Francisco Hernández-Quiroz: Epistemic Kolmogorov Complexity

Organized by the Centre for formal epistemology, Institute of Philosophy, CAS

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Francisco Hernández-Quiroz (Department of Mathematics, National Autonomous University of Mexico): Epistemic Kolmogorov Complexity

Abstract

In this talk, I will present a measure analogous to Kolmogorov Complexity for theorems of decidable theories. I call this measure Epistemic Kolmorgorv Complexity since it has the virtue of attributing more informational content to theorems that are more difficult to prove. This proposal runs counter to the notion that all the logical consequences of the same assumptions are equally informative. The difference in informational content can be regarded as another measure of the epistemic contribution of inference. Furthermore, I derive a notion of conditional informational content that may explain why some formulas in classical propositional calculus are regarded as particularly valuable in proofs.