Domination requires the truth of the conjunction [D1 & D2]. Zalabardo denies the truth of the conjunction by rejecting the second conjunct, D2.
But the first thing to notice is that ~ [D1&D2] alone cannot surely confer differential support for sensitivity. For ~ [D1&D2] is consistent with counterexamples to sensitivity. Sosa argued for domination, but he also propounded counterexamples to sensitivity. Sosa replaced sensitivity with safety because safety does not (ostensibly) succumb to counterexamples. On first blush: S knows that p only if S has a safe belief that p. Formally,
$$ Kp \to \left( {Bp \Rightarrow P} \right) $$
But that schema tells only half the story. Because, so far, we have not eliminated the necessity (“□”) of the sensitivity condition. Sosa argues that knowledge doesn’t require sensitivity (i.e. \( [ {\text{K}}p{ \nrightarrow }(\sim\,p \Rightarrow \sim\,Bp)] \)). Thus, Sosa’s safety premise is better represented as:
$$ Kp \to \left( {Bp \Rightarrow P} \right)\& \left( {\sim\square \left( {\sim\,p \Rightarrow \sim\,Bp} \right)} \right) $$
The above principle allows insensitive but safe beliefs to constitute knowledge. In sum: a belief having the property of insensitivity doesn’t affect its epistemic standing. It is therefore the conjunction of domination and Sosa’s counterexamples which are used to differentially support safety as the correct requirement for knowledge. That is, Sosa argues that there are no virtues which are exclusive to sensitivity AND there are some virtues which are exclusive to safety. Sosa’s best-known counterexample to sensitivity is this:
CHUTE: “On the way to the elevator I release a trash bag down the chute of my high rise condo. Presumably I know my bag will soon be in the basement. But what if, having been released, it still (incredibly) were not to arrive there? That presumably would be because it had been snagged somehow in the chute on the way down (an incredibly rare occurrence), or some such happenstance. But none such could affect my predictive belief as I release it, so I would still predict that the bag would soon arrive in the basement. My belief seems not to be sensitive, therefore, but constitutes knowledge anyhow, and can correctly be said to do so.” (Sosa 1999, p. 145)
Does safety accommodate CHUTE? Safety theorists will need the following verdict: if the chute is a regular smooth chute, then the bag-snagging world is not close. Conversely, if the chute has structural irregularities which leave it prone to bag-snagging, then the bag-snagging world is close. Notice that if the chute is prone to bag-snagging, then the example may also fail to elicit the intuition that the subject knows. If this is the case, then our safety intuition in CHUTE is covariant with the epistemic intuition that the subject knows the target proposition.Footnote 13
Nevertheless, even if the chute is smooth, the closest error worlds in CHUTE are not nearly as distant as the error worlds in which you or I falsely believe that we’re not a disembodied brain-in-a-vat, for example. That is, on a similarity ordering of possible worlds, the error worlds in CHUTE are not radically dissimilar to the actual world. After all, not that much would have to change—modally speaking—for the bag to snag. The error world is not distant enough for it to be uncontroversial that safety is satisfied. The worry, therefore, is that there is no principled way of excluding bag-snagging worlds from the domain of close worlds. The case rests on our intuitions about whether the error worlds are “close”, and here –I suspect—the case may fail to elicit clear reactions in either direction.
I want to concede that safety as Zalabardo formulates it fails to straightforwardly accommodate CHUTE (This concession is benign since I shall argue that sensitivity can’t be differentially supported). If this is so, then there are construals of safety which do accommodate CHUTE. Note first that Zalabardo construes safety strongly. For example, Zalabardo argues that S’s belief that p is safe just in case in every world in which S believes that p that is at a distance of d or less from actuality, p is true (p. 3). The inclusion of the universal quantifier “all” makes this safety condition modally strong because that quantifier prohibits the existence of any error world up to distance d or less from α. If CHUTE is a counterexample to sensitivity, then—so it goes—CHUTE is a counterexample to strong safety (for there exists at least one close possible bag-snagging world in which one falsely believes that the bag is in the basement). Hence, it has been claimed, CHUTE doesn’t motivate strong safety over sensitivity. However, we can see straight away that by adopting the non-standard translation key (NST) safety theorists needn’t endorse strong safety. Consider, for example, a more liberal version of safety:
Weak safety: S’s belief that p is weakly safe just in case in most worlds in which S believes that p that are at a distance of d or less from α, p is true.Footnote 14
CHUTE is not a counterexample to weak safety, because in most close possible worlds, one’s belief in the target proposition is true (Pritchard 2012, 2015). Indeed, in virtually all close possible worlds in which one believes that [the bag is in the basement], one’s belief in this proposition is true. This matters. Because when we assume strong safety, it seems that both sensitivity and safety conditions are roughly on par in the number of counterexamples to their necessity. However, the question of how many worlds are relevant to safety arises because safety theorists embrace NST. By embracing NST for safety, we can see straight away that there arises the question of how strongly or weakly safety ought to be construed. It is thus open to safety theorists to argue that sensitivity fails to dominate weak safety. To argue, in other words, that there are cases of knowledge possession which pass the weak safety test, but which fail the sensitivity test. In effect, to argue as follows:
(D1*) [Kp & (Bp) weakly safe] → (Bp) sensitive.
(D2*) [~ Kp & ~ (Bp) weakly safe] → ~(Bp) sensitive.
It cannot be said that sensitivity reaps every advantage reaped by weak safety. If sensitivity entails weak safety, while that guarantees D1, entailment doesn’t guarantee D1*. Entailment doesn’t stop sensitivity failing to dominate weak safety. And if sensitivity doesn’t dominate weak safety, then we can’t differentially support sensitivity.
Note, however, that there are cases of knowledge failure which are explained by strong safety but not by weak safety. Consider, for example, the following LOTTERY case. Imagine one buys a lottery ticket where the odds of winning are 60 million to 1. Despite these long odds, one’s pessimistic belief that L[I am in possession of a losing ticket] intuitively falls short of knowledge before the result is announced. Nevertheless, in most close worlds one’s belief that L is true, and so one’s belief that L is weakly safe. In contrast, so it goes, there exists at least one close world in which one has a false belief that L, hence one’s belief that L violates strong safety.Footnote 15 Strong safety succeeds here where weak safety fails, such that the retreat from strong to weak safety may seem ad-hoc.
Two points here. First, it is unclear that safety theorists are wedded to a construal of safety which can’t accommodate both CHUTE and LOTTERY. Consider Duncan Pritchard’s defence of safety (2008, 2012, 2015). Pritchard construes safety as an anti-veritic luck condition, one which explains cases of knowledge failure such as LOTTERY and Gettier-type cases. Importantly, Pritchard understands luck as a modal notion which admits of degrees, where the degree of luck pertaining to an event is proportionate to the modal proximity of worlds in which that same event fails to obtain. Pritchard’s safety condition is motivated by an extensive modal account of luck (see Pritchard 2015). Let’s focus on the account’s implications.
What is arguably problematic about LOTTERY is the very close modal proximity of the worlds in which one falsely believes that L. After all, as Pritchard reminds us, the closeness of lottery error worlds explains the lure of the game. In this case, we need only one error world to render the belief veritically lucky in a way which precludes knowledge. In contrast, it is not obvious that CHUTE error worlds are very similar to the actual world (Indeed, it’s controversial whether error worlds in CHUTE are even close) and hence the degree of luck at stake doesn’t undermine knowledge. Safety may handle CHUTE by requiring the elimination of all very close error worlds, with that tolerance gradually increasing as one moves further away from the actual world (Pritchard 2015, p. 101). By the time we reach the close error worlds in CHUTE, safety needn’t display complete intolerance of error.Footnote 16 Safety, at this point, still requires that one doesn’t falsely believe the target proposition at most close worlds. It is just that LOTTERY violates the safety condition in virtue of safety displaying complete intolerance towards falsity at worlds which are very close to the actual world. Weak safety is now supplemented with a strong safety condition, one which applies only to worlds which are very close to the actual world.Footnote 17
The second point, and notwithstanding Pritchard’s proposal, is that we need to judge the plausibility of weak safety overall. While weak safety doesn’t explain LOTTERY, weak safety does explain a class of cases of knowledge failure (Gettier cases, lucky guesses etc.) and—being a less demanding condition than strong safety—it trivially fares no worse than strong safety at corroborating intuitive cases of knowledge possession.Footnote 18 On this point, we must remember that the issue we are considering here is whether sensitivity can be supported over safety as a necessary condition for knowledge. CHUTE may undermine the necessity of strong safety, but LOTTERY—as a case of knowledge failure—undermines the sufficiency rather than the necessity of weak safety.
Weak safety is an improvement on strong safety as a candidate necessary condition for knowledge because weak safety succumbs to fewer counterexamples.Footnote 19 In sum: weak safety avoids at least one of the counterexamples which Sosa levied against sensitivity. This is not to vindicate weak safety as a necessary condition for knowledge, for it too might be vulnerable to counterexamples. However, at least one prominent counterexample to sensitivity doesn’t affect weak safety, such that Zalabardo’s case for differentially supporting sensitivity is undermined.