Somebody here might find this interesting, I dunno. We’ll see.
My friend asks me if I would like to join him on an African Safari this summer. I tell him, ‘You know I won’t be able to afford that!’ Then he says, ‘No I don’t. You own a lottery ticket, after all. Grand Prize, £8,000,000!’ Who spoke truly? Explain why. Relate your answer and explanation to contextualism, subject-sensitive invariantism, and classical invariantism.
I shall identify three particular answers to this ‘lottery puzzle’ - contextualism, subject-sensitive invariantism (SSI) and classical invariantism - clarifying each by giving their respective treatments of the puzzle. I shall then defend a modified version of contextualism against two objections given by John Hawthorne in his Knowledge and Lotteries. I shall finish by explaining why I think contextualism offers the best available treatment of the puzzle. Note that we can state our puzzle in dialogue form:
Dougal: Do you want to go on African Safari this summer?
Ted: You know I won’t be able to afford that!
Dougal: No I don’t. You own a lottery ticket, after all.
We need an account of how a subject, S, can come to know a proposition, p, at a time, t. I shall assume that on any account something like the following is required, but not necessarily sufficient, for knowledge. We can call this the justified true belief (JTB) account.
- S believes that p
- S has a justification for their belief that p
- p is true
We need to distinguish between the ascriber and the subject of the knowledge ascription. If Ted says that Dougal knows something, Dougal is the subject, Ted the ascriber. We can ascribe knowledge to ourselves, ‘I know that p’. We can now distinguish three particular theories.
- Contextualism: Take the word ‘clean’. Standing in my kitchen, I say ‘this kitchen is clean’. Suppose a surgeon wandered in and said ‘I can’t perform surgery in here, it isn’t clean’. Who spoke correctly? We might be inclined to say that we both spoke correctly, its just that the standard of cleanliness required to qualify as ‘clean’ varies between contexts. For the purposes of passing a house inspection, my kitchen is clean; for the purposes of a medical operation, it isn’t.
Contextualists claim that ‘knows’ is context dependent in this sense. We will develop this throughout the essay, so I will just offer a rough sketch here. Each ascriber has an ‘epistemic standard’. Say I have low standards. I am inclined to ascribe a lot of knowledge to people. Say Jack has high standards. He will be inclined to ascribe a lot less knowledge to people. So of the same subject, S, I can say ‘S knows that p’, Jack can say ‘S does not know that p’ and we can both speak correctly. Whether S knows that p depends upon the ascriber. Each ascriber has his own standards, so the word ‘knows’ does not express the same relationship between ‘S’ and ‘p’ in both statements. So whether S knows p varies with context. It is crucial to note that it is the standards of the ascriber that determines whether S ‘knows’ p, not the standards of S.
Hopefully the contextualist treatment of the puzzle will clarify this. Let us assume that Ted is in a low standards context. The notion of an epistemic standard is still vague. The idea is as follows. Ted is considering whether he can afford to go on Safari. He owns a lottery ticket, but he isn’t considering this right now. The possibility that he might win the lottery is not relevant to Ted at this point. According to contextualism, Ted could correctly say ‘I know I can’t afford to go on Safari’. This is what being in a low standards context means: not considering any number of possibilities that would lead to a denial of knowledge ascriptions. I shall consider what makes a possibility relevant later. Given this, in our dialogue Ted speaks truly. In Ted’s context, the word ‘knows’ expresses a relationship that holds between Dougal and the proposition ‘Ted won’t be able to afford to go on Safari’. Now, consider what happens when Dougal mentions that Ted owns a lottery ticket. Presumably this means that Dougal was always aware that Ted owned the ticket. This means the possibility that Ted might win the lottery is relevant to Dougal. So, given Dougal denies of himself that he knows Ted won’t be able to afford to go on Safari, Dougal speaks correctly. In Dougal’s context, the word ‘knows’ expresses a relationship that does not hold between Dougal and the proposition ‘Ted won’t be able to afford to go on Safari’. So, the contextualist treatment is the following: both Ted and Dougal speak correctly. This isn’t contradictory because the word ‘knows’ is context dependent: it expresses different relationships in Ted’s low standards context and in Dougal’s high standards context.
- SSI: To a contextualist, the epistemic standard of the ascriber determines whether S knows p at t. This standard is determined by what possibilities are relevant to the ascriber at t. SSI is the view that only the standards of the subject matter, where we think of these standards in a similar way to the contextualist. We retain the JTB account from before and add that the strength of justification required for knowledge depends upon the epistemic standards of the subject. Crucially, ‘knows’ is now context independent: it doesn’t vary with the ascriber, as only the subject matters. At t either S knows that p or does not know that p.
Let us examine the SSI treatment of the puzzle. Again, let us assume that for Ted the possibility that we might win the lottery is, prior to the dialogue, irrelevant. If Ted were to say ‘I know I can’t afford to go on Safari’ this would be a true statement. But he ascribes this knowledge to Dougal, who, as before, is aware of the lottery winning possibility. This makes it relevant so Ted’s statement is false. When Dougal says of himself that he doesn’t know, given the above, this is correct. So Ted speaks falsely, Dougal truly. Note that Ted and Dougal could never both speak truly on the SSI account as to claim so would be contradictory.
- Classical Invariantism: SSI is a form of invariantism, which is just the claim that the relationship expressed by ‘knows’ is invariant between contexts. SSI adds to the basic invariantist account that certain factors about what possibilities are relevant to the subject are important. Classical invariantism denies this, and will affirm something like the JTB account. This view is just the traditional one in epistemology so I won’t spend time explaining it. With regard to the puzzle, as with SSI it needs to be the case that either Ted or Dougal speak truly. For a sceptical invariantist, Dougal will speak truly. For a non-sceptical invariantist the situation is less clear, though in general there will be situations like the one given where a knowledge ascription will turn out to be true.
I am going to argue that the contextualist treatment is the best available, but I will first deal with two objections. Once I have dealt with these objections I will explain why contextualism should be preferred to SSI and classical invariatism.
Objection 1: Contextualism, knowledge and assertion.
In his Knowledge and Lotteries, John Hawthorne objects that contextualism severs the link between assertion and knowledge. We have the notion of an assertion being proper or improper. But just what is it to assert something properly? The following principle seems tempting:
Proper Assertion: S properly asserts that p iff S knows that p.
This seems intuitively sensible. To assert that p is to claim that p is the case. So wouldn’t it be improper to claim that p without knowing that p? We need to note that the following principle also seems intuitively valid:
Closure: If S knows that p, and knows that q follows from p, then S is in a position to know that q.
Contextualists hold this principle, but only within a fixed context. Say Ted initially knows he won’t be able to afford to go on Safari, where Ted ascribes knowledge to himself. If he were to deduce that he won’t win the lottery, without the lottery possibility (i.e. the possibility that he might win) becoming relevant, he would know that he won’t win the lottery. However this generally isn’t possible: a possibility we are considering must be relevant. So Ted doesn’t know that he won’t win the lottery, but we have moved to a higher standards context, so there is no closure failure.
Let us illustrate the problem with regard to our puzzle. Ted is in a low standards context, Dougal a high one. Suppose I were in a low standards context. I can truly say ‘Ted knows he won’t be able to afford to go on Safari’. Suppose Ted were to assert that he won’t win the lottery. Now, due to closure, Ted knows that he won’t win the lottery. So, according to our principle, Ted should have made a proper assertion. But it seems there is a sense in which Ted should not have asserted this. Consider Dougal: he would deny that Ted knows that he won’t win the lottery, making Ted’s assertion improper. We have a result that shouldn’t be surprising if we consider our principle of proper assertion. Given we use the word ‘knows’ in the principle, whether an assertion is proper or not must vary with context, as ‘knows’ varies with context. The problem is that the propriety of an assertion is not usually thought to vary with context. We might think that to assert ‘I know I won’t win the lottery’ is always improper, despite what contextualism says about our ability to know this.
I wish to defend contextualism by denying that this is a problem. I am going to argue that we should view proper assertion as context dependent. Consider what motivates contextualism about ‘knows’. Remember that a surgeon’s need for a sterile environment for surgery doesn’t mean my kitchen isn’t clean for my purposes. We wanted to say that both the surgeon and myself speak truly. I would like to consider the concept of an epistemic standard as follows. A lower standard context is one in which fewer possibilities are relevant. What determines whether a possibility is relevant are my practical interests or purposes. When I am in the process of booking a summer holiday I have certain interests; I want to get the best deal etc. That I might win the lottery is irrelevant to me - it can’t dictate my course of action. Consider what happens when I have booked the holiday and discuss my plans with a friend. He asks ‘why aren’t you going on Safari’? I say ‘You know I can’t afford it.’ My friend replies ‘that’s not true, you have a lottery ticket’, I agree with this. My interests are now more theoretical, less practical, and I am made aware of the lottery possibility. I no longer take my friend to know I can’t afford it. This is what I take to motivate contextualism about knows.
Now consider assertion, and its role in deliberation. We make assertions in, for example, practical reasoning and theoretical speculation. Take the former. I make assertions when engaged in practical reasoning in order to determine what to do. This makes my purposes important. Parallel to the story about ‘knows’, when I consider where to go on holiday it seems perfectly proper to assert that I know I can’t afford to go on Safari. To assert anything else would be bad practical reasoning: I certainly shouldn’t put off booking my holiday by the possibility that I might win the lottery. Indeed, it seems I could even properly assert that I know I won’t win the lottery: again, the possibility has no role to play in practical reasoning in this type of situation. Here, lottery possibilities are ‘deliberatively irrelevant’. Consider theoretical speculation. My purposes are now to consider all possibilities. Now, the assertions I made previously would be incorrect if asserted in such a situation. Here lottery possibilities are ‘deliberatively relevant’. So, it seems clear that we can tell a story where our norms of proper assertion track the truth-value of knowledge ascriptions. We can put forward the following principle:
Proper Assertion*: S properly asserts that p in a context C iff S knows that p in the same C (where we treat ‘knows’ as a contextualist would).
Returning to the puzzle, that Dougal considers Ted’s assertion improper is because in Dougal’s context Ted doesn’t know that he won’t be able to go on Safari. Dougal’s standards determine whether Ted knows and whether Ted’s assertion is proper. Ted, however, can consider his own assertion proper along with an ascription of knowledge to himself. It should be clear that we are just telling the same story for ‘proper assertion’ as for ‘knows’.
I am not claiming that a contextualist needs to make ‘proper assertion’ context dependent. But I feel this move has a certain consistency, as what motivates it are just similar considerations to those motivating contextualism about ‘knows’. Defending this combined contextualism about knows and correct assertion will be a task of this essay.
Objection 2: Contextualism and propositional attitude reporting.
In his Knowledge and Lotteries, Hawthorne thinks the following principle about ‘knows’ is correct:
Disquotational Truth-Schema for Knows (DSK): “If an English speaker, E, sincerely utters a sentence s of the form ‘A knows that p’…. then E believes of A that A knows that p and expresses that belief by s.”
Hawthorne thinks that a contextualist cannot endorse this principle. Why is it attractive? If I say of Jack that he knows that whiskey is bad for him then it seems intuitively true that I believe of Jack that he knows this. So why can’t contextualists endorse this?
Add Jack to our dialogue, where Jack is in a low standards context. Suppose Ted can say ‘Jack knows Ted can’t afford to go on Safari’. So, using DSK, we would say that Ted believes that Jack knows this. DSK is meant to be true in all contexts, so Dougal should be able to accept it. Therefore, Dougal should be able to say of Ted that he believes that Jack knows that Ted can’t afford to go on Safari. But Dougal can say no such thing: Jack knows nothing of the sort. Jack does not know that Ted can’t afford to go on Safari, where ‘knows’ refers to Dougal’s context.
As a reply to the first objection I moved to the context dependence of proper assertion. I think a similar move is needed here: we need to find a way of recognising that ‘knows’ is context dependent in the above principle. Let us consider how, as contextualists, we would apply DSK. When Ted says of Jack that he knows ‘Ted can’t afford to go on Safari’ this expresses a particular relation between ‘Jack’ and the proposition that he knows. Ted forms the belief as in DSK. This belief is a belief about Jack and the relation that holds between Jack and the proposition. Now consider how Dougal views the situation. He is presumably aware of all this, and of DSK. Dougal isn’t going to deny that Ted has a belief. And what belief Ted actually has isn’t something that can vary between contexts. At this point, a contextualist could argue, when Dougal considers what Ted believes the qualification ‘knows by his standards’ will become embedded in the belief ascription. Dougal is going to think that Ted believes that Jack knows, by Ted’s standards, that Ted can’t afford to go on Safari. So, what Dougal could say truly is ‘Ted believes that Jack knows, by Ted’s standards, that Ted can’t afford to go on Safari’. Now, the claim cannot be that any person in such a situation would really say this. Dougal would be likely to say ‘Ted believes that Jack knows that Ted can’t afford to go on Safari, but he doesn’t really know that’. This is a particular instance of the problem of ‘semantic blindness’: English speakers, generally, treat ‘knows’ as context independent. I am going to briefly consider this problem later. But, for now, the contextualist can endorse the following:
DSK*: If an English speaker, E, sincerely utters a sentence s of the form ‘A knows that p’…. then E believes of A that A knows, by E’s standards, that p and expresses that belief by s. Another English speaker, F, can report of E that E believes that A knows, by E’s standards, that p.
We have modified DSK so that a contextualist can say something similar, capturing what makes DSK so appealing. I have told a story explaining why we could modify DSK in such a way. Both of my replies to Hawthorne’s objections share the common feature that they won’t convince anyone to become a contextualist. The first extends contextualism to proper assertion; the second shows that contextualists are committed to extensive ‘semantic blindness’. So why should we be contextualists?
Blindness and why we should be contextualists.
Picture another scenario. Suppose Ted is driving to the bank on a Friday afternoon to deposit a cheque. He notices a long queue, remembers the bank was open on a Saturday recently and is in no rush to cash the cheque. Suppose Dougal is doing the exact same thing, notices the queue, possessing the same purpose and the same memory. But Dougal urgently needs to cash the cheque, otherwise he will go bankrupt. This puts Ted in a low standards situation, Dougal in a high standards situation. SSI would say that Ted knows the bank will be open on Saturday, Dougal doesn’t. But Dougal would be expected to assert that Ted does not know that the bank will be open on Saturday. This assertion, by SSI, is false. But it seems to be a fairly sensible assertion. We can think of this as a type of blindness: we sometimes are too pessimistic with our knowledge attributions.
In his 2005 paper Stanley presents the above blindness as a problem for SSI and suggests a response that somebody holding SSI could make. When we enquire into whether a subject knows that p we don’t do so disinterestedly; we want to establish whether p is the case. What we are asking is ‘if the subject had my interests, would they know that p?’ As such, we tend to project our standards onto the subject, hence the pessimism. Dougal wants to establish whether the bank is open on Saturday. If Ted had Dougal’s interests, he wouldn’t know this; hence Dougal denies that Ted has knowledge. We can at least ‘explain away’ the blindness.
My question: given this highly plausible description of ‘epistemic practice’, why hold that this is just a projection? Rather, why isn’t it the case that our standards determine what people know? Is this story not just the story I gave about epistemic standards? I think Stanley is largely correct about the purpose of enquiring into what people know. But if the entire purpose of such enquiry is to determine what S would know if S had my interests, why can’t we just say that what S knows is determined by my interests. As before, maybe I want to plan my holiday: I need to know where I can go. So I try to establish where I can go, with lottery possibilities being irrelevant. It is my standards that are important. Of course, to someone else, it is his or her standards that matter. But this is just the claim that ‘knows’ is context dependent. So, if Stanley properly characterises epistemic practice, this seems to give support to contextualism.
Now, none of this is conclusive. Maybe this doesn’t properly characterise epistemic practice. All I want is a sense of why contextualism might be preferable to SSI. In order to deal with the problem of blindness, SSI is led to posit a description of epistemic practice that seems to lend support to contextualism. Remember the case of the surgeon and the kitchen. Why do we enquire into the cleanliness of things? It is for practical purposes. The interests of the surgeon determine whether the kitchen is clean for the purposes of surgery. My interests determine whether the kitchen is clean for the purposes of everyday use. Whether the kitchen is clean or not depends upon the purposes of the enquirer. Whether a subject knows that p or not depends upon the interests of the ascriber. If the purpose of epistemic enquiry is practical, we have an argument for contextualism.
We can now consider the charge of ‘semantic blindness’ levelled at contextualists. I don’t have a full reply to this, partly because I think we need to accept that people do treat ‘knows’ as context independent. When I consider that I own a lottery ticket I may well say ‘I never knew I couldn’t afford to go on Safari after all’. But, consider the case of ‘clean’ we take as paradigmatically context dependent. When pressed by the surgeon I may well say ‘Ok, my kitchen isn’t clean after all’. This, superficially, appears to be no different to the case of ‘knows’. So my reply is that the charge of semantic blindness about ‘knows’ is only as strong as the similar charge about ‘clean’. Generally, to claim any word is context dependent will lead to the charge of semantic blindness. I won’t undertake the task of showing that there are context dependent terms here, but if there are such terms we do have what seems a good response to the objection.
As for classic invariantism, the problem for this view is how to deal with scepticism. By closure, either Ted knows he won’t win the lottery or he doesn’t know he can’t afford to go on Safari. But how could he know he will not win the lottery when there is a non-zero chance that he will? We end up with another type of ‘blindness’: many ordinary knowledge ascriptions are false. Note we don’t need to use a lottery scenario. There is a non-zero chance that this essay will suddenly turn into a whale due to a freak quantum event. So once this essay is filed away, do you know its still in your drawer? Maybe there is a response to this problem. But I know of no response that I find satisfying. I think this gives a prima facie reason to reject classical invariantism, if we have an available alternative. This leaves us with a choice between contextualism and SSI. Given my criticisms of SSI, I think we have a reason to accept contextualism, which we have modified to cope with Hawthorne’s two objections. So the best available answer to the lottery puzzle is the contextualist one: both Ted and Dougal speak truly.
Bibliography
Hawthorne, John - Knowledge and Lotteries (Oxford University Press, 2004)
Lewis, David - ‘Elusive Knowledge’, in Australasian Journal of Philosophy 74 [1996], pp. 549–67
Stanley, Jason - ‘Interest-Relative Invariantism’, in Knowledge and Practical Interests (Oxford University Press, 2005)
Williamson, Timothy - ‘Contextualism, Subject-Sensitive Invariantism and Knowledge of Knowledge’, in Philosophical Quarterly 55 [2005], pp. 213–235
Williamson, Timothy - Knowledge and its Limits (Oxford University Press, 2000)
Cohen, Stewart – ‘Contextualism, Skepticism, and the Structure of Reasons’, in Philosophical Perspectives 131 [1999], pp. 57-89