39 citations · 84 across the 10 of their papers we have counts for
12 papers · 1 filter
Epistemology as Information Theory: From Leibniz to Omega
G. J. Chaitin
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…
How real are real numbers?
G. J. Chaitin
We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Emile Borel (1871-1956).
Irreducible Complexity in Pure Mathematics
G. J. Chaitin
By using ideas on complexity and randomness originally suggested by the mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of algorithmic information is able to…
Leibniz, Randomness and the Halting Probability
G. J. Chaitin
This paper, which is dedicated to Alan Turing on the 50th anniversary of his death, gives an overview and discusses the philosophical implications of incompleteness, uncomputabilit…
Meta Math! The Quest for Omega
G. J. Chaitin
This book presents a personal account of the mathematics and metamathematics of the 20th century leading up to the discovery of the halting probability Omega. The emphasis is on hi…
Leibniz, Information, Math and Physics
G. J. Chaitin
The information-theoretic point of view proposed by Leibniz in 1686 and developed by algorithmic information theory (AIT) suggests that mathematics and physics are not that differe…