WP3. Epistemic Risk and the Safety Principle on Knowledge

One prominent objection against (at least some formulations of) the safety principle— roughly, the principle that if S knows that p, not easily would S believe that p without p being true—is that it is incompatible with multi-premise closure. The idea is that if for each premise there is a small risk of error (even a negligible one), for a sufficiently large conjunction of premises the risk that at least one conjunct obtains and hence that one gets things wrong is large, given how big the conjunction is, which is incompatible with knowing the conclusion by competent deduction from the premises.

This problem is very closely connected to the well-known lottery paradox, which in its knowledge version goes as follows: if you know that a given lottery ticket will be a loser (in a lottery with exactly one winner), then you can know this for every ticket (i.e., you can know the relevant conjunction of lottery propositions), but since you also know that one ticket will be winner, you know inconsistent propositions, namely that all tickets will lose and that one ticket will be a winner, but knowing inconsistent propositions is not possible—see Kyburg (1961) for the original statement; Nelkin (2000) for extensive discussion of the knowledge version of the paradox. The related lottery problem is the problem of explaining why mere reflection on the long odds that one will lose the lottery does not yield knowledge that one will lose. The two problems are connected insofar as by solving the lottery problem one can thereby solve the lottery paradox, because by giving an adequate explanation of why we don’t know that we won’t win the lottery on the basis of statistical evidence, one can explain why the premises of the knowledge version of the lottery paradox are false.

WP3 will investigate several ways to characterize lottery propositions as veritically risky and solutions to the lottery problem in these terms. In particular, it will analyze several ways to argue that lottery propositions feature knowledge-undermining risk, where the specific way in which that risk undermines knowledge is understood in terms of a failure of the safety principle. In other words, WP3 will analyze several safety-based solutions to the lottery problem. What safety theorists typically do is to tailor the notion of easy possibility (or risk of occurrence) in terms of occurrence in close possible worlds, so as to formulate possible-world versions of the principle that aim to explain why highly improbable events (such as winning the lottery) can still occur in close possible worlds and hence still count as easily possible (i.e., risky) despite the odds. The working hypothesis of WP3 will be that no formulation of safety in terms of possible worlds provides a satisfactory solution to the lottery problem.

On a more positive note, WP3 will explore an alternative way to solve the lottery problem and hence the lottery paradox by elaborating on the idea that lottery propositions give rise to defeating unsafe doubts. In general, if one believes p, a corresponding unsafe doubt is the belief that p could easily be false. The hypothesis, then, is that although it is psychologically possible to hold both beliefs, i.e., the belief that p and the belief that p could easily be false, if one holds one such an unsafe doubt, one does not know that p however reliably one has formed the belief that p. In a way, what the relevant unsafe doubt does is to defeat the positive epistemic status of one’s belief, and this is exactly what happens in lottery case. Of course, the claim is not that lottery players lack knowledge of the results because, necessarily, they actually have unsafe doubts that their tickets could easily be winners. The hypothesis that will be explored is that unsafe doubts can (and often do) play the role of normative defeaters, i.e., they are beliefs one ought to have, and this applies specifically to lottery players who form their beliefs that their tickets will win merely on the basis of statistical evidence—for discussion on knowledge and defeat more generally see González de Prado (forthcoming-b; 2016; 2017).