A Paradox of Evidential Equivalence

Abstract

Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. While there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does.

Chance and the Continuum Hypothesis

“…Moreover, a puzzle due to David Builes ( 2020 ) gives independent reason to question the tenability of perfect independence in an infinite sequence of fair coin flips. 5 The contrary intuition is, once more, an extrapolation from the symmetries of finite cases --a risky step that has failed us time and again.…”

Solving a Paradox of Evidential Equivalence

“…What is philosophically interesting is that other methods seem to give inconsistent verdicts. Builes (2020) argues that a case like Infinitely Many Coins presents a paradox. Builes presents an argument that your credence that your coin landed Heads should be 0 and a contrary argument that your credence that your coin landed Heads should be 1 2 .…”