Abstract
A necessary criterion of Duncan Pritchard’s Anti-luck Virtue Epistemology is his safety condition. A believer cannot know p unless her belief is safe. Her belief is safe only if p could not have easily been false. But “easily” is not to be understood probabilistically. The chance that p is false might be extremely low and yet p remains unsafe. This is what happens, Pritchard argues, in lottery examples and explains why knowledge is not a function of the probabilistic strength of one’s evidence. This paper argues that, contra Pritchard, modality holds no epistemic advantage over this type of “probabilistic evidentialism” that he criticizes. I begin with a review of Pritchard’s argument supporting modality over probability; second, I explain the problems with this argument, and third, I offer an alternative explanation of the lottery example (which purportedly shows modality is superior to probability). At the completion of the paper, modality and probability are on equal epistemic footing.
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Notes
Pritchard varies on just how close the lottery winning world is to the losing one. At times he says it is ‘nearby’ (2005, 2008b) sometimes ‘very close’ (2008a, 2012) and other times ‘very close nearby’ (2009). (I should add, these changes are often for helpful and clarifying purposes.) What really matters for us though, is that whatever the distance, the lottery losing and lottery winning worlds are (1) close enough to one another that an agent’s belief in losing the lottery, formed via reflection on the odds, even if true, is unsafe, and (2) the lottery winning and losing worlds are closer to one another than are the worlds in which the paper correctly prints the lottery results and the world in which the paper mistakenly prints the lottery results.
“Recall that the lottery puzzle arises because it seems that forming one’s belief that one is the owner of a losing ticket to a fair lottery with long odds by reflecting on the low probabilities involved does not seem to lead one to knowledge… Compare, for example, this belief with a parallel belief that one has lost formed on the basis of reading the result in a reliable newspaper…” (2009: 35).
“[T]here is a crucial difference between forming one’s belief that one has lost the lottery by reflecting on the odds involved and forming that same belief by reading a reliable newspaper. After all, the former belief is unsafe, unlike the latter belief.”(2009: 36).
“[I]t seems that forming one’s belief that one is the owner of a losing ticket…by reflecting on the low probabilities involved does not seem to lead one to knowledge… Compare, for example, this belief with a parallel belief that one has lost formed on the basis of reading the result in a reliable newspaper. It seems that in this second case one can come to know… [T]he moral I draw from the lottery case is that knowledge is not a function of the probabilistic strength of one’s evidence…” (2009: 35–36).
For although it is highly unlikely that one should win the lottery, it is nevertheless true that there is a nearby possible world in which one does win the lottery because very little needs to be different to turn the actual (non-lottery-winning) world into the appropriate (lottery-winning) possible world (for example, a few numbered balls just need to fall into slightly different holes on the machine that draws the lottery numbers)” (my emphasis) (2005: 129).
“The point here is that reliable newspapers…have checks built-into prevent misprints…it isn’t very plausible to suppose that the possible worlds where our hero forms a false belief in the target proposition are close ones” (2009: 36).
This is not the only example of a lottery misprint. For instance, “When Jim and Dorothy Sprague looked in the newspaper Sunday morning, they saw that their ticket for Saturday night's $4.3 million lottery drawing matched all six numbers. It turns out, the newspaper had mistakenly published wrong numbers” (Oswalt 2011). And here is another, “When Debra Revis, of Colorado, checked the Daily Sentinel to see if her lottery numbers had won, she had no idea there had been a misprint… She saw that 5 of her numbers matched the 6 in the paper, so she called her son to find out if there was a prize for matching 5 numbers… Out of curiosity, he asked her to read out the numbers she had played, and when she read him the final number, he told her that all six matched, and that she had actually won the jackpot”(Smith 2015). These example are from a quick Googler search; there are surely others. Are these papers reliable? Pritchard might try to argue they are not main stream and don’t qualify. He does say the following, “As it happens, I don’t doubt that there are newspapers—local ‘rags’ with one permanent member of staff, say which are produced in such a way that (a mistake) is a near-by possibility…”(2009: 36). These papers may be local, but they are not ‘rags’ with one staff member. And, generally speaking, the local papers are where we read the lottery results. So if the lottery intuition is to have any force, we should think of it in terms of checking the average local paper.
Sosa’s original example was designed to challenge the sensitivity principle. It has since been used by others (see, for example, Greco 2007) to challenge Pritchard’s safety principle.
Johnathan Vogel also has an example with a similar structure to the lottery case. Vogel suggests that, intuitively, we can know that 60 golfers will not get a hole-in-one on the difficult, ‘Heartbreaker’ hole (1999: 168) We might think this is so even if there is some close world in which 60 golfers in a row do get that hole-in-one. For further discussion on Vogel’s case, amongst other challenges to Pritchard’s Safety, see Greco (2007).
As mentioned, depending on the text at issue, Pritchard seems to think the lottery winning and losing worlds are either ‘very close nearby’, ‘very close’ or ‘nearby’. I use ‘very close nearby’ for it seems to be what he considers the best, or most precise, description.
“The moral I draw from the lottery case is that knowledge is not a function of the probabilistic strength of one’s evidence (in the sense that the greater this probabilistic strength, the more likely it is that you know)…” (2009: 36).
Some might point out that even if I am right that paper checking adds probabilistic evidence, the amount it adds is so small as to be insignificant. Since the odds of winning the lottery are already so low, any additional odds in this direction will have little impact. This is a fair enough response, but it does not hurt my argument. This is because the point is that Pritchard’s premise, which claims that checking the paper comes with lesser probabilistic evidence than reflection, is a false premise. And this premise is false if the odds from paper checking and reflection are relatively equal; what matters is paper checking does not provide less probabilistic support than reflection.
Newspaper errors, as we have seen, are not uncommon (even from the most ‘reliable’ presses). In spite of this, most tend toward trusting the paper unless some defeater suggests problems in a particular instance.
The lottery and newspaper contexts conflict, insofar as the former highlights certainty and the latter pushes it aside. When two conflicting contexts collide, discovering how one comes to trump the other is an interesting and complex question, one which we do not have time to address. But for whatever reason, it seems clear that, in the collision under consideration, the newspaper context trumps the lottery context.
The retraction problem is just one objection to explanations that appeal to knowledge ascriptions, attributions, intuitions therein, and pragmatic implicature. There are other problems. Again, see Dinges (2017); and also, Bach (1999), Davis (2006, 2007a, b, 2014), Gerken (2017), Fallis (2012) and Simons (2010). The focus on the retraction problem in this paper offers an example of just one of many possible objections that might arise when appealing to the just mentioned “pragmatic” justifications. As suggested, there will likely remain a divide between those who are generally sympathetic to Hazlett, Pritchard, and others’ use of pragmatic implicature on the one hand, and then those who are not so sympathetic on the other.
There might be special circumstances in which the saliency of winning the lottery is not as salient as usual. If, for instance, you bought a lottery ticket at noon, and at 12:05 pm, you were asked if you could afford an expensive weekend trip to Paris. In circumstances like this, the possibility of winning the lottery might not be as heightened as usual, but I am reluctant to say that (in typical circumstances) the chance of winning is not salient at all. You might respond to the “weekend vacation question” in the following manner: Even though you recognize the possibility of winning, you know the odds are so small you might as well forget about it. We arguably use a similar strategy regarding other small risks. For instance, when we get on an airplane or in the car, we might recognize the possibility of dying, it might even be salient to us, and yet we go forth, perhaps telling ourselves that the odds, after all, are very low.
Yes, some persons might purchase lottery tickets not because they think they will win, but rather, for enjoyment or entertainment. Notwithstanding, I would argue that such enjoyment or entertainment is tied to the possibility of winning. Persons who think they are going to lose might still happily dream of what they would do if they won. And they might have fun joking with friends about the possibility of winning. In both such aforementioned cases, the possibility of winning is salient, even if the agent does not think winning the lottery will come to fruition.
Dinges (and others who take a similar position) might object and ask “which rule makes it the case that claims about winning the lottery imply the ability to eliminate other possibilities.” (a reviewer of this paper made this suggestion.) I admit that I do not know which rule. Rather, I am relying on the following type of intuitions about lottery conversations: If an agent says, “I know I lost the lottery,” this agent might be meet with, “You can’t know that. How do you know you aren’t holding the winning ticket?” Because this seems plausible, it also seems plausible that the just mentioned knowledge claim implied being able to eliminate the possibility of “holding a winning ticket.” The assumption of this implication explains why an interlocuter would respond with, “But how do you know you are not holding the winning ticket?” Even though not all hold this intuition, (i.e. the intuition that claiming, “I know I lost the lottery” implies the ability to eliminate all possibilities of winning) it is common enough that the point seems worth making. For instance, those who agree with Hazlett seem likely to support a pragmatic explanation of the lottery problem.
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Priest, M. Lotteries, Possible Worlds, and Probability. Erkenn 87, 2097–2118 (2022). https://doi.org/10.1007/s10670-020-00292-7
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DOI: https://doi.org/10.1007/s10670-020-00292-7