Annual Logic Lecture
In addition to its other speakers and sessions, the
Logic Group funds an annual event in which a
visiting researcher gives a talk (open to the
public) and, over the course of a few days, engages
in various working sessions with the group.
2011/2012 Annual Speaker: Jeremy Avigad, Carnegie Mellon University.
Understanding, formal verification, and the philosophy of mathematics
2 Mar, 2pm-4pm
Location: Class of 1947 room (in the library)
Abstract:
The philosophy of mathematics has long been
focused on determining the methods that are
appropriate for justifying claims of mathematical
knowledge, and the metaphysical considerations
that render them so. But, as of late, many
philosopher's have called attention to the fact
that a much broader range of normative judgements
arise in ordinary mathematical practice; for
example, questions can be interesting, theorems
important, proofs explanatory, concepts powerful,
and so on. The associated values are often
loosely classified as aspects of "mathematical
understanding".
Meanwhile, In a branch of computer science known
as "formal verification," the practice of
interactive theorem proving has given rise to
software tools and systems designed to support the
development of complex formal axiomatic
proofs. Such efforts require one to develop models
of mathematical language and inference that are
more robust than the the simple foundational
models of the last century.
In this talk, I will explore some of the insights
that emerge from this work, and some of the ways
that these insights can inform, and be informed
by, philosophical theories of mathematical
understanding.
Associated papers:
* Previous speakers
2010/2011: Angelika Kratzer, University of Massachusetts.
Title: Epistemic modals: embedded, modified, and plain.
2009/2010: Michael Glanzberg, University of California at Davis.
Title: Semantics, truth, and truth in a model.
2008/2009: Greg Restall, University of Melbourne.
Title: Normative inferentialist modal logic: from pragmatics
to two-dimensional semantics.
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