June 2012 On Tarski's foundations of the geometry of solids
Arianna Betti, Iris Loeb
Bull. Symbolic Logic 18(2): 230-260 (June 2012). DOI: 10.2178/bsl/1333560806


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.


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Arianna Betti. Iris Loeb. "On Tarski's foundations of the geometry of solids." Bull. Symbolic Logic 18 (2) 230 - 260, June 2012. https://doi.org/10.2178/bsl/1333560806


Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1246.03024
MathSciNet: MR2931673
Digital Object Identifier: 10.2178/bsl/1333560806

Rights: Copyright © 2012 Association for Symbolic Logic


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Vol.18 • No. 2 • June 2012
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