Abstract
On the 1st of May 1915 the philosopher Ludwig Wittgenstein wrote in his diary the following sentence: ‘Not to occupy himself with problems which do not concern him is one of the principal skills of the philosopher’.2 But does this not also apply to the problems of the individual sciences and especially to those of mathematics? Wittgenstein does not seem to have been of this opinion, at least not with regard to the foundations of mathematics; at that time and for years to come he occupied himself intensively with the foundations of mathematics. Since he did not, however, inform us of his reasons for so doing, I would like, once again, to make the question of whether the basic principles of mathematics are a legitimate subject for philosophical investigation the subject of my own deliberations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cf. Friedrich Kambartel, Erfahrung und Struktur, Bausteine zu einer Kritik des Empirismus und Formalismus, Frankfurt a.M. 1968, p. 235.
Thoralf Skolem, “Some remarks on the foundation of set theory”, Proc. Int. Congr. of Mathematicians (Cambridge, Mass. 1950) Providence, R.I. 1952, vo1.2, p. 701f.
Cf. Heinrich Scholz, “Die Sonderstellung der Logik-Kalkule irn Bereich der elementaren logistischen Kalkiilforschung”, in: Travaux du XIe Congrès International de Philosophie(Congres Descartes), 6: Logique et Mathèmatiques, Paris 1937, 20, pp. 40–42
Paul Lorenzen, “Equality and Abstraction”, Ratio 4(1962), pp. 77–81
Paul Bernays, “Die Philosophie der Mathematik und die Hilbertsche Beweistheorie”, Blatter fur Deutsche Philosophie 4 (1930/31), pp. 326–367
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Kluwer Academic Publishers
About this chapter
Cite this chapter
Thiel, C. (1989). Philosophy and the Problem of the Foundations of Mathematics. In: Butts, R.E., Brown, J.R. (eds) Constructivism and Science. The University of Western Ontario Series in Philosophy of Science, vol 44. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0959-5_6
Download citation
DOI: https://doi.org/10.1007/978-94-009-0959-5_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6921-2
Online ISBN: 978-94-009-0959-5
eBook Packages: Springer Book Archive