**NB:** A

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version of this announcement (suitable for posting) is also available.

## Set-Theoretic Knowledge: Beyond True and False

### Akihiro Kanamori

Boston University

###
Friday, October 7, 2005

Rockefeller Room 002, 3 pm

Tea 4:30 pm, Math Lounge

Joint Mathematics and Philosophy Colloquium
Note different time and format

**Abstract: ** Modern mathematics is, to my mind, a
complex edifice based on conceptual constructions. With its richness,
variety, and complexity any discussion of the nature of mathematics
cannot but accede to the primacy of its history and practice. The
applicability of mathematics may be a driving motivation, but in the
end mathematics is autonomous. Mathematics is in a broad sense
self-generating and self-authenticating, and alone competent to
address issues of its correctness and authority.

What brings us
mathematical knowledge? The carriers of mathematical knowledge are
proofs, more generally arguments and constructions, as embedded in
larger contexts. Mathematical knowledge does not consist of theorem
statement, and certainly does not consist of more and more ``epistemic
access'', somehow, to ``abstract objects'' and their workings.
Mathematicians and teachers of higher mathematics know this, but it
should be said. Issues about competence and intuition can be raised as
well as factors about the general dissemination of analogical or
inductive reasoning, but in the end, what can be directly conveyed as
knowledge are proofs.

The talk will describe how proofs are the
carriers of mathematical knowledge, with the first half devoted to set
theory, and the second half, to modern mathematics in general. Some
elementary set theory and knowledge of the set theoretic axioms would
be helpful for following the first half, but the second half requires
little background.

This talk will be accessible to graduate students.