Leibniz as a precursor to Chaitin’s Algorithmic Information Theory 1

Gregory Chaitin, one of the founders of Algorithmic Information Theory (AIT), traces some of the key components of the idea of digital information back to the ideas of Gottfried Wilhelm Leibniz (1646‒1716), among them the idea of a computer program, an information-theoretic notion of complexity, and the idea of irreducibility. This chapter consists in a critical examination of these claims of anticipation. It is argued that Leibniz anticipates some of Chaitin ’s views even more than he recognizes, undermining some of the criticisms he makes of Leibniz ’s metaphysics; but that where they disagree, Leibniz ’s philosophy of science is in fact more insightful and less naïve than Chaitin ’s. Moreover, rather than being fatal to Leibniz ’s metaphysics, the application of AIT to physics can be seen to deliver results consistent with Leibniz ’s defence of contingency, as is shown by a development of ideas about causality as the transfer of information first proposed by the late John Collier.