Introduction
According to a rough-and-ready formulation of the safety principle:
Safety: If one knows that p, then one's belief that p is not only true in the actual world, but also true in relevant nearby possible worlds (where the subject forms the belief with the same method as in the actual world.)Footnote 1
Recent discussions have primarily focused on whether or not a principle like Safety can be successfully defended as a necessary condition for knowledge.Footnote 2 This paper investigates another related issue, i.e. the lottery problem. Very generally speaking, the problem is of explaining why true beliefs based merely on excellent probabilistic evidence don't seem to constitute knowledge. Suppose that someone called Lottie buys a fair lottery ticket. The odds of losing the lottery are massive. Before the result is announced, Lottie forms a true belief that she will lose, based (only) on considerations regarding the very high probability of losing the lottery. Many find it intuitive that Lottie's belief doesn't constitute knowledge, regardless of the very high probability in favor of its truth. This is puzzling because in many other cases where the odds of one's belief being true are lower than in Lottie's case, knowledge does seem to be present. Thus, we would often think that one can know that one loses the lottery purely based on reading the lottery result in a reliable newspaper (cf. Cohen Reference Cohen1998: 292–3). This is so even if the odds of the newspaper misprinting the result may be even higher than the probability of winning the lottery – that is, the odds of forming a true belief conditional on the newspaper result is lower than that conditional on the probability of losing.
This lottery problem has received much attention among epistemologists.Footnote 3 It is a desideratum of a theory of knowledge like safety to be able to tackle this perennial problem – in particular, to explain the intuition that Lottie lacks (or seems to lack) knowledge. In section 1, I introduce some background regarding safety and the lottery problem. In section 2 through section 4, I reject three existing safety-based solutions to the problem, due to Pritchard (Reference Pritchard2007, Reference Pritchard and Hendricks2008, Reference Pritchard2015), Sosa (Reference Sosa2015) and Broncano-Berrocal (Reference Broncano-Berrocal2019), respectively. Section 5 presents an account of knowledge that incorporates a safety principle with another condition regarding one's awareness of (nearby) error-possibilities. It is argued that this account enjoys a number of theoretical advantages, including its capacity to tackle the lottery problem. Finally, section 6 addresses some potential objections.
1. Background
Consider the following versions of the safety principle:
Safety(weak): If one knows that p, then one's belief that p is not only true in the actual world, but also true in most nearby possible worlds (where the subject forms the belief with the same method as in the actual world).
Safety(strong): If one knows that p, then one's belief that p is not only true in the actual world, but also true in all nearby possible worlds (where the subject forms the belief with the same method as in the actual world).
For a safety theorist, an obvious way to explain the lack of knowledge in Lottie's case is to appeal to Safety(strong). Notice that although Lottie's belief that she will lose is true in most nearby possible worlds, thus satisfying Safety(weak), given that there is a small number of nearby worlds where she will win, the belief is not true in all nearby worlds. Hence, the belief is not Safety(strong)-safe, which corresponds to the intuition that Lottie lacks knowledge.
However, Greco (Reference Greco2007) points out that Safety(strong) is problematic because it rules out certain cases of inductive knowledge. Consider:
Chute Case
After dropping a trash bag down the garbage chute of her apartment building, S believes truly that the bag will be in the basement later. Her basis for the belief is inductive: her past experience, background knowledge about the chute, etc. However, it could be the case that her belief is false: it is possible that the bag snags on its way down, though very unlikely. (Adapted from Sosa Reference Sosa1999: 145)
As per Safety(strong), S's belief is unsafe. In a small range of close worlds, the bag would snag on its way down, rendering S's belief false. Therefore, Safety(strong) implies that S does not have inductive knowledge that her bag will be in the basement, which seems quite implausible.
To summarize, safety theorists are caught in a dilemma. On the first horn, by sticking to Safety(strong), one can properly predict the lack of knowledge in Lottie's case, but this form of safety excludes inductive knowledge. On the second horn, Safety(weak) helps to preserve inductive knowledge, but this version of safety is too weak to explain the lack of knowledge in Lottie's case.
2. Pritchard's solution
Duncan Pritchard proposes the following safety principle to resolve the dilemma:
Safety(weighed): If one knows that p, then one's belief that p is not only true in the actual world, but also true in all very close possible worlds and most close possible worlds. (Pritchard Reference Pritchard2007: 292; see also Pritchard Reference Pritchard2015: 102)Footnote 4
While preserving Safety(weak) as a component, Safety(weighed) puts additional weight on the “very close” possible worlds, such that a safe belief is intolerant of errors in any of these worlds. Pritchard thinks that Safety(weighed) judges both Lottie's case and Chute Case correctly. In the former, not-p worlds are very close to the actual world. As he puts it, a “world in which I win the lottery is a world just like this one, where all that need be different is that a few coloured balls fall in a slightly different configuration” (Pritchard Reference Pritchard2007: 292). Thus, Lottie's belief that she will lose does not satisfy Safety(weighed), so she lacks knowledge.
With regard to Chute Case, since it is assumed that it is unlikely for the bag to get caught,Footnote 5 we can imagine that there is some very minor dysfunction in the lift shaft, but one that is so slight that hardly any bag would snag on it. Under these circumstances, many details would have to be changed for the bag to snag on the chute, and so not-p world is not very close to the actual world. If so, the subject's belief that the bag will be in the basement is safe according to Safety(weighed), reflecting the intuition that she knows.Footnote 6
In summary, if Pritchard is correct, it is really the degree of modal closeness of error-possibilities that plays a crucial role in determining whether one knows or not. In Lottie's case, not-p world being very close to the actual world makes her belief unsafe (as per Safety(weighed)), and so she fails to know. By contrast, the subjects in Chute Case and the newspaper example can come to know insofar as the error-possibilities are relatively remote.
Now, Pritchard's judgments of modal closeness are made on a primitively intuitive level. These judgements rely on the amount of relevant changes involved in a possible world compared with the actual world. It would be better to specify a more principled way of determining possible world similarity/closeness, so that one can evaluate safety in a more principled manner, thus avoiding the worry of ad hocness (cf. Baumann Reference Baumann2008; Kvanvig Reference Kvanvig2008; McEvoy Reference McEvoy2009). Setting this issue aside, however, I want to argue that what epistemically distinguishes Lottie's case from Chute Case (as well as the newspaper example) is not the degree of modal closeness of error-possibilities. This is so even if we grant Pritchard's methodology of determining modal closeness. Specifically, in what follows I will revise Lottie's case in a way that the error-possibilities are no longer ‘very close’ to the actual world. Despite this revision, it will be clear that Lottie still lacks knowledge. Therefore, Pritchard's diagnosis of the lottery problem fails. Consider:
Inflated Lottery Ball
The lottery that Lottie plays works as follows. A player picks three different numbers from 1 to 100. The lottery result is announced via a big lottery machine, which contains 100 balls with different numbers (from 1 to 100) marked on their surfaces. Upon operation, the machine completely randomly picks three balls as the lottery result. Anyone whose ticket numbers match the numbers on the announced three balls will win.
The day before the announcement, Lottie buys a lottery ticket. One of her chosen numbers is 13. A few minutes later, at t1, by realizing the extremely low probability of winning the lottery, Lottie forms a belief that she will lose. A couple of hours later, at t2, due to some very peculiar chemical effect, ball number 13 in the lottery machine inflates a bit, so that it becomes very difficult for this ball to be drawn. That is, the chute in the machine that delivers the drawn balls is too narrow for ball 13 at its current size to successfully go through. Thus, for ball number 13 to be a candidate of drawn balls, quite a few changes need to be made: someone needs to open the machine before the announcement, detect the abnormal size of the ball, and promptly fix the problem, etc.
Now, I take it as quite intuitive that, from t1 to the moment when Lottie learns the lottery result, she does not know that she will lose the lottery. After all, her belief is always based on the same probabilistic considerations. She does not gain any new evidence that she will lose, nor is there any new input to her belief-forming process, etc. Sure, the fact that ball 13 inflated at t2 may make it even more unlikely that the numbers Lottie picked will win. Notice, however, that the moral of the lottery example is precisely that high probability in favor of the truth of one's belief does not imply that the belief is knowledge. Given that the probability of her losing the lottery is already extremely high, there is no reason to think that any increased probability would turn Lottie into a knower.
However, Safety(weighed) delivers a rather strange and implausible verdict here. Given that after t2 quite a few changes need to be made for ball 13 to be drawn, a possible world where Lottie's belief becomes false (i.e. a world in which she wins the lottery) becomes relatively remote. It is no longer the case that for Lottie to win, only a few colored balls need to fall in a slightly different configuration, as Pritchard (Reference Pritchard2007: 292) conceives in the original Lottie case. Rather, at least after t2, many changes need to be made for Lottie's numbers (especially number 13) to win. This means that, after t2, Lottie's belief that she will lose becomes safe according to Safety(weighed), and so, the belief suddenly becomes a good candidate for knowledge. In fact, following Pritchard's analysis, all the players whose lottery tickets contain number 13 and who believe that they will lose (purely on the basis of the high probability of losing) may come to know that they will lose after t2;Footnote 7 whereas all the other counterpart players whose numbers do not contain 13 continue to be ignorant. These results are particularly bizarre, since, as we may assume, all the players form the belief based on the same probabilistic reasons, and are not aware that anything happened to the machine, etc.
To clarify, one does not have to be an internalist to find the above results generated by Safety(weighed) to be implausible; advocates of various versions of externalism should find them unacceptable as well. Throughout t1 to the announcement of the lottery result, Lottie's belief is caused by the same belief-forming process and is the result of the same cognitive abilities. Therefore, process reliabilism (cf. Goldman Reference Goldman and Pappas1979) and virtue reliabilism (Greco Reference Greco2010; Sosa Reference Sosa2015) would not suggest that Lottie can suddenly come to know at t2. Also, even at t2, the fact that Lottie's belief is formed by way of properly functioning cognitive faculties, in a congenial epistemic environment, according to a good design plan, remains unchanged. Thus, on proper functionalism (Plantinga Reference Plantinga1993), she doesn't suddenly come to know at t2 either.Footnote 8 Finally, no matter at t1 or t2, were Lottie to win the lottery, she would still believe that she will lose. So, sensitivity (Nozick Reference Nozick1981) also does not lead to the result that she can suddenly know at t2. In sum, all these prominent externalist accounts predict differently than Safety(weighed), which further casts doubts on the plausibility of the latter. It thus turns out that both intuition and theoretical considerations count against Safety(weighed)'s verdict on Inflated Lottery Ball.Footnote 9
To conclude, Inflated Lottery Ball delivers a useful lesson. In particular, it shows that whether Lottie knows or not is not determined by the degree of modal closeness of not-p worlds, contrary to what Safety(weighed) suggests. The modal closeness of these worlds can be stipulated, so that they are relatively remote from the actuality, just as not-p worlds seem to be relatively remote in the above Chute Case and the newspaper example. Even with such a stipulation, however, the point that Lottie lacks knowledge, whereas the latter examples feature knowledge, remains unchanged. Therefore, what makes Lottie's case epistemically distinctive is not the degree of modal closeness. The latter is a red herring; one needs to look somewhere else to handle the lottery problem.
3. Sosa's solution
Let us turn to Sosa. Sosa (Reference Sosa2015: 120) thinks that Safety(weak) is more plausible than other formulations of safety. Consequently, he is committed to the claim that Lottie's belief is safe. Interestingly, however, he thinks that this is a correct result because Lottie does know that she will lose. He then offers an error theory to explain why many tend to have the intuition that Lottie does not know.
According to the error theory, it is the (weaker) safety condition (i.e. Safety(weak)) that is required for knowledge, instead of sensitivity. According to the latter:
Sensitivity: If S knows that p, then S's belief that p, formed via method M, is sensitive, i.e. in the nearest possible worlds where p is false, S does not believe p via M.
Lottie's belief that she will lose is insensitive: If her belief were false – i.e. if she were holding a winning ticket – she would still believe that she will lose (based on the probabilistic information). However, as aforementioned, her belief is (weakly) safe. Moreover, Sosa thinks that safety and sensitivity are easily confused, because it is easy to assume, incorrectly, that the conditional of safety (i.e. Bp□→p) and that of sensitivity (i.e. ~p□→~Bp) contrapose (cf. Sosa Reference Sosa1999: note 1). But they are really inequivalent conditions. And it is the (weaker) safety that is a correct necessary condition for knowledge. Therefore, in Lottie's case, people are misled into thinking that she does not know, simply because they have confused the correct (weaker) safety condition with the incorrect sensitivity condition. The former correctly judges that Lottie's belief is safe, whereas the latter misleadingly predicts that the belief is insensitive.
Sosa's explanation is not without difficulties. First, it is an empirical claim that those who have the intuition that Lottie does not know are confusing sensitivity with safety. Such an empirical claim needs to be confirmed by empirical evidence regarding folk psychology; otherwise the claim remains as a speculation.
More importantly, Sosa's above diagnosis leads to some implausible inconsistencies. To illustrate, notice that just as in Lottie's case, in the above descriptions of Chute Case (see section 1), the subject's belief is also weakly safe but insensitive. Specifically, if her belief were false, she would still hold the same belief that the bag will be in the basement later (via the same inductive method); hence, the belief is insensitive.Footnote 10 At the same time, recall that the belief is true in most relevant nearby worlds, so the belief is safe according to Safety(weak). These results imply that, just as in Lottie's case, it should be expected that in Chute Case people tend to incorrectly think that the belief does not constitute knowledge, due to confusing safety with sensitivity. However, notice that contrary to Lottie's case, it is almost unanimously agreed that there is inductive knowledge in Chute Case. So, it is hard to see how Sosa could consistently deal with both Lottie's case and an example like Chute Case. If safety and sensitivity are being confused vis-à-vis Lottie's case, there is no consistent reason to think such confusion does not exist in the other example, given that both cases seem to feature (weakly) safe but insensitive beliefs.
4. Broncano-Berrocal's solution
Broncano-Berrocal (Reference Broncano-Berrocal2019) presents an alternative version of safety, which indirectly tracks “appropriate determining conditions,” as opposed to directly tracking truths of beliefs:
Indirect Safety: If S knows that p via a method of belief formation M, then the determining conditions in the actual world are appropriate and in nearly all (if not all) close possible worlds in which S continues to believe that p via M, the determining conditions for S's belief that p continue to be appropriate. (Broncano-Berrocal Reference Broncano-Berrocal2019: 48)
Broncano-Berrocal thinks that with Indirect Safety (IS), one can properly solve the lottery problem. Before considering his arguments, some clarifications are in order. “Appropriate determining conditions,” as Broncano-Berrocal defines the terms, are the kind of conditions that determine whether an agent's doxastic state matches the facts. In perceptual cases, for example, such conditions include proper lighting conditions, distance and the size of an object, etc. Determining conditions are to be differentiated from mere “enabling conditions,” such as the existence of oxygen – which enables, without determining – a belief-formation. Furthermore, Broncano-Berrocal (Reference Broncano-Berrocal2019) makes another crucial distinction between “conditions that make success likely” and “conditions that make success in the right way likely.” As he understands it, only the latter refers to conditions that allow a performance to constitute an achievement. To illustrate, suppose that all the targets in an archery field are replaced with powerful electromagnets, such that anyone who releases a (metallic) arrow will hit the target easily, regardless of the archer's abilities (Broncano-Berrocal Reference Broncano-Berrocal2019). Here, obviously the conditions that one is in make the success (i.e. hitting the target) extremely likely. In that sense, the conditions are appropriate for hitting the target. However, the conditions are inappropriate for one's shots to be considered as “successful in the right way,” or be considered as achievements, simply because the presence of electromagnets are unduly helpful to one's shots.
Analogously, Broncano-Berrocal thinks that knowledge must track appropriate determining conditions that allow one to attain true belief in the right way, such that the true belief can be considered as cognitive achievement. This, according to him, is not obtained in the lottery case. For basing one's belief on the mere statistical evidence gives rise to inappropriate conditions in which one's true belief cannot be counted as cognitive achievement. Put simply, mere statistical evidence is unduly helpful to getting truth, just as the presence of electromagnets is unduly helpful to hitting the target. I will let Broncano-Berrocal speak for himself:
More specifically, the kind of circumstances in which one merely bases one's beliefs on (strong) statistical evidence are analogous to the kind of circumstances in which one shoots metallic arrows in a field with powerful electromagnets. In both cases, the circumstances make success (shooting an arrow accurately) and cognitive success (believing correctly that one will lose the lottery) very likely, almost guaranteed. In other words, in both cases the circumstances are appropriate for succeeding simpliciter, cognitively or non-cognitively. However, they are inappropriate for succeeding in the right way, i.e., for achievement or cognitive achievement (knowledge).
As before, the reason is that, like the effect of the electromagnets, strong statistical evidence is unduly helpful. It is helpful because it makes one get things right in a great number of instances of belief formation, just as the electromagnets make one hit the bull's eye in many instances of shooting. It is undue (in the sense of improper) because, just as the electromagnets prevent each particular successful shot from being explained in the right way by the competent exercise of the archer's shooting abilities, mere statistical evidence makes the exercise of our cognitive abilities irrelevant in the explanation of why we come to get things right on each particular occasion. (Broncano-Berrocal Reference Broncano-Berrocal2019: 49; italics original)Footnote 11
Thus, Lottie's belief does not track the required appropriate determining conditions, and so it is unsafe according to IS, which explains why Lottie does not know.
However, I find Broncano-Berrocal's diagnosis of the lottery problem still problematic. In particular, the claim that the conditions (or circumstances) in the lottery case are such that one's true belief is not a cognitive achievement seems dubious. To illustrate, notice that in the standard lottery case, there are two cognitive steps required for forming the belief that one will lose the lottery:
(1) Via a certain method, one comes to believe that the odds of her ticket losing the lottery are massive. (Call this belief(probability).)
(2) Based on belief(probability), one believes that she will lose the lottery. (Call the latter belief(losing).)
Discussions of the lottery problem frequently (and narrowly) focus on (2). With more attention being paid to (1), however, we will find Broncano-Berrocal's diagnosis implausible. Consider:
Amy and Bill
Sally gives Amy and Bill each a lottery ticket, without telling them any information about the odds involved for winning. Amy is epistemically careful. She asks herself: “Couldn't the probability of losing not be so high?” Back at home, she decides to use her brilliant mathematical abilities to calculate the odds. Half an hour later, she gets the correct answer: 1 out of 1 million chance for winning. She then realizes that the chance of losing is too high, and thus believes that she will lose. Bill, with his pessimistic character, does not do any calculation, investigation, or the like. He just tells himself: “I doubt I could be the lucky guy. The odds of losing must be pretty high, anyway …” It turns out that the odds of their tickets’ losing are the same, and neither of them won.
This story shows that one may form belief(probability) in different ways, either haphazardly or carefully. Such a difference, as it appears, does not affect whether one knows she will lose or not. To the extent that both Amy and Bill base their belief(losing) merely on the probability involved, it seems neither of them know that they will lose.Footnote 12 That said, it is clear that Amy's, but not Bill's, belief(losing) constitutes cognitive achievement. Put colloquially, it is Amy who earned her true belief(losing) with her distinctive cognitive abilities. She deserves the credit.
Hold on, though. To the extent that Amy forms her belief(losing) based purely on the probability, aren't the conditions still “unduly helpful,” rendering the belief not cognitive achievement? I think such a response misses the point. Amy's (true) belief(losing) can be counted as cognitive achievement because she did a brilliant job in the first step – figuring out what the probability is. And such etiology matters. To illustrate, consider a swimmer who wins a gold medal in an Olympic 100 m freestyle. Suppose that she performed very well in the first half of the race (let's say her average speed in this period far exceeds the world record.) Then, her winning the gold medal certainly constitutes achievement, even if her performance in the latter half of the race is not as impressive as the first half. What matters is that her excellent performance during the first half is causally/explanatorily responsible for her winning the race. Analogously, just because Amy bases her belief(losing) purely on the probability – a step that Broncano-Berrocal deems as ‘unduly helpful’ – does not mask the fact that she did a wonderful job in the previous step of calculating the probability. To the extent that the latter is explanatorily/causally responsible for Amy's formation of (true) belief(losing), this belief does constitute cognitive achievement.
Thus, contra Broncano-Berrocal, at least sometimes one's belief(losing) could be cognitive achievement. Or, in his terms, the conditions do not have to be such that they are inappropriate for the belief to constitute achievement. Therefore, his solution to the lottery problem fails. And such failure leaves us with an interesting question: If one's belief(losing) could be cognitive achievement, then how to explain the intuition that the belief is not knowledge? To answer this question, we may compare Amy and Bill again. Notice that, although they have taken different routes to come to believe that the chance of losing is very high, their commonality is that they are both aware of the possibility of winning the lottery (i.e. the possibility in which their belief is false.) As I shall argue in the next section, it is precisely such awareness that serves to explain why subjects like Amy and Bill both fail to know, despite their differences in terms of achievement.
5. Safety-awareness account
In this section, I will propose an alternative way to solve the lottery problem on behalf of a safety theorist. In fact, as will be shown, the benefits of my account are not restricted to resolving the lottery problem; it has a broader appeal.
First off, some preliminaries. Recall that Pritchard adopts Safety(weighed) as opposed to Safety(weak) because he thinks that the latter cannot properly solve the lottery problem. But abandoning Safety(weak) straightaway solely on the basis of its inability to solving this problem seems a bit too quick. For one thing, setting aside the lottery cases, Safety(weak) seems remarkably more attractive than the other formulations of safety introduced in sections 1 and 2. Compared to Safety(weighed), Safety(weak) does not rely on the murky distinction between “close possible worlds” and “very close possible worlds.” As critics (e.g. Baumann Reference Baumann2008; Xu Reference XuForthcoming) have pointed out, giving a plausible and systematic account of “closeness relation” is not an easy task. Safety(weighed), however, seems to exacerbate the difficulty here by introducing the additional distinction between “close” and “very close” worlds. (If giving an account of “closeness relation” is already challenging, how could one get a good grip on the yet more complicated distinction here?) In a word, although “closeness relation” is a crucial component in a safety principle, it would be preferable for a safety theorist to let such relation play a relatively minimal role, without adding further complexities to it.Footnote 13 In this regard, Safety(weak) seems better than Safety(weighed).
Also, compared to Safety(strong), Safety(weak) moderately requires truths of beliefs in the majority of nearby worlds – as opposed to all of them – and so the latter nicely accommodates inductive knowledge.
Perhaps more importantly, the problem with Safety(weak) vis-à-vis the lottery cases is that it fails as a sufficient condition, rather than as a necessary condition. That is, Lottie's belief that she will lose is Safety(weak)-safe but does not amount to knowledge, which points out that this form of safety is insufficient for knowledge. Hence, a safety theorist has the option of retaining Safety(weak) and handling the lottery problem with other theoretical resources.Footnote 14
So, what else could be added to Safety(weak) to solve the lottery problem? Or, what is lacking in this account that prevents it from tackling the problem? To answer these questions, observe first that safety in general is an externalist modal condition, such that whether a belief is safe or not depends on the facts in the world – in particular, the facts which may secure modal stability of one's belief. Thus, safety leaves out factors regarding one's own perspective on the modal stability of her beliefs. More specifically, safety leaves out whether or not a subject herself is aware of any error-possibilities of her beliefs. I think once this “subject's part” is taken into account, a solution to the lottery problem on behalf of a safety theorist will naturally emerge.Footnote 15
Thus, notice that in lottery cases, since we assume that the subject forms her belief that she will lose on the basis of the probabilistic considerations alone, she is de facto aware of the (nearby) possibility of winning the lottery, where “awareness” can be simply construed as “belief.” That is, the subject believes (either implicitly or explicitly) that there is some close error-possibility in which she wins the lottery and thus her belief that she will lose is false. This is true even in Inflated Lottery Ball. Since Lottie does not know anything happened with ball 13, she is misled to believe that there is some close possibility in which she wins the lottery.
Some clarifications must be considered. First, it is not intended here that Lottie's awareness/belief must explicitly involve such terms as “close possibility” or “nearby possible world.” It is unlikely that ordinary people who play the lottery would form beliefs that precisely involve such concepts. The point is rather that what Lottie believes can be analyzed or interpreted in terms of “close possibility” or “nearby possible world.” For example, it is plausible that an ordinary player like Lottie would believe that there need not be many changes for her to win the lottery (“I just need to pick slightly different numbers!”), and such a belief can then be interpreted as belief regarding nearby/close error-possibilities.
Second, understanding “awareness” as belief means that my technical usage of the term “awareness” is, to some extent, detached from how this word is used in ordinary life. Ordinarily, “awareness” is factive – e.g., one cannot be said to be aware that it is raining outside if it is not really raining outside (Silva Reference Silva2019: 725). However, since awareness in the current context is understood as belief, just as belief is non-factive, the sense of “awareness” here also inherits the feature of being non-factive. This is not itself a problem against the account that I will present below. After all, the purpose of my theorizing is not conceptual analysis of the term “awareness.” (If the reader finds my usage of “awareness” unpalatable, simply substitute the phrase “awareness of nearby error-possibility” with “belief that there is nearby error-possibility.”) Indeed, as will be shown momentarily, the non-factive feature of my “awareness” allows the following account to accommodate the phenomenon of misleading defeat.
With these points in mind, let us consider the following proposal:
Safety-Awareness Account (SAA)
S knows that p, only if
(1) Safety(weak): S's belief that p is not only true in the actual world, but also true in most nearby possible worlds (where the subject forms the belief with the same method as in the actual world).
(2) Lack-of-Awareness: S is not aware of nearby error-possibilities, i.e. nearby possible worlds in which her belief that p is false.
(Notice that the phrase “Lack-of-Awareness” is not to be construed literally in terms of its face value. In many contexts, if one lacks awareness of something, it may sound as if the person is being negligent – e.g. “He lacks awareness of how serious the current situation is.” In this way, “lack of awareness” may sound undesirable and negative.Footnote 16 But it certainly seems odd that something undesirable and negative is necessary for knowledge. Indeed, in my usage of the term, “Lack-of-Awareness” essentially means “no-defeater,” which I will explain below.)
Now, SAA handles the aforementioned problematic cases nicely.Footnote 17 In Lottie's cases, again, her belief that she will lose satisfies Safety(weak), but since she is aware of some nearby error-possibilities of winning the lottery, her belief violates Lack-of-Awareness. So, she fails to know that she will lose. Turning to Chute Case and the newspaper example, since it is assumed that these examples feature knowledge, presumably the chute is functioning properly and the newspaper is a reliable one (otherwise there is no reason to think that the subjects know in these cases.) Yet, given these assumptions, there appears no special reason to think that these subjects are aware of any nearby error-possibilities under these ordinary circumstances.Footnote 18 So, the subjects’ beliefs plausibly satisfy Lack-of-Awareness. This, coupled with the point that the subjects’ beliefs are Safety(weak)-safe, implies that the current proposal preserves inductive knowledge and renders it possible to know one loses the lottery by reading a reliable newspaper.
Furthermore, adding Lack-of-Awareness to Safety(weak) is not an ad-hoc maneuver. For as mentioned earlier, the former can be independently defended as a “no-defeater condition.” That is, when S is aware of a nearby error-possibility where her belief that p is false, it seems quite plausible that she simultaneously acquires a (doxastic) defeater against her belief that p. Hence, her belief that p does not constitute knowledge. In this way, the notion of “awareness of nearby error-possibility” helps the safety theorist to accommodate the important phenomenon of knowledge-defeat, as any theory of knowledge should do. To illustrate, consider a paradigmatic example of knowledge-defeat from Chisholm (Reference Chisholm1966: 48). (See also Lasonen-Aarnio Reference Lasonen-Aarnio2010). At a time t1 Suzy comes to know that a certain object is red based on perception (she has normal perceptual abilities, the lighting is normal, etc.). At a slightly later time t2, she believes based on someone's false testimony that the object is illuminated by peculiar red lighting, lighting that would make objects of any color look red. In our terminology, it can be said that at t2 Suzy loses her knowledge that the object is red, because she is misled to believe(/aware) that some nearby error-possibilities exist – the possibilities in which the object is illuminated by the red lighting, without itself being red.
Indeed, understanding Lack-of-Awareness as a no-defeater condition also delivers fresh insights in solving the lottery problem. Although there are various attempts of addressing this problem in the literature, few have attempted to consider the case as one that involves the phenomenon of defeat. However, such an attempt seems to be both justified and interesting. In particular, we may claim that, the reason Lottie does not seem to know is because she has a doxastic, modal defeater – a defeater that essentially involves such contents as “I could be the winner,” “My belief of losing the lottery could turn out to be false,” etc. Furthermore, notice that “could” here – as explained above – refers to a relatively close error-possibility, at least from the subject's own perspective. And plausibly, such a defeater goes some way in undermining the epistemic status of Lottie's belief that she will lose. Specifically, due to the defeater's modal character, Lottie's mere probabilistic evidence becomes insufficient for adequately supporting (epistemically) her belief. It is insufficient in the sense that she must gain additional resources to eliminate the error-possibility of winning (say, by learning from the lottery announcement that she is indeed not the winner). And lacking such resources, she fails to know that she will lose. Put another way, the modal defeater functions in a way that it places a particular kind of epistemic demand on the subject – i.e. a demand for eliminating the close error-possibility.
6. Some lingering worries
6.1. Is SAA too permissive?
The set-up of the standard lottery cases – specifically, the point that Lottie forms her belief that she will lose based purely on statistical/probabilistic evidence – guarantees that Lottie is aware of the possibility of winning. In fact, even if a lottery player's belief is not formed on such a basis, it is hard for one who has minimal background information regarding a lottery to not be aware of the possibility of winning (unless one already knows the lottery is rigged). Being aware of such possibility is just part of the game, so to speak. Furthermore, I have argued that such awareness can be plausibly analyzed or interpreted in terms of awareness of nearby error-possibility, thus rendering Lottie's belief a violation of Lack-of-Awareness. That said, we may still conceive cases where one does not have such awareness. And such cases may put some pressure on SAA. The most reasonable counterexample I could think of goes as follows.
Imagine a five-year-old named Tom. Tom has no background information whatsoever about how lottery works. One day, his dad gives him a lottery ticket. His mom, who believes that the ticket is not a winner (based purely on the probabilistic considerations), tells Tom that he will lose the lottery. Tom trusts his mom, as usual, and comes to believe that he will lose the lottery.
Here, it seems far-fetched to say that little Tom is aware of the nearby possibility of winning the lottery. Indeed, we could even stipulate that he doesn't quite understand what “winning the lottery” really means – he just trusts his mom and literally believes that he will lose. So, Tom's belief satisfies Lack-of-Awareness. Assuming the belief is also Safety(weak)-safe, it seems that SAA implies that Tom can come to know that he will lose the lottery. But isn't this implausibly permissive? After all, even Tom's testifier – his mom – doesn't know that the ticket is not a winner. Then, how could a child who knows even less in general about the lottery than his mom have the fortune of knowing that he will lose? It thus seems that whether one is aware of nearby error-possibility or not doesn't matter.
In reply, I think that the reason why Tom doesn't know is fundamentally different from why we tend to think that the subject in the standard lottery case – or, for that matter, someone like Tom's mom – doesn't know. Put simply, these cases warrant different theoretical treatments. In the following, I will offer two resolutions, leaving it to the reader to decide which one is better.
First, since the above alleged counterexample only puts pressure on the sufficiency of SAA, we may appeal to some other account to explain it away. Consider transmission theory about testimony, the idea that if a hearer knows that p based on a speaker's testimony, the speaker must also know that p.Footnote 19 On this view, Tom doesn't know simply because Tom's testifier – his mom – doesn't know. Transmission theory is compatible with SAA, to the extent that SAA is not aimed at giving sufficient conditions for knowledge.
Second, and perhaps more ambitiously, a SAA-theorist may avail herself with a relatively more refined version of Safety(weak). In his criticisms of Pritchard's early “anti-luck epistemology,” Greco (Reference Greco2007: 302) argues that “safety must have its seat in S's cognitive abilities (or virtue) ….” What he means by “seat” here can be understood as one's “method” (broadly construed) that gives rise to the belief. In other words, not just any method can give rise to a safe belief. For a belief to be properly safe, in Greco's sense, it must be produced by a virtuous method that manifests the subject's cognitive abilities. (See also Greco Reference Greco and Fernández2016.)
Indeed, I find Greco's arguments for the above point plausible: Sometimes one's belief can be “safe” just by default, without manifesting the subject's cognitive abilities at all. A wishful thinker's belief that p is “safe,” if the world happens to be arranged in a way that p is stably true across nearby possible worlds (see Greco Reference Greco2007: 302). Plausibly, restricting safety to “virtuous method” avoids counting beliefs of this kind as knowledge.
Now, what counts as a “virtuous method” is a tricky issue that I cannot fully address here (cf. Hirvelä Reference Hirvelä2019, Reference Hirvelä2020). But it seems plausible to take Tom's belief as not being formed via a virtuous method. This is because a virtuously formed testimonial belief at least requires an adequate understanding of the content of the testimony. Given the set-up of the example, however, Tom does not have relevant background information about how a lottery works. He (almost blindly) trusts his mom that he will lose, without proper linguistic-interpretive understanding of what the testimony really means. (Notice that if he does understand properly, he should also be aware of the possibility of winning, in which case the imagined scenario would not be a counterexample at all.) Hence, Tom's belief is not properly safe, according to our more sophisticated safety principle. And this explains why he doesn't know he will lose. Compare this with another scenario where Tom's mom says to him: “Your granny has come to visit you – she is downstairs!” Assuming what mom says is true and that Tom accepts her testimony, we may take him to know that his granny has come to visit him. For even a five-year-old may have the linguistic-interpretive abilities to understand the content of the testimony here: he knows which individual is his grandma, he understands what is meant by “visiting him,” etc. In this way, Tom's testimonial belief that his granny is visiting him is virtuously formed and is properly safe.Footnote 20
6.2. Is SAA too demanding?
Another worry takes a different direction. Notice that most (if not all) human cognitive faculties are fallible. Thus, for a subject S and a belief p that she holds, S may (at least implicitly) believe that p is possibly false. But then, isn't such awareness an awareness of “nearby error-possibility”? If so, skepticism seems to be a result of Lack-of-Awareness. And so, the latter cannot be what is required for knowledge.
We may call the fact that human cognitive faculties are fallible a kind of “generic error-possibility.” Merely being aware of such a fact is not a violation of Lack-of-Awareness. For such a generic error-possibility cannot be evaluated as either nearby or remote – it is just a brute fact. One needs to look at a particular scenario that one is aware of – a scenario which instantiates the generic error-possibility – in order to determine whether what one is aware of is remote or nearby. And crucially, in the kind of good cases where knowledge is intuitively present, the scenario one is aware of tends to be remote. Take memory as an example. Right now, I am (episodically) remembering that I met my colleague Joe a moment ago. Indeed, I just had a conversation with him in the hallway of our department building. My memory of meeting him is remarkably vivid and clear. And I, let's assume, have normally functioning, though not infallible, memory systems. Granted, even under this benign circumstance, there is still the possibility of me misremembering – a possibility that I could be aware of. But what would such a possibility look like? Presumably, we could only conceive of rather remote ones: Perhaps a few hours ago someone managed to put a hallucination drug in my coffee mug, so that now I am hallucinating that I just met Joe? Or perhaps a demon just controlled my mind, etc. Assuming that the actual world is just the way we think it is, these possibilities are clearly remote ones – they involve too many changes from the actuality. Fortunately, being aware of such remote error-possibilities doesn't violate Lack-of-Awareness, as the latter only concerns nearby ones. Thus, to the extent that in the good cases error-possibilities one could be aware of do tend to be remote, embracing Lack-of-Awareness does not commit one to skepticism.
Relatedly, it's worth noting that the present observation also helps to address some other problematic cases in epistemology.Footnote 21 Take Greco's (Reference Greco2007: 300) typing monkey case as an example: “A monkey sits down at my computer and starts banging away at the keyboard. I believe that he won't type out a perfect copy of War and Peace.” (Vogel Reference Vogel1999: 165 presents a similar example.) Here, intuitively, my belief constitutes knowledge, even if I am aware of the possibility of the monkey typing out War and Peace. SAA can explain the presence of knowledge here: the possible world in which the monkey types out the book is fairly far away from the actual world.Footnote 22 After all, given the length of War and Peace, in the relevant error-possibility the monkey would have to type numerous keys differently compared with the actual world (assuming that in the actual world the monkey is not typing out anything close to War and Peace.) Thus, the error-possibility involves many relevant changes compared with the actual world, so that even if I am aware of it, my awareness does not lead to a violation of Lack-of-Awareness. In addition, plausibly my belief is true in most nearby possible worlds where I continue to hold the same belief. In this way, the belief is also Safety(weak)-safe. SAA thus correctly predicts knowledge in the present example.Footnote 23
