Knowledge , Safety , and Questions

Safety-based theories of knowledge face a difficulty surrounding necessary truths: no subject could have easily falsely believed such a proposition. Failing to predict that ill-grounded beliefs in such propositions do not constitute knowledge, standard safety theories are therefore less informative than desired. Some have suggested that the subjects at issue could easily have believed some related false proposition; but they have given no indication as to what makes a proposition related. I suggest a solution to this problem: a belief is safe iff its subject could not easily have believed a false answer to the same question.

fair, serves as an oracle.He comes to the view that if the next toss of his coin lands heads he wi l be freed tomor ow, but that he wi l not be freed until later in the week if the coin lands tails.He tosses the coin, it lands tails, and he comes to the view that he wi l be in prison tomor ow night.If this is the only reason Crazy believes he wi l be in prison tomor ow night, then he does not know that he wi l be, even though his belief is safe.
So the idea is not that knowledge consists in safe belief: rather, it seems that safety is a consequence of knowledge.More ecifica ly, the safety of a knowledgea le belief might be thought to fo low from the fact that knowledge must have an ap ropriate doxastic-cum-epistemic basis or ground.If a belief has such a basis-which, if it is to be knowledge it mustthen, the ar ument goes, if its object were false, that basis for belief would not have been availa le, and the belief would not have been held.So the belief in question could not easily have been falsely held, and knowledgea le beliefs are safe.
That this is the central idea underlying safety theories can serve to explain the fo lowing otherwise potentia ly puzzling claim of Wi liamson's: In many cases, someone with no idea of what knowledge is would be unable to determine whether safety obtained.[…] One may have to decide whether safety obtains [in such cases] by first deciding whether knowledge obtains, rather than vice versa (2009, p. 305).
If safety theorists such as Wi liamson were proposing to reduce knowledge to safely true belief, this might be thought to be pro lematic; but if instead safety is held to be a consequence of knowledge, then it can simply be maintained that certain possibilities are more similar to the actual case (and therefore could easily have obtained) than others (which could not) because they hold fixed whether knowledge obtains in those cases, and so they hold fixed the actual grounds for belief.
Nonetheless, even if safety is not thought to be sufficient for knowledge, the claim that safety is necessary for knowledge yields determinate predictions, and so is informative.For it is possi le to ar ue, and in some sense explain the fact, that a belief does not constitute knowledge by showing that it is not safe.If Jai bird could easily have been paroled tomor ow morning, his belief that he wi l be in prison tomor ow night would not constitute knowledge since it could easily have been false, not being connected to its truth in an ap ropriate manner.

The Problem of Necessary Truths
There is, however, a pro lem.Any belief in a necessary truth is safe.While this fact does not present the theory with any counterexamples, it does make the safety condition, as formulated above, utterly trivial and uninformative in these cases.We cannot ar ue that a belief in a necessary truth is not knowledge on the grounds that it isn't safe.For instance, if Crazy Mathematician thinks her actua ly fair coin is an oracle, then she might come to the view that Fermat's Last Theorem is true if, and only if, the next toss of her coin lands heads: if it then does land heads and she comes to believe that Fermat's Last Theorem holds, her belief does not constitute knowledge; yet we cannot ar ue that it does not by ap eal to the safety condition articulated above, for her belief couldn't have been false, and so, a fortio i, could not easily have been false.This pro lem of necessary truths might be thought to restrict the interest of the safety requirement on knowledge. 4i liamson (2000, p. 181-182) responds to this pro lem by su gesting that what matters for the safety of a belief is not whether that very belief could easily have been false but whether the subject could easily have had a false belief in a related proposition.5This, it seems to me, is cor ect in so far as it goes.But it is va ue.Which propositions count as related?
My proposal, roughly eaking, is that a proposition is related to the proposition that p if, and only if, it is an answer to the same question.One way to fi l this out is to say that a belief that p is safe if, and only if, the subject could not easily have had a false belief on the question whether p.As we sha l see, if this ecific proposal is adopted, pro lematic cases wi l remain: but perhaps a slightly more general idea wi l suffice; and in any case, even the ecific proposal yields a non-trivial constraint on our knowledge of necessities.But we wi l come to a l of this in due course.

Questions
First, we must ask: What is a question?It wi l be useful to ap roach this issue via the distinct but related question, What is a proposition?Propositions are quite familiar to philosophers.They are the objects of certain eech acts, e.g. the declarative eech act of assertion; they are what we assert when we assert something.They also occur semantica ly embe ded in indirect discourse constructions such as "Amy said that it is snowing, " and in certain attitude ascriptions, e.g."John believes that it is raining." Fina ly, they are the objects of certain psychological attitudes, such as belief-namely, the propositional attitudes.
More substantively, there has been some dispute about what propositions are.For instance, there is an internal disagreement amongst those who think of them as structured entities about what the nature of their constituents might be, with neo-Russe lians holding that they comprise objects, properties, and relations as parts, and neo-Fregeans maintain-ing that the constituents in question are rather modes of presentation of such worl ly entities: however, those working in formal semantics have found it useful to think of propositions as (unstructured) sets of possi le worlds; and in any case, everyone can at least agree that they deter ine sets of worlds.
Similarly, then, a question is the object of a certain kind of eech act, e.g. the inter ogative act of asking: it is what we ask when we ask a question.It is also, semantica ly eaking, the object of the verb in certain lin uistic constructions, e.g."John wondered who took the last cookie, " and "Mary asked whether it was raining." And Jane Friedman (2013) has recently ar ued that questions are the objects of certain kinds of psychological attitudes-attitudes such as wondering, which she ca ls interrogati e attitudes.
Formal theorists (e.g.Ham lin, 1973) have found it useful to think of questions as sets of their (complete) answers, that is, as sets of propositions that (completely) answer them.Thus, if propositions are sets of possi le worlds, questions are families (or sets) of (certain) such sets; and in any case, everyone can agree that they deter ine such sets of sets of worlds.Thus, we may say that questions are, or determine, partitions of the domain of possi le worlds. 6ome answers are complete and others are incomplete.Sup ose I host a party, that Amy, Bob, and Charlie come, and that Doug and Emily do not.(And let's sup ose that there are no other people.)Then the question, Who came to the party?can be answered completely by saying that Amy, Bob, and Charlie did.Another possi le complete answer is that Charlie and Doug did.This alternative answer is not a cor ect answer, but it is a possi ly cor ect, complete answer.By contrast, the proposition that Amy came to the party cor ectly answers the question, but does not answer it completely.

A Solution
With this background in place, we can now say what it is for a belief to be safe.A first, simple proposal is that S's belief that p is safe if, and only if, S could not easily have had a false belief on the question of whether p-that is, the question whose two complete answers are p and not p.This deals with some instances of the pro lem of necessary truths, for instance, the case of the Crazy Mathematician discussed above.The subject's belief in that case is safe in the Ichikawa-Steup sense above, but intuitively it does not constitute knowledge.Yet the new account of safety readily accounts for the failure of knowledge in this case, since the Crazy Mathematician could easily have had a false belief on the question of whether Fermat's Last Theorem is true; indeed, she would have done had the coin she tossed landed tails (which it could easily have done).Thus, her belief is not safe in the new sense; and since its being so is necessary for it to constitute knowledge, she does not know Fermat's Last Theorem.
However, there remain pro lematic cases.Consider the fo lowing example, due to Roland and Cogburn, which involves Sam, whose calculator is broken so that it always tells the user that whatever number entered is prime.Sam uses his calculator to randomly check whether or not [some prime number p] is prime, and it answers affirmatively.As a result, Sam forms the true belief that [p] is a prime number (2011, p. 550).
In this case of the Broken Calculator, Sam could not easily have formed a false belief on the question of whether p is prime, since he could not easily have formed the belief that it is not prime: accordingly, his belief is safe, not only in the Ichikawa/Steup sense, but also in the sense just articulated; and Broken Calculator therefore shows that the safety constraint so construed is not sufficient for knowledge.
There are two things that might be said in response to this case.The first, more ambitious reply, begins by noting that the proposition that p is prime does not only answer the question whether p is prime; it is also a partial answer to the question, Which numbers are prime?Moreover, Sam could easily have had a false belief on this question: after a l, he selects p as the number to check at random; and had he decided to check some composite number c instead, he would have formed a false belief in (partial) answer to the question of which numbers are prime-namely, the false belief that c is prime.
This su gests that a more subtle safety condition on knowledge might be articulated as fo lows: a subject S's belief that p is safe if, and only if, S could not easily have believed a false answer to the question Q to which p is saliently an answer.Clearly, though, this su gestion does not determine precisely which question this is; so it does not yet resolve the va ueness of the Wi liamsonian proposal mentioned above.Nonetheless, there are a number of ways in which the proposal might be made more concrete, thereby resolving at least some of the underlying va ueness; and the ap eal to a salient question might provide a means of unifying the various propositions that are relevant to the safety of the belief at issue in a given case.
The second, more modest reply is to note that our aim was to find an informative constraint on knowledge of necessary truths; and, as we have seen in connection with Crazy Mathematician, the simple proposal that a subject S's belief that p is safe if and only if S could not easily have had a false belief on the question of whether p provides just that.Thus, in particular, if the case of Crazy Jai bird does not undermine safety-based ap roaches to knowledge, then the case of the Broken Calculator shouldn't be taken to undermine the proposal advanced here either.On the cur ent proposal, safe belief is not sufficient for knowledge, but it is both necessary and non-trivial, even when it comes to our knowledge of necessities-and that is exactly what was sought. 7

Concluding Remarks
I am not the first to propose that the theory of knowledge may benefit from the deployment of the notion of a question.Jonathan Schaffer (2007) has ar ued that knowledge is a three-place relation between a subject, a proposition, and a question. 8If he is right, then (assuming safety is a necessary condition on knowledge) that might explain why we need to ap eal to questions when explaining the notion of safety.Nevertheless, my proposal is different from-indeed, less committal than-Schaffer's, in two ecific (though not entirely unrelated) re ects.First, even on the ambitious proposal, I am not su gesting anything about the semantics in general, or the logical form in particular, of knowledge attributions.Accordingly, while the question that is salient might be determined by some feature of the context of eech, this is by no means required; it might, for instance, be fixed by some feature of the situation in which the subject finds him or herself. 9Second, my proposal, whether modest or ambitious, is concerned directly with safety, not knowledge; it therefore has no immediate implications for those who reject safety-based ap roaches to epistemology.Accordingly, those who reject Schaffer's position may nonetheless find something of value in what I have said here.
Other theorists have ap ealed tacitly to questions, while failing to do so explicitly.Thus, Nozick, for instance, in chara erizing his sensitivity-based account of knowledge, suggests that a subject who knows that p is such that she would believe that p if she were to "have a belief whether (or not) p" (1981, p. 179) in a case in which p; and she would not have the belief that p in the case in which not p.But the quoted phrase is not quite grammatical as it stands; what's needed for fu l acceptability is the insertion of (e.g.) "on the question (of)" between "belief " and "whether." With questions now being granted the philosophical re ectability long afforded to propositions, we can have no qualms about explicitly recognizing their role in the theory of knowledge. 10n any case, the notion of a question has, until recently, been relatively neglected in philosophical theorizing.I have found a new ap lication for it-in explicating the notion of safety in such a way that safety theorists of knowledge have a (relatively) precise and non-trivial theory of our knowledge of necessary truths.This not only constitutes an advance on this ecific topic; it also provides some further, if modest, inductive evidence of the theoretical utility of questions more genera ly. 11