Logical ignorance and logical learning


Authors
Richard Pettigrew
Bristol University
Abstract
According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Ian Hacking (1967), I develop a version of Bayesianism that permits logical ignorance. This includes an account of the synchronic norms that govern a logically ignorant individual at any given time, as well as an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations.
Keywords logical omniscience  Bayesian epistemology  Dutch Book argument  Probabilism  Bayesian updating  conditionalization  epistemology of logic  accuracy  value of information
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