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Michiel Renger (TU/e)
| Speaker: |
Michiel Renger (TU/e)
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| Date: |
Wednesday July 15, 2009
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| Title: |
The role of Intuition
in Mathematical Practice
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Abstract
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After a relatively short period
of genious mathematical and scientific work, Newton spent the rest of
his life arguing that mathematical concepts have no meaning outside the
physical realm. Nowadays, the continental (Leibnizian) view seems to
have prevailed: most mathematicians are accustomed to working with
abstract concepts that may not be directly related to any phenomena in
the “real” world. But how can a purely mental inquiry in abstract
concepts possibly yield objective truths?
This question has been a central theme in the philosophy of mathematics
since the very birth of western philosophy and mathematics in Ancient
Greece. In the first part of this talk, I will present some of the
major philosophical views on this subject: classical and modern
platonism, Kantianism, formalism, intuitionism and instrumentalism/
pragmatism. More specifically, I will discuss how mathematical
intuition plays a fundamental role in these philosophies. In the second
part of this talk, I will show a number of counterintuitive results in
fundamental set theory. These results show that either the axioms are
'wrong' (as Gödel thought), or our intuition must be wrong.
(No prerequisite knowledge of philosophy of mathematics is needed in
order to follow this talk)
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