On Tarski's foundations of the geometry of solids

Bulletin of Symbolic Logic 18 (2):230-260 (2012)
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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, no. 4, pp. 481—540] according to which Tarski has made a certain mistake.

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Arianna Betti
University of Amsterdam

Citations of this work

Ordinary Truth in Tarski and Næss.Joseph Ulatowski - 2016 - In Adrian Kuzniar & Joanna Odrowąż-Sypniewska (eds.), Uncovering Facts and Values. Brill. pp. 67-90.

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References found in this work

Parts: A Study in Ontology.Peter Simons - 1987 - Oxford, England: Oxford University Press.
Parts : a Study in Ontology.Peter Simons - 1987 - Revue de Métaphysique et de Morale 2:277-279.
Process and Reality.Arthur E. Murphy - 1931 - Humana Mente 6 (21):102-106.

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