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)

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.

The Paradox of the Surprise Examination has been a testing ground for a variety of frameworks in formal epistemology, from epistemic logic to probability theory to game theory and more. In this paper, I treat a related paradox, the Paradox of the Undiscoverable Position, as a test case for the possible-worlds style representation of epistemic states. I argue that the paradox can be solved in this framework, further illustrating the power of possible-worlds style modeling. The solution also illustrates an important (...) distinction between anti-performatory and unassimilable announcements of information. (shrink)

outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.

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)

Roy A. Sorensen has advanced an ingenious variation of the prediction or surprise event paradox, which he calls the designated student paradox. Sorensen reduces the temporal dimension of the problem by eliminating reference to future occasions on which an announced surprise event might occur, and substituting a surprise location to which epistemic agents have progressively limited spatial-perceptual access, in order to sidestep what he regards as inessential solutions to the standard formulation.

This paper proposes a new framework to solve the surprise examination paradox. I survey preliminary the main contributions to the literature related to the paradox. I introduce then a distinction between a monist and a dichotomic analysis of the paradox. With the help of a matrix notation, I also present a dichotomy that leads to distinguish two basically and structurally different notions of surprise, which are respectively based on a conjoint and a disjoint structure. I describe then how Quine’s solution (...) applies to the version of the paradox corresponding to the conjoint structure. Lastly, I expose a solution to the paradox based on the disjoint structure. (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)

This paper proposes a new framework to solve the surprise examination paradox. I survey preliminary the main contributions to the literature related to the paradox. I introduce then a distinction between a monist and a dichotomic analysis of the paradox. With the help of a matrix notation, I also present a dichotomy that leads to distinguish two basically and structurally different notions of surprise, which are respectively based on a conjoint and a disjoint structure. I describe then how Quine's solution (...) and Hall's reduction apply to the version of the paradox corresponding to the conjoint structure. Lastly, I expose a solution to the version of the paradox based on the disjoint structure. (shrink)

Can victims of the oracle paradox, which is known primarily through its unexpected hanging and surprise examination versions, extricate themselves from their difficulties of reasoning? No. For they do not, contrary to recent opinion, commit errors of fallacious elimination. As I shall argue, the difficulties of reasoning faced by these victims do not originate in the domain of concepts, propositions and their entailment relations; nor do they result from misapprehensions about limitations on what can be known. The difficulties of reasoning (...) flow, instead, from conflicts that arise in the practical dimension of life. The oracle paradox is in this way more evocative of problems faced in the theory of computation than it is like the celebrated Russell’s paradox. (shrink)

The paradox of the Unexpected Hanging, related prediction paradoxes, and the Sorites paradoxes all involve reasoning about ordered collections of entities: days ordered by date in the case of the Unexpected Hanging; men ordered by the number of hairs on their heads the case of the bald man version of the Sorites. The reasoning then assigns each entity a value that depends on the previously assigned value of one of the neighboring entities. The final result is paradoxical because it conflicts (...) with the obviously correct, commonsensical value. The paradox is due to the serial procedure of assigning a value based on the newly assigned value of the neighbor. An alternative procedure is to assign each value based only on the original values of neighbors - a parallel procedure. That procedure does not give paradoxical answers. (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.