Bulletin of Symbolic Logic

On Tarski's foundations of the geometry of solids

Arianna Betti and Iris Loeb

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Abstract

The paper [Tarski: Les fondements de la géométrie des corps, Annales de la Société Polonaise de Mathématiques, pp. 29—34, 1929] is in many ways remarkable. We address three historico-philosophical issues that force themselves upon the reader. First we argue that in this paper Tarski did not live up to his own methodological ideals, but displayed instead a much more pragmatic approach. Second we show that Leśniewski's philosophy and systems do not play the significant role that one may be tempted to assign to them at first glance. Especially the role of background logic must be at least partially allocated to Russell's systems of Principia mathematica. This analysis leads us, third, to a threefold distinction of the technical ways in which the domain of discourse comes to be embodied in a theory. Having all of this in place, we discuss why we have to reject the argument in [Gruszczyński and Pietruszczak: Full development of Tarski's Geometry of Solids, The Bulletin of Symbolic Logic, vol. 4 (2008), no. 4, pp. 481—540] according to which Tarski has made a certain mistake.

Article information

Source
Bull. Symbolic Logic, Volume 18, Issue 2 (2012), 230-260.

Dates
First available in Project Euclid: 4 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1333560806

Digital Object Identifier
doi:10.2178/bsl/1333560806

Mathematical Reviews number (MathSciNet)
MR2931673

Zentralblatt MATH identifier
1246.03024

Citation

Betti, Arianna; Loeb, Iris. On Tarski's foundations of the geometry of solids. Bull. Symbolic Logic 18 (2012), no. 2, 230--260. doi:10.2178/bsl/1333560806. https://projecteuclid.org/euclid.bsl/1333560806


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