Foundations of Science

, Volume 3, Issue 2, pp 207–229

Unification of Mathematical Theories

  • Krzysztof Wójtowicz
Article

DOI: 10.1023/A:1009665705969

Cite this article as:
Wójtowicz, K. Foundations of Science (1998) 3: 207. doi:10.1023/A:1009665705969
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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 lawsformalismmathematical realismquasi-empiricismreverse mathematicsset theoryunification

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Krzysztof Wójtowicz
    • 1
  1. 1.Institute of PhilosophyUniversity of Warsow, Krakowskie Przedmiescie 3WarszawaPoland