Leibniz, Randomness and the Halting Probability
G. J. Chaitin (IBM Research)
TL;DR
This paper discusses the philosophical implications of incompleteness, uncomputability, and randomness, with a focus on Leibniz's ideas and their relation to the halting probability, honoring Alan Turing's legacy.
Contribution
It provides an overview connecting Leibniz's philosophy with modern concepts of uncomputability and randomness, highlighting their implications for understanding the halting probability.
Findings
Explores the connection between Leibniz's philosophy and modern computability theory.
Discusses the implications of uncomputability and randomness for mathematical philosophy.
Highlights the significance of the halting probability in understanding randomness.
Abstract
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, uncomputability and randomness.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Mathematical and Theoretical Analysis · Philosophy and History of Science