A Fundamental Duality in the Exact Sciences: An Introduction to Mathematical Metaphysics

David Ellerman (University of Ljubljana)

There is a fundamental duality that runs through the exact sciences. At the logical level, it is the duality between (Boolean) logic of subsets and the logic of partitions. The quantitative versions of the dual logics are logical probability theory and logical information theory. The duality accounts for the duality in the category of Sets and its opposite Sets^{op}. The partial order in the two dual logics gives the two fundamental canonical functions and the claim is that all canonical morphisms in Sets arise from those two morphisms. In physics, there is the notion of "definiteness all the way down" which arises in classical physics (Boolean logic of subsets) and dually there is the notion of definiteness only down to a certain level and then objective indefiniteness that arises in quantum physics (logic of partitions).

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