2005/06/27 by G. J. Chaitin, Gregory J. Chaitin, Chaitin, G. J. · 5 citations
Arts and Humanities · Computer Science · Mathematics · Neuroscience · #68Q30 #Cognitive Science and Education Research #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Overview (math.HO) #Philosophy and History of Science #math.HO #msc:68Q30
paper · pdf · doi:10.48550/arxiv.math/0506552
Alan Turing Lecture on Computing and Philosophy, E-CAP'05
openalex publication_date 2005/06/27 · arxiv created 2005/06/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1686 in his Discours de Metaphysique, Leibniz points out that if an arbitrarily complex theory is permitted then the notion of "theory" becomes vacuous because there is always a theory. This idea is developed in the modern theory of algorithmic information, which deals with the size of computer programs and provides a new view of Godel's work on incompleteness and Turing's work on uncomputability. Of particular interest is the halting probability Omega, whose bits are irreducible, i.e., 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 giant computer. There are also connections with recent "digital physics" speculations that the universe might actually be discrete, not continuous. This systeme du monde is presented as a coherent whole in my book Meta Math!, which will be published this fall.