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Ockham Efficiency Theorem for Empirical



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Ockham Efficiency Theorem for Empirical Methods Conceived as Empirically Driven Countable State Stochastic Processes Kevin Kelly Conor Mayo Wilson November 29 2008 Abstract Ockham s razor is the principle that all other things being equal it is rational to prefer simpler scientific theories to more complex ones In a series of a papers Kelly Glymour and Schulte argue that scientists who heed Ockham s razor make fewer errors and retract their opinions less often than do their complexity preferring counterparts The centerpiece of their argument is the Ockham Efficiency Theorem which provides a precise explanation of errors retractions and Ockham s razor within a model of scientific inquiry developed by formal learning theorists Kelly Glymour and Schulte s previous arguments however were restricted in two important ways 1 they applied only to deterministic rather than randomized methods for choosing scientific theories from data and 2 they failed to successfully model inference from statistical data with error In this paper we full address the first issue by extending the Ockham Efficiency Theorem to prove that amongst any set of randomized strategies a systematic preference for simpler theories minimizes the number of errors and retractions one commits before converging to the true theory By incorporating probabilistic elements into the model employed by formal learning theorists moreover we take a large step towards addressing the second issue as well 1 Introduction From the Copernican revolution to Einstein s jettisoning of absolute space from mechanics some of the most celebrated advances in the history of science were motivated in part by a desire to simplify existing theories The systematic preference for simpler theories moreover still dominates scientific practice today Faced with multiple competing theories that are all compatible with existing experimental and observational evidence scientists eschew complexity in favor of theories with fewer laws fewer free



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