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 Hacking (Philos Sci 34(4):311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: (i) an account of the synchronic norms that govern a logically ignorant individual at any given time; (ii) 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; and (iii) an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations.
Highlights
I am grateful to the following people for helping me to think through the issues in this paper: Branden Fitelson, Liam Kofi Bright, Catrin Campbell-Moore, Jason Konek, Johannes Stern, Kevin Dorst, Julia Staffel, Jennifer Carr, Sophie Horowitz, David Christensen, and Kenny Easwaran
I will adopt and expand Ian Hacking’s approach to this issue (Hacking 1967). Hacking applied his approach primarily to synchronic credal norms; I will expand it to diachronic norms as well; and I will explain how we might appeal to an application of Good’s Value of Information Theorem (Good 1967) in order to say when it is appropriate to criticize an individual for their logical ignorance, and to recover what is right about the demand for logical omniscience as a requirement of ideal rationality
In the Dutch Book Argument, we show that, if your credences violate Probabilism, they require you to make a dominated series of choices; that is, they require you to make each of a series of choices where there is an alternative series of choices you could have made instead that would leave you better off at all possible worlds: in particular, you must choose to accept each of a series of bets where refusing each bet would leave you better off
Summary
Synthese anything logically equivalent to it; if we believe something, we should believe all its logical consequences, and we should be no more confident in something than we are in any of its logical consequences; and so on. I will adopt and expand Ian Hacking’s approach to this issue (Hacking 1967) Hacking applied his approach primarily to synchronic credal norms; I will expand it to diachronic norms as well; and I will explain how we might appeal to an application of Good’s Value of Information Theorem (Good 1967) in order to say when it is appropriate to criticize an individual for their logical ignorance, and to recover what is right about the demand for logical omniscience as a requirement of ideal rationality
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
