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On Tarski's Foundations of the Geometry of Solids

Published online by Cambridge University Press:  15 January 2014

Arianna Betti  and
Iris Loeb
Arianna Betti
Affiliation:
Faculty of Philosophy, Vu University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The NetherlandsE-mail: [email protected], E-mail: [email protected]
Iris Loeb
Affiliation:
Faculty of Philosophy, Vu University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The NetherlandsE-mail: [email protected], E-mail: [email protected]
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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 ofTarski'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.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 18 , Issue 2 , June 2012 , pp. 230 - 260
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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