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)

While social epistemology is a diverse field, much of it still understands knowledge as an individual status—albeit an individual status that crucially depends on various social factors (such as testimony). Further, the literature on group knowledge until now has primarily focused on limited, specialized groups that may be said to know this or that as a group. I wish to argue, to the contrary, that all knowledge-attributions ascribe a collective status; and that this follows more or less directly from an (...) essential function of entitlement-ascriptions: Ascriptions of knowledge and entitlement serve a primarily social function in that they facilitate coordination by maintaining consensus around true beliefs, true theories, and truth-producing methodologies. This conclusion will shed light on ways in which traditional theories of knowledge (such as foundationalism and coherentism) fail to capture a central function of our epistemic practice. (shrink)

An opinionated introduction to philosophical issues connected to common knowledge.

According to we-mode accounts of collective intentionality, an experience is a "we-experience"—that is, part of a jointly attentional episode—in virtue of the way or mode in which the content of the experience is given to the subject of experience. These accounts are supposed to explain how a we-experience can have the phenomenal character of being given to the subject "as ours" rather than merely "as my experience" (Zahavi 2015), and do so in a relatively conceptually and cognitively undemanding way. Galotti (...) and Frith (2013) and Schmitz (2017) present we-mode accounts that are supposed to, in particular, avoid the need for the subjects of experience to have common knowledge of each other’s perceptual beliefs. In this paper, drawing in part on Schutz’s (1932/1967; 1953) writings on "the pure We-relationship", I argue that appeal to a we-mode does not render common knowledge unnecessary. To explain when we-experiences are veridical, we-mode accounts must (i) explain how a we-experience can enable rational interpersonal coordination in some high-risk situations and (ii) explain why what is experienced is "out in the open" between the subjects of the we-experience. To do this, proponents of we-mode accounts need an account of common knowledge. In addition, they must explain why certain inferences hold between we-mode and I-mode attitudes. In light of this, we-mode accounts fare no better than content accounts in illuminating how basic forms of collective intentionality are possible. (shrink)

Some people commonly know a proposition just in case they all know it, they all know that they all know it, they all know that they all know that they all know it, and so on. They commonly believe a proposition just in case they all believe it, they all believe that they all believe it, they all believe that they all believe that they all believe it, and so on. A long tradition in economic theory, theoretical computer science, linguistics (...) and philosophy has held that people have some approximation of common knowledge or common belief in a range of circumstances, for example, when they are looking at an object together, or when they have just discussed something explicitly in conversation. In this paper, I argue that people do not have any approximation of common knowledge or common belief in these circumstances. The argument suggests that people never have any approximation of common knowledge or common belief. (shrink)

The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to do (...) by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

This paper argues for several related theses. First, the epistemological position that knowledge requires safe belief can be motivated by views in the philosophy of science, according to which good explanations show that their explananda are robust. This motivation goes via the idea—recently defended on both conceptual and empirical grounds—that knowledge attributions play a crucial role in explaining successful action. Second, motivating the safety requirement in this way creates a choice point—depending on how we understand robustness, we'll end up with (...) different conceptions of safety in epistemology. Lastly, and most controversially, there's an attractive choice at this point that will not vindicate some of the most influential applications of the safety-theoretic framework in epistemology, e.g., Williamson's arguments against the KK principle, and luminosity. (shrink)

What is it for a group to believe something? A summative account assumes that for a group to believe that p most members of the group must believe that p. Accounts of this type are commonly proposed in interpretation of everyday ascriptions of beliefs to groups. I argue that a nonsummative account corresponds better to our unexamined understanding of such ascriptions. In particular I propose what I refer to as the joint acceptance model of group belief. I argue that group (...) beliefs according to the joint acceptance model are important phenomena whose aetiology and development require investigation. There is an analogous phenomenon of social or group preference, which social choice theory tends to ignore. (shrink)

This paper is intended to show how epistemologists can profit from the study of ways in which 'know' is vague. Topics include the kk thesis, Incorrigibility of sense data, A resemblance between infinity and vagueness, Common knowledge, Naive holism, Question-Begging, Epistemic universalizability, The prediction paradox, The completability of epistemology, And harman's social knowledge cases.

What is common knowledge? According to the dominant iterative model, a group of people commonly knows that p if and only if they each individually know that p, and they furthermore each know that they each know that p, and so on to infinity. According to the integrative model proposed in this paper, a group commonly knows that p when its members are united in a state of mind of the type whose contents must be true. Epistemic integration within a (...) group is enabled by symmetrical signalling processes such as eye contact. In conversational dyads, symmetrical processing operates on pairs of signals produced by the two sides in a familiar format: speakers generate content for joint attention in main channel communication, and addressees evaluate that content in backchannel communication. Processes of reinforcement learning shape our pairwise signalling, driving the accumulation of common knowledge, both in response to extrinsic reward for coordinated action, and in response to the intrinsic reward of curiosity. Where the iterative model caps the epistemic performance of the group at the level of its weakest member, the integrative model of common knowledge shows how groups working together can outperform their strongest member working alone. (shrink)

Traditional definitions of common ground in terms of iterative de re attitudes do not apply to conversations where at least one conversational participant is not acquainted with the other(s). I propose and compare two potential refinements of traditional definitions based on Abelard’s distinction between generality in sensu composito and in sensu diviso.

Philosophers using game-theoretical models of human interactions have, I argue, often overestimated what sheer rationality can achieve. (References are made to David Gauthier, David Lewis, and others.) In particular I argue that in coordination problems rational agents will not necessarily reach a unique outcome that is most preferred by all, nor a unique 'coordination equilibrium' (Lewis), nor a unique Nash equilibrium. Nor are things helped by the addition of a successful precedent, or by common knowledge of generally accepted personal principles. (...) Commitments like those generated by agreements may be necessary for rational expectations to arise. Social conventions, construed as group principles (following the analysis in my book On Social Facts), would suffice for this task. (shrink)

This paper argues for two models of agreement which develop the idea that there is an agreement where one party gives a conditional undertaking and the other responds with an unconditional undertaking. The models accommodate plausible justifications for making and complying with agreements.

Defined and formalized several decades ago, widely used in philosophy and game theory, the concept of common knowledge is still considered as problematic, although not always for the right reasons. I suggest that the epistemic status of a group of human agents in a state of common knowledge has not been thoroughly analyzed. In particular, every existing account of common knowledge, whether formal or not, is either too strong to fit cognitively limited individuals, or too weak to adequately describe their (...) state. I provide a realistic definition of common knowledge, based on a formalization of David Lewis’ seminal account and show that it is formally equivalent to probabilistic common belief. This leads to a philosophical analysis of common knowledge which answers several common criticisms and sheds light on its nature. (shrink)

In this paper I provide a theory of the speech act of assertion according to which assertion is a species of joint action. In doing so I rely on a theory of joint action developed in more detail elsewhere. Here we need to distinguish between the genus, joint action, and an important species of joint action, namely, what I call joint epistemic action. In the case of the latter, but not necessarily the former, participating agents have epistemic goals, e.g., the (...) acquisition of knowledge. It is joint epistemic action that assertion is a species of. (shrink)

The rational choice paradigm has proved to be a fruitful means of analysis and explanation in various disciplines concerned with questions of practical rationality, but in various attempts to extend its fields of application the deficiencies of the original account of rational choice have become evident. This paper tries to give a systematic overview of ways in which the rational choice paradigm can be extended and modified.

Epistemic iteration principles are principles according to which some or another epistemic operator automatically iterates---e.g., if it is known that P, then it is known that P, or there is evidence that P, then there is evidence that there is evidence that P. This article provides a survey of various arguments for and against epistemic iteration principles, with a focus on arguments relevant to a wide range of such principles.

A number of authors, Including Thomas Schelling and David Lewis, have envisaged a model of the generation of action in coordination problems in which salience plays a crucial role. Empirical studies suggest that human subjects are likely to try for the salient combination of actions, a tendency leading to fortunate results. Does rationality dictate that one aim at the salient combination? Some have thought so, Thus proclaiming that salience is all that is needed to resolve coordination problems for agents who (...) are rational in the sense of game theory. I argue against this position; rational agents will not necessarily aim for the salient. It remains to explain how the salient comes to be chosen by human beings. Various possibilities are noted. One involves a mechanism invoked by Hume and Wittgenstein in other contexts: we may project an unreasoned compulsion onto reason, falsely believing that rationality dictates our choice of the salient. (shrink)

This paper reviews some of the growing body of work in the analytic philosophy of social phenomena, with special reference to the question whether adequate accounts of particular social phenomena can be given in terms that are individualistic in a sense that is specified. The discussion focusses on accounts of what have come to be known as shared intention and action. There is also some consideration of accounts of social convention and collective belief. Particular attention is paid to the need (...) to explain the association of certain rights and obligations with the phenomena at issue. (shrink)

Computer software is written in languages like C, Java or Haskell. In many cases social software is expressed in natural language. The paper explores connections between the areas of natural language analysis and analysis of social protocols, and proposes an extended program for natural language semantics, where the goals of natural language communication are derived from the demands of specific social protocols.

The problem of cooperation for rational actors comprises two sub problems: the problem of the intentional object (under what description does each actor perceive the situation?) and the problem of common knowledge for finite minds (how much belief iteration is required?). I will argue that subdoxastic signalling can solve the problem of the intentional object as long as this is confined to a simple coordination problem. In a more complex environment like an assurance game signals may become unreliable. Mutual beliefs (...) can then bolster the earlier attained equilibrium. I will first address these two problems by means of an example, in order to draw some more general lessons about combining evolutionary theory and rationality later on. (shrink)