文档介绍：Epistemology as Information Theory:
From Leibniz to Ω∗
Gregory Chaitin†
Abstract
In 1686 in his Discours de m´etaphysique, Leibniz points out that
if an plex theory is permitted then the notion of “the-
ory” es vacuous because there is always a theory. This idea
is developed in the modern theory of algorithmic information, which
deals with the size puter programs and provides a new view of
G¨odel’s work on pleteness and Turing’s work on putabil-
ity. Of particular interest is the halting probability Ω, whose bits
are irreducible, ., maximally unknowable mathematical facts. More
generally, these ideas constitute a kind of “digital philosophy” related
to recent attempts of Edward Fredkin, Stephen Wolfram and others to
view the world as a puter. There are also connections with
recent “digital physics” speculations that the universe might actually
be discrete, not continuous. This syst`eme du monde is presented as a
coherent whole in my book Meta Math!, which will be published this
fall.
Introduction
I am happy to be here with you enjoying the delicate Scandinavian summer; if
we were a little farther north there wouldn’t be any darkness at all. And I am
especially delighted to be here delivering the Alan Turing Lecture. Turing’s
∗Alan Turing Lecture puting and Philosophy, E-CAP’05, puting
and Philosophy Conference, M¨alardalen University, V¨aster˚as, Sweden, June 2005.
†IBM T. J. Watson Research Center, P. O. Box 218, Yorktown Heights, NY 10598,
., ******@us..
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famous 1936 paper is an intellectual milestone that seems larger and more
important with every passing
People are not merely content to enjoy the beautiful summers in the far
north, they also want and need to understand, and so they create myths.
In this part of the world those myths involve Thor and Odin and the other
Norse gods. In this talk, I’m going to present another myth, what the French
call a syst`eme du monde, a system of the world