'Post this letter!' does not entail 'Post this letter or drink up my wine!' (the Ross Paradox) because one can be in a state with the content of the former without being in a state with the content of the latter; in turn, because the latter can rationalize drinking up my wine but the former cannot; in turn, because practical rationalization flows toward one's present situation, in contrast with the flow of theoretical rationalization from one's present situation. Formally, this (...) is implemented with a semantics for imperatives involving a partition to set up an issue of significance and a proposition to establish how to settle it. I characterize a series of languages and language-games to implement all this, and appeal to an 'endorsement-theoretic' conception of modals as quantifiers over mental states to explain why 'You must post this letter' does not entail 'You must either post this letter or drink up my wine'. (shrink)

1 Background for the Uninitiated RICHMOND CAMPBELL Paradoxes are intrinsically fascinating. They are also distinctively ...

This book develops a framework for analysing strategic rationality, a notion central to contemporary game theory, which is the formal study of the interaction of rational agents and which has proved extremely fruitful in economics, political theory and business management. The author argues that a logical paradox lies at the root of a number of persistent puzzles in game theory, in particular those concerning rational agents who seek to establish some kind of reputation. Building on the work of (...) Parsons, Burge, Gaifman and Barwise and Etchemendy, Robert Koons constructs a context-sensitive solution to the whole family of liar-like paradoxes including, for the first time, a detailed account of how the interpretation of paradoxical statements is fixed by context. This analysis provides an understanding of how the rational agent model can account for the emergence of rules, practices and institutions. (shrink)

According to some, there is a problem concerning the emotions we feel toward fictional entities such as Anna Karenina, Werther and the like. We feel pity, fear, and sadness toward them, but how is that possible? “We are saddened, but how can we be? What are we sad about? How can we feel genuinely and involuntarily sad, and weep, as we do know that no one has suffered or died?” (Radford, in: Proceedings of the Aristotelian Society, 1975). This is the (...) paradox of fiction which is based on the assumption that emotions, to be genuine and rational, should be directed toward existent beings. But if beliefs about existence are necessary for us to be rationally moved by something, and such beliefs are lacking when we are moved by fiction (because we do not believe fictional characters and events to be real), then our capacity for an emotional response to fiction is irrational. Consequently, our emotional attitude toward future generations should be considered as irrational as well. But is this really the case? Are there good arguments to consider future and fictional entities as similar from this point of view? Or would it be better to distinguish the two? Is there such a thing as a paradox of the future? If so, how does it relate to the more famous paradox of fiction? (shrink)

My aim in this paper is to develop a unified solution to two paradoxes of bounded rationality. The first is the regress problem that incorporating cognitive bounds into models of rational decisionmaking generates a regress of higher-order decision problems. The second is the problem of rational irrationality: it sometimes seems rational for bounded agents to act irrationally on the basis of rational deliberation. I review two strategies which have been brought to bear on these problems: the way of weakening (...) which responds by weakening rational norms, and the way of indirection which responds by letting the rationality of behavior be determined by the rationality of the deliberative processes which produced it. Then I propose and defend a third way to confront the paradoxes: the way of level separation. (shrink)

Any organised society needs some method for determining common policy: public decisions must be forged from private preferences, and particular interests must find a reconciliation in the general good. A society is tolerable only if its decisions are reached by a rational path; for, just as a reasonable man decides his private life on the basis of reasonable procedures, so a reasonable society must formulate its communal behaviour on the basis of reasonable principles. If the Principle of Rationality is (...) violated, society collapses into an anarchic tohubohu, governed by naked power or arbitrary caprice. (shrink)

This paper provides a new solution to the epistemic paradox of belief-instability, a problem of rational choice which has recently received considerable attention (versions of the problem have been discussed by — among others — Tyler Burge, Earl Conee, and Roy Sorensen). The problem involves an ideally rational agent who has good reason to believe the truth of something of the form:[Ap] p if and only if it is not the case that I accept or believe p.

Sorensen provides a panoramic view of paradoxes of theoretical and practical rationality. These puzzles are organized as apparent counterexamples to attractive principles such as the principle of charity, the transitivity of preferences, and the principle that we should maximize expected utility. The following paradoxes are discussed: fearing fictions, the surprise test paradox, Pascal’s Wager, Pollock’s Ever Better wine, Newcomb’s problem, the iterated prisoner’s dilemma, Kavka’s paradoxes of deterrence, backward inductions, the bottle imp, the preface paradox, Moore’s problem, (...) Buridan’s ass, Condorcet’s paradox of cyclical majorities, the St. Petersburg paradox, weakness of will, the Ellsberg paradox, Allais’s paradox, and Peter Cave’s puzzle of self-fulfilling beliefs. (shrink)

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the (...) epistemic situation when a given node is reached can be thought of as the result of a joint act of learning (via public announcements) that the node is reached. We then use the notion of “stable belief”, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann’s and compatible with the implicit assumptions (the “epistemic openness of the future”) underlying Stalnaker’s criticism of Aumann’s proof. The “dynamic” nature of our concept of rationality explains why our condition avoids the apparent circularity of the “backward induction paradox”: it is consistent to (continue to) believe in a player’s rationality after updating with his irrationality. (shrink)

This article shows that there is a liar-like paradox that arises for rational credence that relies only on very weak logical and credal principles. The paradox depends on a weak rational reflection principle, logical principles governing conjunction, and principles governing the relationship between rational credence and proof. To respond to this paradox, we must either reject even very weak rational reflection principles or reject some highly plausible logical or credal principle.

Discusses Soren Kierkegaard's use of irrationality in his pseudonymous writings to bolster important truths about rationality.

This article provides a straightforward diagnosis and resolution of the lottery paradox and the epistemic version of the paradox of the preface. In doing so, The article takes some steps in relating the notion of probability to the notion of epistemic justification.

Current incentive structures are more favorably aligned with the world’s problems than with their solutions. We conceptualize this as the paradox of incentives to argue the need for new thinking and restructuring of incentives to break the paradox during the COVID-19 pandemic and beyond, and create new opportunities for societal transformation.

G. E. Moore observed that to assert, 'I went to the pictures last Tuesday but I don't believe that I did' would be 'absurd'. Over half a century later, such sayings continue to perplex philosophers. In the definitive treatment of the famous paradox, Green and Williams explain its history and relevance and present new essays by leading thinkers in the area.

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on plausibility models. Similarly to other epistemic statements, dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we "simulate" the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought (...) of as the result of a joint act of learning that the node is reached. We then use the notion of "stable belief, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann's and compatible with the implicit assumptions underlying Stalnaker's criticism of Aumann's proof. The "dynamic" nature of our concept of rationality explains why our condition avoids the apparent circularity of the "backward induction paradox": it is consistent to believe in a player's rationality after updating with his irrationality. (shrink)

To the normal reasons that we think can justify one in preferring something, x (namely, that x has objectively preferable properties, or has properties that one prefers things to have, or that x's obtaining would advance one's preferences), I argue that it can be a justifying reason to prefer x that one's very preferring of x would advance one's preferences. Here, one prefers x not because of the properties of x, but because of the properties of one's having the preference (...) for x. So-revising one's preferences is rational in paradoxical choice situations like Kavka's Deterrence Paradox. I then try to meet the following objections: that this is stoicist, incoherent, bad faith; that it conflates instrumental and intrinsic value, gives wrong solutions to the problems presented by paradoxical choice situations, entails vicious regresses of value justification, falsifies value realism, makes valuing x unresponsive to x's properties, causes value conflict, conflicts with other standards of rationality, violates decision theory, counsels immorality, makes moral paradox, treats value change as voluntary, conflates first- and second-order values, is psychologically unrealistic, and wrongly presumes that paradoxical choice situations can even occur. (shrink)

Jim buys a ticket in a million-ticket lottery. He knows it is a fair lottery, but, given the odds, he believes he will lose. When the winning ticket is chosen, it is not his. Did he know his ticket would lose? It seems that he did not. After all, if he knew his ticket would lose, why would he have bought it? Further, if he knew his ticket would lose, then, given that his ticket is no different in its chances (...) of winning from any other ticket, it seems that by parity of reasoning he should also know that every other ticket would lose. But of course he doesn’t know that; in fact, he knows that not every ticket will lose. (shrink)

I offer a model of self‐knowledge that provides a solution to Moore's paradox. First, I distinguish two versions of the paradox and I discuss two approaches to it, neither of which solves both versions of the paradox. Next, I propose a model of self‐knowledge according to which, when I have a certain belief, I form the higher‐order belief that I have it on the basis of the very evidence that grounds my first‐order belief. Then, I argue that (...) the model in question can account for both versions of Moore's paradox. Moore's paradox, I conclude, tells us something about our conceptions of rationality and self‐knowledge. For it teaches us that we take it to be constitutive of being rational that one can have privileged access to one's own mind and it reveals that having privileged access to one's own mind is a matter of forming first‐order beliefs and corresponding second‐order beliefs on the same basis. (shrink)

This article examines the prisoner's dilemma paradox and argues that confessing is the rational choice, despite this probably entailing a less-than-ideal outcome.

We argue that giving up on the closure of rational belief under conjunction comes with a substantial price. Either rational belief is closed under conjunction, or else the epistemology of belief has a serious diachronic deficit over and above the synchronic failures of conjunctive closure. The argument for this, which can be viewed as a sequel to the preface paradox, is called the ‘review paradox'; it is presented in four distinct, but closely related versions.

This paper investigates the responses of GPT-4, a state-of-the-art AI language model, to ten prominent philosophical paradoxes, and evaluates its capacity to reason and make decisions in complex and uncertain situations. In addition to analyzing GPT-4's solutions to the paradoxes, this paper assesses the model's Theory of Mind (ToM) capabilities by testing its understanding of mental states, intentions, and beliefs in scenarios ranging from classic ToM tests to complex, real-world simulations. Through these tests, we gain insight into AI's potential for (...) social reasoning and its capacity for more sophisticated forms of human-AI interaction. The paper also explores the limitations and biases of AI-generated reasoning and its implications for our comprehension of complex philosophical problems. (shrink)

We talk and think about our beliefs both in a categorical and in a graded way. How do the two kinds of belief hang together? The most straightforward answer is that we believe something categorically if we believe it to a high enough degree. But this seemingly obvious, near-platitudinous claim is known to give rise to a paradox commonly known as the 'lottery paradox' – at least when it is coupled with some further seeming near-platitudes about belief. How (...) to resolve that paradox has been a matter of intense philosophical debate for over fifty years. This volume offers a collection of newly commissioned essays on the subject, all of which provide compelling reasons for rethinking many of the fundamentals of the debate. (shrink)

How much would you pay to play a lottery with an “infinite expected payoff?” In the case of the century old, St. Petersburg Paradox, the answer is that the vast majority of people would only pay a small amount. The authors seek to understand this paradox by providing an explanation consistent with a broad, process‐level model of human decision‐making under risk.

Evidentialism is the doctrine that rational belief should be proportioned to one’s evidence. By “one’s evidence,” I mean evidence that we possess and know that we possess. I specifically exclude from “evidence” the following: information of which we are unaware that our brain might rely on in constructing experience or in the formation of beliefs. My initial interest is with the doctrine of Evidentialism as it applies to a quandary that arises in the Sci-Fi movie Contact, the “Contact Paradox” (...) as I will call it. In this movie one of the main characters, Ellie, is a cosmologist working in a radio-telescope research facility searching for signals from intelligent life in the cosmos. The entity whose epistemological status is at issue in her quandary is her deceased father but there is an obvious parallel between the quandary of a rational believer in God and Ellie’s quandary, a parallel extensively explored in the movie itself. My first thesis is that in Ellie’s case Evidentialism is false: in certain cases, it is rational to believe in the existence of an entity in spite of the fact that the empirical evidence overall is contrary, and the Contact Paradox is one such case. Later in the paper I turn attention to the issue of Evidentialism regarding beliefs in the existence of God. My second thesis is that Evidentialism is false there as well. (shrink)

The renowned paradox of voting arises when one tries to explain the decision to go out and vote in an exclusively instrumental framework. Instead of postulating that voters always derive utility from the act of voting, I want to search for the reasons that underlie the absence or presence of a preference for voting. In my noninstrumental account of expressive rationality, citizens want to express who they are and what they care about. Whether or not one votes therefore (...) depends on the force of one’s commitments to principles, norms, ideologies or particular persons. This has been confirmed by empirical research showing that citizens vote because they feel they have to, not because they like doing so. Complementing instrumental rationality, this concept of expressive rationality gives a fuller, deeper and more adequate view of the way citizens make political decisions, thereby solving the paradox of voting. (shrink)

Wilhelm Vossenkuhl; XI*—The Paradox in Kant's Rational Religion, Proceedings of the Aristotelian Society, Volume 88, Issue 1, 1 June 1988, Pages 179–192, https.

The author discusses the meaning of the paradox, which rises as a result of the controversy between the principles of scientific ethos (R. Merton) and fallibilism (K. Popper). She argues that the justification of the moral authority of science should not depend on this paradox. The author uses Max Weber’s concept of substantive rationality to consider the idea of social legitimation of science. She argues for understanding expertise as a special mode of scientific knowledge which aims at (...) justifying the authority of science in the society. (shrink)

Self-deception is one of the topics that lends itself best to the task of exploring the possibilities of cross-fertilization between 'continental philosophy' and 'analytic philosophy'. Fifty years ago, in Being and Nothingness, Sartre defined the core notion of 'Bad Faith' as lying to oneself. On the other side of the Atlantic, self-deception has become one of the most exciting puzzles in the philosophy of mind, and a number of paradoxes encountered by the theory of rational choice involve that very same (...) notion. One of the objectives is to show that bridges can be thrown over the gap between the two traditions, but also that both of them make self-deception too intrapsychic and suffer from a serious individualistic bias. The conference was intended to explore the intersubjective and social dimensions of self-deception. (shrink)

This collection focuses on relations between probability or Bayesian credence on the one hand and rational belief or knowledge on the other, relations undergirding epistemic lottery paradoxes. A co...

The ancient puzzle of the Liar was shown by Tarski to be a genuine paradox or antinomy. I show, analogously, that certain puzzles of contemporary game theory are genuinely paradoxical, i.e., certain very plausible principles of rationality, which are in fact presupposed by game theorists, are inconsistent as naively formulated. ;I use Godel theory to construct three versions of this new paradox, in which the role of 'true' in the Liar paradox is played, respectively, by 'provable', (...) 'self-evident', and 'justifiable'. I also construct in modal operator logic a paradox involving reflexive empirical reasoning. Unlike the paradox of the Liar, the paradox of reflexive reasoning does not depend on self-reference. ;I consider various solutions to the Liar paradox and evaluate how well these solutions cope with the paradox of reflexive reasoning. I then formalize the solution to the paradoxes which I favor: the indexical-hierarchical approach, first sketched out by Charles Parsons and Tyler Burge. In this solution, occurrences of the predicate 'true' in sentence-tokens are contextually relativized to levels of a hierarchy. Drawing also on some brief remarks of Bertrand Russell and Charles Parsons, I develop an account of the kind of schematic generality needed for this theory to be statable. ;Finally, I demonstrate that the principles shown to be paradoxical are in fact presupposed by contemporary game theorists in their reliance on the notion of common knowledge or, more precisely, mutual belief. I create novel analyses of and corresponding solutions to several recalcitrant puzzles within game theory, including the "chain-store paradox". (shrink)

This article discusses rationality gaps triggered by self-referential/cyclic choice, the latter being understood as choosing according to a norm that refers to the choosing itself. The Crocodile Paradox is reformulated and analyzed as a game—named CP—whose Nash equilibrium is shown to trigger a cyclic choice and to invite a rationality gap. It is shown that choosing the Nash equilibrium of CP conforms to the principles Wolfgang Spohn and Haim Gaifman introduced to, allegedly, guarantee acyclicity but, in fact, (...) does not prevent self-referential/cyclic choice and rationality gaps. It is shown that CP is a counter-example to Gaifman's solution of the rationality gaps problem. (shrink)