On the Duality between Existence and Information
21 Pages Posted: 1 Nov 2015
Date Written: October 30, 2015
Recent developments in pure mathematics (category theory) and in mathematical logic (partition logic) have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets (mis-specified as the logic of "propositions") and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction (a pair of elements in different blocks) of a partition, and that leads to a whole stream of dualities or analogies -- including the development of new logical foundations for information theory parallel to Boole's development of logical finite probability theory.
After outlining these dual concepts in mathematical terms, we turn to a more metaphysical speculation about two dual notions of reality, a fully definite notion using Boolean logic and appropriate for classical physics, and the other objectively indefinite notion using partition logic which turns out to be appropriate for quantum mechanics. The existence-information duality is used to intuitively illustrate these two dual notions of reality. The elucidation of the objectively indefinite notion of reality leads to the "killer application" of the existence-information duality, namely the interpretation of quantum mechanics.
Keywords: partition logic, subset logic, duality, logical information theory, quantum mechanics
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