The Lottery Paradox and the Pragmatics of Belief

Abstract

The thesis that high probability suffices for rational belief, while initially plausible, is known to face the Lottery Paradox. The present paper proposes an amended version of that thesis which escapes the Lottery Paradox. The amendment is argued to be plausible on independent grounds.

The Psychological Dimension of the Lottery Paradox

“…One might easily have thoughts of Pope Frances without reflecting on mortality statistics, but thoughts of lottery tickets with specified odds naturally demand verbatim representation and reflective cognition. This feature of lottery tickets plays a key role in Igor Douven's (2012) treatment of the paradox. Douven holds that high probability generally suffices for rational belief, but he argues that it is irrational to believe outright that one's ticket will lose, because such a belief would violate principles of what he calls 'epistemic hygienics'.…”

Implicatures and Naturalness

“…And all of the cardinal number items (13-16) do strike us as being more infelicitous than, for instance, item 6, but not quite as infelicitous as the quantifier or conventional items. More generally, that felicitousness is a matter of degree should be uncontroversial and is directly related to the claim made in Douven (2012) that implicatures can vary in strength. The latter claim was defended in terms of explanation quality-an implicature can be part of the best explanation of why the speaker said what she said in the context in which she said it, but the extent to which the best explanation stands out as being the best can vary, and can have a significant impact on people's willingness to infer the truth of that explanation, as has recently been verified experimentally in Douven and Mirabile (2019).…”

The relationship between belief and credence

“…Nonetheless, worries loom. The first is the lottery paradox (Chandler, 2010; Douven, 2012; Douven & Williamson, 2006; Kyburg, 1961; Leitgeb, 2014b; Smith, 2010a; Weintraub, 2001; Weisberg, 2015, Section 5). Suppose you have a lottery ticket; uncontroversially, you should have a high credence your ticket will lose (a fair 100‐ticket lottery puts your credence at 0.99, and we can increase the number of tickets).…”

“…Nonetheless, worries loom. The first is the lottery paradox (Chandler, 2010;Douven, 2012;Douven & Williamson, 2006;Kyburg, 1961;Leitgeb, 2014b;Smith, 2010a;Weintraub, 2001;Weisberg, 2015, Section 5).…”