The Platonistic Standpoint in Mathematics

David Booth and Renatus Ziegler
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David Booth: Three Fold Foundation 307
Renatus Ziegler: Mathematisch-Astronomische Sektion am Geotheanum

A chapter in Finsler Set Theory: Platonism and Circularity, 1996, pp 73-77 from Springer

Abstract: Abstract In Wittenberg’s interesting paper Über adäquate Problemstellungen in der Mathematischen Grundlagenforschung [1953] and in the subsequent discussion (Wittenberg et al. [1954]) there is a clear description of a view of mathematics which is called naive or uncritical Platonism, “inhaltlich”, theological, Platonic philosophy, classical philosophy, and by E. Specker [1954] the “an sich” philosophy. It is said, for example, in Wittenberg’s answer that these views embrace the opinion “that this philosophy seizes upon objective relationships, that in itself it describes a factual situation, which as such remains removed from our powers of discretion”. This “Platonic standpoint” is, however, rejected even if with regret. Why? First of all because of the antinomies!

Keywords: Number Class; Imaginary Number; Arbitrary Restriction; Objective Relationship; Classical Philosophy (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-3-0348-9031-1_7

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