Anaid Ochoa

Safety accounts of knowledge intend to explain why certain true and intuitively justified beliefs fail to be knowledge in terms of such beliefs falling prey to a modal veritic type of luck. In particular, they explain why true and intuitively justified beliefs in “lottery propositions” (highly likely propositions reporting that a particular statistical outcome obtains) are not knowledge. In this paper, I argue that there is a type of case involving lottery propositions that inevitably lies beyond the scope of any reasonable safety account of epistemic luck. I offer counterexamples to accounts of epistemic luck in terms of safety conditions that involve both “locally” and “globally” reliable ways of forming beliefs in nearby worlds. All such counterexamples present a lottery case illustrating the next possibility: the process of selecting the lottery winner might be such that any world in which it delivers a different outcome is extremely far away from the actual world. In addition to being a case of safe ignorance, this type of lottery case shows that, ultimately, either veritic epistemic luck is not unsafe true belief or beliefs in lottery propositions are not epistemically luckily true.

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.

There is a wide consensus among epistemologists that we fail to know lottery propositions (that is, highly likely propositions solely supported by statistical evidence), but there is no agreed-upon explanation of why we fail to know them. Yet, paradoxes surrounding lotteries continue pressing on the need to identify the correct explanation. This dissertation evaluates various explanations of why we do not know lottery propositions, which normally take one of two forms. The first argues that lottery beliefs are true by mere epistemic luck (roughly, luck, chance, or accident in possessing a true belief in a proposition p, which prevents us from knowing p), and provides an account of epistemic luck that entails that lottery beliefs are epistemically luckily true. Here I evaluate and reject an explanation that relies on the largely dominant account of epistemically lucky beliefs as “unsafe true beliefs”. The second argues that lottery beliefs are unjustified (where being justified in believing p is necessary for knowing p), and provides an account of justification with a condition that lottery beliefs or propositions do not satisfy. I divide conditions on justification into “probabilistic” and “non-probabilistic” and argue, contrary to Douven and Williamson (2016), that justification can have a probabilistic condition that lottery beliefs fail to satisfy, thus restoring such accounts as a theoretical possibility to solve the “lottery paradox”. I also argue that among the dominant candidates of non-probabilistic conditions, Smith’s (2016) normic support condition on justification is the only suitable one to explain why we do not know lottery propositions. Alternatively, if lottery propositions are justified, there is nonetheless a solution to the lottery paradox compatible with their possessing such epistemic status, which consists in rejecting the “aggregativity of justification”. I argue that this principle is incorrect, and that preserving it obstructs solving what I identify as the most basic form of the lottery paradox. Finally, I address the legal correlates of lottery propositions –i.e., litigated claims supported by bare statistical evidence. I divide explanations of why such claims do not meet a given standard of proof into two types: externalist and internalist. I present independent problems for two externalist explanations –Pritchard’s (2018, 2022) modal explanation and Blome-Tillmann’s (2017) knowledge-first explanation, and argue that they face such problems in virtue of being externalist. This finding motivates the need to evaluate externalist accounts qua externalist to determine if an externalist account is a viable solution to the “proof paradox”.

Safety accounts of knowledge intend to explain why certain true and intuitively justified beliefs fail to be knowledge in terms of such beliefs falling prey to a modal veritic type of luck. In particular, they explain why true and intuitively justified beliefs in “lottery propositions” (highly likely propositions reporting that a particular statistical outcome obtains) are not knowledge. In this paper, I argue that there is a type of case involving lottery propositions that inevitably lies beyond the scope of any reasonable safety account of epistemic luck. I offer counterexamples to accounts of epistemic luck in terms of safety conditions that involve both “locally” and “globally” reliable ways of forming beliefs in nearby worlds. All such counterexamples present a lottery case illustrating the next possibility: the process of selecting the lottery winner might be such that any world in which it delivers a different outcome is extremely far away from the actual world. In addition to being a case of safe ignorance, this type of lottery case shows that, ultimately, either veritic epistemic luck is not unsafe true belief or beliefs in lottery propositions are not epistemically luckily true.