Another way to bring out my contrast between 'Moral Roots and Alienating Aspirations' is to consider the practical significance of higher-order evidence.
Suppose it seems to you that you ought to phi, but you also think that your judgment in this case could well be biased or otherwise impaired. You believe that other people in similar circumstances to yours have turned out to be mistaken. Moreover, others you consider to be moral experts -- reliably more insightful than yourself -- are unanimous in insisting that you should not phi. What should you do?
Objectivists must allow that appearances can be misleading, and so higher-order evidence can undermine our first-order beliefs. In the above scenario, it looks like your all-things-considered judgment should be that the totality of reasons that exist weigh against phi-ing, even though you do not currently have access to all those reasons yourself. The reasons in your possession count in favour of phi-ing, but as a realist you acknowledge that there may be other reasons beyond your grasp, and the views of experts can give you some indication of what the totality of reasons really favours.
What of the 'rooted' conservative/subjectivist? Here it is less clear. There may still be some room for overriding your personal judgments, e.g. if they rest on some merely empirical or logical error, and so do not really reflect your core values. But if we accept the Vellemanian position that what fundamentally matters is making sense to oneself, then there seems something deeply problematic about acting on mere "meta-reasons", i.e. the abstract promise of reasons out there that you have not fully grasped. You can't really make sense of your action, because even though there is abstract evidence that you did what is for the best, you do not yourself possess the grounds for this judgment; you don't, in other words, understand why it is for the best. So it may seem that you acted for reasons that are not, in some vital sense, your own.
This practical difference marks a vivid distinction between the two metaethical views. Whether we act for the sake of making internal sense to ourselves, or to make the external world better, will influence our receptivity to meta-reasons, and hence what decisions we make.
I take this to count in favour of objectivism, since it seems clear that we should be receptive to meta-reasons. As Dan Moller writes in 'Meta-reasoning and Practical Deliberation' [pdf] (p.26):Failing to act on second-level reasoning means, by definition, acting on the basis of flawed deliberations when there is evidence of how improving those deliberations would affect the outcome. To return to the general [who is biased towards cowardice by the recent deaths of his friends], he presumably cares about discharging his duties as a soldier with integrity, so why shouldn’t he pursue every available opportunity to improve his decision-making? It is true that in that pursuit he may cut himself off from ultimate comprehension of the reasoning that leads to the conclusion to send in the troops, but accepting that limitation would in this circumstance express precisely a commitment to his deepest values and identity as a soldier, not any sort of compromise or abdication.
Isn't the alternative a bit solipsistic?
Friday, May 16, 2008
Acting on Meta-reasons
Wednesday, May 14, 2008
Epistemic Conservatism and Meta-coherence
Some commenters in the thread on 'structure and similarity' proposed that we should work with whatever concepts we happen to start with -- green rather than grue, or vice versa -- and only change if there's a compelling reason to do so: "I do not have to assume that the way I cut up the world now is the best way (in fact I'm pretty sure it isn't), I just have to consider if the [change] that you are proposing has useful consequences."
However, this runs headlong into a problem that I highlighted in a previous post: that principles of metacoherence mean that such humble meta-beliefs rationally undermine our first-order beliefs. Or, as I put it in my comment:If you think that both inductive arguments are equally reasonable, and that there's no sense in which X is objectively more similar to Y than Z, then you have no grounds for believing one conclusion rather than the other (e.g. that future emeralds will be green rather than grue). By the principle of metacoherence, you should be agnostic.
I introduce this notion in my global rationality paper:Sometimes we may be in a position to realize that our initial judgments should be revised. I may initially be taken in by a visual illusion, and falsely believe that the two lines I see are of different lengths. Learning how the illusion worked would undercut the evidence of my senses. I would come to see that the prima facie evidence was misleading, and the belief I formed on its basis likely false. Principles of meta-coherence suggest that it would be irrational to continue accepting the appearances after learning them to be deceptive, or more generally to hold a belief concurrently with the meta-belief that the former is unjustified or otherwise likely false.
As I further explain in my post 'Meta-Coherence vs. Humble Convictions':It's [meta-]incoherent to believe that P whilst also believing that the weight of evidence fails to support P, since this is just to judge both [on the lower level] that P is true and [on the higher level] that P is probably not true after all.
If, faced with alternative possibilities, you nonetheless retain your belief in P, you must represent this to yourself as being because you judge that P is more likely true, and not just because you happened to have the belief in the past and don't feel like revising it. You can't consciously be an epistemic conservative, because the realization that you believe P partly for non-truth-related reasons will instantly lower your degree of belief in P, to match your assessment of the (subjective) probability that P is really true.
Some form of epistemic conservatism may be true nonetheless, in the trivial sense that we think our existing beliefs are true, and it will take positive work to convince us otherwise. But from a first-personal perspective, the reason we hold on to our existing beliefs is not the egoistic fact that they are our beliefs, but rather the "fact" (as it seems to us) that they are true. If you lose your confidence in the truth of a belief, and are "pretty sure" it's mistaken, then you can't sincerely believe it any more. You can't now appeal to epistemic conservatism as a way to hold onto your belief without judging it to be true. That's incoherent.
Monday, April 28, 2008
Meta-Coherence vs. Humble Convictions
G.A. Cohen points out that Oxford-trained philosophers tend to believe in the analytic/synthetic distinction, whereas Harvard-trained philosophers tend not to. As an Oxfordian himself, he believes in the distinction. But he could have gone to Harvard instead, and so ended up a Quinean. Should this fact undermine his belief?
More detail is required. Here are two possibilities:
(1) The reasons upon which the Harvardians' beliefs rest are, impartially considered, no less weighty than the reasons behind the Oxfordian view. (The difference in their beliefs is merely explained by the fact that each side is more familiar with their own reasons.) If you think this is the situation, then this should immediately undermine your belief. It's [meta-]incoherent to believe that P whilst also believing that the weight of evidence fails to support P, since this is just to judge both [on the lower level] that P is true and [on the higher level] that P is probably not true after all.
(2) Alternatively, you might judge that, all things considered, the weight of reasons really does support the Oxfordian view here. So you're lucky you didn't go to Harvard, in much the same way that it's lucky you weren't born into a society of Flat Earthers (or a religious cult). If you'd been raised and trained differently, you would have been less sensitive to where the weight of reasons truly lies.
As a reflective agent, to truly believe something you must consider it to be epistemically superior to its negation. You must therefore hold that anyone who believes otherwise is ipso facto your epistemic inferior in this respect. (They are failing to believe what is best supported by reasons.)
Conversely: humility + metacoherence = agnosticism.
One might initially be tempted to retain one's convictions even whilst modestly admitting that others' views are equally well supported (all things considered). Cohen thinks this is a fairly common stance (e.g. between Protestant and Catholic friends). But you cannot coherently maintain this combination of first-order belief and higher-order humility. Which you should give up will of course depend on the details of the case.
For example, it seems plausible to me that a proper appreciation of religious pluralism should undermine common grounds for religious belief (e.g. 'religious experience' -- why think that yours is any more reliable than Akbar's?). But this is arguably just because there are independent grounds for skepticism, which actual pluralism makes more salient. The existence of geocentrist cults, by contrast, does nothing whatsoever to undermine heliocentrism.
Friday, March 07, 2008
Meta-Evidence, Rationality and Guidance
How should we revise our conclusions upon learning that an (apparently) equally reliable epistemic agent came to a different conclusion? The Equal Weight View steps back from the fray and suggests that if we have no prior/independent reason to consider ourselves more likely right, we should 'split the difference'.
The Asymmetric No Independent Weight View claims that both parties should believe whatever the first-order evidence in fact supported all along. So if you were reasonable in your initial assessment of the evidence, you can reasonably give no weight at all to my (unreasonable, as it happens) opinion.
A third option, Tom Kelly's Total Evidence View, allows that we often should take higher-order evidence into account -- for peer disagreement is evidence that we have evaluated the first-order evidence incorrectly. However, TEV denies that this automatically swamps all first-order evidence. Instead, what's reasonable to believe is determined by one's total evidence (both first- and higher-order, combined).
When put like that, TEV seems clearly right. But it may be unhelpful in practice, if we cannot actually tell where the weight of (first order) evidence lies. Here are some fun cases from last week's epistemology class which put pressure on the view:
Case 1 (ordinary peer disagreement): You and I are expert weather forecasters with the same data set, training, and track record. Nonetheless, we disagree in our current forecasts. Should we revise our judgments on this basis?
Case 2 (chancy curse): As above, but an oracle tells us that long before we were born, a fair coin was flipped which would definitely curse one of us with all the phenomenology of having evaluated the data correctly, but ensure error.
Case 3 (simple curse): As in case 2, but without the coin flip. That is, all we know is that it was determined long ago -- by some unknown method -- that one of us would have all the phenomenology of having evaluated the data correctly, but be guaranteed to make an error.
It seems like the higher-order evidence swamps in case 2, obliging us to split the difference. But then case 3 may seem relevantly similar, and this in turn is effectively no different from case 1 (esp. if determinism is true). So if we want to avoid the Equal Weight View, we must either reject the intuition that we're rationally on a par in case 2, or else explain how to avoid the slippery slope through case 3. Any suggestions?
See also: How Objective is Rationality?
Monday, February 18, 2008
Guest Post: Peer Disagreement
[The following is a guest post from Barry Maguire, discussing the view that one ought to 'split the difference' upon disagreeing with an epistemic peer, giving 'equal weight' to your own judgment and theirs...]
Here is something of a response to an objection to the equal weight view, based on a suggestion by Adam Elga last week. Consider first the following distinction: between epistemically identical agents, who have identical background information, local evidence, computational faculties, dispositions to err, and so on; and seemingly equivalent agents, who have equivalent epistemic capacities with respect to some issue as far as they both can tell.1
Two epistemically identical agents could not come to differing conclusions about some issue. Our world does not contain any epistemically identical agents, for any candidates would at least differ in some small degree in their background information and dispositions. Two seemingly equivalent agents obviously could differ in their conclusions. Suppose you are one of two seemingly equivalent agents, and you have come to different conclusions with respect to the some question. In such a case, one of the following sorts of things has gone wrong: either one of you has made a computational error of some kind (perhaps simply making a faulty inference, perhaps failing properly to attent to the evidence), or one of you has better evidence than the other. I want to make a claim about the latter sort of case. So suppose, for now, that you are the two most pedantic and punctilious persons you know. Suppose, further, that you have widely divergent backgrounds and perspectives on the question. It seems reasonable for you both to conclude on the basis of your divergent results that one of you has better evidence than the other. Suppose you both do so conclude.
Now lets call the two agents under discussion ‘you’ and ‘Sally.’ Suppose you are an equal weight view theorist. Then you should split the difference between your conclusion and Sally’s. Well and good. But: now suppose that Sally invites ten friends to reflect on the question. All twelve of you are seemingly equivalent epistemic agents. Suppose all ten of Sally’s friends independently come to the same conclusion as Sally. Should you move further towards her view?
Here is reason why you might not. You previously considered yourself and these eleven others to be seemingly equivalent epistemic agents. This allowed room for the possibility that some of the twelve had evidence or capacities that the others lacked. But the point was that no-one had any discernible epistemic advantage. Now you find that you come to one conclusion, and the other eleven come to some different conclusion. If you were epistemically identical, apart from your disposition to err, this result would almost certainly be reason for you to move more than half way to the other conclusion. But this case is different. Here there is the possibility that you have evidence that all the others lack, or on the other hand that all eleven of the others share exactly the same piece of evidence that you lack. Moreover, it is possible that you have some higher-order piece of evidence which indicates the likelihood of one of these results. And if so – and here’s the claim – you should move no further in your view for the eleven than you did for Sally. For you moved towards Sally on the basis of your assessment of the relevance of the evidence you judged that she had and you lacked. By hypothesis, her ten friends have come to their conclusions on the basis of this same piece of evidence. So if you changed your position on the basis of the indication from Sally that you were lacking this evidence, you need make no further change when you find others indicating that you were lacking this evidence. So, further, if Sally had introduced a hundred other friends, or a million, and they all agreed with each other and disagreed with you, still: if you judge it likely that either you have some evidence they all lack or they all share the same piece of evidence that you lack, then you should move no further from your view for the hundred, or the million, than for the one.
Now there is a further wrinkle here. We are talking about the significance of higher-order evidence – evidence that there is evidence – and it itself comes in degrees. Suppose that knowledge of the missing evidence would move you 10 points. Presumably the higher-order evidence from Sally is defeasible: it does not itself entail the first-order evidence. So it might be that Sally’s higher-order evidence only moves you 7 points. Then her friends would make a difference, for they would provide further higher-order evidence. If there were a million of them, you might be moved the full 10 points. This seems right: more higher-order evidence is more evidence of a sort. However note two things. Firstly, the missing evidence may be rather paltry. Perhaps the difference between your conclusion and Sally’s was 100 points. Then even all her friends’ conclusions would not move you more than 10% towards her view. Secondly, if you were certain of the relation between Sally’s higher-order and lower-order evidence then, as before, her million friends would move you not at all.
1 If you like we can further distinguish fine and coarse seemingly equivalent agents: fine agents are seemingly equivalent on each assessable parameter – background evidence, local evidence, etc.; these themselves can admit of more or less fine-grained interpretations – coarse agents are equivalent across the range. I don’t think this distinction affects the current point.- Barry.
Saturday, August 18, 2007
Explaining Beliefs
Why do we believe the things we do? Fans of evolutionary psychology might be tempted to construct an evolutionary story about how such-and-such a belief might have proven beneficial to our ancestors on the African savannah. (Freudians and others might construct other stories.) But this is usually the wrong level to focus on. Evolution has equipped us with reliable general faculties of sense and reason. This means that the specific conclusions we reach are better explained by what's justified than by what's adaptive. In other words, if a belief is justified then no further explanation is necessary. It is only blatantly unreasonable beliefs that call out for special explanation -- perhaps in terms of evolved biases, developed disorders, social pressures, or the like.
This is important because people often treat evolution (and causal explanations in general) as an argument for moral skepticism: whatever caused our beliefs, it presumably isn't the abstract moral facts themselves!* But such arguments are question-begging, for they presuppose the skeptical view that our moral beliefs aren't justified.** Indeed, I think there's an important sense in which our philosophical beliefs are caused by the facts: we are responsive to considerations of rational coherence, which is precisely what the truth itself consists in.
* = It's also suspicious that only moral philosophy is singled out here. Logic is no less abstract, after all. Not to mention the belief in skepticism itself.
** = It works better as an argument against Platonism, though.
Here's the vital point: if philosophical truth just is what's maximally reasonable, then the skeptic needs to show that no moral views are more reasonable than their competition (for this would suffice to explain our knowing them). But of course merely pointing to Darwin does no such thing.
Tuesday, October 17, 2006
The Epistemic Argument against Vigilantism
I'm currently working on an essay that develops the arguments against political vigilantism initially presented in my post on 'the ethics of activism'. In this post I want to focus on the Epistemic Principle: No matter how awful X seems to you, if you can't rationally convince your fellow citizens then you're probably wrong about it, and so have no business engaging in coercion.
As background, note the fact of widespread first-order moral/political disagreement, which serves to motivate a liberal-procedural metapolitics. We need some way to adjudicate political conflicts, and reach collective decisions about what ought to be done. The best process will be the one that most reliably distinguishes good proposals from bad ones. I will assume that the liberal-democratic process is the best that is realistically available.
Thus, if the process is functioning adequately, we should find that it generally approves good proposals and rejects bad ones. This means that if you cannot rationally persuade your fellow citizens to your position, chances are that this is because you’re in error. Of course, we are engaged in a very high level of statistical abstraction here – in any particular case, there could be reasons that defeat the democratic presumption. For example, the populace might be demonstrably biased or ignorant in some crucial respect. But then, bringing this to their attention should, ideally, suffice to overcome it, unless we are to despair of our fellow citizens as fundamentally unreasonable. Still, the possibility must be granted that a small group of educated radicals might be in a manifestly better epistemic position than the general populace with regard to determining the common good. If they knew this to be so, could that justify radicalism?
The worry, of course, is that many other radical groups mistakenly believe themselves to be in such a position. They are subjectively every bit as certain in their “knowledge” as the correct group is. So the question remains how to distinguish them. However, it’s important to note that, in principle, the ability to distinguish the two situations need not hold symmetrically. Although the justified believer must be able to distinguish their position from that of being unjustified, the converse need not necessarily be the case. As Sosa writes:Suppose I could now about as easily be dead, having barely escaped a potentially fatal accident. Obviously, we cannot distinguish being alive from being dead by believing oneself alive when alive, and dead when dead. But that is no obstacle to our knowing ourselves alive when alive.
Similarly, we may at times be so muddle-headed that we do not even realize it (for example while dreaming). But the possibility of overlooking such a deficit does nothing to undermine our introspective appreciation of wakeful clarity. As a general rule, our positive awareness of an introspective property is not threatened by the fact that we would be unaware of lacking the property. The full force of one’s actual awareness and appreciation suffices to guarantee that the property is really there. It’s no reflection on your actual situation if others (perhaps including your counterfactual selves or counterparts) are less discerning.
Perhaps the justified radical is in a similar position. She has a deep appreciation of the moral-political facts, we may suppose, and it’s not her fault that others lack such discernment. Even though others are in such a poor epistemic position that they don’t even realize it, this fact does not reflect on the epistemic situation of the fully-aware radical. She, at least, is in a position to tell the difference, even if the others aren’t.
But there are generally tests that one can do to confirm one’s positive awareness and clarity of thought. For example, it may help to focus one’s attention on the details of the property allegedly observed – presumably the deluded will find themselves unable to perform this feat, and thereby become aware of their deficit at last. So we should want to put our political beliefs to a similar ‘test’, which they should have no trouble passing if they’re really as self-evident as we believe. The justified radical will be able to specify the justificatory grounds of her proposals with clarity and logical rigour lacking in the attempts of her opponents. Others might offer justifications that they personally find equally convincing, but only because they are unaware of their flaws.
Are these two situations really subjectively discernible though, even asymmetrically? Is fine-grained epistemic justification, or complex rational insight, the kind of property that is open to introspective awareness? Or must the asymmetry argument be restricted in application to more black-and-white cases (e.g. death vs. life, or muddled dreaming vs. wakeful clarity)? Is it really true that moral justification is internally accessible, so that the phenomenal experience or subjective ‘what it is like’ quality of having justified moral-political beliefs is different in kind from what it is like to have prima facie defensible but ultimately unjustified beliefs on these topics? This seems implausible. So the subjective position of the radical – no matter how convinced they may feel that such-and-such is an intolerable moral outrage – is insufficient to justify coercive action. Their beliefs must pass a more objective test. Whatever test is appropriate here is presumably the test that should be instituted in the political system. So this leads us back to procedural liberalism.
Although there does seem to be a problem for radicalism here, it may not be purely epistemic in nature. After all, it seems reasonable to retain one’s political beliefs even in the face of democratic defeat. (On the view I defend, one must abide by the outcome of a just process, but one need not whole-heartedly agree with it.) We might explain this away by suggesting that the high stakes involved in political action demand more stringent justification than is required for mere belief. The differing prescriptions may also be grounded in a utilitarian fashion. Given the fallibility of mainstream opinion, the advancement of social knowledge might be best served by having individuals persist in trying to support their discredited views – even when this is individually “irrational” in the sense that any given dissenter is statistically unlikely to ultimately prove correct.* Such behaviour is at least collectively rational, so we have reason to support epistemic norms that would allow individuals to retain beliefs that are too ungrounded to serve as a basis for coercive action.
* = I've heard of similar defences of dogmatism by philosophers of science. Can anyone provide a reference here?
Anyway, I'd be very interested to hear what others think about (1) my extension of Sosa's asymmetry argument, and its application to political disagreements; and (2) the collectivist explanation for why we think it epistemically acceptable to hold on to democratically discredited beliefs. [Or (3) any other issues that arise from this discussion...]
Monday, October 16, 2006
Experience and Testimony
People commonly talk about "private" evidence, had on the basis of personal experiences that aren't accessible to other people. But I'm not convinced that there is any such thing. Suppose that a subject S has an experience E, and thereupon concludes that C. ('E' might be a religious experience, for instance, and 'C' the proposition that God exists.) If S then tells me about her experience in sufficient detail, and I trust that she is sincere, then surely I have just as much evidence as S does for C. We both recognize the objective fact: (O) "S had an experience E". So where's the asymmetry? We may state this as a dilemma: either O is good evidence for C, or it is not. If it is, then I (and S) should believe C. If it isn't, then S (and I) should not believe C. Either way, there's no epistemic difference between S and I. There's no "private" evidence that she cannot share through testimony.
Few of us would think it epistemically justified to believe in aliens or deities on the basis of your neighbour's "experience" of being abducted by aliens or visited by God. But your neighbour has no further, private evidence, and hence is in the same epistemic position as you. That is, they shouldn't believe in these things on their basis of their experiences either. What everyone alike should conclude is that the neighbour was hallucinating, dreaming, or some such.
I assume here that justification is a relation between propositions. When we say that a conclusion is justified by experience, this is really shorthand for saying that it's justified by the proposition that one had such an experience. There's nothing essentially "private" about such propositions, of course; knowledge of them can be transmitted through testimony just as for any other proposition. I can come to know that S had experience E, simply by S telling me so!
The defender of private evidence will need to claim that justification can be non-propositional. They will want to say that it is the first-personal event of having experience E, rather than the objective fact that this event occurred, which justifies one's belief in C. But that sounds bizarre to me. What is it about the subjective "having" of experiences that's so special, or that's of evidential import?
Monday, May 22, 2006
Self-Deprecating Testimony
Suppose someone tells you that they're an unreliable source. Should you believe them?
This isn't so bad as the liar paradox. The statement might be true, after all. Or it might just as well be false.
If they are a reliable source (but simply misleading you in this particular case) then the statement is false, so you shouldn't believe it. On the other hand, if they're an unreliable source (but having a rare moment of honesty) then the statement is true, so you should believe it. Oddly enough, the statement itself doesn't seem to provide you with any information at all about which of these cases is more likely.* All it tells you is that the person is certainly not perfectly reliable, nor perfectly unreliable (in the sense of reliably telling only falsehoods).
* = You might think we should have a default disposition towards believing others. But that might just as well be described as a default assumption that their testimony is reliable -- which should lead us to disbelieve them in the present case. Actually, that sounds right. If someone said to me "most things I say are false", I would think it more likely that that particular thing they just said was false. So perhaps we should simply disregard such self-deprecating testimony?
Monday, May 15, 2006
Global Strategies and Indirect Reasons
Building on my previous post: Suppose there is some worthwhile goal G (e.g. happiness or general utility), which is best achieved by an "indirect" strategy, i.e. by aiming at goals S other than G itself. What is the normative status of the strategically recommended goals S, especially in those particular instances where they conflict with G?
We have reason to achieve G. But I am more likely to achieve G by adopting S as my goal instead. So there are instrumental reasons to aim at S rather than G. If I know all this, my apparent and objective reasons will coincide, so the demands of rationality coincide with what is objectively best: namely, to achieve G by aiming at S instead.
This may seem puzzling. Rationality tells us to aim at the good, or do what seems best, i.e. maximize expected utility (for whatever scale of "utility" we're interested in). But the whole idea of the indirect strategy is to be guided by reliable rules rather than direct utility calculations. One effectively commits to occasionally acting irrationally (in the 'local' sense), though it is rational/optimal to make this commitment. Parfit thus calls it "rational irrationality".
But we may question whether it is really irrational to abide by the rules (against apparent utility) after all. We adopt the indirect strategy because we recognize that our direct calculations are unreliable. The over-zealous sherriff might think that torturing a terrorist suspect would have a high expected utility. But if he recalls his own unreliability on such matters, he should lower the expected utility accordingly. As a good indirect utilitarian, he believes that in situations subjectively indiscernible from his own, the best results will generally be obtained by respecting human rights and following a strict "no torture" policy. Taking this "meta" information into account, then, he should reach the all-things-considered conclusion that expected utility is maximized by refraining from torture.
Global reasons thus entail local reasons. It's not a matter of following strategy S no matter what seems most likely to achieve G. A broadened perspective will lead the agent to recognize that S is what's most likely to achieve G. The conflict is only with prima facie "seemings". His all-things-considered judgment of "what seems best" should in fact coincide with his general strategy. So "rational irrationality" need not be genuinely irrational at all. It is only irrational in the restricted, "local" sense whereby we only take into account first-order evidence or considerations, and fail to consider higher-order issues of reliability and so forth. But rationality, simpliciter, is surely an "all things considered" rationality. And when we consider all things, the apparent conflict dissolves.
Wednesday, August 31, 2005
The Surprise Examination Paradox
I really like this one. Here's how it goes: your teacher tells you (i) she's going to give the class a surprise exam next week, and (ii) you won't be able to work out beforehand on which day it will be. Using this information, you work out that it can't be on Friday (the last day), or else you'd be able to know this as soon as class ended the day before, contrary to the second condition. With Friday excluded from consideration, Thursday is now the last possible day, so we can exclude it by the same reasoning. Similarly for Wednesday, Tuesday, and finally Monday. So you conclude that there cannot be any such exam. This chain of reasoning guarantees that when the teacher finally gives the exam (say, on Wednesday), you're all surprised, just like she said you'd be.
I originally thought that this paradox would only arise when the speaker was known to be fallible. The reason you can't know beforehand what day the exam will be, is because when running through the reasoning, you come to suspect that what the teacher said is false. But what if the teacher was known to be infallibly truthful? Imagine it is God that makes the announcement (and suppose we know that God cannot speak falsehoods). My thought was that the announcement would then simply be false, i.e. the exclusionary argument proves that this statement could never be made by a being known to be infallible.
But I've changed my mind about this. It seems that if God were to make such a statement, we would be thrown into confusion by it, and would be unable to work out on what day the surprise exam would be. So the statement would turn out true, even though we know the speaker is truthful and so cannot (unlike before) suspect that there will be no exam. (But then what's wrong with the exclusionary reasoning? Most puzzling!)
A commenter over at Opinatrety distills the core of the problem:I have a coin in my hand. But you will never know if I really have a coin in my hand before I open it.
So you do not know if I have a coin in my hand or not. Then, I open it. Yes, there is a coin. My statements are right.
As he notes, the trick lies in saying 'you will never know'. By saying that, you throw the listener into a state of epistemic conclusion, thereby ensuring the truth of that very statement. Even the known-infallible God could do this, by saying to you: "X is true, but you cannot know it". After all, you'd then reason, "If God says I cannot know X, and he's never wrong, then there must be something dodgy about it... I'd better suspend belief" -- so then you don't know X any more! Even though you were told it from an infallible source! Tricky.
