[FOM] ASL Annual Meeting
urquhart at cs.toronto.edu
Tue Jun 10 10:14:54 EDT 2003
I got back last week from
the Annual meeting of the ASL, held
on the campus of the University of Illinois
at Chicago. It was a well organised and enjoyable
meeting. In the list of registered participants,
I counted 7 philosophers, 13 computer scientists,
and 66 mathematicians, roughly (there were quite
a few people of indeterminate affiliation).
The talks were fairly varied, and there were special
sessions in Algebraic Logic and Universal Algebra,
Computability Theory and Effective Mathematics,
and Model Theory. In addition, there was a first-rate series
of 3 tutorials on Kolmogorov complexity by Jack Lutz,
and (at least) two plenary talks on foundational issues.
The first of these plenary talks was by Michael Makkai,
and advocated a structuralist view of mathematical
objects based on Category theory. Some of his research
seems to be inspired by possible applications in physics,
and I would be interested to learn more. Harvey Friedman
tells me that Makkai may post to FOM, so I am
looking forward to hearing more.
The most interesting plenary talk to me was by Leonid Levin,
who gave a fine exposition on "Forbidden information."
The general thrust of this talk was to reject the following
reaction to Goedel's incompleteness theorem: "Goedel has shown
that formal methods don't work, so we'll have to use informal
(physical?) methods instead." Greg Chaitin, for example, argues
somewhat along these lines.
The last paragraph of Levin's abstract reads as follows:
"In this framework one can ask if the Hilbert-Goedel task of
a consistent completion of a formal system is really possible
for PA, as it is for an artificial system R just mentioned.
A negative answer follows from the existence of a specific sequence
that has infinite mutual information with ALL total extensions
of a universal partial recursive predicate. It plays the role
of a password: no substantial information about it can be guessed,
no matter what methods are allowed. This "robust" version of
Incompleteness Theorem is, however, trickier to prove than
the old one."
The Annual Meeting of the ASL is a good time to reflect on where
the logic community is going collectively. I'd like to hear
from other logicians, both those who attended the meeting, and those
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