Article

Foundations of Science

, Volume 3, Issue 2, pp 207-229

First online:

Unification of Mathematical Theories

  • Krzysztof WójtowiczAffiliated withInstitute of Philosophy, University of Warsow, Krakowskie Przedmiescie 3

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Abstract

In this article the problem of unification of mathematical theories is discussed. We argue, that specific problems arise here, which are quite different than the problems in the case of empirical sciences. In particular, the notion of unification depends on the philosophical standpoint. We give an analysis of the notion of unification from the point of view of formalism, Gödel's platonism and Quine's realism. In particular we show, that the concept of “having the same object of study” should be made precise in the case of mathematical theories. In the appendix we give a working proposal of a certain understanding of this notion.

bridge laws formalism mathematical realism quasi-empiricism reverse mathematics set theory unification