Justification does not aggregate: de-generalizing the lottery paradox
摘要
This paper challenges the aggregation of justification—the claim that if propositions p and q are individually justified for a subject, their conjunction (p&q) is also justified—as a solution to the lottery paradox. Two arguments against aggregativity are presented, in light of Douven and Williamson’s 2006 proof aiming to show that defeaters of lottery propositions cannot be purely structural (roughly, reducible to logical or probabilistic notions), which assumes that justification aggregates. First, since evidential support (necessary for justification) does not aggregate, justification also fails to aggregate. Further, any restriction of aggregativity possibly invoked in Douven and Williamson’s proof is untenable. Second, accepting aggregativity obstructs solutions to the lottery paradox in its “most basic form” (where the paradox involving the notion of justification is a meta-level paradox). Moreover, Douven and Williamson’s treatment of the paradox diverts attention from viable solutions. These arguments strongly support reinterpreting their proof as a reductio of aggregativity (rather than a reductio of propositions having structural defeaters, as they intended). The paper concludes by proposing and defending a restricted aggregativity principle to solve the lottery paradox.