NPP > CONFERENCES > BIYCLC > Vol. 4 (2008)

#### Article Title

#### Keywords

philosophy, analytic philosophy, philosophy of mathematics

#### Abstract

The traditional view regarding the philosophy of mathematics in the twentieth century is the dogma of three schools: Logicism, Intuitionism and Formalism. The problem with this dogma is not, at least not first and foremost, that it is wrong, but that it is biased and essentially incomplete. 'Biased' because it was formulated by one of the involved parties, namely the logical empiricists - if I see it right - in order to make their own position look more agreeable by comparison with Intuitionism and Formalism. 'Essentially incomplete' because there was - and still exists - beside Frege's Logicism, Brouwer's Intuitionism and Hilbert's Formalism at least one further position, namely Husserl's phenomenological approach to the foundations of arithmetic, which is also philosophically interesting. In what follows, I want to do two things: First, I will show that the standard dogma regarding the foundations of mathematics is not only incomplete, but also inaccurate, misleading and basically wrong with respect to the three schools themselves. In doing this I hope to make room for Husserl and his phenomenological approach as a viable alternative in the foundations of arithmetic. Second, I will show how Husserl's phenomenological point of view is a position that fits exactly in between Frege's "logicism", properly understood, and Hilbert's mature proof theory, in which his so called "formalism" turns out to be only a means to an end and not a goal in itself.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Majer, Ulrich
(2008)
"Husserl Between Frege’s Logicism And Hilbert’s Formalism,"
*Baltic International Yearbook of Cognition, Logic and Communication*:
Vol. 4.
http://dx.doi.org/10.4148/biyclc.v4i0.128

#### References

Føllesdal, Dagﬁnn. 1994. ‘Husserl and Frege: A Contribution to Elucidating the Origins of Phenomenological Philosophy’. In Leila Haaparanta (ed.) ‘Mind, Meaning and Mathematics’, No. 237 in Synthese Library. Kluwer.

Frege, Gottlob. 1880/81. ‘Booles rechnende Logik und die Begriffsschrift’. In Hermes et al. 1969.

Frege, Gottlob. 1882a. ‘Über die die wissenschaftliche Berechtigung einer Begriffsschrift’. Zeitschrift für Philosophie und philosophische Kritik 81 S: 48–56.

Frege, Gottlob. 1882b. ‘Booles logische Formelsprache und meine Begriffsschrift’. In Hermes et al. 1969.

Frege, Gottlob. 1882/83. ‘Über den Zweck der Begriffsschrift’. Supp. zur Jenaische Zeitschrift für Naturwissenschaft, 16 (Neue Folge 9).

Hermes, Hans, Kambartel, Friedrich & Kaulbach, Friedrich (eds.). 1969. Gottlob Frege. Nachgelassene Schriften. Hamburg: Felix Meiner.

Majer, Ulrich. ‘Frege’s reception of Leibniz’s characteristica universalis and his idea of a Begriffsschrift’. To appear in the proceedings of “The Leibniz reception in the sciences and philosophy of science in the 19th and 20th centuries”, edited by R. Kroemer.

Majer, Ulrich. 1997. ‘Husserl and Hilbert on completeness: A neglected chapter in early twentieth century foundation of mathematics’. Synthese 110: 417–438.

http://dx.doi.org/10.1023/A:1004962922108

Patzig, Günther. 1969. ‘Leibniz, Frege und die sogenannte lingua characteristica universalis’. Studia Leibniziana Supplement III: 103–112.

Weyl, Hermann. 1968. Gesammelte Abhandlungen, vol. 1, ed. Komaravolu Chandrasekharan. Springer.