Keep Changing Your Beliefs, Aiming for the Truth

We investigate the process of truth-seeking by iterated belief revision with higher-level doxastic information. We elaborate further on the main results in Baltag and Smets (Proceedings of TARK, 2009a, Proceedings of WOLLIC’09 LNAI 5514, 2009b), applying them to the issue of convergence to truth. We study the conditions under which the belief revision induced by a series of truthful iterated upgrades eventually stabilizes on true beliefs. We give two different conditions ensuring that beliefs converge to “full” (complete) truth, as well as a condition ensuring only that they converge to true (but not necessarily complete) beliefs.     

Games with Zero-knowledge Signaling

We observe that in certain two-player repeated games of incomplete information, where information may be incomplete on both sides, it is possible for an informed player to signal his status as an informed player to the other without revealing any information about the choice of chance. The key to obtaining such a class of games is to relax the assumption that the players’ moves are observable. We show that in such cases players can achieve a kind of signaling that is “zero-knowledge”, in the sense that the other player becomes convinced that her opponent is informed without ever learning the choice of chance. Moreover, such “zero-knowledge signaling” has all of the statistical properties associated with zero-knowledge proofs in intereactive protocols. In particular, under the general assumption that moves are unobservable, such signaling leads to a class of equilibria in repeated games that are separatingin regard to the status of player 1–informed or uninformed–but only for player 2; any other player in a network, being unable to observe the moves of player 2, remains uncertain as to the status of player 1. Special Issue Formal Epistemology II. Edited by Branden Fitelson     

To Believe in Belief

Summary  Take the following version of scientific realism: we have good reason to believe that (some of the) current scientific theories tell us something specific about the underlying, i.e. unobservable, structures of the world, for instance that there are electrons with a certain electric charge, or that there are viruses that cause certain diseases. Popper, the rationalist, would not have adhered to the proposed formulation of scientific realism in terms of the rationality of existential beliefs concerning unobservables. Popper did not believe in belief. According to Van Fraassen, the empiricist, one may yet have a rational existential belief concerning unobservables, given a liberal notion of rationality of belief. In this paper I will investigate to what extent a reassessment of both Popper’s rejection of the rationality of belief and Van Fraassen’s reformulation of the rationality of belief, points towards a new and pragmatist dissolution of the ‘problem of scientific realism’.     

Socially Constructed Technology

The concepts of omniscience and omnipotence are defined in 2 × 2 ordinal games, and implications for the optimal play of these games, when one player is omniscient or omnipotent and the other player is aware of his omniscience or omnipotence, are derived. Intuitively, omniscience allows a player to predict the strategy choice of an opponent in advance of play, and omnipotence allows a player, after initial strategy choices are made, to continue to move after the other player is forced to stop. Omniscience and its awareness by an opponent may hurt both players, but this problem can always be rectified if the other player is omniscient. This pathology can also be rectified if at least one of the two players is omnipotent, which can override the effects of omniscience. In some games, one player's omnipotence ‐ versus the other's ‐ helps him, whereas in other games the outcome induced does not depend on which player is omnipotent. Deducing whether a player is superior (omniscient or omnipotent) from the nature of his game playing alone raises several problems, however, suggesting the difficulty of devising tests for detecting superior ability in games.     

Cynicism and Morality

Our attitude towards cynicism is ambivalent: On the one hand we condemn it as a character failing and a trend that is undermining political and social life; on the other hand, we are often impressed by the apparent realism and honesty of the cynic. My aim in this paper is to offer an account of cynicism that can explain both our attraction and aversion. After defending a particular conception of cynicism, I argue that most of the work in explaining the fault of cynicism can be done by referring not to the cynic’s beliefs about humanity, but to the attitude cultivated as a response to that belief. This attitude is hostile to the virtues of faith, hope and charity, upon which relationships and our sense of moral community depend. In conclusion, I suggest that holding the cynical belief is itself immoral, and that cynicism is disrespectful and destructive of morality.     

Contraction in Interrogative Belief Revision

In the paper “On the role of the research agenda in epistemic change”, Olsson and Westlund have suggested that the notion of epistemic state employed in the standard framework of belief revision (Alchourrón et al. 1985; G?rdenfors 1988) should be extended to include a representation of the agent’s research agenda (Olsson and Westlund 2006). The resulting framework will here be referred to as interrogative belief revision. In this paper, I attempt to deal with the problem of how research agendas should change in contraction, a problem largely left open by Olsson and Westlund. Two desiderata of an appropriate solution are suggested: one is a principle of continuity, stating that changes in the research agenda should somehow reflect that certain long term research interests are kept fixed. The other desideratum, which is based on part of Olsson and Westlund’s motivation for adding research agendas to the epistemic states, is that we should be able to account for how contraction may serve to open up new, fruitful hypotheses for investigation. In order to achieve these desiderata, I base my solution on a revised version of Olsson and Westlund’s notion of epistemic state.     

An Impossibility Theorem on Beliefs in Games

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob’s assumption is wrongThis is formalized to show that any belief model of a certain kind must have a ‘hole.’ An interpretation of the result is that if the analyst’s tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen     

Thomason’s Paradox for Belief,and Two Consequence Relations

Thomason (1979/2010)’s argument against competence psychologism in semantics envisages a representation of a subject’s competence as follows: he understands his own language in the sense that he can identify the semantic content of each of its sentences, which requires that the relation between expression and content be recursive. Then if the scientist constructs a theory that is meant to represent the body of the subject’s beliefs, construed as assent to the content of the pertinent sentences, and that theory satisfies certain ‘natural assumptions’, then it implies that the subject is inconsistent if the beliefs include arithmetic. I challenge the result by insisting that the motivation for Thomason’s principle (ii), via Moore’s Paradox, leads to a more complex representation, in which stating the facts and expressing one’s beliefs are treated differently. Certain logical connections among expressions of assent, and between expression and statement, are a matter of consequence on pain of pragmatic incoherence, not consequence on pain of classical logical inconsistency. But while this salvages the possibility that a modification of the above sort of representation could be adequate, Thomason’s devastating conclusion returns if the scientist identifies himself as the subject of that representation, even when paying heed to the requirement of pragmatic coherence of the sort highlighted by Moore’s Paradox.     

Should knowledge entail belief?

The appropriateness of S5 as a logic of knowledge has been attacked at some length in the philosophical literature. Here one particular attack based on the interplay between knowledge and belief is considered: Suppose that knowledge satisfies S5, belief satisfies KD45, and both the entailment property (knowledge implies belief) and positive certainty (if the agent believes something, she believes she knows it) hold. Then it can be shown that belief reduces to knowledge: it is impossible to have false beliefs. While the entialment property has typically been viewed as perhaps the least controversial of these assumptions, an argument is presented that it can plausibly be viewed as the culprit. More precisely, it is shown that this attack fails if we weaken the entailment property so that it applies only to objective (nonmodal) formulas, rather than to arbitrary formulas. Since the standard arguments in favor of the entailment property are typically given only for objective formulas, this observation suggests that care must be taken in applying intuitions that seem reasonable in the case of objective formulas to arbitrary formulas.Research sponsored in part by the Air Force office of Scientific Research (AFSC), under Contract F49620-91-C-0080. The United States Government is authorized to reproduce and distribute reprints for governmental purposes.     

A. F. Losevs personalistische ontologie

A. F. Losev, one of the most important Russian philosophers and historians of ancient aesthetics and culture in the 20th century, develops in his ‘Dialectics of the Myth’ (Dialektika mifa), 1930, a personalistic ontology by using elements of neoplatonic philosophy and Orthodox Christian belief. According to Losev reality in all its different expressions and ontological strata must be understood as “mythical”, i.e. as “living mutual exchange of subject and object”. The subjective and personal aspect of reality is not grounded in man’s epistemic relation to it alone; reality in itself has to be characterized as personal and subjective. The main philosophical opponent is Descartes, the founder of “modern rationalism and mechanism”.

     

Television Viewing and Adolescents’ Judgment of Sexual Request Scripts: A Latent Growth Curve Analysis in Early and Middle Adolescence

A longitudinal study was conducted to explore the relationship between television viewing and beliefs about expressing sexual desire in dating situations. In three consecutive years, a panel of early adolescents (N = 883) and a panel of middle adolescents (N = 651) rated the effectiveness of a sexual approach and a romantic approach. Latent growth curve analyses indicate that between the ages of 12 and 15 there is a growing belief in the effectiveness of the sexual approach, which was related to respondents’ maturity status but unrelated to television viewing, and a weakening belief in the effectiveness of the romantic strategy, a decline that appeared to be quickened by television viewing in the female sample and slowed down by television viewing in the male sample. Between the ages of 15 and 18 television viewing reinforces a respondent’s belief in the effectiveness of both the sexual and the romantic strategy. Steven Eggermont, Ph.D., is a postdoctoral fellow of the K.U. Leuven Research Fund at The Leuven School for Mass Communication Research.     

Bounded Revision: Two-Dimensional Belief Change Between Conservative and Moderate Revision

This paper presents the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is that the input sentence is accepted as far as (and just a little further than) the reference sentence is ‘cotenable’ with it. Bounded revision satisfies the AGM axioms as well as the Same Beliefs Condition (SBC) saying that the set of beliefs accepted after the revision does not depend on the reference sentence (although the posterior belief state does depend on it). Bounded revision satisfies the Darwiche–Pearl (DP) axioms for iterated belief change. If the reference sentence is fixed to be a tautology or a contradiction, two well-known one-dimensional revision operations result. Bounded revision thus naturally fills the space between conservative revision (also known as natural revision) and moderate revision (also known as lexicographic revision). I compare this approach to the two-dimensional model of ‘revision by comparison’ investigated by Fermé and Rott (Artif Intell 157:5–47, 2004) that satisfies neither the SBC nor the DP axioms. I conclude that two-dimensional revision operations add substantially to the expressive power of qualitative approaches that do not make use of numbers as measures of degrees of belief.     

Clearing conceptual space for cognitivist motivational internalism

Cognitivist motivational internalism is the thesis that, if one believes that 'It is right to ϕ', then one will be motivated to ϕ. This thesis—which captures the practical nature of morality—is in tension with a Humean constraint on belief: belief cannot motivate action without the assistance of a conceptually independent desire. When defending cognitivist motivational internalism it is tempting to either argue that the Humean constraint only applies to non-moral beliefs or that moral beliefs only motivate ceteris paribus. But succumbing to the first temptation places one under a burden to justify what is motivationally exceptional about moral beliefs and succumbing to the second temptation saddles one with a thesis that fails to do justice to the practicality intuition that cognitivist motivational internalism is suppose to capture. In this paper, I offer a way of defending cognitivist motivational internalism, which does not require accepting that there is anything motivationally unusual about moral beliefs. I argue that no belief satisfies the Humean constraint: all beliefs are capable of motivating without the assistance of a conceptually independent desire.     

Common knowledge of payoff uncertainty in games

Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as ‘player i has approximate knowledge about the utility functions of player j.’ We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called ‘mixed iterated strict weak dominance.’     

Tracking, Epistemic Dispositions and the Conditional Analysis

According to Nozick’s tracking theory of knowledge, an agent a knows that p just in case her belief that p is true and also satisfies the two tracking conditionals that had p been false, she would not have believed that p, and had p been true under slightly different circumstances, she would still have believed that p. In this paper I wish to highlight an interesting but generally ignored feature of this theory: namely that it is reminiscent of a dispositional account of knowledge: it invites us to think of knowledge as a manifestation of a cognitive disposition to form true beliefs. Indeed, given a general account of dispositions in terms of subjunctive conditionals, the two tracking conditionals are satisfied just in case the belief in question results from some cognitive disposition to form true beliefs. Recently, such a conditional account of dispositions has, however, been criticised for its vulnerability to so-called ‘masked’, ‘mimicked’ and ‘finkish’ counterexamples. I show how the classical counterexamples to Nozick’s theory divide smoothly into four corresponding categories of counterexamples from epistemic masking, mimicking and finkishness. This provides strong evidence for the thesis that satisfaction of the two tracking conditionals is symptomatic of knowledge and that knowledge is instead constituted by a dispositional capability to form true beliefs. The attempt to capture such a cognitive, dispositional capability in terms of the tracking conditionals, although providing a good approximation in a wide variety of cases, still comes apart from the real thing whenever the epistemic layout is characterised by masking-, mimicking- and finkish mechanisms. In the last part of the paper I explore the prospect of improving the tracking theory in the light of these findings.     

The Intrinsic Quantum Nature of Nash Equilibrium Mixtures

In classical game theory the idea that players randomize between their actions according to a particular optimal probability distribution has always been viewed as puzzling. In this paper, we establish a fundamental connection between n-person normal form games and quantum mechanics (QM), which eliminates the conceptual problems of these random strategies. While the two theories have been regarded as distinct, our main theorem proves that if we do not give any other piece of information to a player in a game, than the payoff matrix—the axiom of “no-supplementary data” holds—then the state of mind of a rational player is algebraically isomorphic to a pure quantum state. The “no supplementary data” axiom is captured in a Lukasiewicz’s three-valued Kripke semantics wherein statements about whether a strategy or a belief of a player is rational are initially indeterminate i.e. neither true, nor false. As a corollary, we show that in a mixed Nash equilibrium, the knowledge structure of a player implies that probabilities must verify the standard “Born rule” postulate of QM. The puzzling “indifference condition” wherein each player must be rationally indifferent between all the pure actions of the support of his equilibrium strategy is resolved by his state of mind being described by a “quantum superposition” prior a player is asked to make a definite choice in a “measurement”. Finally, these results demonstrate that there is an intrinsic limitation to the predictions of game theory, on a par with the “irreducible randomness” of quantum physics.     

Evidence does not equal knowledge

Timothy Williamson has argued that a person S’s total evidence is constituted solely by propositions that S knows. This theory of evidence entails that a false belief can not be a part of S’s evidence base for a conclusion. I argue by counterexample that this thesis (E = K for now) forces an implausible separation between what it means for a belief to be justified and rational from one’s perspective and what it means to base one’s beliefs on the evidence. Furthermore, I argue that E = K entails the implausible result that there are cases in which a well-evidenced belief necessarily can not serve as evidence for a further proposition.     

Belief, faith, and acceptance

Belief is a central focus of inquiry in the philosophy of religion and indeed in the field of religion itself. No one conception of belief is central in all these cases, and sometimes the term ‘belief’ is used where ‘faith’ or ‘acceptance’ would better express what is intended. This paper sketches the major concepts in the philosophy of religion that are expressed by these three terms. In doing so, it distinguishes propositional belief (belief that) from both objectual belief (believing something to have a property) and, more importantly, belief in (a trusting attitude that is illustrated by at least many paradigm cases of belief in God). Faith is shown to have a similar complexity, and even propositional faith divides into importantly different categories. Acceptance differs from both belief and faith in that at least one kind of acceptance is behavioral in a way neither of the other two elements is. Acceptance of a proposition, it is argued, does not entail believing it, nor does believing entail acceptance in any distinctive sense of the latter term. In characterizing these three notions (and related ones), the paper provides some basic materials important both for understanding a person’s religious position and for appraising its rationality. The nature of religious faith and some of the conditions for its rationality, including some deriving from elements of an ethics of belief, are explored in some detail.