Abstract
Husserl’s philosophy of mathematics is interpreted as dealing with forms not unlike Aristotle’s forms. They can be somehow immediately present in one’s consciousness. Husserl’s ideas are compared for similarities and dissimilarities with those of Aristotle, Mach, Russell and Wittgenstein. Husserl’s main development is seen as making these forms more and more robust conceptually. It parallels the overall development of mathematics in the last 200 years from a study of numbers and space into a study of different structures. This development culminates in Husserl’s unfinished project of a theory of all theories. This project has closer connections with Hilbert’s axiomatic theorizing than with the ideas of the intuitionists.
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- 1.
Mark van Atten has challenged my attribution of actualism to Gödel. His evidence nevertheless supports my case. It is all from Gödel’s paper on the general theory of relativity, where the relevant sense of possibility is a physical one, not conceptual (logical). Of course a philosophical actualist can speak of other physically possible worlds, meaning simply possible systems satisfying a given physical theory.
- 2.
I have profited from comments of several of the participants in our meeting, and I thank all of them. All my scholarly sins are original.
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Hintikka, J. (2010). How Can a Phenomenologist Have a Philosophy of Mathematics?. In: Hartimo, M. (eds) Phenomenology and Mathematics. Phaenomenologica, vol 195. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3729-9_5
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