The scope of Aumann’s (1976) Agreement Theorem is needlessly limited by its restriction to Conditioning as the update rule. Here we prove the theorem in a more comprehensive framework, in which the evolution of probabilities is represented directly, without deriving new probabilities from new certainties. The framework allows arbitrary update rules subject only to Goldstein’s (1983) requirement that current expectations agree with current expectations of future expectations.

This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which (...) are natural formalizations of Aumann’s original result. Furthermore, a sound and complete axiomatization of a dynamic agreement logic is provided, in which one of these agreement theorems can be derived syntactically. These technical results are used to show the importance of explicitly representing the dynamics behind the agreement theorem, and lead to a clarification of some conceptual issues surrounding the agreement theorem, in particular concerning the role of common knowledge. The formalization of the agreement theorem thus constitutes a concrete example of the so-called dynamic turn in logic. (shrink)

Robert Aumann presents his Agreement Theorem as the key conditional: “if two people have the same priors and their posteriors for an event A are common knowledge, then these posteriors are equal” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s proof but are not explicit in the key conditional: (1) that agents commonly know, of some prior μ, that it is the common prior; (2) that agents commonly know that each (...) of them updates on the prior by conditionalization; (3) that agents commonly know that if an agent knows a proposition, she knows that she knows that proposition (the “K K” principle); (4) that agents commonly know that they each update only on true propositions. It is shown that natural weakenings of any one of these strong assumptions can lead to countermodels to Aumann’s key conditional. Examples are given in which agents who have a common prior and commonly know what probability they each assign to a proposition nevertheless assign that proposition unequal probabilities. To alter Aumann’s famous slogan: people can “agree to disagree”, even if they share a common prior. The epistemological significance of these examples is presented in terms of their role in a defense of the Uniqueness Thesis: If an agent whose total evidence is E is fully rational in taking doxastic attitude D to P, then necessarily, any subject with total evidence E who takes a different attitude to P is less than fully rational. (shrink)

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts, content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but (...) in agreement. We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic versus semantic formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence. (shrink)

An intricate, long, and occasionally heated debate surrounds Boltzmann’s H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt’s 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In (...) the first part, I discuss the development of Boltzmann’s research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt’s challenge and Boltzmann’s response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject. (shrink)

Is the restricted, consistent, version of the T-scheme sufficient for an ‘implicit definition’ of truth? In a sense, the answer is yes (Haack 1978 , Quine 1953 ). Section 4 of Ketland 1999 mentions this but gives a result saying that the T-scheme does not implicitly define truth in the stronger sense relevant for Beth’s Definability Theorem. This insinuates that the T-scheme fares worse than the compositional truth theory as an implicit definition. However, the insinuation is mistaken. For, as (...) Bays rightly points out, the result given extends to the compositional truth theory also. So, as regards implicit definability, both kinds of truth theory are equivalent. Some further discussion of this topic is mentioned (Gupta 2008 , Ketland 2003 , McGee 1991 ), all in agreement with Bays’s analysis. (shrink)

Standard models in epistemic game theory make strong assumptions about agents’ knowledge of their own beliefs. Agents are typically assumed to be introspectively omniscient: if an agent believes an event with probability p, she is certain that she believes it with probability p. This paper investigates the extent to which this assumption can be relaxed while preserving some standard epistemic results. Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth” axiom, together with the property of balancedness, (...) a significant relaxation of introspective omniscience. I provide an example which shows that Geanakoplos’s statement is incorrect. I then introduce a new property, local balancedness, which allows us both to correct Geanakoplos’s result, and to extend it to cases where the truth axiom may fail. I exploit this general Agreement Theorem to provide novel epistemic conditions for correlated and Nash equilibrium, both of which relax the assumption of introspective omniscience. In all three cases, the results are also extended to infinite state spaces. (This is Chapter 5 of my 2014 Oxford DPhil (PhD) thesis.). (shrink)

The hidden-variables model constructed by Karl Hess and Walter Philipp is claimed by its authors to exploit a "loophole" in Bell's theorem; according to Hess and Philipp, the parameters employed in their model extend beyond those considered by Bell. Furthermore, they claim that their model satisfies Einstein locality and is free of any "suspicion of spooky action at a distance." Both of these claims are false; the Hess-Philipp model achieves agreement with the quantum-mechanical predictions, not by circumventing Bell's (...) theorem, but via Parameter Dependence. (shrink)

How can collective decisions be made among individuals with conflicting preferences or judgments? Arrow’s impossibility theorem and other social-choice-theoretic results suggest that, for many collective decision problems, there are no attractive democratic solutions. In response, deliberative democrats argue that group deliberation makes collective decisions more tractable. How can deliberation accomplish this? In this paper, I explore the distinction between two different types of agreement and discuss how they can facilitate collective decision making. Deliberative democrats have traditionally defended the (...) hypothesis that group deliberation generates consensus on what decision option should be chosen: "substantive agreement". But substantive agreement is not only empirically unrealistic, but also logically unnecessary for meaningful collective decision making. An alternative, less demanding hypothesis is that, under certain conditions, group deliberation generates consensus on how a decision problem should be conceptualized: "meta-agreement". I assess the latter hypothesis, explain how it can be empirically tested, and cite some evidence consistent with it. My discussion addresses two contexts of democratic decision making: preference aggregation and judgment aggregation. (shrink)

The failure of Bell's theorem for Clifford algebra valued local variables is further consolidated by proving that the conditions of remote parameter independence and remote outcome independence are duly respected within the recently constructed exact, local realistic model for the EPR-Bohm correlations. Since the conjunction of these two conditions is equivalent to the locality condition of Bell, this provides an independent geometric proof of the local causality of the model, at the level of microstates. In addition to local causality, (...) the model respects at least seven other conceptual and operational requirements, arising either from the predictions of quantum mechanics or the premises of Bell's theorem, including the Malus's law for sequential spin measurements. Since the agreement between the predictions of the model and those of quantum mechanics is quantitatively precise in all respects, the ensemble interpretation of the entangled singlet state becomes amenable. (shrink)

The author clarifies the thesis of the social constructivists and shows how it is overlapping with some ideas of its critics. Based on established agreement between social constructivism and evolutionary epistemology, she argues that the conceptual elements of mathematical knowledge are social constructs.

No-lose theorems state that---no matter what the result of an experiment will be---there will be a relevant epistemic gain if the experiment is performed. Here I provide an analysis of such theorems, looking at examples from particle physics. I argue that no-lose theorems indicate the pursuitworthiness of experiments by partially decoupling the expected epistemic gain of an experiment from the ex-ante probability that the primarily intended outcome is achieved. While an experiment's pursuitworthiness typically depends on the ex-ante probability that the (...) intended outcome is realized, this is not the case if there is a no-lose theorem in place. I argue that this works only if (1) the theorem's win condition is attainable with reasonable effort, (2) the theorem's underlying assumptions are plausible, and (3) all potential experimental outcomes are epistemically relevant. I also explore the consequences of no-lose theorems for considerations of scientific pursuitworthiness. First, no-lose theorems can play an important role in assessing the risk associated with investing into a research project. Second, no-lose experiments can enhance scientists' agreement about the pursuitworthiness of experiments. My analysis also shows that no-lose theorems can face a number of limitations in these contexts. (shrink)

Two players bargain to select a utility allocation in some set X⊂R+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\subset {\mathbb {R}}_+^2$$\end{document}. Bargaining takes place in infinite discrete time, where each period t is divided into two sub-periods. In the first sub-period, the players play a simultaneous-move game to determine that period’s proposer, and bargaining takes place in the second sub-period. Rejection triggers a one-period delay and move to t+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t+1$$\end{document}. For (...) every x∈X∩R++2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x\in X\cap {\mathbb {R}}^2_{++}$$\end{document}, there exists a cutoff δ<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta <1$$\end{document}, such that if at least one player has a discount factor above δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}, then for every y∈X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y\in X$$\end{document} that satisfies y≥x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y\ge x$$\end{document} there exists a subgame perfect equilibrium with immediate agreement on y. The equilibrium is supported by “dictatorial threats.” These threats can be dispensed with if X is the unit simplex and the target-vector is Pareto efficient. The results can be modified in a way that allows for arbitrarily long delays in equilibrium. (shrink)

The coherence of general good turns out to conflict with the widely accepted Pareto principle. This chapter explains the conflict and resolves it in favour of coherence. It also presents an example of a head‐on collision between coherence and the Pareto principle. The example relies on an auxiliary assumption, but one that is very plausible. The principle of personal good is immune to the difficulty raised by the probability agreement theorem. The theorem presents welfare economics with a (...) dilemma: it must abandon either the coherence of social preferences or else the traditional Pareto principle. Either way, it will have to repudiate Harsanyi's theorem. The ex‐ante school of welfare economists abandons coherence. This is the best established school. The ex‐ante school cleaves to the traditional Pareto principle. Consequently, it has to accept incoherent social preferences. (shrink)

In a Bayesian dialogue two individuals report their Bayesian updated belief about a certain event back and forth, at each step taking into account the additional information contained in the updated belief announced by the other at the previous step. Such a process, which operates through a reduction of the set of possible states of the world, converges to a commonly known posterior belief, which can be interpreted as a dynamic foundation for Aumann’s agreement result. Certainly, if two (...) individuals have diverging interests, truthfully reporting one’s Bayesian updated belief at every step might not be optimal. This observation could lead to the intuition that always truthfully reporting one’s Bayesian updated belief were the best that two individuals could do if they had perfectly coinciding interests and these were in line with coming to know the truth. This article provides an example which shows this intuition to be wrong. In this example, at some step of the process, one individual has an incentive to deviate from truthfully reporting his Bayesian updated belief. However, not in order to hide the truth, but to help it come out at the end: to prevent the process from settling into a commonly known belief—the “Aumann conditions”—on a certain subset of the set of possible states of the world, and this way make it converge to a subset of the set of possible states of the world on which it will be commonly known whether the event in question has occurred or not. The strategic movement described in this example is similar to a conversational implicature: the correct interpretation of the deviation from truthfully reporting the Bayesian updated belief thrives on it being common knowledge that the announced probability cannot possibly be the speaker’s Bayesian updated belief at this step. Finally, the argument is embedded in a game-theoretic model. (shrink)

This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The (...) static agreement result is, however, finitely derivable in an extended modal logic. We provide the full derivation. We finally consider dynamic agreement results. We show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via public announcements. (shrink)

Some arguments against the assumption that ordinary people may share common knowledge are sound. The apparent cost of such arguments is the rejection of scientific theories that appeal to common knowledge. My proposal is to accept the arguments without rejecting the theories. On my proposal, common knowledge is shared by ideally rational people, who are not just mathematically simple versions of ordinary people. They are qualitatively different from us, and theorizing about them does not lead to predictions about our behavior. (...) Nevertheless, models of action that assume common knowledge have a role to play in our understanding of collective rationality. (shrink)

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in (...) Sections 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought- only monotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense. (shrink)

Writers on collective action are in broad agreement that in order for a group of agents to form a collective intention, the members of that group must have beliefs about the beliefs of the other members. But in spite of the fact that this so-called "interactive knowledge" is central to virtually every account of collective intention, writers on this subject have not offered a detailed account of the nature of interactive knowledge. In this paper, we argue that such an (...) account is necessary for any adequate analysis of collective intention. Furthermore, we argue that an application of Robert Aumann's theory of interactive knowledge may be used to address several puzzling features of collective intention. CiteULike Connotea Del.icio.us What's this? (shrink)

We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically notof the Cartesian product form). We apply these representationsto (1)streams of commodity baskets through time, (2)uncertain social (...) prospects, (3)uncertain individual prospects. Concerning(1), we propose a finite horizon variant of Koopmans’s (1960) axiomatization of infinite discounted utility sums. The main results concern(2). We push the classic comparison between the exanteand expostsocial welfare criteria one step further by avoiding any expected utility assumptions, and as a consequence obtain what appears to be the strongest existing form of Harsanyi’s (1955) Aggregation Theorem. Concerning(3), we derive a subjective probability for Anscombe and Aumann’s (1963) finite case by merely assuming that there are two epistemically independent sources of uncertainty. (shrink)

Recent scholarship has shown that the success of Pascal’s wager rests on precarious grounds. To avoid notorious problems, it must appeal to considerations such as what probability we assign to the existence of various gods and what religion we think provides the greatest happiness in this life. Rational judgments concerning these matters are subject to change over time. Some claim that the wager therefore cannot support a steadfast commitment to God. I argue that this conclusion does not follow. By drawing (...) upon the line of reasoning employed in getting married, I explain how unstable considerations can provide a sufficient rational foundation for a stable commitment. (shrink)

Noncontextual hidden variables theories, assigning simultaneous values to all quantum mechanical observables, are inconsistent by theorems of Gleason and others. These theorems do not exclude contextual hidden variables theories, in which a complete state assigns values to physical quantities only relative to contexts. However, any contextual theory obeying a certain factorisability conditions implies one of Bell's Inequalities, thereby precluding complete agreement with quantum mechanical predictions. The present paper distinguishes two kinds of contextual theories, ‘algebraic’ and ‘environmental’, and investigates when (...) factorisability is reasonable. Some statements by Fine about the philosophical significance of Bell's Inequalities are then assessed. (shrink)

ABSTRACT One striking feature of On the Genealogy of Morals is how it is written. Nietzsche employs a literary style that provokes his readers' emotions. In Beyond Selflessness, Christopher Janaway argues that such a literary approach is integral to Nietzsche's philosophical goals. Feeling the emotions Nietzsche's style arouses is necessary for understanding the views he defends. I argue that Janaway's position is mistaken. The evidence at our disposal fails to establish that emotion is ever necessary for cognition. However, I maintain (...) that we do have good evidence for a slightly weaker claim. The emotionally sensitive person is epistemically better off than the cold and dispassionate person. There are some truths he or she will be more likely to believe and will have better reasons for believing. I conclude that Janaway is right to defend the philosophical importance of Nietzsche's literary writing style. His error is simply that he overstates the case. (shrink)

This paper describes the first three-year experience of the Consortium Ethics Program (CEP-1) of the University of Pittsburgh Center for Medical Ethics, and also outlines plans for the second three-year phase (CEP-2) of this experiment in continuing ethics education. In existence since 1990, the CEP has the primary goal of creating a cost-effective, permanent ethics resource network, by utilizing the educational resources of a university bioethics center and the practical expertise of a regional hospital council. The CEP's conception and specific (...) components stem from recognition of the need to make each hospital a major focus of educational efforts, and to provide academic support for the in-house activities of the representatives from each institution. (shrink)

Recent attention to the relationship between aesthetic value and cognitive value has focused on whether the latter can affect the former. In this article, I approach the issue from the opposite direction. I investigate whether the aesthetic value of a work can influence its cognitive value. More narrowly, I consider whether a work's aesthetic value ever contributes to or detracts from its philosophical value, which I take to include the truth of its claims, the strength of its arguments, and its (...) internal consistency. I argue that aesthetic value does have such an impact, at least sometimes and to some degree. The aesthetic merits of some works help to preserve their consistency, and the aesthetic defects of other works render them self-contradictory. (shrink)

The paper is about some epistemological ideas of David Hume. At first, I give a review of his most influential epistemological conceptions: his exposition of the problem of induction in the context of his investigation of the nature of empirical reasonings, his analysis of epistemic status of the principle of causation, and his skeptical arguments concerning existence of external world and demonstrative knowledge. Then I discuss those Hume’s epistemological ideas which, as I believe, are usually not rightly understood in literature (...) about Hume’s philosophy. They are connected to his theory of probabilistic reasonings. It is quite common to contrast his theory with approach of Thomas Bayes, but I try to show that in reality Hume’s theory is in perfect agreement with the Bayes’ theorem. In order to do this I interpret a topic of probability of our belief in testimonies of miracles, which Hume discusses, in terms of Bayes’ theorem: P(miracle/testimony) = P(testimony/miracle) x P(miracle) // P(testimony). According to this interpretation a probability of veracity of testimony of a miracle diminishes with diminishing of probability of miracles and diminishes when probability of testimonies increases. That’s very Hume’s position. At the end of the paper I discuss Hume’s insights on non-rational aspects of human cognition, which had anticipated some recent developments in cognitive psychology. In this context I also consider a possibility of justification of our principles of empirical cognition in Hume’s epistemology. I argue that Hume gave a kind of justification of them after all in terms of final causes, and quite legitimate. (shrink)

Since Lewis’s (1969) and Aumann’s (1976) pioneering contributions, the concepts of common knowledge and common belief have been discussed extensively in the literature, both syntactically and semantically1. At the individual level the difference between knowledge and belief is usually identified with the presence or absence of the Truth Axiom ( iA → A), which is interpreted as ”if individual i believes that A, then A is true”. In such a case the individual is often said to know that A (...) (thus it is possible for an individual to believe a false proposition but she cannot know a false proposition). Going to the interpersonal level, the literature then distinguishes between common knowledge and common belief on the basis of whether or not the Truth Axiom is postulated at the individual level. However, while at the individual level the Truth Axiom captures merely a relationship between the individuals’ beliefs and the external world, at the interpersonal level it has very strong implications. For example, the following is a consequence of the Truth Axiom: i jA → iA, that is, if individual i believes that individual j believes that A, then individual i herself believes that A. Thus, in contrast to other axioms, the Truth Axiom does not merely reflect individual agents’ “logic of belief”. (The reason why the Truth Axiom is much stronger in an interpersonal context than appears at first glance is that it amounts to assuming that agreement of any individual’s belief with the truth is common knowledge). Given its logical force, it is not surprising to find that it has strong implications for the logic of common knowledge. In particular, if each individual’s beliefs satisfy the strongest logic of knowledge (namely S5 or KT5), the associated common knowledge operator satisfies this logic too. Such is not the case for belief: bereft of the Truth Axiom, even the strongest logic for individual belief (KD45) is insufficient to ensure the satisfaction of the “Negative Introspection” axiom for common belief: ¬ ∗A → ∗¬ ∗A (where ∗ denotes the common belief operator).. (shrink)

Encounters with art can change us in ways both big and small. This paper focuses on one of the more dramatic cases. I argue that works of art can inspire what L. A. Paul calls transformations, classic examples of which include getting married, having a child, and undergoing a religious conversion. Two features distinguish transformations from other changes we undergo. First, they involve the discovery of something new. Second, they result in a change in our core preferences. These two features (...) make transformations hard to motivate. I argue, however, that art can help on both fronts. First, works of art can guide our attempt to imagine unfamiliar ways of living. Second, they can attract us to values we currently reject. I conclude by observing that what makes art powerful also makes it dangerous. Transformations are not always for the good, and art's ability to inspire them can be put to immoral ends. (shrink)

We propose a model of unawareness that remains close to the paradigm of Aumann’s model for knowledge [R. J. Aumann, International Journal of Game Theory 28 (1999) 263-300]: just as Aumann uses a correspondence on a state space to define an agent’s knowledge operator on events, we use a correspondence on a state space to define an agent’s awareness operator on events. This is made possible by three ideas. First, like the model of [A. Heifetz, M. Meier, and B. (...) Schipper, Journal of Economic Theory 130 (2006) 78-94], ours is based on a space of partial specifications of the world, partially ordered by a relation of further specification or refinement, and the idea that agents may be aware of some coarser-grained specifications while unaware of some finer-grained specifications; however, our model is based on a different implementation of this idea, related to forcing in set theory. Second, we depart from a tradition in the literature, initiated by [S. Modica and A. Rustichini, Theory and Decision 37 (1994) 107- 124] and adopted by Heifetz et al. and [J. Li, Journal of Economic Theory 144 (2009) 977-993], of taking awareness to be definable in terms of knowledge. Third, we show that the negative conclusion of a well- known impossibility theorem concerning unawareness in [Dekel, Lipman, and Rustichini, Econometrica 66 (1998) 159-173] can be escaped by a slight weakening of a key axiom. Together these points demonstrate that a correspondence on a partial-state space is sufficient to model unawareness of events. Indeed, we prove a representation theorem showing that any abstract Boolean algebra equipped with awareness, knowledge, and belief operators satisfying some plausible axioms is representable as the algebra of events arising from a partial-state space with awareness, knowledge, and belief correspondences. (shrink)

This paper illuminates the central arguments in Sartre's UNESCO address, 'The Singular Universal." The address begins by asking whether objective facts tell us everything there is to know about Kierkegaard. Sartre's answer is negative. The question then arises as to whether we can lay hold of Kierkegaard's "irreducible subjectivity" by seeing him as alive for us today, i.e., as transhistorical. Sartre's answer here is affirmative. However, a close inspection of this answer exposes a deeper level to the address. The struggle (...) to find a place for Kierkegaard within the world of objective knowledge is an allegory. It mirrors Sartre's struggle to find a place for his existentialism within the Marxism that dominates his later thinking. (shrink)

This paper provides an account of Kierkegaard’s central criticism of the Danish Hegelians. Contrary to recent scholarship, it is argued that this criticism has a substantive theoretical basis and is not merely personal or ad hominem in nature. In particular, Kierkegaard is seen as criticizing the Hegelians for endorsing an unacceptable form of intellectual elitism, one that gives them pride of place in the realm of religion by dint of their philosophical knowledge. A problem arises, however, because this criticism threatens (...) to apply to Kierkegaard himself. It is shown that Kierkegaard manages to escape this problem by virtue of the humorous aspect of his work. (shrink)

Works of art can be difficult in several ways. One important way is by making us face up to unsettling truths. Such works typically receive praise. I maintain, however, that sometimes they deserve moral censure. The crux of my argument is that, just as we have a right to know the truth in certain contexts, so too we have a right not to know it. Provided our ignorance does not harm or seriously endanger others, the decision about whether to know (...) the truth ought to be left to us. Within this limit, therefore, difficult art is morally problematic if it intentionally targets those who have chosen not to know. To illustrate the problem, I discuss the literary writings of Søren Kierkegaard, which aim to deceive readers into seeing unpleasant truths about themselves that they seek to ignore. (shrink)

Suppose a committee has to take a stand on a complex issue, where the decision presupposes answering a number of sub-questions. There is an agreement within the committee which sub-questions should be posed. All questions are of the ”yes or no?”-type and the main question is to be given the yes-answer if and only if each sub-question is answered with “yes”. Two different voting procedures can be used. On one procedure, the committee members vote on each sub-question and the (...) voting results then determine the committee’s conclusion on the main issue. This premise-based procedure (or pbp, for short) can be contrasted with the conclusion-based procedure (cbp), on which the members directly vote on the conclusion, with the vote of each member being guided by her views on the relevant sub-questions. The problem we want to examine concerns the relative advantages and disadvantages of the two procedures from the epistemic point of view. In some cases one can assume that the question before the committee has a right answer, which the committee is trying to reach. Is one of the two procedures better when it comes to tracking the truth? As it turns out, the answer to this query is not univocal: On the basis of Condorcet’s jury theorem we shall show that the premise-based procedure is clearly superior if we want to reach truth for the right reasons, i.e. without making any mistakes on the road to the conclusion. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be special cases in which using the conclusion-based procedure turns out to be more reliable. But for the most part, the premise-based procedure will still retain its superiority. In this respect, our results disconfirm the tentative conjectures that have been put forward in Pettit and Rabinowicz (2001). (shrink)

This paper critically engages Philip Mirowki's essay, "The scientific dimensions of social knowledge and their distant echoes in 20th-century American philosophy of science." It argues that although the cold war context of anti-democratic elitism best suited for making decisions about engaging in nuclear war may seem to be politically and ideologically motivated, in fact we need to carefully consider the arguments underlying the new rational choice based political philosophies of the post-WWII era typified by Arrow's impossibility theorem. A distrust (...) of democratic decision-making principles may be developed by social scientists whose leanings may be toward the left or right side of the spectrum of political practices. (shrink)

Kierkegaard faces an apparent dilemma. On the one hand, he concurs with the biblical injunction: we are to love our neighbors as ourselves. He takes this to imply that self-love and neighbor-love should be roughly symmetrical, similar in kind as well as degree. On the other hand, he recommends relating to others and to ourselves in disparate ways. We should be lenient, charitable, and forgiving when interacting with neighbors; the opposite when dealing with ourselves. The goal of my paper is (...) to solve this puzzle. I first consider addressing it by appealing to Gene Outka’s idea that equal love does not entail identical treatment. After rejecting this solution, I offer my own: Asymmetry between the two loves is not a moral ideal for Kierkegaard but a rehabilitative strategy. He recommends being more latitudinarian with others than with ourselves to correct against a common tendency toward the opposite extreme. (shrink)

In The Ethics of Authorship, Daniel Berthold depicts G. W. F. Hegel and Søren Kierkegaard as endorsing two postmodern principles. The first is an ethical ideal. Authors should abdicate their traditional privileged position as arbiters of their texts’ meaning. They should allow readers to determine this meaning for themselves. Only by doing so will they help readers attain genuine selfhood. The second principle is a claim about language. To wit, language cannot express an author’s thoughts. I argue that if the (...) claim about language holds, the ethical ideal becomes superfluous. In addition, if Berthold has identified Hegel and Kierkegaard’s views regarding the issues in question by reading their works, then either they failed to execute their ethical project or their views about language are false. (shrink)

Fisher’s ‘fundamental theorem of natural selection’ is notoriously abstract, and, no less notoriously, many take it to be false. In this paper, I explicate the theorem, examine the role that it played in Fisher’s general project for biology, and analyze why it was so very fundamental for Fisher. I defend Ewens (1989) and Lessard (1997) in the view that the theorem is in fact a true theorem if, as Fisher claimed, ‘the terms employed’ are ‘used strictly (...) as defined’ (1930, p. 38). Finally, I explain the role that projects such as Fisher’s play in the progress of scientific inquiry. (shrink)

Following the pattern set by the early German Romantics, Kierkegaard conveys many of his insights through literature rather than academic prose. What makes him a valuable member of this tradition is the theory he develops to support it, his so-called “theory of indirect communication.” The most exciting aspect of this theory concerns the alleged importance of indirect communication: Kierkegaard claims that there are some projects only it can accomplish. This paper provides a critical account of two arguments Kierkegaard offers in (...) defense of this claim. The first argument is that he needs to use indirect communication in order to discourage people from losing themselves in the “crowd”. The second argument is that he needs to use it in order to help people out of a “monstrous illusion”. It is shown that while both arguments justify Kierkegaard’s decision to use indirect communication, neither one supports the original claim about its indispensability. (shrink)

In Religion of Existence, Noreen Khawaja suggests that Kierkegaard is an “ascetic” thinker. By this, she means that he regards religious striving as (1) requiring ceaseless renewal and (2) being an end in itself rather than a means to some further end. In this paper, I raise challenges to both parts of Khawaja’s proposal. I argue that the first part stands in tension with Kierkegaard’s assertion that his infinitely demanding account of religious existence is meant merely as a “corrective.” The (...) second part, I maintain, does not fit well with his claim that our eternal salvation is at stake in religious striving. (shrink)

The dissertation under comment is a contribution to the area of Set Theory concerned with the interactions between the method of Forcing and the so-called Large Cardinal axioms.The dissertation is divided into two thematic blocks. In Block I we analyze the large-cardinal hierarchy between the first supercompact cardinal and Vopěnka’s Principle. In turn, Block II is devoted to the investigation of some problems arising from Singular Cardinal Combinatorics.We commence Part I by investigating the Identity Crisis phenomenon in the region comprised (...) between the first supercompact cardinal and Vopěnka’s Principle. As a result, we generalize Magidor’s classical theorems [2] to this higher region of the large-cardinal hierarchy. Also, our analysis allows to settle all the questions that were left open in [1]. Finally, we conclude Part I by presenting a general theory of preservation of $C^{}$ -extendible cardinals under class forcing iterations. From this analysis we derive several applications. For instance, our arguments are used to show that an extendible cardinal is consistent with “ $^{\mathrm {HOD}}<\lambda ^+$, for every regular cardinal $\lambda $.” In particular, if Woodin’s HOD Conjecture holds, and therefore it is provable in ZFC + “There exists an extendible cardinal” that above the first extendible cardinal every singular cardinal $\lambda $ is singular in HOD and $^{\textrm {{HOD}}}=\lambda ^+$, there may still be no agreement at all between V and HOD about successors of regular cardinals.In Part II and Part III we analyse the relationship between the Singular Cardinal Hypothesis with other relevant combinatorial principles at the level of successors of singular cardinals. Two of these are the Tree Property and the Reflection of Stationary sets, which are central in Infinite Combinatorics.Specifically, Part II is devoted to prove the consistency of the Tree Property at both $\kappa ^+$ and $\kappa ^{++}$, whenever $\kappa $ is a strong limit singular cardinal witnessing an arbitrary failure of the SCH. This generalizes the main result of [3] in two senses: it allows arbitrary cofinalities for $\kappa $ and arbitrary failures for the SCH.In the last part of the dissertation we introduce the notion of $\Sigma $ -Prikry forcing. This new concept allows an abstract and uniform approach to the theory of Prikry-type forcings and encompasses several classical examples of Prikry-type forcing notions, such as the classical Prikry forcing, the Gitik-Sharon poset, or the Extender Based Prikry forcing, among many others.Our motivation in this part of the dissertation is to prove an iteration theorem at the level of the successor of a singular cardinal. Specifically, we aim for a theorem asserting that every $\kappa ^{++}$ -length iteration with support of size $\leq \kappa $ has the $\kappa ^{++}$ -cc, provided the iterates belong to a relevant class of $\kappa ^{++}$ -cc forcings. While there are a myriad of works on this vein for regular cardinals, this contrasts with the dearth of investigations in the parallel context of singular cardinals. Our main contribution is the proof that such a result is available whenever the class of forcings under consideration is the family of $\Sigma $ -Prikry forcings. Finally, and as an application, we prove that it is consistent—modulo large cardinals—the existence of a strong limit cardinal $\kappa $ with countable cofinality such that $\mathrm {SCH}_\kappa $ fails and every finite family of stationary subsets of $\kappa ^+$ reflects simultaneously. (shrink)

Like many 19th c. thinkers, Kierkegaard embraces a cognitivist view of art. He thinks works of art matter because they can teach us in important ways. This chapter defends two striking features of Kierkegaard’s version of this theory. First, works of art do not teach “directly” by telling us truths and offering us evidence. Instead, they educate us “indirect-ly” by helping us make our own discoveries. Second, the fact that art does not teach in a straightforward manner is no defect. (...) On the contrary, it is precisely because art teaches indirectly that it teaches better than philosophy and science do. (shrink)

This dissertation concerns Kierkegaard’s theory of indirect communication. A central aspect of this theory is what I call the “indispensability thesis”: there are some projects only indirect communication can accomplish. The purpose of the dissertation is to disclose and assess the rationale behind the indispensability thesis. -/- A pair of questions guides the project. First, to what does ‘indirect communication’ refer? Two acceptable responses exist: (1) Kierkegaard’s version of Socrates’ midwifery method and (2) Kierkegaard’s use of artful literary devices. Second, (...) for what end does Kierkegaard use indirect communication? There are two acceptable responses here as well: (1) helping others become religious and (2) making others aware of the nature of existence. -/- These responses are interrelated. First, Kierkegaard’s notion of religion places restrictions on the means he can use to get readers to become religious. These restrictions ultimately entail that the only viable form of religious pedagogy is the midwifery method. Second, Kierkegaard engages in the midwifery method in part by making readers aware of the nature of existence (especially religious existence). But given the problems plaguing his readers, he thinks a straightforward approach to this project will likely fail. An approach that used artful literary devices such as deception and humor would be more successful. Third, Kierkegaard believes that there is one aspect of religious existence (viz. subjectivity) that people can come to know only first-hand. As such, he cannot directly impart knowledge of subjectivity to his readers. He argues that this means he must use the midwifery method. And he thinks the most productive way to do so is to provide readers with the kind of fictional narratives found in his early pseudonymous writings. Thus artful rhetorical devices play a role here as well. -/- All of Kierkegaard’s arguments for the indispensability thesis turn on debatable assumptions. But the arguments concerning artful rhetorical devices have the additional defect of being merely probabilistic in nature. They lack the strength to support the indispensability thesis even if we grant the relevant background assumptions. Therefore, to the degree that the indispensability thesis has merit, it lies with the arguments concerning the midwifery method. (shrink)

Drawing on insights from Søren Kierkegaard, Art and Selfhood: A Kierkegaardian Account defends the idea that art matters in our society today because it can play a pivotal role in helping us become better and more authentic versions of ourselves.

ABSTRACT Kierkegaard seeks to inspire transformations. His aim is to get us to devote our lives to God or the Good rather than our own personal enjoyment – to abandon the aesthetic life in favour of the ethical or religious one. Drawing on Laurie Paul and Agnes Callard’s recent work, I maintain that two obstacles stand in Kierkegaard’s way. First, transformations involve adopting a new perspective on the world, one we cannot fully grasp ahead of time. Second, transformations also involve (...) coming to care about something we do not yet care about. On my interpretation, Kierkegaard sees art, especially literature, as central to overcoming both obstacles. Good stories afford us a glimpse into what it would look and feel like to live in ways other than we currently do. In addition, they have the power to attract us to points of view we would ordinarily reject. (shrink)

On one standard view, paraphrasing Kierkegaard requires no special literary talent. It demands no particular flair for the poetic. However, Kierkegaard himself rejects this view. He says we cannot paraphrase in a straightforward fashion some of the ideas he expresses in a literary format. To use the words of Johannes Climacus, these ideas defy direct communication. In this paper, I piece together and defend the justification Kierkegaard offers for this position. I trace its origins to concerns raised by Lessing and (...) Mendelssohn about the relationship between form and content in works of art. I maintain that Kierkegaard follows early German Romantic thinkers in applying these aesthetic concerns to philosophical writing. By way of conclusion, I discuss the implications of Kierkegaard’s position for contemporary scholarship. (shrink)

Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. (...) Furthermore, we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum. (shrink)

It is well known that Gödel’s incompleteness theorems hold for ∑1-definable theories containing Peano arithmetic. We generalize Gödel’s incompleteness theorems for arithmetically definable theories. First, we prove that every ∑n+1-definable ∑n-sound theory is incomplete. Secondly, we generalize and improve Jeroslow and Hájek’s results. That is, we prove that every consistent theory having ∏n+1set of theorems has a true but unprovable ∏nsentence. Lastly, we prove that no ∑n+1-definable ∑n-sound theory can prove its own ∑n-soundness. These three results are generalizations of Rosser’s (...) improvement of the first incompleteness theorem, Gödel’s first incompleteness theorem, and the second incompleteness theorem, respectively. (shrink)