THE ETERNAL COIN: A PUZZLE ABOUT SELF-LOCATING CONDITIONAL CREDENCE

Abstract

The setup: The Eternal Coin has existed throughout an infinite past, and will continue to exist throughout an infinite future. It is fair, and it is tossed every day. It is causally isolated from you: you can never gain any evidence relevant to questions about how it lands. Suppose you are ideally rational and that Cr is your conditional credence function, conditional on the setup. Let H be the centred proposition the Coin lands Heads today; let F be the Coin will land Heads on every future day; and let P be the Coin has landed Heads on every past day. What are Cr(H|F) and Cr(H|P)? On the assumption that these conditional credences are well-defined, there are two answers worth considering: 1Neither of the arguments is irresistible, of course. The phenomena that motivate taking selflocating credence as irreducible can perhaps be accommodated in a Fregean theory of propositions that allows for distinctive first-personal modes of presentation. And some of the phenomena that motivate taking conditional credence as irreducible can be accommodated in a theory that uses non-standard real numbers (including infinitesimals) to measure unconditional credence (McGee 1994). For my purposes it does not matter whether these reductions are successful. I will assume that unconditional and conditional credences are standard real numbers; if you favour the nonstandard approach, you should translate everything I say by inserting ‘the standard part of’ in front of every expression that I treat as denoting a real number.