by their mode of referring and in particular by the more or less important use of the reconstructed reference, the reference to the sets and collections, that I will distinguish from the direct reference, the reference to the world of the facts in a broad sense. The direct reference, in traditional mathematics as well as in non standard mathematics (for the main part) is ritually performed in the classical form of modelling, consisting in confronting the facts to a small paradise (a set) correctly structured. So the discourse on the model acts like a metaphor of the modelized reality.

Keywords: Traditional Mathematic; Standard Mathematics; Reconstructed Reference; Variable Selon; Colombeau Generalize Function (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-211-49905-4_3

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