On Tarski's Foundations of the Geometry of Solids

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...

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Bibliographic Details
Published in:The bulletin of symbolic logic 2012-06, Vol.18 (2), p.230-260
Main Authors: Betti, Arianna, Loeb, Iris
Format: Article
Language:English
Subjects:
Axioms
Discourse communities
Geometric shapes
Geometry
Mathematical logic
Mereology
Philosophical axioms
Primitive notions
Spheres
Universes of discourse
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Summary: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 Lesniewski'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.
ISSN:1079-8986
1943-5894
DOI:10.2178/bsl/1333560806