Some formulations of the surprise paradox involve a pair of unnecessary and controversial assumptions. After casting doubt on these assumptions, I propose a solution to the paradox.

One tradition of solving the surprise exam paradox, started by Robert Binkley and continued by Doris Olin, Roy Sorensen and Jelle Gerbrandy, construes surpriseepistemically and relies upon the oddity of propositions akin to G. E. Moore’s paradoxical ‘p and I don’t believe that p.’ Here I argue for an analysis that evolves from Olin’s. My analysis is different from hers or indeed any of those in the tradition because it explicitly recognizes that there are two distinct reductios (...) at work in the student’s paradoxical argument against the teacher. The weak reductio is easy to fault. Its invalidity determines the structure of the strong reductio, so-calledbecause it is more difficult to refute, but ultimately unsound because of reasons associated with Moore-paradoxicality. Previous commentators have not always appreciated this difference, with the result that the strong reductio is not addressed, or the response to the weak reductio is superfl uous. This is one reason why other analyses in the tradition are vulnerable to objections to which mine is not. (shrink)

One tradition of solving the surprise exam paradox, started by Robert Binkley and continued by Doris Olin, Roy Sorensen and Jelle Gerbrandy, construes surpriseepistemically and relies upon the oddity of propositions akin to G. E. Moore’s paradoxical ‘p and I don’t believe that p.’ Here I argue for an analysis that evolves from Olin’s. My analysis is different from hers or indeed any of those in the tradition because it explicitly recognizes that there are two distinct reductios (...) at work in the student’s paradoxical argument against the teacher. The weak reductio is easy to fault. Its invalidity determines the structure of the strong reductio, so-calledbecause it is more difficult to refute, but ultimately unsound because of reasons associated with Moore-paradoxicality. Previous commentators have not always appreciated this difference, with the result that the strong reductio is not addressed, or the response to the weak reductio is superfl uous. This is one reason why other analyses in the tradition are vulnerable to objections to which mine is not. (shrink)

One tradition of solving the surprise exam paradox, started by Robert Binkley and continued by Doris Olin, Roy Sorensen and Jelle Gerbrandy, construes surpriseepistemically and relies upon the oddity of propositions akin to G. E. Moore’s paradoxical ‘p and I don’t believe that p.’ Here I argue for an analysis that evolves from Olin’s. My analysis is different from hers or indeed any of those in the tradition because it explicitly recognizes that there are two distinct reductios (...) at work in the student’s paradoxical argument against the teacher. The weak reductio is easy to fault. Its invalidity determines the structure of the strong reductio, so-calledbecause it is more difficult to refute, but ultimately unsound because of reasons associated with Moore-paradoxicality. Previous commentators have not always appreciated this difference, with the result that the strong reductio is not addressed, or the response to the weak reductio is superfl uous. This is one reason why other analyses in the tradition are vulnerable to objections to which mine is not. (shrink)

The students’ argument against the possibility of a surprise exam assumes that the following would not occur: the teacher decides to give the exam on a certain day; the teacher believes that the exam would be a surprise on that day; but, actually, the exam would not be a surprise on that day. I give a reason to reject this assumption, and I point out that an attempt to reformulate the surprise (...) class='Hi'>exam paradox in order to allow for the assumption does not result in an acceptable argument. (shrink)

The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed (...) from the literature: the 'Unprojectible Announcement Argument,' the 'Wright & Sudbury Argument,' and the 'Epistemic Blindspot Argument.' The reason that the Surprise Exam Paradox has persisted this long is not because any of these arguments is problematic. On the contrary, each of them is correct. The reason that it has persisted so long is because each argument is only part of the solution. The correct solution requires all three of them to be combined together. Once they are, we may see exactly why the No Friday Argument fails and therefore why we have a solution to the Surprise Exam Paradox that should stick. (shrink)

We represent the well-known surprise exam paradox in constructive and computable mathematics and offer solutions. One solution is based on Brouwer’s continuity principle in constructive mathematics, and the other involves type 2 Turing computability in classical mathematics. We also discuss the backward induction paradox for extensive form games in constructive logic.

In this paper, I analyze the "surprise exam paradox". I think that the paradox can be avoided and I am going to focus on three points: 1) A conflict arises between reasoning and the confidence in the person that makes the original statement. If we examine the situation by reasoning we conclude that the statement is not going to come true, because we trust the person that states it. However, if it is not possible to happen, (...) it happens, and the person told the truth; 2) There is a disjunction among the days of the week: “or it is the first day or it is the second day or … it is the last day” (or Monday or Tuesday or Wednesday or Thursday or Friday). If I still have not been given the exam by Friday, the only possible conclusion is that the exam will be given on Friday. On Thursday, however, thesituation is completely different; 3) It seems that this paradox is a case of contingent futures, which branching time logics usually solve. The truth-value of the sentences is only relative to the branch that takes place in the end. (shrink)

There are two curious features about the backward induction argument (BIA) to the effect that repeated non-cooperation is the rational solution to the finite iterated prisoner’s dilemma (FIPD). First, however compelling the argument may seem, one remains hesitant either to recommend this solu- tion to players who are about to engage in cooperation or to explain cooperation as a deviation from rational play in real-life FIPD’s. Second, there seems to be a similarity between the BIA for the FIPD and the (...) surprise exam paradox (SEP) and one cannot help but wonder whether the former is indeed no more than an instance of the latter. I argue that there is an important difference between the BIA for the FIPD and the SEP, but that a comparison to the SEP can help us understand why the conclusion of the BIA for the FIPD strikes us as a counterintuitive solution to real-life FIPD’s. (shrink)

I identify an assumption that the students should not rely on: if the teacher believes that the exam would not be a surprise on a certain day, the teacher will not give the exam on that day. The reason I present for not making this assumption does not involve doubting the moral goodness of the teacher. But it does involve making a value judgment.

In this paper, I present a response to the surprise exam paradox which may be of some use to someone. It is somewhat frightening for me.

Will a surprise exam happen in the next school week? The memory skepticism solution says, “The students should expect a rational student on the penultimate evening of that week to open themselves up to the possibility that the exam may have happened already, rather than predicting that the exam will happen tomorrow.”.

In this paper, we provide a Bayesian analysis of the well-known surprise exam paradox. Central to our analysis is a probabilistic account of what it means for the student to accept the teacher's announcement that he will receive a surprise exam. According to this account, the student can be said to have accepted the teacher's announcement provided he adopts a subjective probability distribution relative to which he expects to receive the exam on a day (...) on which he expects not to receive it. We show that as long as expectation is not equated with subjective certainty there will be contexts in which it is possible for the student to accept the teacher's announcement, in this sense. In addition, we show how a Bayesian modeling of the scenario can yield plausible explanations of the following three intuitive claims: (1) the teacher's announcement becomes easier to accept the more days there are in class; (2) a strict interpretation of the teacher's announcement does not provide the student with any categorical information as to the date of the exam; and (3) the teacher's announcement contains less information about the date of the exam the more days there are in class. To conclude, we show how the surprise exam paradox can be seen as one among the larger class of paradoxes of doxastic fallibilism, foremost among which is the paradox of the preface. (shrink)

Before the semester begins, a teacher tells his students: “There will be exactly one exam this semester. It will not take place on a day that is an immediate-successor of a day that you are currently in a position to know is not the exam-day”. Both the students and the teacher know – it is common knowledge – that no exam can be given on the first day of the semester. Since the teacher is truthful and reliable, (...) it seems that the students can know that what he says is true. However, in that case, assuming the students can know that they know whatever it is they know (KK) and assuming their knowledge is closed under entailment (closure), the students can reason from what they know to the conclusion that no exam will take place during the semester. This conclusion contradicts what they supposedly know: that there will be an exam. This puzzle, we argue, gives rise to a new consideration for the rejection of KK. We discuss unique features of the argument, especially in comparison to Timothy Williamson's rejection of KK in light of other versions of the surprise exam paradox. (shrink)

The surprise exam paradox is an apparently sound argument to the apparently absurd conclusion that a surprise exam cannot be given within a finite exam period. A closer look at the logic of the paradox shows the argument breaking down immediately. So why do the beginning stages of the argument appear sound in the first place? This paper presents an account of the paradox on which its allure is rooted in a common (...) probabilistic mistake: the base rate fallacy. The account predicts that the paradoxical argument should get less and less convincing as it goes along—a prediction I take to be welcome. On a bleaker note, the account suggests that the base rate fallacy may be more widespread than previously thought. (shrink)

The Surprise Exam Paradox is well-known: a teacher announces that there will be a surprise exam the following week; the students argue by an intuitively sound reasoning that this is impossible; and yet they can be surprised by the teacher. We suggest that a solution can be found scattered in the literature, in part anticipated by Wright and Sudbury, informally developed by Sorensen, and more recently discussed, and dismissed, by Williamson. In a nutshell, the solution (...) consists in realising that the teacher's announcement is a blindspot that can only be known if the week is at least 2 days long. Along the way, we criticise Williamson's own treatment of the paradox. In Williamson's view, the Surprise is similar to the Paradox of the Glimpse and, because of their similarities, both these paradoxes ought to receive a uniform treatment-one that involves locating an illicit application of the KK Principle. We argue that there's no deep analogy between the Surprise and the Glimpse and that, even if there were, the Surprise reasoning reaches a paradoxical conclusion before the KK Principle is used. Rather, in both the Surprise and the Glimpse, the blame should be put on other epistemic principles-respectively, a knowledge retention and a margin for error principle. (shrink)

We’ve all been at parties where there's one cookie left on what was once a plate full of cookies, a cookie no one will eat simply because everyone is following a rule of etiquette, according to which you’re not supposed to eat the last cookie. Or at least we think everyone is following this rule, but maybe not. In this paper I present a new paradox, the Cookie Paradox, which is an argument that seems to prove that in (...) any situation in which everyone is truly following the rule, no one eats any cookies at all, no matter how many there are to be eaten. The ‘Cookie Argument’ resembles the more familiar argument that surprise exams are impossible, but it's not exactly the same. I argue that the biggest difference is that, unlike the surprise exam argument, the Cookie Argument is actually sound! I conclude the paper by explaining how it could be possible for a group of people to engage in behavior (eating cookies) that guarantees that at least one of the members of the group will violate a rule, even when it's common knowledge in the group that everyone is committed to following that very rule. (shrink)

The leading idea of this article is that one cannot acquire knowledge of any non-epistemic fact by virtue of knowing that one that knows something. The lines of reasoning involved in the surprise exam paradox and in Williamson’s _reductio_ of the KK-principle, which demand that one can, are thereby undermined, and new type of counter-example to epistemic closure emerges.

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we (...) explore a variation on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we (...) explore a variation on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s (...) paradox. The references and recommended readings provide gateways for further exploration. (shrink)

The professor announces a surprise exam for the upcoming week; her clever student purports to demonstrate by reductio that she cannot possibly give such an exam. Diagnosing his puzzling argument reveals a deeper puzzle: Is the student justified in believing the announcement? It would seem so, particularly if the upcoming 'week' is long enough. On the other hand, a plausible principle states that if, at the outset, the student is justified in believing some proposition, then he is (...) also justified in believing that he will continue to be justified in believing that proposition. It follows from this 'confidence' principle that the student is not justified in believing the announcement, regardless of the number of days in the week. I argue that the key to resolving this dilemma is to distinguish the confidence principle from a slightly weaker principle governing the student's justified degrees of belief. Representing these degrees of belief as probabilities, and taking 'justified belief' to mean 'justified degree of belief above a certain threshold', I show that we can uphold the weaker, probabilistic analog to the confidence principle, and maintain that, provided the 'week' is long enough, the student can justifiably believe the announcement. The resulting probabilistic analysis of the story leads to a new diagnosis of the logical flaw in the student's reasoning, and suggests, finally, that even those early stages of it which are logically impeccable exhibit another kind of flaw: circularity. (shrink)

This paper proposes a game-theoretic solution of the surprise examination problem. It is argued that the game of “matching pennies” provides a useful model for the interaction of a teacher who wants her exam to be surprising and students who want to avoid being surprised. A distinction is drawn between prudential and evidential versions of the problem. In both, the teacher should not assign a probability of zero to giving the exam on the last day. This representation (...) of the problem provides a diagnosis of where the backwards induction argument, which “proves” that no surprise exam is possible, is mistaken. (shrink)

Despite having been solved numerous times, the surprise quiz paradox persists in the intellectual imagination as a riddle. This dialogue aims to dispel the fallacies of the paradox in an intuitive way through the causal format of a dialogue. Along the way, two contributions are made to the literature. Even if the student knew there would be a quiz at the end of a quizless Thursday, the fact that the quiz will be a surprise Friday would (...) provide a Gettier-style defeater for his supposed knowledge that he will have a quiz Friday. In addition, pace Sorensen (1988), the dialogue explains why the temporal retention of knowledge is essential to the puzzle and not a mere accident. (shrink)

Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal (...) characterisations of the surprise notion, crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes. (shrink)

In this book Jody Azzouni challenges existing epistemological conventions about knowledge: what it means to know something, who or what is seen as knowing, and how we talk about it. He argues that the classic restrictive conditions philosophers routinely place on knowers only hold in special cases, and suggests that knowledge can be equally attributed to children, sophisticated animals, unsophisticated animals, and machinery or devices. Through this perspective and a close examination of its relation to linguistics and psychology, Azzouni freshly (...) approaches longstanding epistemological puzzles including the dogmatism paradox, Gettier puzzles, Agrippa's trilemma, and the surprise-exam paradox. (shrink)

Backwards induction is an intriguing form of argument. It is used in a number of different contexts. One of these is the surprise exam paradox. Another is game theory. But its use is problematic, at least sometimes. The purpose of this paper is to determine what, exactly, backwards induction is, and hence to evaluate it. Let us start by rehearsing informally some of its problematic applications.

This paper considers two explanations for why the main character of Flora Nwapa’s novel One is Enough does not answer the question of how many times her mother-in-law has visited. One of these is a variation on the surprise exam paradox.

This is a collection of eighteen solicited papers on the topics of the title: circularity, definition, and truth. The papers are loosely connected in subject matter, but present a great variety of issues, theories, and approaches. Amongst the many subjects discussed are: the revision theory of truth and applications of revision rules, partiality and fixed point constructions, substitutional quantification, fuzzy logic, negation, belief revision, context dependence, hierarchies, Tarski on truth, deflationism, correspondence theories of truth, and normative aspects of truth. The (...) Liar paradox figures prominently in this collection, but is not alone. Other familiar paradoxes are also discussed, including paradoxes of definability, the Sorites paradox, and the Surprise Exam paradox. So-called paradoxes of rationality, such as the Prisoner’s Dilemma, receive attention as well. (shrink)

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s (...) paradox. The references and recommended readings provide gateways for further exploration. (shrink)

In this paper I consider the surprise examination paradox from a practical perspective, paying special attention to the communicative role of the teacher’s promise to the students. This perspective, which places the promise within a practice, rather than viewing it in the abstract, imposes constraints on adequate solutions to the paradox. In the light of these constraints, I examine various solutions which have been offered, and suggest two of my own.

In this paper, I consider a popular version of the clever student’s reasoning in the surprise examination case, and demonstrate that a valid argument can be constructed. The valid argument is a reductio ad absurdum with the proposition that the student knows on the morning of the first day that the teacher’s announcement is fulfilled as its reductio. But it would not give rise to any paradox. In the process, I criticize Saul Kripke’s solution and Timothy Williamson’s attack (...) on a key step of the student’s reasoning. I then consider the condemned prisoner case in W. V. Quine’s paper ‘On a So-Called Paradox’. I argue that the prisoner’s reasoning as conceived by Quine is more relevant and reasonable than the student’s argument in the popular version of the surprise examination case. I also argue that Quine’s criticism of the prisoner’s reasoning is correct, and therefore that the condemned prisoner case, and the surprise examination case as well, would not generate any paradox. (shrink)

A teacher announced to his pupils that on exactly one of the days of the following school week (Monday through Friday) he would give them a test. But it would be a surprise test; on the evening before the test they would not know that the test would take place the next day. One of the brighter students in the class then argued that the teacher could never give them the test. "It can't be Friday," she said, "since in (...) that case we'll expect it on Thurday evening. But then it can't be Thursday, since having already eliminated Friday we'll know Wednesday evening that it has to be Thursday. And by similar reasoning we can also eliminate Wednesday, Tuesday, and Monday. So there can't be a test!" The students were somewhat baffled by the situation. The teacher was well-known to be truthful, so if he said there would be a test, then it was safe to assume that there would be one. On the other hand, he also said that the test would be a surprise. But it seemed that whenever he gave the test, it wouldn't be a surprise. Well, the teacher gave the test on Tuesday, and, sure enough, the students were surprised. (shrink)

This paper presents a dichotomic analysis of the surprise examination paradox. In section 1, I analyse the surprise notion in detail. I introduce then in section 2, the distinction between a monist and dichotomic analysis of the paradox. I also present there a dichotomy leading to distinguish two basically and structurally different versions of the paradox, respectively based on a conjoint and a disjoint definition of the surprise. In section 3, I describe the solution (...) to SEP corresponding to the conjoint definition. Lastly, I expose in section 4, the solution to SEP based on the disjoint definition. (shrink)

Presents a /simple/ epistemic solution to the paradox of the surprise test, suitable for undergraduates. Given the Gazette's audience, recalcitrant versions, such as Sorenson's, would have been inappropriate to even mention. It is also classified under "logical paradoxes," because it can be argued that given the existence of logical, rather than epistemic, solutions, so also the paradox is logical, rather than epistemic. -/- The author was not sent proofs, because the /Gazette/ was then run on a "shoestring (...) budget"; the 2009 article is just as intended, and the journal is now typeset well. (shrink)

In this paper, I raise and respond to the question of why females are underrepresented in parts of philosophy which one might classify as feminine.