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)

Conventions and leaders are believed to be the two pillars of justice and order in society. This paper evaluates this proposition and draws attention to two intriguing ways in which these pillars can malfunction. The argument is constructed by creating two new games, Greta’s Dilemma and the Incarceration Game. An awareness of these problems can help us use our ‘moral intention’ to reexamine our own collective behavior and to design prior conventions, which limit the power of the leader.

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.

Chalmers and Hájek argue that on an epistemic reading of Ramsey’s test for the rational acceptability of conditionals, it is faulty. They claim that applying the test to each of a certain pair of conditionals requires one to think that one is omniscient or infallible, unless one forms irrational Moore-paradoxical beliefs. I show that this claim is false. The epistemic Ramsey test is indeed faulty. Applying it requires that one think of anyone as all-believing and if one is rational, to (...) think of anyone as infallible-if-rational. But this is not because of Moore-paradoxical beliefs. Rather it is because applying the test requires a certain supposition about conscious belief. It is important to understand the nature of this supposition. (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 mooronic solution to the surprise quiz paradox says students know there will be a surprise quiz one day this week but they lose this knowledge on the penultimate day. This is because ‘there will be a surprise quiz one day this week’ then becomes an instance of Moore's paradox. This view has surprising consequences. Furthermore, even though the surprise quiz announcement becomes an instance of Moore's paradox on the penultimate day, this does not prevent the students from knowing the (...) quiz is coming. I conclude that the first stage of the paradoxical argument succeeds and the mooronic solution fails. (shrink)

In an information state where various agents have both factual knowledge and knowledge about each other, announcements can be made that change the state of information. Such informative announcements can have the curious property that they become false because they are announced. The most typical example of that is 'fact p is true and you don't know that', after which you know that p, which entails the negation of the announcement formula. The announcement of such a formula in a given (...) information state is called an unsuccessful update. A successful formula is a formula that always becomes common knowledge after being announced. Analysis of information systems and 'philosophical puzzles' reveals a growing number of dynamic phenomena that can be described or explained by unsuccessful updates. This increases our understanding of such philosophical problems. We also investigate the syntactic characterization of the successful formulas. (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)

Harman and Lewis credit Kripke with having formulated a puzzle that seems to show that knowledge entails dogmatism. The puzzle is widely regarded as having been solved. In this paper we argue that this standard solution, in its various versions, addresses only a limited aspect of the puzzle and holds no promise of fully resolving it. Analyzing this failure and the proper rendering of the puzzle, it is suggested that it poses a significant challenge for the defense of epistemic closure.

In this article, the author attempts to explicate the notion of the best known Talmudic inference rule called qal wa-omer. He claims that this rule assumes a massive-parallel deduction, and for formalizing it, he builds up a case of massive-parallel proof theory, the proof-theoretic cellular automata, where he draws conclusions without using axioms.

This is a presentation about the impacts of Logic and Theory of Computation. It starts by some explanations about Theory of Computation and its relations with the other subjects in science. Then we have some explanations about paradoxes and some historical points. In continuation, we present some of the most important paradoxes. Forthcoming, Five subjects around the relations between Logic and Theory of computation is introduced. Finally, we present a new approach to solve P vs NP problem via Paradoxes (Presentation (...) 6/20/2022 In Persian, Online seminar of The Iranian Association for Logic (IAL) . (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)

The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that stands between knowing (...) the truth of the premises of a valid inference and knowledge of its conclusion is inferring it from the premises, the evidence for each of the premises may jointly count against the conclusion. The intuitive view regarding inferred knowledge says one thing, the evidence says another. One epistemological framework that seems to have the resources to resolve this tension endorses the view that knowledge always requires conclusive evidence. A second framework resolves the tension by limiting the scope of the closure principle. Only inferences drawn directly from propositions contained in the scope of a single knowledge operator are considered closed. The aim of the present essay is to revive the unpopular third option, the idea that knowledge is open. The essay proceeds by arguing that in different ways the two former frameworks only succeed in relocating the problem, not in resolving it. The first framework, the infallibilist view, relocates the problem to a sharp separation between knowledge of the occurrences of events from knowledge of their chance of occurring, a separation leading to several significant additional problems. The fallibilist view, the second framework, in endorsing closure neglects to take into full account the ways in which evidence fails to be transitive. For instance, evidence can count in favor of a conjunction while counting against each of its conjuncts. This fact, which is argued for in the essay on probabilistic as well as non-probabilistic grounds, is used as the foundation of an argument against closed knowledge that can be used as a way to understand several of the most fundamental challenges of epistemology. Not only can an open knowledge view that is based on open evidence resolve all these problems in a simple and natural way, it can also respond to formidable challenges that significantly hinder other open knowledge views. There are good reasons, then, to view both knowledge and evidence as open. (shrink)

The appropriationist approach to history of philosophy is often accused of being antihistorical and thus unreliable. The appropriationists are only concerned with their own philosophical problems, and they make discriminating use of the historical data as far as it serves their needs. Its rival, the contextualist approach, claims to be an honest, dedicated and reliable treatment of history. The contextualists are willing to make use of the tedious methodology of Classical studies as long as it promises to uncover the true (...) historical data. In this paper I present a case where the contextualists have failed to surpass their rival appropriationists in their quest for veracity. The case is the debate about Aristotle’s De Interpretatione 9, which took place in 1950-1980s. In this debate the contextualists were unable to offer any other results except for those which have already been suggested by the appropriationists. In addition I demonstrate how the contextualists selectively used the arsenal of Classical methodology not to uncover the truth, but to justify their own preconceived interpretations. (shrink)

This paper deals with the problem of future contingents, and focuses on two classical logical principles, excluded middle and bivalence. One may think that different attitudes are to be adopted towards these two principles in order to solve the problem. According to what seems to be a widely held hypothesis, excluded middle must be accepted while bivalence must be rejected. The paper goes against that line of thought. In the first place, it shows how the rejection of bivalence leads to (...) implausible consequences if excluded middle is accepted. In the second place, it addresses the question of why one should reject bivalence, and finds no satisfactory answer. /// Este artículo trata el problema de los futuros contingentes, y se enfoca en dos principios lógicos clásicos: el tercero excluido y la bivalencia. Se podría pensar que una solución del problema requiere actitudes diferentes hacia estos dos principios. Según una hipótesis que parece ampliamente compartida, el tercero excluido debe ser aceptado, mientras que la bivalencia debe ser rechazada. Este artículo argumenta en contra de esta línea de pensamiento. En primer lugar, se aborda cómo el rechazo de la bivalencia lleva a consecuencias poco plausibles si el tercero excluido es aceptado. En segundo lugar, se enfrenta la cuestión de por qué se debería rechazar la bivalencia, sin encontrar una respuesta satisfactoria. (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)

RÉSUMÉ: Les philosophes, au cours des cinquante dernières années, se sont efforcés de démontrer qu’un professeur peut, d’une manière cohérente et exacte, annoncer à ses étudiants qu’un examen surprise aura lieu lors d’une journée non spécifiée d’une période donnée, le problème étant qu’une telle annonce peut sembler s’annuler ellemême lorsqu’elle est soumise à une induction régressive. Deux grandes approches, l’une épistémique et l’autre logique, one été développées à ce propos. Le présent article adopte une approche logique, mais repose aussi d’une (...) manière cruciale sur une compréhension épistémique du problème, pour essayer de montrer que l’annonce du professeur peut effectivement être cohérente et exacte. (shrink)

Here, by introducing a version of “Unexpected hanging paradox” first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support it. Finally, we propose a claim in Theory of Computation about the consistency of this Theory. One of the major claim is:Theory of Computation and Classical Logic leads us to a contradiction.

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)

This paper offers a new solution to the Surprise Test Paradox. The paradox arises thanks to an ingenious argument that seems to show that surprise tests are impossible. My solution to the paradox states that it relies on a questionable closure principle. This closure principle says that if one knows something and competently deduces something else, one knows the further thing. This principle has been endorsed by John Hawthorne and Timothy Williamson, among others, and I trace its motivation back to (...) work by Alvin Goldman. I provide counterexamples to the principle and explain the flaw in the reasoning of those who defend it. (shrink)

This paper revisits Buridan’s Bridge paradox (Sophismata, chapter 8, Sophism 17), itself close kin to the Liar paradox, a version of which also appears in Bradwardine’s Insolubilia. Prompted by the occurrence of the paradox in Cervantes’s Don Quixote, I discuss and compare four distinct solutions to the problem, namely Bradwardine’s “just false” conception, Buridan’s “contingently true/false” theory, Cervantes’s “both true and false” view, and then the “neither true simpliciter nor false simpliciter” account proposed more recently by Jacquette. All have in (...) common to accept that the Bridge expresses a truth-apt proposition, but only the latter three endorse the transparency of truth. Against some previous commentaries I first show that Buridan’s solution is fully compliant with an account of the paradox within classical logic. I then argue that Cervantes’s insights, as well as Jacquette’s treatment, are both supportive of a dialetheist account, and Jacquette’s in particular of the strict-tolerant account of truth. I defend dialetheist intuitions (whether in LP or ST guise) against two objections: one concerning the future, the other concerning the alleged simplicity of the Bridge compared to the Liar. (shrink)

There is a long tradition of drawing metaphysical conclusions from investigations into language. This paper concerns one contemporary variation on this theme: the alleged ontological significance of cognitivist truth-theoretic accounts of semantic competence. According to such accounts, human speakers’ linguistic behavior is in part empirically explained by their cognizing a truth-theory. Such a theory consists of a finite number of axioms assigning semantic values to lexical items, a finite number of axioms assigning semantic values to complex expressions on the basis (...) of their structure and the semantic values of their constituents, and a finite number of production schemata. The theory enables the derivation of truth-conditions for each sentence of the language: something of roughly the form ‘S is true iff P’.1 The claim that speakers stand in a cognitive relation to such theories is advanced, not as a conceptual analysis of semantic competence or understanding, but rather as an empirical hypothesis about human speakers in particular, one part of a broader empirical account of our linguistic competence and cognition generally. It therefore must mesh with the rest of our theorizing in these areas and whatever relevant data from neighboring inquiries there may be. The precise nature of the cognitive relation a speaker is supposed to bear to a truththeory is a matter of some dispute. I speak of ‘‘cognizing’’ (following. (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 (...) 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)

Michael Tooley presents a major new philosophical theory of the nature of time, offering a powerful alternative to the traditional "tensed" and recent "tenseless" accounts of time. He argues for a dynamic conception of the universe, in which past, present, and future are not merely subjective features of experience. He claims that the past and the present are real, while the future is not. Tooley's approach accounts for time in terms of causation. He therefore claims that the key to understanding (...) the dynamic nature of the universe is to understand the nature of causation. Time, Tense, and Causation is a landmark treatment of one of the oldest and most perplexing intellectual problems, and will be fascinating reading for anyone interested in the character of time. (shrink)

This paper examines causal theories of reference with respect to how plausible an account they give of non-physical natural kind terms such as ‘gene’ as well as of the truth of the associated theoretical claims. I first show that reference fixism for ‘gene’ fails. By this, I mean the claim that the reference of ‘gene’ was stable over longer historical periods, for example, since the classical period of transmission genetics. Second, I show that the theory of partial reference does not (...) do justice to some widely held realist intuitions about classical genetics. This result is at loggerheads with the explicit goals usually associated with partial theories of reference, which is to defend a realist semantics for scientific terms. Thirdly, I show that, contrary to received wisdom and perhaps contrary to physics and chemistry, neither reference fixism nor partial reference are necessary in order to hold on to scientific realism about biology. I pinpoint the reasons for this in the nature of biological kinds, which do not even remotely resemble natural kinds (i.e., Lockean real essences) as traditionally conceived. (shrink)

John Cook Wilson (1849–1915) was Wykeham Professor of Logic at New College, Oxford and the founder of ‘Oxford Realism’, a philosophical movement that flourished at Oxford during the first decades of the 20th century. Although trained as a classicist and a mathematician, his most important contribution was to the theory of knowledge, where he argued that knowledge is factive and not definable in terms of belief, and he criticized ‘hybrid’ and ‘externalist’ accounts. He also argued for direct realism in perception, (...) criticizing both empiricism and idealism, and argued for a moderate nominalist view of universals as being in rebus and only ‘apprehended’ by their particulars. His influence helped swaying Oxford away from idealism and, through figures such as H. A. Prichard, Gilbert Ryle, or J. L. Austin, his ideas were also to some extent at the origin of ‘moral intuitionism’ and ‘ordinary language philosophy’ which defined much of Oxford philosophy until the second half of the twentieth-century. Nevertheless, his name and legacy were all but forgotten for generations after World War II. Still, his views on knowledge are with us today, being in part at work in the writings of philosophers as diverse as John McDowell, Charles Travis, and Timothy Williamson. (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)

RÉSUMÉ: Les philosophes, au cours des cinquante dernières années, se sont efforcés de démontrer qu’un professeur peut, d’une manière cohérente et exacte, annoncer à ses étudiants qu’un examen surprise aura lieu lors d’une journée non spécifiée d’une période donnée, le problème étant qu’une telle annonce peut sembler s’annuler ellemême lorsqu’elle est soumise à une induction régressive. Deux grandes approches, l’une épistémique et l’autre logique, one été développées à ce propos. Le présent article adopte une approche logique, mais repose aussi d’une (...) manière cruciale sur une compréhension épistémique du problème, pour essayer de montrer que l’annonce du professeur peut effectivement être cohérente et exacte. (shrink)

In what follows, I strive to present the elements of a philosophical doctrine, which can be defined as dialectical contextualism. I proceed first to define the elements of this doctrine: dualities and polar contraries, the principle of dialectical indifference and the one-sidedness bias. I emphasize then the special importance of this doctrine in one specific field of meta-philosophy: the methodology for solving philosophical paradoxes. Finally, I describe several applications of this methodology on the following paradoxes: Hempel's paradox, the surprise examination (...) paradox and the Doomsday Argument. (shrink)

This volume seeks to further the use of formal methods in clarifying one of the central problems of philosophy: that of our free human agency and its place in our indeterministic world. It celebrates the important contributions made in this area by Nuel Belnap, American logician and philosopher. Philosophically, indeterminism and free action can seem far apart, but in Belnap’s work, they are intimately linked. This book explores their philosophical interconnectedness through a selection of original research papers that build forth (...) on Belnap’s logical and philosophical work. Some contributions take the form of critical discussions of Belnap's published work, some develop points made in his publications in new directions, and others provide additional insights on the topics of indeterminism and free action. In Nuel Belnap’s work on indeterminism and free action, three formal frameworks figure prominently: the simple branching histories framework known as "branching time;" its relativistic spatio-temporal extension, branching space-times; and the “seeing to it that” logic of agency. As those frameworks provide the formal background for the contributed papers, the volume introduction gives an overview of the current state of their development. It also introduces case-intensional first order logic, a general intensional logic offering resources for a first-order extension of the mentioned frameworks and a recent research focus of Belnap’s. The volume also contains an extended biographical interview with Nuel Belnap. (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.

In this paper, I propose an accurate description of the cognitive process involved in the one-sidedness fallacy, a widespread type of fallacy. I describe first several characterizations of the one-sidedness fallacy, that are either inductive or deductive, or occurring at a meta-philosophical level. I recall, second, the framework of the cognitive distortions described in Franceschi (2007). I give then a definition of the one-sidedness fallacy, by describing it as a general cognitive distortion: the disqualification of one pole. I show finally (...) how the one-sidedness fallacy distinguishes itself from the confirmation bias. (shrink)