-
PDF
- Split View
-
Views
-
Cite
Cite
DIETER LOHMAR, Elements of a Phenomenological Justification of Logical Principles, including an Appendix with Mathematical Doubts concerning some Proofs of Cantor on the Transfiniteness of the Set of Real Numbers, Philosophia Mathematica, Volume 10, Issue 2, June 2002, Pages 227–250, https://doi.org/10.1093/philmat/10.2.227
Close - Share Icon Share
Abstract
There are two main objections against epistemological foundation of logical principles: 1. Every argument for them must necessarily make use of them. 2. Logical principles cannot be abstracted from experience because they imply elements of meaning that exceed in principle our finite experience (like universality & necessity). In opposition to these objections I argue for Husserl's thesis that logic needs a theory of experience as a foundation. To show the practicability of his attempt I argue that he is able to avoid the two circles mentioned. Motivated by this investigation the Appendix presents some mathematical doubts concerning the proofs by Cantor of the transfiniteness of the set of real numbers.
Author notes
†This article goes back to a paper presented at the symposium Phenomenology and Mathematics, sponsored by ZENO, the Leiden-Utrecht Research Institute for Philosophy, 18 December, 1999. I have to thank all participants in this symposium for their helpful comments. I am grateful especially to Richard Tieszen for his critical comments and his help with the text. An earlier German version of this article is to be found in ‘Warum braucht die Logik eine Theorie der Erfahrung?’ in R. Dostal, L. Embree, J. N. Mohanty, J. J. Kockelmanns and O. K. Wiegand, eds., Phenomenology on German Idealism, Hermcneutics and Logic Dordrecht: Kluwer, 1999, pp. 149-169.
