How is cultural progress possible? Historically, no other animal has progressed as humans have. Conventional wisdom suggests that by having language, people accumulate knowledge, which produces progress. Such Formal stage 10 wisdom begs fundamental questions. Thus, we assert the cultural necessity of levels of support, or scaffolding, for people to develop higher stages of hierarchical complexity. The resulting, wider accessibility to higher-stage action and knowledge, which requires higher stages of development to understand, enables social and scientific progress. With (...) memes and downward assimilation, larger proportions of society gain access to advanced thinking with support, in turn enabling cultural progress. (shrink)

Common knowledge is ubiquitous in our lives and yet there remains considerable uncertainty about how to model or understand it. Standard analyses of common knowledge end up being challenged by either regress or circularity which then give rise to well-known paradoxes of practical reasoning, such as the Two Generals’ Paradox. This paper argues that the nature and utility of common knowledge can be illuminated by appeal to Wittgenstein’s Hinge Epistemology. It is argued that those (...) things that we standardly think of as being common knowledge in our lives are the same as those that Wittgenstein identified as hinge certainties. This identification of common knowledge with hinge certainties allows us to resolve the regress problem for common knowledge and explain how the Two Generals’ Paradox arises. (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)

Most reductionist accounts of intentional joint action include a condition that it must be common knowledge between participants that they have certain intentions and beliefs that cause and coordinate the joint action. However, this condition has typically simply been taken for granted rather than argued for. The condition is not necessary for ensuring that participants are jointly responsible for the action in which each participates, nor for ensuring that each treats the others as partners rather than as social (...) tools. It is thus something of a mystery why the condition is so widely accepted. By rejecting three arguments that could potentially support it, I argue that reductionists should get rid of the condition. I show that two of the arguments fail. While the third argument is intuitively compelling, it builds on key premises that are unavailable to the reductionist. (shrink)

Typically, common knowledge is taken as grounds for the acceptability of a claim, while appeals to popularity are seen as fallacious attempts to support a claim. This paper poses the question of whether there is any categorical difference between appeals to common knowledge and appeals to popular opinion as argumentative moves. In answering this question, I argue that appeals to common knowledge do not, on their own, provide adequate grounds for a claim’s acceptability.

This paper investigates the epistemic assumptions that David Lewis makes in his account of social conventions. In particular, I focus on the assumption that the agents have common knowledge of the convention to which they are parties. While evolutionary analyses show that the common knowledge assumption is unnecessary in certain classes of games, Lewis’ original account (and, more recently, Cubitt and Sugden’s reconstruction) stresses the importance of including it in the definition of convention. I discuss arguments (...) pro et contra to argue that, although the assumption might be relevant to a descriptively adequate account of social convention, it is not required for its rational reconstruction. I then point out that Lewis’ account, properly speaking, is of common reason to believe, rather than of common knowledge, and argue that, in order to formalize aptly the distinction between reason to believe and belief, standard formal epistemic models need to be supplemented with so-called awareness structures. Finally, I stress that the notion of knowledge implicit in Lewis’ text involves interesting elements that cannot be captured in the standard propositional formalizations, but need the full expressive force of quantified epistemic logic. (shrink)

David Lewis is widely credited with the first formulation of common knowledge and the first rigorous analysis of convention. However, common knowledge and convention entered mainstream game theory only when they were formulated, later and independently, by other theorists. As a result, some of the most distinctive and valuable features of Lewis' game theory have been overlooked. We re-examine this theory by reconstructing key parts in a more formal way, extending it, and showing how it differs (...) from more recent game theory. In contrast to current theories of common knowledge, Lewis' theory is based on an explicit analysis of the modes of reasoning that are accessible to rational individuals and so can be used to analyse the genesis of common knowledge. Lewis' analysis of convention emphasises the role of inductive reasoning and of salience in the maintenance of conventions over time. Footnotes Earlier versions of this paper were presented at the 13th Amsterdam Colloquium at the University of Amsterdam, at a workshop on social norms at Wissenschaftskolleg zu Berlin, and at seminars at Tilburg University and the University of Bristol. We are grateful for comments from participants at those meetings, from two anonymous referees, and from Michael Bacharach, Nick Bardsley, Cristina Bicchieri, Luc Bovens, Simon Grant, David McCarthy, Shepley Orr, Brian Skyrms, Peter Vanderschraaf, Peter Wakker and Jörgen Weibull. Robert Sugden's work was supported by the Leverhulme Trust. (shrink)

The two of us commonly know a proposition just in case (i) we both know it, (ii) we both know that we both know it, (iii) we both know that we both know that we both know it, and so on. In a recent paper titled ‘Uncommon Knowledge’, Harvey Lederman (2018) argues against the possibility of common knowledge. His argument rests on the empirical claim that there are minor individual variations in how we perceive things. This motivates (...) a principle about perception: when two people are perceiving something and it perceptually appears a certain way to one of them, then for all that person knows, it perceptually appears a slightly different way to the other. In this paper, I challenge Lederman’s perceptual principle and thereby his argument. In particular, I argue that there are some circumstances in which things perceptually appear a certain way to me and nonetheless I know that they don’t perceptually appear in a slightly different way to you. Indeed, I argue that not only are there exceptions to the perceptual principle, but they are widespread. (shrink)

An opinionated introduction to philosophical issues connected to common knowledge.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 34.2 (2001) 93-112 [Access article in PDF] Enthymemes, Common Knowledge, and Plausible Inference Douglas Walton The study of enthymemes has always been regarded as important in logic, critical thinking, and rhetoric, but too often it is the formal or mechanistic aspect of it that has been in the forefront. This investigation will show that there is a kind of plausibilistic script-based reasoning, of a (...) kind that has mainly been studied in artificial intelligence, that should have a much more important role to play in the study of enthymemes. But then curiously, as will also be shown, this plausibilistic type of reasoning was familiar in the ancient world, to the Sophists, as well as to leading philosophers such as Plato and Aristotle. By linking this ancient notion of plausibility to the modern notion used in computer science, this investigation reveals an important basis for the enthymeme that has a type of logical structure in its own right, but also has an informal aspect.An enthymeme, in current usage, is an argument that has one or more premises, or possibly a conclusion, not explicitly stated in the text, but that needs to have these propositions explicitly stated to extract the complete argument from the text. Sometimes enthymemes are described as arguments with "missing premises." That vocabulary is awkward, however, because the nonexplicit statement that needs to be added can be a conclusion, at least in a minority of cases. To make the exposition below smoother, the term nonexplicit assumption will be used to cover either the case of a nonexplicit premise or that of a nonexplicit conclusion. The problem with enthymemes is that if the nonexplicit assumptions in an argument are supposed to be propositions used by the arguer (as opposed to just the propositions needed to make the argument structurally correct, according to some standard), reasonable people can have differences of opinion on what the nonexplicit assumptions are supposed to be. The problem is that filling in the missing parts of enthymemes depends on interpreting the natural language [End Page 93] in which the argument was put forward to try to determine what the speaker meant to say.The solution to the problem comes through the recognition that enthymemes rest not only on formal (structural) criteria, but also on informal criteria. One of the most important of these informal criteria is something often called "common knowledge" (Govier 1992; Freeman 1995). But as shown below in a set of selected case studies of enthymemes, "common knowledge" is not really a kind of knowledge at all. It is really plausibility, or eikos, something well known in the ancient world and often misleadingly translated as "probability." Curiously, Aristotle's original doctrine of the enthymeme was based on this notion of plausibility. This historical fact has often been a source of puzzlement and confusion, and sometimes it has even been taken to indicate a defect or contradiction in Aristotle's treatment of the enthymeme. However, the goal of this investigation is not primarily historical. It is to work out one of the most important required steps toward a solution to the problem of enthymemes. But to do this, it is necessary to come back to the ancient notion of plausible inference. 1. The problem with enthymemes Once you have any formal theory of inference, like syllogistic, for example, you will be confronted by cases of arguments in everyday discourse that meet all the requirements for a structurally correct inference except that some part or parts, usually a premise or a conclusion, is missing. By "missing" is meant that the proposition in question has not been explicitly stated in the text of discourse, even though it may be clear enough that the speaker (writer) was relying on it, or including it, as part of the argument. The classic example is the following inference: All men are mortal; therefore, Socrates is mortal. To evaluate such an argument, surely some account of the "hidden" or "missing" assumption needs to be taken. The problem with enthymemes (Burke 1985; Gough and Tindale 1985; Hitchcock 1985) is that, if given carte... (shrink)

We develop a logical system that captures two different interpretations of what extensive games model, and we apply this to a long-standing debate in game theory between those who defend the claim that common knowledge of rationality leads to backward induction or subgame perfect (Nash) equilibria and those who reject this claim. We show that a defense of the claim à la Aumann (1995) rests on a conception of extensive game playing as a one-shot event in combination with (...) a principle of rationality that is incompatible with it, while a rejection of the claim à la Reny (1988) assumes a temporally extended, many-moment interpretation of extensive games in combination with implausible belief revision policies. In addition, the logical system provides an original inductive and implicit axiomatization of rationality in extensive games based on relations of dominance rather than the usual direct axiomatization of rationality as maximization of expected utility. (shrink)

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.’.

For as long as there have been theories about common knowledge, they have been exposed to a certain amount of skepticism. Recent more sophisticated arguments question whether agents can acquire common attitudes and whether they are needed in social reasoning. I argue that this skepticism arises from assumptions about practical reasoning that, considered in themselves, are at worst implausible and at best controversial. A proper approach to the acquisition of attitudes and their deployment in decision making leaves (...) room for common attitudes. Postulating them is no worse off than similar idealizations that are usefully made in logic and economics. (shrink)

We show the faithful embedding of common knowledge logic CKL into game logic GL, that is, CKL is embedded into GL and GL is a conservative extension of the fragment obtained by this embedding. Then many results in GL are available in CKL, and vice versa. For example, an epistemic consideration of Nash equilibrium for a game with pure strategies in GL is carried over to CKL. Another important application is to obtain a Gentzen-style sequent calculus formulation of (...) CKL and its cut-elimination. The faithful embedding theorem is proved for the KD4-type propositional CKL and GL, but it holds for some variants of them. (shrink)

The meaning of an utterance is often enriched by the pragmatic context in which it is uttered. This is because in ordinary conversations we routinely and uncontroversially compress what we say, safe in the knowledge that those interpreting us will ‘add in’ the content we intend to communicate. Does the same thing hold true in the case of legal utterances like ‘This constitution protects the personal rights of the citizen’ or ‘the parliament shall have the power to lay and (...) collect taxes’? This article addresses this question from the perspective of the constitutional originalist—the person who holds that the meaning of a constitutional text is fixed at some historical moment. In doing so, it advances four theses. First, it argues that every originalist theory is committed to some degree of pragmatic enrichment, the debate is about how much. Second, that in determining which content gets ‘added in’, originalists typically hold to a common knowledge standard for enrichment, protestations... (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)

We study the relationship between common knowledge and the sequence of iterated mutual knowledge from a topological point of view. It is shown that common knowledge is not equivalent to the limit of the sequence of iterated mutual knowledge. On that account the new epistemic operator limit knowledge is introduced and analyzed in the context of games. Indeed, an example is constructed where the behavioral implications of limit knowledge of rationality strictly refine (...) those of common knowledge of rationality. More generally, it is then shown that limit knowledge of rationality is capable of characterizing any solution concept for some appropriate epistemic-topological conditions. Finally, some perspectives of a topologically enriched epistemic framework for games are discussed. (shrink)

The importance of the notion of common knowledge in sustaining cooperative outcomes in strategic situations is well appreciated. However, the systematic analysis of the extent to which small departures from common knowledge affect equilibrium in games has only recently been attempted.We review the main themes in this literature, in particular, the notion of common p-belief. We outline both the analytical issues raised, and the potential applicability of such ideas to game theory, computer science and the (...) philosophy of language. (shrink)

One does not simply predict where the other will go, which is wherever the first predicts the second to predict the first to go, and so ad infinitum. Not "What would I do if I were she?" but "What would I do if I were she wondering what she would do if she were wondering what I would do if I were she...?".

We argue that common knowledge, of the kind used in reasoning in law and computing is best analyzed using a dialogue model of argumentation (Walton & Krabbe 1995). In this model, implicit premises resting on common knowledge are analyzed as endoxa or widely accepted opinions and generalizations (Tardini 2005). We argue that, in this sense, common knowledge is not really knowledge of the kind represent by belief and/or knowledge of the epistemic kind (...) studied in current epistemology. This paper takes a different approach, defining it in relation to a common commitment store of two participants in a rule-governed dialogue in which two parties engage in rational argumentation (Jackson & Jacobs 1980; van Eemeren & Grootendorst 2004). A theme of the paper is how arguments containing common knowledge premises can be studied with the help of argumentation schemes for arguments from generally accepted opinion and expert opinion. It is argued that common knowledge is a species of provi- sional acceptance of a premise that is not in dispute at a given point in a dia- logue, but may later be defeated as the discussion proceeds . (shrink)

Current dynamic epistemic logics often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions regarding common knowledge express the essence of what communication achieves. We present some methods that yield so-called reduction axioms for common knowledge. We investigate the expressive power of public announcement logic with relativized common knowledge, and present reduction axioms that give a detailed account of the dynamics of common knowledge in (...) some major communication types. (shrink)

In this paper we present a finitary sequent calculus for the S5 multi-modal system with common knowledge. The sequent calculus is based on indexed hypersequents which are standard hypersequents refined with indices that serve to show the multi-agent feature of the system S5. The calculus has a non-analytic right introduction rule. We prove that the calculus is contraction- and weakening-free, that (almost all) its logical rules are invertible, and finally that it enjoys a syntactic cut-elimination procedure. Moreover, the (...) use of the non-analytic rule can be restricted so that the calculus can be considered as suitable for proof search. (shrink)

Current dynamic epistemic logics often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions regarding common knowledge express the essence of what communication achieves. We present some methods that yield so-called reduction axioms for common knowledge. We investigate the expressive power of public announcement logic with relativized common knowledge, and present reduction axioms that give a detailed account of the dynamics of common knowledge in (...) some major communication types. (shrink)

Two approaches for defining common knowledge coexist in the literature: the infinite iteration definition and the circular or fixed point one. In particular, an original modelization of the fixed point definition was proposed by Barwise in the context of a non-well-founded set theory and the infinite iteration approach has been technically analyzed within multi-modal epistemic logic using neighbourhood semantics by Lismont. This paper exhibits a relation between these two ways of modelling common knowledge which seem at (...) first quite different. (shrink)

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)

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.’.

Although most of us know that human beings cannot and should not be replaced by computers, we have great difficulties saying why this is so. This paradox is largely the result of institutionalizing several fundamental misconceptions as to the nature of both trustworthy objective and moral knowledge. Unless we transcend this paradox, we run the increasing risks of becoming very good at counting without being able to say what is worth counting and why. The degree to which this is (...) occurring is the degree to which the computer revolution is already over — and the degree to which we human beings have lost. (shrink)

In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on [6] we introduce formal axiomatic systems for common information logics and prove that these systems are sound and complete. Analyzing the common information operation we show that it can be understood as greatest open fixed points for knowledge formulas. Using obtained results we explore monotonicity, omniscience problem, and inward monotonocity, describe their (...) connections and give dividing examples. Also we find algorithms recognizing these properties for some particular cases. (shrink)

This paper reveals a serious flaw in the consequentialist solution to the inefficacy problem in moral philosophy. The consequentialist solution is based on expected utility theory. In current philosophical literature, the debate focuses on the empirical plausibility of the solution. Most philosophers consider the cases of collective actions as of the same type as a horse-racing game, where expected utility theory is adequate to solve the choice problem. However, these cases should be considered as of the same type as a (...) coordination game, where the assumption of common knowledge is also required. However, the assumption is implausible—it is impossible to obtain common knowledge of rationality in cases such as voting. (shrink)

Suppose a speaker S and an audience A are in a communication coordination problem. That is, for some proposition p, they each prefer that S mean that p and that A believe p in response. How do they coordinate their thought and action to solve the problem? The Gricean answer is that they reason their way to the solution. Pragmatics makes a similar assumption. “Pragmatics involves perception augmented by some species of ‘ampliative’ inference … a sort of reasoning”. There are (...) two objections. The first is that it is not plausible to attribute such reasoning to speakers and audiences. The second objection grants, for the sake of argument, that speakers and audiences reason in the required ways. The objection is that this is not sufficient to solve coordination problems since a speaker and an audience may not know how each has reasoned. The problem is well-known in game theory, which typically solves it by assuming the parties’ preferences are common knowledge. Common knowledge is the recursive belief state in which people are know something, know they know it, know they know they know it, ad infinitum. I propose a similar solution. When people interact as speaker and audience, common knowledge arises from their perceptions of each other as fulfilling the roles of speaker and audience. The account of how common knowledge arises entails Grice’s general characterization of conversational implicatures. More precisely, it entails speakers and audiences involved in communication coordination problems typically commonly know that a relevant instance of the conditions holds. The common knowledge approach requires attributing reasoning to speakers and audiences, but it keeps those attributions to a plausible minimum. Thus the common knowledge approach is a viable alternative to current approaches that attribute extensive reasoning to speakers and audiences.A common knowledge-based approach to pragmatics would answer at least the following question: What informative generalizations are possible about the role of contexts in generating common knowledge relevant to conversational implicatures? The question is important. “Much has been learned about these domains of psychology from a focus on the problem of altruistic cooperation and the mechanisms of reciprocity. We hope that comparable insights are waiting to be discovered by psychologists as they investigate the problem of mutualistic cooperation, and the mechanisms of common knowledge are—as we might say—put out there”. (shrink)

In this paper it is shown how a formal theory of interpretation in Montague’s style can be reconciled with a view on meaning as a social construct. We sketch a formal theory in which agents can have their own theory of interpretation and in which groups can have common theories of interpretation. Frege solved the problem how different persons can have access to the same proposition by placing the proposition in a Platonic realm, independent from all language users but (...) accessible to all of them. Here we explore the alternative of letting meaning be socially constructed. The meaning of a sentence is accessible to each member of a linguistic community because the way the sentence is to be interpreted is common knowledge among the members of that community. Misunderstandings can arise when the semantic knowledge of two or more individuals is not completely in sync. (shrink)

We sketch recent insights in dynamic epistemic logic and use them to shed new light on old ideas about common knowledge as a prerequisite for linguistic communication.

Studies in Communication Sciences, 6, 2006, 3-26 . [link to online version posted].

This chapter makes the case for a relational version of an experientialist view of joint attention. On an experientialist view of joint attention, shifting from solitary attention to joint attention involves a shift in the nature of your perceptual experience of the object attended to. A relational analysis of such a view explains the latter shift in terms of the idea that, in joint attention, it is a constituent of your experience that the other person is, with you, jointly attending (...) to the object. We need such an analysis of joint attention to explain the possibility of success in tasks such as coordinated attack. (shrink)

The importance of the notion of common knowledge in sustaining cooperative outcomes in strategic situations is well appreciated. However, the systematic analysis of the extent to which small departures from common knowledge affect equilibrium in games has only recently been attempted.We review the main themes in this literature, in particular, the notion of common p-belief. We outline both the analytical issues raised, and the potential applicability of such ideas to game theory, computer science and the (...) philosophy of language. (shrink)