tag:blogger.com,1999:blog-6642011.post112547044787685923..comments2023-10-29T10:32:36.914-04:00Comments on Philosophy, et cetera: The Surprise Examination ParadoxRichard Y Chappellhttp://www.blogger.com/profile/16725218276285291235noreply@blogger.comBlogger46125tag:blogger.com,1999:blog-6642011.post-80807186177712411622008-05-25T01:01:00.000-04:002008-05-25T01:01:00.000-04:00Thanks. I've created a new thread for the question...Thanks. I've created a new thread for the question: <A HREF="http://www.philosophyetc.net/2008/05/is-knowledge-ever-indefeasible.html" REL="nofollow">Is Knowledge (Ever) Indefeasible?</A>Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-9063921389330398492008-05-24T22:47:00.000-04:002008-05-24T22:47:00.000-04:00Okay, at this stage we can only continue the debat...Okay, at this stage we can only continue the debate by straying too far away from the topic of the original post. It was fun while it lasted.Pablohttps://www.blogger.com/profile/10363127923767597327noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-53863035064089317812008-05-24T22:39:00.000-04:002008-05-24T22:39:00.000-04:00That the students superknow anything.That the students superknow anything.Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-13955899620591208472008-05-24T22:36:00.000-04:002008-05-24T22:36:00.000-04:00As I was assuming, knowledge is indefeasible justi...As I was assuming, knowledge is indefeasible justified true belief. If you deny that knowledge is indefeasible, fine; just assume the term 'know' and its cognates in my previous comment express the concept of <EM>superknowledge</EM>, where someone superknows P iff she indefeasibly knows P. What step in my argument, thus restated, would you deny?Pablohttps://www.blogger.com/profile/10363127923767597327noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-76503640974486363882008-05-24T21:35:00.000-04:002008-05-24T21:35:00.000-04:00"If someone knows that Q, that person cannot be th..."<I>If someone knows that Q, that person cannot be thrown into a state of epistemic confusion regarding Q.</I>"<BR/><BR/>Why think that? Seems false to me. The students may initially know (i.e. have a non-gettiered justified true belief) that the teacher is truthful and hence that her assertion (1) is true, only to have (the warrant for) both these beliefs undermined by her later utterence of (2).<BR/><BR/>We know from other cases that knowledge can be 'lost' in virtue of acquiring new defeaters for one's belief. So why not in this case?Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-15493781165457932342008-05-24T21:26:00.000-04:002008-05-24T21:26:00.000-04:00The teacher is truthful. The students know that s...The teacher is truthful. The students know that she is. Necessarily, if a truthful agent asserts P, then P is true. The students know this analytic truth. The teacher has asserted (1), and the students know this too. So the students know that (1). If someone knows that Q, that person cannot be thrown into a state of epistemic confusion regarding Q. Only if the students are in a state of epistemic confusion regarding (1) can (2) be true. The students are not in a state of epistemic confusion regarding (1). So (2) cannot be true. So the scenario is logically impossible.Pablohttps://www.blogger.com/profile/10363127923767597327noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-551502861667133802008-05-24T18:58:00.000-04:002008-05-24T18:58:00.000-04:00If an infallible being (or one I consider infallib...If an infallible being (or one I consider infallible) tells me that <I>I cannot know that P</I>, then that <I>undercuts</I> my other grounds for believing P, and throws me into a state of epistemic confusion. It raises doubts of a sort that, we may think, are incompatible with knowledge.<BR/><BR/>The case where P is "2+2=4" is unclear. It's possible that my antecedent belief in P is <I>so robust</I> that I would sooner doubt the infallibility of the being than my knowledge of P. In <I>that</I> case, the agent would be speaking falsely in asserting that I cannot know P; so the scenario would be impossible as you suggest. But I do not think our knowledge is <I>always</I> so robust and impervious to epistemic confusion. Especially on contingent matters, like the question whether there will be an exam on Friday, I see no reason at all to deny that one's epistemic position may be undercut, and thus the scenario described is possible.Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-3473729740063127422008-05-24T14:54:00.000-04:002008-05-24T14:54:00.000-04:00[I have consolidated the two previous comments and...[I have consolidated the two previous comments and corrected an omission.]<BR/><BR/>The point is that the students' belief in claim (1) will not (in light of (2)) constitute knowledge.<BR/><BR/>What are your grounds for saying that the students' belief in claim (1) will not constitute knowledge in light of (2)? Would you also be prepared to say that, if a truthful being told you that 2 + 2 = 4, your belief in that proposition would not constitute knowledge? If not, what's the difference between the two cases?<BR/><BR/>(Notice, incidentally, that I didn't ask whether the students could consistently believe that the teacher is truthful. The question is whether we, in the real world, can consistently believe that proposition. I claim that we can't because there is no logically possible world in which both (1) and (2) are true. Since there is no such world, there are no possible students considering whether they can consistently believe that their teacher is truthful and correctly reaching the conclusion that she is.)Pablohttps://www.blogger.com/profile/10363127923767597327noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-49066363262603948212008-05-24T13:56:00.000-04:002008-05-24T13:56:00.000-04:00Yes, they can consistently believe that, and indee...Yes, they can consistently believe that, and indeed be right in doing so because both claims turn out true. The point is that the students' belief in claim (1) will not (in light of (2)) constitute knowledge.Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-35831147377220126102008-05-24T13:27:00.000-04:002008-05-24T13:27:00.000-04:00Richard, your response to Covaithe presupposes tha...Richard, your response to Covaithe presupposes that the two statements come out true. I am contesting that presupposition.<BR/><BR/>Suppose, to simplify, that the teacher tells the students that he will take an exam on Friday and that they won't know that he will take an exam on Friday. Would you still deny that, as I claimed, it's impossible to consistently believe that the teacher is truthful?Pablohttps://www.blogger.com/profile/10363127923767597327noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-6912112706488399772008-05-24T12:06:00.000-04:002008-05-24T12:06:00.000-04:00Pablo - see my responses to Covaithe, upthread. In...Pablo - see my responses to Covaithe, upthread. In the original case, both statements from the teacher turn out to be <B>true</B>. There is an exam, and the students really <I>didn't</I> (and couldn't)* know beforehand when it would be.<BR/><BR/>This can really happen. And a situation cannot be logically impossible if it is actual.<BR/><BR/>* = in your simplified version, it's less clear whether the true conclusion <I>cannot</I> be known. It can at least be reliably guessed at, as per my previous comment. But the latter half of my original post argues that we still couldn't have knowledge in such a case.Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-21594991481345667602008-05-24T11:50:00.000-04:002008-05-24T11:50:00.000-04:00The teacher makes two relevant statements:(1) the ...The teacher makes two relevant statements:<BR/><BR/>(1) the exam will be this week; and<BR/><BR/>(2) the students won't know when the exam will be.<BR/><BR/>We are supposed to assume that the teacher is truthful, so we must assume that (1) and (2) are true. If (1) is true, then given the assumptions I made explicit in my parenthetical remark above, if follows necessarily that the exam will be on Friday. (I’m assuming the simpler version I proposed.) The students can draw elementary inferences and are aware of the relevant assumptions, so they must know this. Yet this is contradicted by proposition (2). It seems to me that there is no paradox here, but simply a description of a problem predicated on a logical impossibility. One might as well imagine a “paradox” involving a truthful being who claims that 2 + 2 = 5.Pablohttps://www.blogger.com/profile/10363127923767597327noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-2267159752936798812008-05-24T11:21:00.000-04:002008-05-24T11:21:00.000-04:00Then again, perhaps there is the following differe...Then again, perhaps there is the following difference:<BR/><BR/>In the simple (only one option remaining) case, even if you can't attain "knowledge" for tricky reasons, you can at least settle on a most likely hypothesis (they have a coin in their hand; the test will be Friday), and almost certainly turn out to be right about it.<BR/><BR/>In the original case, though, it seems like you really can't narrow down the 5 options to any better than a chance guess between them (and the sixth option of no test at all).Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-29930278663122021852008-05-24T11:17:00.000-04:002008-05-24T11:17:00.000-04:00Not really, or at least that's the suggestion of t...Not really, or at least that's the suggestion of the last part of my post, with the discussion of: "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."Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-24594272716339397862008-05-24T11:15:00.000-04:002008-05-24T11:15:00.000-04:00Suppose it is now Thursday and your teacher tells ...Suppose it is now Thursday and your teacher tells you, after the class is over for that day, that (i) she's going to give the class a surprise exam this week, and (ii) you won't be able to work out beforehand on which day it will be. (Assume that the week ends on Sunday and that there are no classes on weekends.)<BR/><BR/><EM>Does the original version of the paradox add anything to this simplified version?</EM>Pablohttps://www.blogger.com/profile/10363127923767597327noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-43459084375147256462008-05-24T11:01:00.000-04:002008-05-24T11:01:00.000-04:00There's nothing wrong with the ordinary conception...There's nothing wrong with the ordinary conception of knowledge, and no reason not to use it here.<BR/><BR/>Now, knowledge entails truth, so your option #1 is clearly ruled out.<BR/><BR/>My own solution is something more like your #2. But note that the claim is not just that the students "do not in fact know" the day of the test, but that they <I>could not</I> know it (i.e. by means of any chain of good reasoning). This is puzzling, because the exclusionary argument <I>looks</I> like good reasoning, so the question is why it is not in fact so, or at least why it can't yield knowledge in the reasoner. (It sounds like you might be sympathetic to the answer I give here. No?)Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-67385683576557400612008-05-24T00:57:00.000-04:002008-05-24T00:57:00.000-04:00To be more clear:I claim that any notion of knowle...To be more clear:<BR/><BR/>I claim that any notion of knowledge you try and offer will fail to generate the paradox in one of three ways.<BR/><BR/>1) The notion of knowledge will allow the reasoner to know contradictory things. Thus the teacher's statement is flat out false since the students know the test will occur on monday and on tuesday and on wednesday and etc..<BR/><BR/>2) The notion of knowledge you offer will avoid allowing inconsistant beliefs in a fashion that prevents it from making the inferences needed in the problem, e.g., you will defined knowledge in such a way that it 'forsees' the problem it is about to get into and rejects the reasoning that leads to the knowledge the test will be on some particular day. Once again no problem the teacher says something true and fufills it by giving the test on the day the students in fact did not know the test would occur.<BR/><BR/>3) You will define knowledge in a fashion that is internally inconsistent to avoid the first two problems. Once again we fail to have a problem.TruePathhttps://www.blogger.com/profile/12167366567189261911noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-19237206695131030092008-05-24T00:50:00.000-04:002008-05-24T00:50:00.000-04:00WHAT DO YOU MEAN BY KNOW??I was just using surpris...WHAT DO YOU MEAN BY KNOW??<BR/><BR/>I was just using surprise as a synonym for not know. The exact same reasoning applies just the same.<BR/><BR/>If you mean an actual teacher talking to actual students and using our natural language concept of know no problem (they are failible, probabilities build up and the students indeed don't know on the day of the students).<BR/><BR/>If you want to go any farther beyond this <B>you can't rely on our intuitive notion of knowledge</B> because like most other natural language terms it's vague and imprecisce in exactly these sorts of extreme cases. Thus in order to generate a paradox you need to:<BR/><BR/>1) List out some predicate K that your agent supposedly posseses.<BR/><BR/>2) Given me reasons to believe it's logically possible for the agent to actually have a predicate like this.<BR/><BR/>3) Give me reason to believe with respect to that predicate that the teacher/god's claim is true.<BR/><BR/>------<BR/><BR/>The problem is that once you depart from our intuitive notion of knowledge the argument that the statement is necessarily true is no longer obvious. In particular if you allow a bizarre notion of knowledge that lets the student know that the quiz will be on monday and know that it will be on tuesday and etc.. then the statement made by the teacher is simply straight out false.<BR/><BR/>On the other hand if you demand as one of your axioms of knowledge that it not reach contradictory results then your system can never infer that the student knows the test will even be on friday since use of such a scheme must already be blocked by some part of your definition of knowledge.<BR/><BR/>----<BR/><BR/>Ultimately though I did agree you *could* make a paradox out of this by making in complicated in a fashion that lets you embed the liar. This seems to be what you are sorta reaching at, well more preciscely you want to demand the existance of a predicate K that functions as a truth predicate for it's own theory. But this isn't a paradox about the surprise examination it's a well known restriction on what sorts of consistant theories you can have (remember all the Kripke stuff about crazy hierarchies with multi-valued logics ....he did this because it's impossible to have a predicate that obeys the constraints you want).<BR/><BR/>------<BR/><BR/>In short if you want to give me the supposed features your notion of knowledge has that generate a paradox I'd be glad to continue the debate. If you can't I think that's very strong evidence that there is no such paradox, i.e., it's been successfully dissolved.TruePathhttps://www.blogger.com/profile/12167366567189261911noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-87789826623941957642008-05-23T14:13:00.000-04:002008-05-23T14:13:00.000-04:00Why do you keep talking about 'surprise'? I mean, ...Why do you keep talking about 'surprise'? I mean, I know it's in the title of the paradox. But the actual <I>substance</I>, as I spell it out above, is simply in terms of what's <I>knowable</I>. Not what can be known or worked out <I>using such-and-such formal methods</I>, but just what can be known or worked out, <I>simpliciter</I>.<BR/><BR/>The paradox here, unlike your God case, is that what the teacher says is <B>true</B>. There <B>will</B> be an examination during the week, and you <B>won't</B> be able to work out beforehand which day it is on. This contradicts the apparently sound exclusionary reasoning, so the challenge is to show why the exclusionary reasoning actually fails. (My solution invokes the notion of agents being thrown into a state of epistemic confusion, which prevents their knowing things they otherwise might.)Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-89253189950085816842008-05-23T10:26:00.000-04:002008-05-23T10:26:00.000-04:00In fact I think I'm going to go post my full argum...In fact I think I'm going to go post my full argument at my blog rather than just give half-assed versions here. Both of this issue and the other one (http://infiniteinjury.org/blog)<BR/><BR/>Note that I do think this was a very interesting philosophical problem to start with, I just think it was solved way back when.TruePathhttps://www.blogger.com/profile/12167366567189261911noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-19908644687829937232008-05-23T10:25:00.000-04:002008-05-23T10:25:00.000-04:00Alright so despite what I think is a dissolution o...Alright so despite what I think is a dissolution of the problem one might still think there is a sneaky way to define the notion so the paradox returns. I argue this can't be so once we sufficiently preciscify our notions.<BR/><BR/>Suppose our agent A has a well defined belief state in response to being in the situation of waking up on day D and not having had a test yet. If we supply a coherent notion (rational/knowledge/whatever) that specifies a coherent constraint on this agent's belief that means there is some function like the above that is consistant with every requirement we want to hold of his beliefs.<BR/><BR/>Either the agent's belief about when the quiz will be always satisfies B(D)=D or it does not (i.e. he thinks the quiz will be today every day or he does not). If he thinks the quiz will be today every day then it is impossible for any teacher to give a surprise quiz. If he has a day where B(D) neq D then the surprise quiz can be given. <B>If at any point this story fails you specified an incoherent set of constraints about how the agent's beliefs are constrained to behave</B>.TruePathhttps://www.blogger.com/profile/12167366567189261911noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-23550997884938726542008-05-23T10:13:00.000-04:002008-05-23T10:13:00.000-04:00I still don't see how it's tricky at all. We just...I still don't see how it's tricky at all. We just need to remove the ambiguity in surprise.<BR/><BR/>Of course if we mean surprise as in literally real individuals will be surprised there is absolutely no problem. Some people experience a certain emotion, no biggie. This is one sense in which the statement can be true.<BR/><BR/>Suppose instead the statement is that I (GOD) will never give a test on the last day of the week nor on any day on which every later day has already been eliminated on these grounds. This statement clearly implies god will not give the test this week so we just proved a truth speaking being could never make such a claim.<BR/><BR/>Alright I presume your response to these two points will be, 'sure but I want to know what happens when GOD tells an ideally rational agent that they will not know when the test will be this week.' But now this just depends on what you mean by ideally rational. In particular will an ideally rational agent infer any conclusion from a contradictory system.<BR/><BR/>I think the only reasonable answer to this question is no (but if you answer yes just work out the specifics of when it is allowed and the paradox will disappear the same way. An ideally rationally agent would, if given a contradictory set of axioms, realize they are contradictory and infer nothing from them. Yet, the supposed 'paradox' arises only by having the ideally rational agent accept propositions that together yield contradiction. Such an agent would simply refuse to reach any conclusion from these propositions all together and could thus be 'surprised' by a friday test. (Not that at worst if the argument did go through it would merely prove that god couldn't make the statement).<BR/><BR/>Ultimately in your version there are two confusions going on. First is the confusion between surprise/know as a formal notion and as the real world concept we find familiar. Secondly is our temptation to assume that a perfectly rational being is just a regular guy who is a big smarter. Being perfectly rational is going to cause the agent to often behave in ways that violate our expectations for people.<BR/><BR/>In particular when I say, "the perfectly rational being realizes it's inconsistent and concludes nothing" you are going to want to yell, "but on thursday night surely he has no doubts anymore." But this rests upon the idea that the perfectly rational being will behave as we do and assign a high credence to shorter deductions. Since on thursday night the deduction the test will be friday is so trivial it tugs at us to say of course the rational being will know about the test tomorrow. However, if we are really going to be serious about the idea of a perfectly rational actor then they absolutely won't give lesser credences to more remote conclusions. <BR/><BR/>I'll actually give you an argument that this in principle can't be a paradox in my next comment.TruePathhttps://www.blogger.com/profile/12167366567189261911noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-41704585085450814332008-05-21T18:30:00.000-04:002008-05-21T18:30:00.000-04:00Truepath comments:"As far as the surprise problem ...Truepath <A HREF="http://www.philosophyetc.net/2008/05/aspiring-to-objectivity.html#comments" REL="nofollow">comments</A>:<BR/><BR/>"<I>As far as the surprise problem I simply don't see the paradox. I mean if by surprise the teacher means "the students will literally be surprised when I give this exam" then we don't have any problem or contradiction. After all it's not contradictory for the students to be surprised on friday, they could just be dumb.<BR/><BR/>Alright well another possibility as to what you mean is the formal approach but we already covered that. So what's left? Well you could try to formulate the approach by asking whether it is rational for the students to be surprised. But since you aren't talking about a stipulative formal system anymore but actual rationality (to the extent that makes sense) you can't force in the assumption the teacher is infallible and the paradox again fails to generate.<BR/><BR/>Perhaps then you say but what about the possible world in which the teacher is really infallible. Well at worst then the consequence of the surprise quiz paradox is that such a world is not possible and it's no worse than the irresistible object and immovable force puzzle.<BR/><BR/>But all this is unnecessery. The burden is on the person presenting the paradox to offer up specifics that do make it troubling and I just don't see them.</I>"<BR/><BR/>I think my main post (above) does just that.Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-1125904689889499952005-09-05T03:18:00.000-04:002005-09-05T03:18:00.000-04:00More specifically, I'd distinguish between "X is t...More specifically, I'd distinguish between "X is true" and "S is in a position to know X". After all, X is known by God, at least. The question is whether <I>we</I> are in a position to know it. And while it <I>normally</I> is the case that if God tells us X then we can thereby know X (because we know God is infallible, etc.), it's always possible for new evidence to come along and cast doubt on this. That's what happens when God adds the further claim, "But you cannot know X". We <I>could</I> have known it, if he hadn't added this further phrase. But because he did add it, this changes our epistemic position with regard to X. We are no longer in a position to accept God's testimony (we are instead thrown into a state of epistemic confusion).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6642011.post-1125835995914148862005-09-04T08:13:00.000-04:002005-09-04T08:13:00.000-04:00Ok, after a bit of thought I agree that God's sent...Ok, after a bit of thought I agree that God's sentence isn't like the liar sentence. Whoops. <BR/><BR/>So, if I understand correctly, you're making a distinction between "X is true" and "X is known to be true", yes? It seems to me that God saying "X is true" naturally implies "X is known to be true". Isn't that why we have God saying it, instead of, say, me, in this example? But then, we have a simple contradiction. Let Y be "X is known to be true". Then, God saying "X is true" implies Y, and God saying "X is not known to be true" is identical with not-Y. God saying both implies Y and not-Y. <BR/><BR/>Unless you're saying "God says X" does not imply "X is known". But if it doesn't, then why are we talking about God?Anonymousnoreply@blogger.com