On Tarski's foundations of the geometry of solids

Abstract

The paper (Tarski:Lesfondementsdelageometriedescorps,AnnalesdelaSoci´´ Polonaise de Math´ ematiques, 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 Lephilosophy 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 (Gruszczyand 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.