Leibniz, complexity and incompleteness

Gregory J. Chaitin

pp. 127-133

in: Causality, meaningful complexity and embodied cognition, Berlin, Springer, 2010

Abstract

Leibniz in 1686 in his Discours de mtaphysique 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 Gdel's work on incompleteness and Turing's work on uncomputability.This will be a first-person account of some doubts and speculations about the nature of mathematics that I have entertained for the past three decades.

Cited authors

Leibniz Gottfried Wilhelm