The central philosophical task posed by conventions is to analyze whatthey are and how they differ from mere regularities of action andcognition. Subsidiary questions include: How do conventions arise? Howare they sustained? How do we select between alternative conventions?Why should one conform to convention? What social good, if any, doconventions serve? How does convention relate to such notions as rule,norm, custom, practice, institution, and social contract? Apart fromits intrinsic interest, convention is important because philosophersfrequently invoke it when discussing other topics. A favoritephilosophical gambit is to argue that, perhaps despite appearances tothe contrary, some phenomenon ultimately results from convention.Notable candidates include: property, government, justice, law,morality, linguistic meaning, necessity, ontology, mathematics, andlogic.

• 1. Issues raised by convention
  • 1.1 Social convention
  • 1.2 Conventionalism
• 2. Truth by convention
• 3. Analyzing social convention
  • 3.1 Hume
  • 3.2 Lewis
• 4. Critical reactions to Lewis
  • 4.1 Regularitiesde facto andde jure
  • 4.2 Alternative conventions?
  • 4.3 Dichotomy or degree?
  • 4.4 Which equilibrium concept?
  • 4.5 Must convention solve a coordination problem?
• 5. Equilibrium selection
  • 5.1 Salience
  • 5.2 Dynamical models
  • 5.3 Experimental methods
• 6. Alternative treatments of convention
  • 6.1 Gilbert: plural subjects
  • 6.2 Miller: collective ends
  • 6.3 Millikan: patterns sustained by weight of precedent
• 7. Conventions of language
  • 7.1 Conventional theories of meaning
  • 7.2 Objections to conventional theories
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Issues raised by convention

In everyday usage, “convention” has various meanings, assuggested by the following list: Republican Party Convention; GenevaConvention; terminological conventions; conventional wisdom; floutingsocietal convention; conventional medicine; conventional weapons;conventions of the horror genre. As Nelson Goodman observes:

The terms “convention” and “conventional” areflagrantly and intricately ambiguous. On the one hand, theconventional is the ordinary, the usual, the traditional, the orthodoxas against the novel, the deviant, the unexpected, the heterodox. Onthe other hand, the conventional is the artificial, the invented, theoptional, as against the natural, the fundamental, the mandatory.(1989, p. 80)

Adding to the confusion, “convention” frequently serves asjargon within economics, anthropology, and sociology. Even withinphilosophy, “convention” plays so many roles that we mustask whether a uniform notion is at work. Generally speaking,philosophical usage emphasizes the second of Goodman’sdisambiguations. A common thread linking most treatments is thatconventions are “up to us,” undetermined by human natureor by intrinsic features of the non-human world. Wechooseour conventions, either explicitly or implicitly.

1.1 Social convention

This concept is the target of David Lewis’s celebrated analysisinConvention (1969). A social convention is a regularitywidely observed by some group of agents. But not every regularity is aconvention. We all eat, sleep, and breathe, yet these are notconventions. In contrast, the fact that everyone in the United Statesdrives on the right side of the road rather than the left is aconvention. We also abide by conventions of etiquette, dress, eating,and so on.

Two putative social conventions commonly cited by philosophers aremoney andlanguage. Aristotle mentions the formerexample in theNicomachean Ethics (V.5.II33a):

Money has become by convention a sort of representative of demand; andthis is why it has the name “money”(“nomisma”)—because it exists not by naturebut by law (nomos) and it is in our power to change it andmake it useless,

and the latter example inDe Interpretatione(16a.20–28):

A name is a spoken sound significant by convention… I say“by convention” because no name is a name naturally butonly when it has become a symbol.

David Hume mentions both examples in theTreatise of HumanNature (p. 490):

[L]anguages [are] gradually establish’d by human conventionswithout any explicit promise. In like manner do gold and silver becomethe common measures of exchange, and are esteem’d sufficientpayment for what is of a hundred times their value.

Although Hume analyzed money at some length in the 1752 “OfMoney,” it now receives systematic attention mainly fromeconomists rather than philosophers.^[1] In contrast, philosophers still lavish great attention upon theextent, if any, to which language rests upon convention. David Lewisoffers a theory of linguistic conventions, while Noam Chomsky andDonald Davidson argue that convention sheds no light upon language.See section 7,Conventions of language.

For many philosophers, a central philosophical task is to elucidatehow we succeed in “creating facts” through ourconventions. For instance, how does convention succeed in conferringvalue upon money or meaning upon linguistic items? Ideally, asatisfying answer to these questions would include both an analysis ofwhat social conventionsare and a description of theparticular conventions underlying some range of“conventional” facts. Hume’s theory of property andLewis’s theory of linguistic meaning serve as paradigmshere.

What are social conventions? A natural first thought is that they areexplicit agreements, such as promises or contracts, enactedeither by parties to the convention or by people suitably related tothose parties (such as their ancestors). This conception underwritesat least one famous conventionalist account: Thomas Hobbes’stheory of government as resulting from asocial contract,into which agents enter so as to leave thestate of nature.However, it seems clear that the vast majority of interesting socialphenomena, including government, involve no explicit historical act ofagreement. Social conventions can arise and persist without overtconvening.

Partly in response to such worries, John Locke emphasized the notionof atacit agreement. A tacit agreement obtains if there hasbeen no explicit agreement but matters are otherwiseas if anexplicit agreement occurred. A principal challenge here is explainingthe precise respects in which matters are just as if an explicitagreement occurred. Moreover, many philosophers argue that appeal evento “as if” agreements cannot explain linguistic meaning.What language would participants in such an agreement employ whenconducting their deliberations? Bertrand Russell observes that“[w]e can hardly suppose a parliament of hitherto speechlesselders meeting together and agreeing to call a cow a cow and a wolf awolf” (1921, p. 190). As W. V. Quine asks, then, “What isconvention when there can be no thought of convening?” (1969, p.xi). Some philosophers take this argument to show that language doesnot rest upon convention. Others, such as Lewis, take it as impetus todevelop a theory of convention that invokes neither explicit nor tacitagreement.

1.2 Conventionalism

Conventionalism about some phenomenon is the doctrine that, perhapsdespite appearances to the contrary, the phenomenon arises from or isdetermined by convention. Conventionalism surfaces in virtually everyarea of philosophy, with respect to such topics as property(Hume’sTreatise of Human Nature), justice(Hume’sTreatise again, Peter Vanderschraaf (2019)),morality (Gilbert Harman (1996), Graham Oddie (1999), Bruno Verbeek(2008)), geometry (Henri Poincaré (1902), Hans Reichenbach(1922), Adolf Grünbaum (1962)), Lawrence Sklar (1977)), pictorialrepresentation (Nelson Goodman (1976)), personal identity (DerekParfit (1984)), ontology (Rudolf Carnap (1937), Nelson Goodman (1978),Hilary Putnam (1987)), arithmetic and mathematical analysis (RudolfCarnap (1937)), necessity (A. J. Ayer (1936)), Alan Sidelle (1989)),and almost any other topic one can imagine. Conventionalism arises inso many different forms that one can say little of substance about itas a general matter. However, a distinctive thesis shared by mostconventionalist theories is that there existalternativeconventions that are in some sense equally good. Our choice of aconvention from among alternatives is undetermined by the nature ofthings, by general rational considerations, or by universal featuresof human physiology, perception, or cognition. This element of freechoice distinguishes conventionalism from doctrines such asprojectivism, transcendental idealism, and constructivism aboutmathematics, all of which hold that, in one way or another, certainphenomena are “due to us.”

A particularly important species of conventionalism, especially withinmetaphysics and epistemology, holds that some phenomenon is partly dueto our conventions about the meaning or proper use of words. Forinstance, Henri Poincaré argues that “the axioms ofgeometry are merely disguised definitions,” concludingthat:

Theaxioms of geometry therefore are neither synthetic apriorijudgments nor experimental facts. They areconventions; our choice among all possible conventions isguided by experimental facts; but it remainsfreeand is limited only by the necessity of avoiding all contradiction.(1902, p. 65)

Poincaré holds that, in practice, we will always find it moreconvenient to choose Euclidean over non-Euclidean geometry. But heinsists that, in principle, we could equally well choose non-Euclideanaxioms. This position greatly influenced the logical positivists,including Rudolf Carnap, Moritz Schlick, and Hans Reichenbach, whogeneralized it to other aspects of science.

Beginning withLogical Syntax of Language (1937/2002), Carnapdeveloped a particularly thoroughgoing version of linguisticconventionalism. Carnap invites us to propose various linguisticframeworks for scientific inquiry. Which framework we choosedetermines fundamental aspects of our logic, mathematics, andontology. For instance, we might choose a framework yielding eitherclassical or intuitionistic logic; we might choose a frameworkquantifying over numbers or one that eschews numbers; we might choosea framework that takes sense data as primitive or one that takesphysical objects as primitive. Questions about logic, mathematics, andontology make no sense outside a linguistic framework, since only bychoosing a framework do we settle upon the ground rules through whichwe can rationally assess such questions. There is no theoretical basisfor deciding between any two linguistic frameworks. It is just amatter for conventional stipulation based upon pragmatic factors likeconvenience.

Conventionalist theories differ along several dimensions. The mostobvious concerns the underlying understanding of conventionsthemselves. In many cases, such as Hume’s theory of property andjustice, the conventions aresocial. In other cases, however,convention lacks any intrinsically social element. For example, bothPoincaré and Carnap seem to regard conventional stipulation assomething that a lone cognitive agent could in principle achieve.

Another important difference between conventionalist theories concernswhat the “conventional” is contrasted with. Optionsinclude: the natural; the mind-independent; the objective; theuniversal; the factual; and the truth-evaluable.

Poincaré’s geometric conventionalism contrasts theconventional with the truth-evaluable. According to Poincaré,there is no underlying fact of the matter about the geometry ofphysical space, so geometric axioms are not evaluable as true orfalse. Rather, the choice of an axiom system is akin to the choice ofa measuring standard, such as the metric system. In manyconventionalist theories, however, the idea is that our conventionssomehowmake certain facts true. Those facts may be“conventional”, “social,” or“institutional” rather than “brute” or“natural,” but they are full-fledged facts nonetheless.For instance, following Hume, it seems plausible to claim thatproperty rights and monetary value are due largely to convention. Yetfew philosophers would hold that claims about property rights ormonetary value are non-truth-evaluable.^[2] As this example illustrates, conventionalism need not reflect an“anti-realist” or “deflationary” stancetowards some subject matter.

Conventionalism often entrainsrelativism. A particularlyclear example is Gilbert Harman’s moral philosophy (1996),according to which moral truths result from social convention.Conventions vary among societies. One society may regard infanticideas horrific, while another may regard it as routine and necessary.Moral statements are true only relative to a conventional standard. Onthe other hand, as the example of property rights illustrates, one canaccept that some fact is due to social convention while denying thatit is relative or non-universal. For instance, one might urge, theconventions of my society make it the case that I own my house, butthis fact is then truesimpliciter, without relativization toa particular societal convention.

A final division among conventionalist theories concerns whether theputative conventions inform pre-existing practice. Hume’s theoryof property purports to unveil actual conventions at work in actualhuman societies. But some conventionalists instead urge that we mustadopt a convention. Carnap’s conventionalist treatmentof logic, mathematics, and ontology illustrates this approach. Carnapexhorts us to replace unformalized natural language withconventionally chosen formal languages. Carnap has no interest indescribing pre-existing practice. Instead, he offers a “rationalreconstruction” of that practice.

2. Truth by convention

Carnap’s conventionalism was the culmination of the logicalpositivists’ efforts to accommodate logic and mathematics withinan empiricist setting. Rejecting the Kantian syntheticapriori, the positivists held that logic and mathematics wereanalytic. Kant had explained theanalytic-synthetic distinction in terms of concept-containment, which struck the positivists aspsychologistic and hence “unscientific.” The positivistsinstead treated analyticity as “truth by virtue ofmeaning.” Specifically, they treated it as the product oflinguistic convention. For instance, we can adopt the stipulativeconvention that “bachelor” means “unmarriedman.” “All bachelors are unmarried men” is true byvirtue of this convention. The positivists sought to extend thisanalysis to far less trivial examples, most notably mathematical andlogical truth. In this regard, they were heavily influenced by GottlobFrege’s logicism and also by Ludwig Wittgenstein’sconception, developed in theTractatus Logico-Philosophicus,of logical truths as tautologous and contentless (sinnloss).Alberto Coffa (1993), Michael Friedman (1999), and Warren Goldfarb(1997) offer detailed discussion of the role played by conventionalismin logical positivism.

Although initially attracted to Carnap’s conventionalism, W.V.Quine eventually launched a sustained attack on it in “Truth byConvention” (1935) and “Carnap and Logical Truth”(1963). Quine’s anti-conventionalist arguments, in conjunctionwith his attack upon the analytic-synthetic distinction, profoundlyimpacted metaphysics and epistemology, casting conventionalisttheories of logic, mathematics, and ontology into generaldisrepute.

One of the Quine’s most widely cited arguments (1936), directedagainst a crude conventionalism about logic, traces back to LewisCarroll. There are infinitely many logical truths. Human beings arefinite, so we can explicitly stipulate only a finite number ofstatements. Thus, in generating all the logical truths we musteventually apply rules of inference to finitely many conventionallystipulated statements. But then we are employing logic to derive logicfrom convention, generating a vicious regress. Quine’s pointhere is not just that logic did notin fact come intoexistence through conventional truth assignment. His point is that itcould not have thus come into existence.

To avoid the Quinean regress, one might propose that we conventionallystipulate a finite number of axiomsand a finite number ofinferences rules, thereby fixing an infinite number of logical truths.The question here is what it means to “stipulate” aninference rule. We can conventionally stipulate that we willhenceforth obey a certain inference rule. But that stipulation doesnot entail that we areentitled to reason in accord with theinference rule. Mere conventional stipulation that we will henceforthobey a inference rule does not ensure that the rule carries truthsinto truths. What if we stipulate that the inference rule carriestruths into truths? Then our stipulation is merely another axiom. Sowe require a new inference rule to draw any consequences from it, andthe regress continues.

While it is doubtful that Carnap or the other positivists held thecrude form of conventionalism attacked by Quine’s argument, theargument suggests that conventionalism about logic requires an accountof “tacit” conventions. If logic is indeed “true byconvention,” then some of the relevant conventions mustapparently be “implicit” in our practice, rather than theresults of explicit stipulation. So we require an account of what an“implicit” convention amounts to. Carnap offers no suchaccount. Jared Warren (2017, 2020) attempts to meet the challenge bydeveloping an account of “implicit” inference rules.

Another Quinean argument holds that “truth by convention”offers no explanatory or predictive advantage over the far lessexciting thesis that certain statements are true due to obviousfeatures of extra-linguistic reality. For instance, we can all agreethat linguistic convention makes it the case that “Everything isidentical to itself” means what it does. But why should wefurthermore hold that thetruth of this sentence is due tolinguistic convention, rather than to the fact that everything isindeed self-identical? According to Quine, Carnap has offered noreason for thinking that such truths are somehow vacuous as opposed tomerely obvious.

A final notable Quinean argument centers on the role of“conventional stipulation” in scientific theorizing.Consider a scientist introducing a new theoretical term bydefinitional stipulation. The new term is embroiled in an evolvingbody of scientific doctrine. As this body of doctrine develops, theoriginal legislated definition occupies no privileged status. We mayreject it in light of new empirical developments. Thus,“conventionality is a passing trait, significant at the movingfront of science but useless in classifying the sentences behind thelines” (1954, p. 119). Hilary Putnam (1962) further developsthis argument, offering the example of “kinetic energy \(=\bfrac{1}{2} mv^{2}\)”. Although that identity began as astipulative definition in Newtonian mechanics, Einsteinian mechanicsdeems it false. Inspired by such examples, Quine rejects as untenableany distinction between statements “true by convention” orotherwise.

Quine therefore rejects Carnap’s picture of science as atwo-stage process: the first stage in which we conventionallystipulate constitutive aspects of our scientific language (such as itsontology or logic) based solely upon pragmatic, non-rational factors;the second in which we deploy our language by subjectingnon-conventional theories to rational scrutiny. For Quine, thistwo-stage picture does not describe even idealized scientific inquiry.There is no clear separation between those aspects of theory choicethat are solely “pragmatic” and those that arerational.

These and other Quinean arguments proved extremely influential.Ultimately, many philosophers became convinced that Carnap’sconventionalist program was fundamentally flawed.^[3] This reaction dovetailed with additional developments inimical toconventionalism. For instance, Hilary Putnam (1963, 1974) and variouslater philosophers, such as Michael Friedman (1983), vigorouslyattacked geometric conventionalism.^[4]

On the other hand, conventionalism still finds defenders. LawrenceSklar (1977) advocates a refurbished version of geometricconventionalism. Alan Sidelle (1989) advocates conventionalism aboutnecessary truth. Michael Dummett (1991), Christopher Peacocke (1987),and Dag Prawitz (1977) follow Gerhard Gentzen in treating certainfundamental inferences as “implicit definitions” of thelogical connectives, a theory somewhat reminiscent of Carnap’sconventionalism about logic. Jared Warren (2020) develops the“implicit definition” approach into a systematic defense ofconventionalism about logic. He also invokes implicit definition toelucidate arithmetical vocabulary (Warren 2015, 2020), defending onthat basis a conventionalist treatment of arithmetical truth. Thus,the issues raised by Quine remain unresolved. Still, it seems safe tosay that philosophers nowadays regard conventionalist solutions withinmetaphysics and epistemology more warily than philosophers from thepre-Quinean era.^[5]

3. Analyzing social convention

Although philosophers have always been interested in socialconventions, Hume’sTreatiseof Human Natureoffered the first systematic analysis of what theyare. Thetopic then lay dormant until Lewis revived it inConvention,providing an analysis heavily influenced by Hume’s but far moredetailed and rigorous. Lewis’s analysis continues to shape thecontemporary discussion. In this section, we briefly discuss Hume andthen discuss Lewis in detail. Henceforth, “convention”means “social convention.”

3.1 Hume

Hume’s analysis of convention, while compressed, has provedremarkably fertile. As Hume puts it in theEnquiryConcerning Human Understanding, a convention is

a sense of common interest; which sense each man feels in his ownbreast, which he remarks in his fellows, and which carries him, inconcurrence with others into a general plan or system of actions,which tends to public utility. (p. 257)

On this definition, a convention prevails in a population when eachmember of the population plays his part in some system of actionsbecause he perceives that it is in his interest to do so, given thatothers perceive it is in their interests to do so. Several features ofthis definition deserve emphasis. First, a convention contributes tothe mutual benefit of its participants. Second, a convention need notresult from explicit promise or agreement. Third, each participantbelieves that other participants obey the convention. Fourth, giventhis belief, each participant has reason to obey the conventionherself. This fourth point emerges even more sharply in theTreatise: “the actions of each of us have a referenceto those of the other, and are perform’d upon the supposition,that something is to be perform’d on the other part” (p.490). Hume illustrates his approach with the memorable example of twomen sitting in a row-boat. In order to move at all, they mustsynchronize their rowing, which they do without any explicitagreement.

Having clarified convention, Hume deploys it to illuminate property,justice, promising, and government. In each case, Hume offers abroadly conventionalist account (see the entry on Hume’s moralphilosophy for details). For instance, property emerges from the stateof nature through a social convention “to bestow stability onthe possession of those external goods, and leave every one in thepeaceable enjoyment of what he may acquire by his fortune andindustry” (Treatise, p. 489). This convention makes itthe case that certain goods are “owned” by certain people,who enjoy exclusive rights to their use or dispensation. Similarly,Hume argues that the obligation to keep one’s promises isintelligible only with reference to convention that, when one employsa certain “form of words” (e.g., “I promise to\(j\)”), one thereby expresses a resolution to \(j\) andsubjects oneself to penalty if one does not \(j\).

In both theTreatise and “Of the OriginalContract,” Hume rejects a Hobbesian conception of government asarising from the state of nature through a social contract. Humeoffers various criticisms, but a particularly fundamental objection isthat Hobbes adopts a misguided order of explanation. Hobbes explainsgovernment as the result of phenomena, such aspromising orcontracting, that themselves rest upon convention and hencecould not arise in a pure state of nature. Hume contends thatpromising and government arise independently, albeit in the same basicway and from the same basic source: convention.^[6]

Perhaps the most notable feature of Hume’s account is that itprovides a detailed model of how social order can arise from rationaldecisions made by individual agents, without any need for eitherexplicit covenant or supervision by a centralized authority. In thisrespect, Hume’s discussion prefigures Adam Smith’s“invisible hand” analysis of the marketplace.

3.2 Lewis

Lewis (1969) develops a broadly Humean perspective by employing game theory,the mathematical theory of strategic interaction among instrumentallyrational agents. Drawing inspiration from Thomas Schelling’sThe Strategy of Conflict (1960), Lewis centers his accountaround the notion of acoordination problem, i.e., asituation in which there are several ways agents may coordinate theiractions for mutual benefit.

Suppose \(A\) and \(B\) want to meet for dinner. They can choosebetween two restaurants, Luigi’s and Fabio’s. Each agentis indifferent between the two restaurants, and each agent prefersmeeting the other one to not meeting. We represent this situationthrough apayoff matrix:

The rows (respectively, columns) represent \(A\)’s(respectively, \(B\)’s) possiblestrategies: in thiscase, their two restaurant options. Each cell contains the respectivepayoffs for \(A\) and \(B\) for a given strategy combination.Since there are two incompatible ways that \(A\) and \(B\) mightachieve a mutually desirable result, the two “players”must coordinate their actions.

In several respects, Restaurant Rendezvous is an unrepresentativecoordination problem. First, \(A\) and \(B\) must perform thesame action in order to achieve the desired result. Second,\(A\) and \(B\) achieve identical payoffs in each circumstance. Thefollowing payoff matrix represents a coordination problem lackingthese two properties:

As an intuitive interpretation, imagine that \(A\) and \(B\) arespeaking on the phone but that they are disconnected. Who should callback? Each would prefer that the other call back, so as to avoidpaying for the call. However, each prefers paying for the call to nottalking at all. If both try to call back, then both will receive abusy signal. The payoff matrix summarizes this situation. This kind ofcase is sometimes called animpure coordination problem,since it enshrines a partial conflict of interest between players.

Coordination problems pervade social interaction. Drivers mustcoordinate so as to avoid collisions. Economics agents eliminate theneed for barter by coordinating upon a common monetary currency. Inmany such cases, there is no way to communicate in advance, and thereis no centralized authority to impose order. For instance, prisonersin POW camps converge without any centralized guidance upon a singlemedium of exchange, such as cigarettes.

Lewis analyzes convention as an arbitrary, self-perpetuating solutionto a recurring coordination problem. It is self-perpetuating becauseno one has reason to deviate from it, given that others conform. Forexample, if everyone else drives on the right, I have reason to aswell, since otherwise I will cause a collision. Lewis’s analysisruns as follows (1969, p. 76):

A regularity \(R\) in the behavior of members of a population \(P\)when they are agents in a recurrent situation \(S\) is a convention ifand only if it is true that, and it is common knowledge in \(P\) that,in any instance of \(S\) among members of \(P\),

(1) everyone conforms to \(R\);

(2) everyone expects everyone else to conform to \(R\);

(3) everyone has approximately the same preferences regarding allpossible combinations of actions;

(4) everyone prefers that everyone conform to \(R\), on condition thatat least all but one conform to \(R\);

(5) everyone would prefer that everyone conform to \(R'\), oncondition that at least all but one conform to \(R'\),

where \(R'\) is some possible regularity in the behavior of members of\(P\) in \(S\), such that no one in any instance of \(S\) amongmembers of \(P\) could conform both to \(R'\) and to \(R\).

Lewis finally settles upon a modified analysis that allows occasionalexceptions to conventions. The literature spawned by Lewis’sdiscussion tends to focus on the exceptionless characterization givenabove.

Lewisian convention is a special case ofNash equilibrium,the central idea behind modern game theory. An assignment ofstrategies to players is a Nash equilibrium iff no agent can improvehis payoff by deviating unilaterally from it. An equilibrium isstrict iff each agentdecreases his payoff bydeviating unilaterally from it. Intuitively, a Nash equilibrium is a“steady state”, since each player behaves optimally, givenhow other players behave. In this sense, Nash equilibrium“solves” the strategic problem posed by a game, so it issometimes called a “solution concept”. However, Lewisianconvention goes well beyond Nash equilibrium. In a Lewisianconvention, everyone prefers thateveryone else conform if atleast all but one conform. Equilibria with this property are sometimescalledcoordination equilibria.

By classifying \(R\) as a convention only if there is some alternativeregularity \(R'\) that could serve as a convention, Lewis codifies theintuitive idea that conventions arearbitrary. This was oneof the most widely heralded features of Lewis’s definition,emphasized by both Quine (1969) and Putnam (1981).

Notably, Lewis introduces the concept ofcommon knowledge.Roughly, \(p\) is common knowledge iff everyone knows \(p\), everyoneknows that everyone knows \(p\), everyone knows that everyone knowsthat everyone knows that \(p\), etc. The subsequent game-theoretic andphilosophical literature offers several different ways of formalizingthis intuitive idea, due to researchers such as Robert Aumann (1976)and Stephen Schiffer (1972). The precise relation between these laterformalizations and Lewis’s own informal remarks iscontroversial. Robin Cubitt and Robert Sugden (2003) argue thatLewis’s conception of common knowledge is radically differentfrom the later formalizations, while Peter Vanderschraaf (1998) andGiacomo Sillari (2005) downplay the differences. See the entry oncommon knowledge for discussion of this controversy and of how common knowledgeinforms both game theory and the philosophical study ofconvention.

In the later paper “Languages and Language” (1975/1983),Lewis significantly altered his analysis of convention. See section 7,Conventions of language, for details.

4. Critical reactions to Lewis

Most subsequent discussions take Lewis’s analysis as a startingpoint, if only as a foil for motivating some alternative. Manyphilosophers simply help themselves to Lewis’s account withoutmodifying it. On the other hand, virtually every element ofLewis’s account has attracted criticism during the past fewdecades. For instance, Ken Binmore (2008) and Richard Moore (2013)attack the “common knowledge” condition in Lewis’sanalysis. In this section, we will review some prominent criticisms ofLewis’s account.

4.1 Regularitiesde facto andde jure

Lewis’s definition of convention demands complete ornear-complete conformity. Many commentators object that this is toostrict, excluding conventions “more honored in the breach thanthe observance.” To take Margaret Gilbert’s example(1989), there might be a convention in my social circle of sendingthank-you notes after a dinner party, even though few people actuallyobserve this convention anymore. Lewis must deny that sendingthank-you notes is a convention, a verdict which Gilbert and othercommentators find unintuitive. Wayne Davis (2003) and Ruth Millikan(2005) develop similar objections.

This objection sometimes accompanies another: that Lewis overlooks theessentiallynormative character of conventions. The idea isthat conventions concern not just how people actually behave but alsohow theyshould behave. In other words, conventions areregularities not (merely)de facto, butde jure. Forinstance, if there is a convention that people stand a certaindistance from one another when conversing, then it seems natural tosay that peopleshould stand that distance when conversing.It is not obvious that Lewis can honor these intuitions, since hisconceptual analysis does not mention normative notions. On this basis,Margaret Gilbert (1989) and Andrei Marmor (1996) conclude that Lewishas not provided sufficient conditions for a convention to prevailamong some group.

A closely related idea is that violations of convention elicit somekind ofsanction, such as tangible punishment or, morecommonly, negative reactive attitudes. Lewis emphasizes theself-perpetuating character of convention: one conformsbecause it is in one’s interest to conform, given that othersconform. But, the argument goes, this emphasis overlooks a distinctenforcement mechanism: non-conformity elicits some kind of sanctionfrom other people.

Lewis (1969, pp. 97–100) anticipates such objections andattempts to forestall them. He argues that conventions will tend tobecome norms. Once a convention prevails in some population, anymember of the population will recognize that others expect him toconform to it and that they prefer he do so. He will also recognizethat by conforming, he will comply with his own preferences. Itfollows that heought to conform, since, other things beingequal, one ought to do what answers both to one’s ownpreferences and to those of other people. Moreover, if people see thathe fails to conform, then they will tend to sanction him throughpunishment, reproach, or distrust, since they will see that he actscontrary both to his own preferences and to theirs. To some extent,this argument recalls Hume’s argument in theTreatisethat conventions of property generate moral norms. Robert Sugden(1986/2004) develops the line of thought in more detail.

Gilbert responds to such arguments by noting that, even if they showthat conventions have a tendency toacquire normative force,they do not show that normativity is essential to convention.Theoretically, it seems possible for rational agents to instantiate aLewisian convention without regarding it as a norm and without makingany effort to enforce the convention through sanctions. Thus, Gilbertconcludes, Lewis’s account does not preserve the intrinsic linkbetween convention and normativity.

Even if one sympathizes with this objection, how to elucidate moresystematically the normativity of convention remains unclear. It doesnot seem to be the normativity of morality, since someone who violatessome convention of, say, etiquette or fashion need not thereby actimmorally. Nor is it straightforwardly reducible to the normativity ofinstrumental rationality: many philosophers want to say that, otherthings being equal, one should conform to convention quiteindependently of whatever one’s beliefs and desires happen tobe. (“You really ought to send a thank-you note.”) What isthis mysterious brand of normativity, which apparently derives fromneither morality nor instrumental rationality? That question is stilla focus of active philosophical research.

4.2 Alternative conventions?

Seumas Miller (2001) deploys an example of Jean-Jacques Rousseau toquestion whether a convention must have a conventional alternative. InRousseau’s example, agents stationed throughout a forest mustdecide whether to hunt stag or hunt hares. Hunting stag yields ahigher pay-off for everyone, but only if all other players hunt stagas well. We can represent a two-person stag hunt through the followingpay-off matrix:

Miller argues that, on Lewis’s definition of“convention,” hunting hares is not a possible convention,since a player who chooses to hunt rabbits does not prefer that theother player do likewise. Miller argues that this result accords withintuition. He furthermore argues that hunting stag \(is\), intuitivelyspeaking, a possible convention. He concludes that Lewis errs byrequiring convention to have a conventional alternative.

Tyler Burge (1975) develops a related but distinct worry. He agreeswith Lewis that convention must have a conventional alternative, buthe denies that participants mustknow of such an alternative.Burge offers as an example a primitive, isolated society with a singlelanguage. Members of this society believe, as a matter of religiousprinciple, that theirs is the only possible language. Nevertheless,Burge argues, their linguistic practice is governed by convention.Burge concludes that Lewis adopts an overly“intellectualist” conception of convention, one thatcredits participants in convention with far more rationalself-understanding than they necessarily possess. While Burge agreeswith Lewis that conventions are arbitrary, he thinks that “thearbitrariness of conventions resides somehow in the ‘logic ofthe situation’ rather than in the participants’psychological life” (p. 253). For Burge, the arbitrariness of aconvention consists in the following facts: the conventions operativewithin a society emerge due to historical accident, not biological,psychological or sociological law; and, with effort comparable to thatexpended in learning the original convention, parties to theconventioncould have instead learned an incompatibleconvention that would have served roughly the same social purpose.

4.3 Dichotomy or degree?

Some authors question whether there is a sharp dichotomy between theconventional and the non-conventional. They urge that conventionalityshould instead be viewed as a matter of degree. Lewis himselfanticipates this viewpoint (1969, pp. 76–80). He articulates a notion ofdegree of conventionality that measures the extent to whichmembers of a population satisfy the various clauses in his definition.However, some authors contend that Lewis does not go far enough inacknowledging the extent to which conventionality is a matter ofdegree. Mandy Simons and Kevin Zollman (2019) target the notion ofarbitrariness. They claim that whether a solution to acoordination problem counts as arbitrary is itself a matter of degree,depending on factors such as how likely the solution is to emerge andhow likely it is to persist if it does emerge. Cailin O’Conner (2021)agrees, articulating an information-theoretic measure of arbitrarinessthat targets likelihood of emergence. Her analysis yields a continuumof arbitrariness rather than a rigid dichotomy between the arbitraryand the non-arbitrary. She maintains that her analysis “pushesstrongly against a framework where we class outcomes into‘conventional’ and ‘not conventional.’ Insteadwe should expect that almost everything is at least a littleconventional, and focus on the diversity of cases within the categoryof ‘convention’(p. 586)”. She applies herdegree-theoretic viewpoint to several social and linguistic phenomena,such as the conventionality of color vocabulary.

4.4 Which equilibrium concept?

The game-theoretic literature contains numerous solution concepts thateither generalize or refine Nash equilibrium. Various commentatorssuggest that a proper analysis of convention requires one of thesealternate solution concepts. For instance, Robert Sugden (1986/2004)analyzes convention as a system of evolutionarily stable strategies.On this approach, not only are conventions self-enforcing, but theyhave an additional stability property: once established, they canresist invasion by deviant agents trying to establish a newconvention. Sugden argues that this approach illuminates a wide rangeof social phenomena, including familiar examples such as money andproperty.

Another widely discussed solution concept iscorrelatedequilibrium, introduced by Robert Aumann (1974, 1987). Toillustrate this generalized concept, consider a modified version ofRestaurant Rendezvous. In the new version (sometimes called“Battle of the Sexes”), each agent prefers a differentrestaurant, although both agents prefer meeting to not meeting. Werepresent this situation with the following payoff matrix:

This game has two “pure” Nash equilibria: one in whichboth players go to Luigi’s, the other in which both go toFabio’s. Intuitively, neither equilibrium is fair, since oneplayer achieves a higher payoff than the other. The game also has a“mixed-strategy” Nash equilibrium: that is, an equilibriumin which each agent chooses his strategy based upon the outcome of arandomizing device. Specifically, the game has a mixed-strategyequilibrium in which \(A\) goes to Luigi’s with probability\(\bfrac{2}{3}\) and \(B\) goes to Luigi’s with probability\(\bfrac{1}{3}\). \(A\)’s expected payoff from this equilibriumis given as follows, where “\(Prob(x, y)\)” denotes theprobability that \(A\) goes to \(x\) and \(B\) goes to \(y\):

Similarly, \(B\)’s expected payoff is \(\bfrac{2}{3}\). Neitherplayer can improve upon this payoff by deviating from themixed-strategy equilibrium, given that the other player is playing herend of the equilibrium. This equilibrium is fair, in that it yieldsthe same expected payoff for both players. But it also yields a lowerexpected payoff for each player than either pure equilibrium, sincethere is a decent chance that the players’ separate randomizingdevices will lead to them to different restaurants.

If the players can contrive to correlate their actions with acommon randomizing device, they can achieve a new equilibriumthat is fair and that Pareto dominates the old mixed-strategyequilibrium. More specifically, suppose that there is asingle coin toss: each player goes to Luigi’s if thetoss is heads, Fabio’s if the toss is tails. The resultingstrategy combination yields an expected payoff of \(\bfrac{3}{2}\) foreach player. Intuitively, this strategy combination is an equilibrium,since no player has reason to deviate unilaterally from it. But thestrategy combination does not count as aNash equilibrium ofthe original game, since in mixed Nash equilibria players’actions must be probabilistically independent. Aumann calls thisstrategy combination acorrelated equilibrium, sinceplayers’ actions are probabilistically correlated. He developsthis intuitive idea in great formal detail, without reliance uponexplicit pre-game communication between players.

Building upon Aumann’s formal treatment, Brian Skyrms (1996) andPeter Vanderschraaf (1998b, 2001) argue that we should treatconvention as a kind of correlated equilibrium. For example, considerthe convention that drivers at traffic intersections correlate theiractions with the color of the traffic signal. As the restaurant andtraffic examples illustrate, correlated equilibria often provide farmore satisfactory solutions to coordination problems than one couldotherwise achieve.

Skyrms (2023) also discusses a solution concept,coarse correlatedequilibrium, that generalizes correlated equilibrium. Thedifference between correlated equilibrium and coarse correlatedequilibrium is this. In a correlated equilibrium, the player receivesa recommendation from the randomizing device, and she cannot improveher expected payoff by deviating from that recommendation. In acoarse correlated equilibrium, the player knows in advancethat deviation from the device’s recommendations does notimprove expected payoffas computed before she receives anyspecific recommendation. Coarse correlated equilibrium allows(while mere correlated equilibrium does not allow) that the agentwould like to deviate from the device’s recommendation after shelearns its specific recommendation. For that reason, coarse correlatedequilibria may not have the kind of stability one would usually expectfrom conventions. Skyrms introduces the termquasi-convention, to highlight that coarse correlatedequilibrium gives rise to a notion sharing some but not all importantfeatures with our intuitive concept of convention.

4.5 Must convention solve a coordination problem?

Wayne Davis (2003), Andrei Marmor (1996, 2009), Seumas Miller (2001),Robert Sugden (1986/2004), and Peter Vanderschraaf (1998) argue thatconventions need not be coordination equilibria. For instance, Davisclaims that fashion conventions do not solve coordination problems,since we do not usually care how other people dress.

To develop this objection, Sugden introducesconventions ofproperty andconventions of reciprocity, neither ofwhich solves coordination problems. He illustrates the former with theHawk-Dove game (also sometimes called “Chicken”):

The intuitive interpretation here is that two people faced with anitem of value 2 must decide whether to fight for it (Hawk) or share it(Dove). If both play Dove, then they split it. If one plays Hawk andthe other Dove, then the Hawk gets the entire good. If they both playHawk, then they again split it, but its value is reduced by half toreflect the cost of fighting. This game has no coordinationequilibrium. However, consider the following strategy for recurringinstances of the game: “If you are already in possession of therelevant item, then playHawk; otherwise, playDove.” It is an equilibrium for both players to playthis strategy. (More technically, following Skyrms (1996), we mightregard this strategy combination as a correlated equilibrium.) Sugdenargues that such an equilibrium might emerge as a convention amongagents who repeatedly play Hawk-Dove. But the equilibrium is not aconvention according to Lewis’s definition. If I play my end ofit, I do not prefer that other people do likewise. I prefer thatothers play Dove. Thus, the equilibrium lacks one of the maincharacteristics emphasized by Lewis: a preference for generalconformity over slight-less-than-general conformity.

Sugden illustrates conventions of reciprocity with thePrisoner’s Dilemma, which has the following payoff matrix:

The original intuitive interpretation of this payoff matrix is thatthe police are separately interrogating two prisoners, each of whommust decide whether to cooperate with the other prisoner by remainingsilent or whether to “defect” by confessing. If bothcooperate, then both receive very light sentences. If both defect,then both receive very harsh sentences. If one defects and the othercooperates, then the defector goes free while the cooperator receivesa harsh sentence. Although this scenario may seem rather contrived, wecan model many common social interactions as instances ofPrisoner’s Dilemma. Sugden offers as an example two academicswho exchange houses for their sabbaticals. Each academic must decidewhether to maintain the other’s house in good condition, eventhough leaving it a mess would be easier.

Prisoner’s Dilemma has no coordination equilibrium. Yet Sugdenargues that the following “tit-for-tat” strategy mightemerge as a convention when players repeatedly play Prisoner’sDilemma over some indefinite period (e.g., two academics with astanding arrangement to exchange houses every summer): co-operate aslong as your opponent cooperates; if your opponent defects, thendefect for some prescribed number of rounds \(r\) as retaliationbefore cooperating again; if your opponent cooperates but you defectby mistake, then accept your opponent’s punishment in the next\(r\) rounds without retaliating. This equilibrium is not a conventionin Lewis’s sense, since one always prefers that one’sopponent cooperate rather than defect.

In response to such examples, Sugden (1986/2004) and Vanderschraaf(1998b) develop generalized game-theoretic analyses that do notrequire convention to solve a coordination problem. In practice, thenecessary revisions to Lewis’s account are not very sweeping,since they basically amount to excising clause (4) from his conceptualanalysis. Vanderschraaf (1998a) argues that these revisions yield atheory closer to Hume’s original account.

Marmor (2009) also questions Lewis’s focus on coordinationproblems. Marmor emphasizes actual games, such as chess, rather thanthe “games” primarily studied by game theorists, such asPrisoner’s Dilemma. According to Marmor, the rules of chess areconventions that do not solve a coordination problem. Chess playingactivity does not involve coordinating one’s actions with thoseof other players, in anything like the sense that driving on the rightside of the road (rather than the left) involves coordination amongagents. Drawing on John Searle’s (1969) discussion of“constitutive rules,” Marmor argues that Lewis hasoverlooked an important class of conventions, which Marmor calls“constitutive conventions,” modeled after the rules of agame. Roughly, a constitutive convention helps“constitute” a social practice, in the sense that it helpsdefine what the practice is and how to engage in it correctly. Marmoroffers a generalized analysis designed to accommodate both Lewisianconventions and constitutive conventions. The analysis resemblesLewis’s, but it makes no mention of coordination problems, andit contains no reference to common knowledge.

5. Equilibrium selection

Lewis requires that a convention be one among several possiblealternatives. Even if one follows Miller in rejecting thatrequirement, it seems clear that there are many cases, such as thechoice of monetary currency, where we must select from among numerouscandidate conventions. This raises the question of how we select aparticular candidate. An analogous question arises for game theorymore generally, since a game may have many Nash equilibria. It isrational to play my part in a Nash equilibrium,if I believe thatother agents will play their parts. But why should I believe thatothers will play their parts in this particular equilibrium? If weassume that players cannot engage in pre-game communication, threebasic answers suggest themselves: players converge upon a uniqueequilibrium through rational reflection on the logic of theirstrategic situation; or they are guided by psychological factorsoutside the ambit of purely rational analysis; or they learn fromprior experience which equilibrium to choose. One might also combinethese three suggestions with one another.

A venerable game-theoretic tradition embraces the first suggestion.The hope is that, if we assume enough common knowledge among playersabout the game’s payoff structure and their own rationality,then, through relativelya priori reasoning, they cansuccessfully predict which equilibrium others will select. An earlyexample of this explanatory tradition is the method of backwardsinduction, introduced by Ernst Zermelo (1913). The traditionculminates in John Harsanyi and Reinhard Selten’sA GeneralTheory of Equilibrium Selection (1988). However, few researchersstill champion this tradition. Its basic flaw is already apparent fromour simplest coordination problem, Restaurant Rendezvous. Nothingintrinsic either to rationality or to the logic of the situationfavors one equilibrium over the other. Indeed, Harsanyi andSelten’s theory dictates that each player choose amixed-strategy randomizing over Luigi’s and Fabio’s.Clearly, then, Harsanyi and Selten cannot explain how, in a widevariety of cases, people converge upon a unique, non-randomizedsolution. Nor does it seem likely that we can overcome this difficultyby emending our analysis of rationality or refining our solutionconcept. Apparently, breaking the tie between otherwise symmetricalequilibria requires us to supplement the austere viewpoint of purerational analysis with some additional input, either from humanpsychology or else from experience.

5.1 Salience

Following Thomas Schelling (1960), who introduced the notion of afocal point, Lewis argues that agents will select thesalient convention. A convention is salient (it is a focalpoint) if it “stands out” from the other choices. Acandidate convention might acquire salience through precedent,explicit agreement, or its own intrinsic properties. Schellingconducted a famous experiment to illustrate the concept of salience.He asked subjects to choose a time and place to meet a friend on agiven day in New York City, without any possibility of priorcommunication about where or when to meet. Most respondents chose noonat Grand Central Station. Somehow, then, this choice stands out as themost conspicuous. As Schelling’s example illustrates, salienceis a “subjective” psychological trait that does not followin any obvious way from the rational structure of the strategicsituation. Hume already anticipated a role for subjectivepsychological traits, noting that our choice of convention oftendepends upon “the imagination, or the more frivolous propertiesof our thought and conception” (Treatise, p. 504, note1).

Salience plays two distinct roles in Lewis’s account,corresponding to the following two questions:How do conventionsarise? andWhy do people conform to convention? Theformer question concerns dynamics (i.e., the factors governing howconventions originate and evolve over time), while the latter concernsstatics (specifically, the rational structure that sustains aconvention at a given moment). Lewis’s answer to the firstquestion is that agents initially select some equilibrium either bychance, agreement, or intrinsic salience. The equilibrium graduallybecomes more salient through precedent, until eventually it becomes aconvention. Lewis’s answer to the second question is that apre-existing convention is so overwhelmingly salient that agentsexpect one another to abide by it, an expectation which furnishesreason to conform.

Philosophers have heavily criticized Lewis’s reliance uponsalience, arguing that the notion of salience is obscure, or thatthere is often no salient option among candidate conventions, or thatprecedence does not confer salience, or that Lewis fails to integratesalience into the formal game-theoretic framework that otherwiseshapes his discussion. Margaret Gilbert (1989) argues that saliencecannot provide a reason for action: merely observing that somepossible convention is salient tells us nothing, because we cannotassume that others will abide by the most salient convention. In asimilar vein, Brian Skyrms (1996) asks how it comes to be commonknowledge that others will choose the salient equilibrium over thealternatives.

Despite these criticisms, many authors over the intervening decades,such as Robert Sugden (1986/2004, 2011) and Ken Binmore and LarrySamuelson (2006), have argued that a satisfactory theory ofequilibrium selection requires something like Lewis’s notion ofsalience. Note also that, even if the foregoing criticisms arelegitimate, they do not impugn Lewis’s analysis of whatconventionsare. They only show that Lewis has not offered acomplete theory of how conventions are chosen, how they evolve, andhow they sustain themselves.

5.2 Dynamical models

Another popular approach to equilibrium selection is broadlydynamical. The dynamical approach, a branch of evolutionarygame theory, develops formal models of how strategy choice evolves ina population whose members repeatedly play some game against eachanother. In contrast with “static” game theory (i.e., thestudy of equilibria), dynamical models incorporate an explicitlytemporal parameter. The basic goal is to study the conditions underwhich dynamical models with various properties tend to converge tostatic equilibria with various properties.

Dynamical models of equilibrium selection differ along severaldimensions. Does the model depict learning by individual players oraggregate trends in the population as a whole? How much rationalitydoes the model attribute to players? Is the model deterministic orstochastic? Do players have limited or unlimited memory of pastevents? How much common knowledge do players have about thegame’s payoff structure? Can players learn about the results ofinteractions in which they do not participate? Do the same playersparticipate in each round of play, or are the players repeatedly drawnanew from a larger population? Is that larger population modeled asfinite or infinite? An overview of the burgeoning and forbiddinglytechnical literature on these questions falls beyond the scope of thisarticle. We confine attention here to three developments: replicatordynamics; fictitious play; and sophisticated Bayesian learning.Interested readers should consult the detailed surveys offered by DrewFudenberg and David Levine (1998) and H. Peyton Young (2004).

Replicator dynamics: In this deterministic model, introducedby Peter Taylor and Leo Jonker (1978), the proportion of playerschoosing some strategy grows proportionally to the difference betweenthat strategy’s mean payoff and the mean payoff for thepopulation as a whole. The model does not describe how the behavior ofindividual players changes over time. Rather, the model describesaggregate trends in the population as a whole.

Astable steady state of a dynamical system is a state \(s\)with the following two features: once the system enters \(s\), itnever leaves it; and once the system approaches “closeenough” to \(s\), then it always remains near \(s\). Thebasin of attraction of \(s\) is the set of states such that,if the dynamical system begins in one of those states, then it willeventually converge towards \(s\). In many cases, the best way tounderstand a dynamical system is to construct a “phaseportrait” diagramming its steady states and their basins ofattraction. In the case of interest to us here, the“state” of a dynamical system is simply the proportion ofplayers choosing each strategy.

Two easy formal results convey the flavor of research on replicatordynamics: every stable steady state of replicator dynamics is a Nashequilibrium; and every evolutionarily stable equilibrium is a stablesteady state of replicator dynamics.

Replicator dynamics originated within evolutionary biology.Subsequently, game theorists such as Larry Samuelson (1997) haveargued that it illuminates social interaction among humans. Withinphilosophy, Brian Skyrms (1996, 1998) argues that replicator dynamicsshows how conventions of property and linguistic meaning could evolvewithout any need for Lewisian “salience.” He placesparticular emphasis uponsignaling games, that is, games inwhich a sender wishes to communicate a message to a receiver, amessage determining which action from among a fixed repertoire thereceiver will perform. (Seesection 7.1 for more detail on signaling games.) For certain signaling games,replicator dynamics almost always converges to an evolutionarilystable signaling convention. Which convention emerges depends solelyupon chance facts about players’ initial propensities to adoptvarious strategies (i.e., the basin of attraction from which thesystem happens to begin). As Skyrms puts it, “[w]hichsignaling system is selected is a matter of chance, not ofsalience” (1996, p. 93).

Despite the popularity of replicator dynamics, critics such as H.Peyton Young (1998) remain skeptical. The most natural motivation forreplicator dynamics is biological. We conceptualize players as animalsgenetically programmed to exhibit certain behaviors. Creatures whoachieve higher payoffs have higher reproductive fitness, and they passtheir strategy choices along to their progeny. Natural selectiontherefore causes certain behaviors to become more prevalent. Underthese assumptions, replicator dynamics seems plausible. But it is notclear that a comparable rationale applies to human interaction, sincehumans generally act not based solely upon their genetic programmingbut rather upon their beliefs and desires. Why should the choices ofindividual human agents yield the pattern described by replicatordynamics?

In response to this worry, theorists try to derive replicator dynamicsfrom models of individual adaptive behavior. Some models posit thatpeople tend to imitate the behavior of others, based either on howpopular or how successful that behavior seems. Other models posit somekind of reinforcement mechanism. Neither approach accords very wellwith the traditional preference among both philosophers and economistsforrational explanations. Samuelson (1997, p. 23) respondsthat such approaches may nevertheless be appropriate “if we areinterested in people, rather than ideally rational agents.” Butit is hardly obvious that our best cognitive science of actual humanpsychology will eschew rational explanation in favor of thepsychological mechanisms currently being invoked to underwritereplicator dynamics.

Fictitious play: George Brown (1951) introduced fictitiousplay as “pre-play” reasoning, in which a player mentallysimulates repeated trials of a game against an imaginary opponent soas to predict her real opponent’s actions. The phrase“fictitious play” has become a misnomer, becauseresearchers now typically apply it to models in which players learnbased upon their actual experience of repeated play. In paradigmaticfictitious play models, each player plays a “best reply”to the observed historical frequency of her opponents’ pastactions. This policy is rational if: the player assumes that eachopponent plays some stationary (either pure or mixed) strategy; theplayer employs Bayesian updating to determine the probability thateach opponent will perform a given action in the next round; and theplayer seeks to maximize her expected payoff for that round based uponher current probability distribution over her opponents’actions. It is easy to show that, if players engaged in fictitiousplay enter into a strict Nash equilibrium, then they stay in itforever. Moreover, there are some circumstances (e.g., zero-sumtwo-person games) in which fictitious play converges to Nashequilibrium behavior. However, as Lloyd Shapley (1964) first showed,there are games in which fictitious play does not always converge toequilibrium behavior.

The literature explores many different variations on this theme. Onecan restrict how many past trials the player remembers or how muchweight the player places upon older trials. One can embed the playerin a large population and restrict how much a player knows aboutinteractions within that population. One can introduce a“neighborhood structure,” so that players interact onlywith their neighbors. One can introduce a stochastic element. Forinstance, building on work of M. I. Friedlin and A. D. Wentzell (1984)and Michihiro Kandori, George Mailath, and Rafael Rob (1993), H.Peyton Young (1993, 1996, 1998) develops a model of how conventionsevolve in which each player chooses a “best reply” withprobability \(1-\varepsilon\) and some random strategy withprobability \(\varepsilon\). One can also generalize the fictitiousplay framework to accommodate correlated equilibrium. PeterVanderschraaf (2001) explores a variant of fictitious play in which aplayer frames hypotheses about correlations between heropponents’ strategies and external events. Applying thisframework to convention, he argues that we can treat the emergence ofcorrelated equilibrium conventions as an instance of rationalbelief-fixation through inductive deliberation.

Fictitious play does not attribute knowledge of other people’spayoffs or their rationality. It does not depict players as reasoningabout the reasoning of others. Instead, it depicts players asperforming a mechanical statistical inference that converts anaction’s observed historical frequency into a prediction aboutits future probability of recurrence. For this reason, critics such asEhud Kalai and Ehud Lehrer (1993) contend that fictitious playattributes to players insufficient recognition that they are engagedinstrategic interaction. For instance, a player who reasonsin accord with fictitious play implicitly assumes that each opponentplays some stationary (either pure or mixed) strategy. This assumptionoverlooks that her opponents are themselves updating their beliefs andactions based upon prior interaction. It also prevents players fromdetecting patterns in the data (such as an opponent who plays onestrategy in odd-numbered trials and another strategy in even-numberedtrials). Moreover, fictitious play instructs a player to maximize herexpected payoff for thecurrent round of play. This“myopic” approach precludes maximizing one’s futureexpected payoff at the price of lowering one’s current payoff(e.g., playing Hawk rather than Dove even if I expect my opponent todo likewise, since I believe that I can eventually “teach”my opponent to back down and play Dove in future rounds).

Sophisticated Bayesian learning: This approach, initiated byPaul Milgrom and John Robert (1991), replaces the rather crudestatistical inference posited by fictitious play with a more refinedconception of inductive deliberation. Specifically, it abandons thequestionable assumption that one faces stationary strategies fromone’s opponents. Ehud Kalai and Ehud Lehrer (1993) offer awidely discussed model of sophisticated Bayesian learning. Playersengaged in an infinitely repeated game constantly update probabilitydistributions defined over the set of possible strategies played bytheir opponents, where a strategy is a function from the set ofpossible histories to the set of possible actions. At each stage, aplayer chooses an action that maximizes the expected value of herpayoffs for theentire future sequence of trials, not justfor the present trial. This approach allows a player to discernpatterns in her opponents’ behavior, including patterns thatdepend upon her own actions. It also allows her to sacrifice currentpayoff for a higher expected long-term payoff. Kalai and Lehrer provethat their procedure almost always converges to somethingapproximating Nash equilibrium, under the crucial assumption (the“grain of truth” assumption) that each player begins byassigning positive probability to all strategies that actuallyoccur.

Critics such as John Nachbar (1997) and Dean Foster and H. PeytonYoung (2001) argue that there is no reason to accept the “grainof truth” assumption. From this perspective, Kalai and Lehrermerely push the problem back to explaining how players converge upon asuitable set of prior probabilities satisfying the “grain oftruth” assumption. Although Kalai and Lehrer’s proofactually requires only a somewhat weakened version of this assumption,the problem persists: sophisticated Bayesian learning converges toNash equilibrium only under special assumptions about players’prior coordinated expectations, assumptions that players might wellfail to satisfy.

Sanjeev Goyal and Maarten Janssen (1996) develop this criticism,connecting it with the philosophical problem of induction, especiallyNelson Goodman’s grue problem. Robert Sugden (1998, 2011)further develops the criticism, targeting not just sophisticatedBayesian learning but virtually every other learning model found inthe current literature. As the grue problem highlights, there are manydifferent way of extrapolating past observations into predictionsabout the future. In philosophy of science, the traditional solutionto this difficulty is that only certain predicates are“projectible.” But Sugden argues that the difficulty ismore acute for strategic interaction, since successful coordinationrequires shared standards of projectibility. For instance, supposethat I repeatedly play a coordination game with an opponent who hastwo different strategy options: \(s_{1}\) and \(s_{2}\). Up until time\(t\), my opponent has always played \(s_{1}\). I might“project” this pattern into the future, predicting that myopponent will henceforth play \(s_{1}\). But I might instead project a“grueified” pattern, such as: “play \(s_{1}\) untiltime \(t\), and then play \(s_{2}\).” Which inductive inferenceI make depends upon which predicates I regard as projectible. There isno guarantee that my opponent shares my standards of projectibility.In effect, then, convergence through inductive deliberation requiresme and my opponent to solve a new coordination problem: coordinatingour standards of projectibility. According to Sugden, existingdynamical models implicitly assume that players have already solvedthis new coordination problem. Sugden concludes that a fullexplanation of equilibrium selection requires something likeLewis’s notion of salience. In particular, it requires sharedpsychological standards regarding which patterns are projectible andwhich are not. Sugden urges, contra Skyrms, that dynamical models ofconvention cannot displace salience from its central role inunderstanding convention.^[7]

5.3 Experimental methods

An increasingly active research tradition uses experimental methods toinvestigate equilibrium selection. The typical goal is to study howclosely human subjects conform to the predictions of some formalmodel. In that spirit, Justin Bruner, Cailin O’Connor, HannahRubin, and Simon Huttegger (2018), building on work of Andreas Blume,Douglas DeJong, Yong-Gwan Kim, and Geoffrey Sprinkle (1998), show thatactual human behavior in several small group signaling games fits wellwith the predictions of replicator dynamics. This study, along withother related studies (e.g. Calvin Cochran and Jeffrey Barrett(2021)), provides empirical evidence that signaling conventions canemerge through “low-rationality” dynamics in at least somecircumstances. Other empirical studies suggest a more significant rolefor high-level rational cognition. For example, Robert Hawkins,Michael Franke, Michael C. Frank, Adele Goldberg, Kenny Smith, ThomasGriffiths, and Noah Goodman (2023) give a Bayesian model ofcommunicative interaction and linguistic convention formation. Throughcomputer simulations coupled with behavioral experiments, they showthat the model can accommodate several phenomena that are otherwisedifficult to explain, such as communicative conventions tailored tospecific interlocutors. We may expect future empirical research toshed further light upon the extent to which various conventionsimplicate high-level rationality as opposed to relatively low-levelpsychological mechanisms.

As the foregoing discussion indicates,equilibrium selection is a diverse, fast-growing area of study.Moreover, it raises difficult questions on the boundary betweeneconomics, philosophy, and psychology, such as how to analyzeinductive reasoning, how much rationality to attribute to socialagents, and so on. It is undeniable that, in a wide variety ofcircumstances, people successfully converge upon a single uniqueconvention amidst a range of alternatives. It seems equally undeniablethat we do not yet fully understand the social and psychologicalmechanisms that accomplish this deceptively simple feat.

6. Alternative treatments of convention

We now survey some alternative theories of convention proposed in thepast few decades. Unlike the rival proposals discussed in section 4,which accept Lewis’s basic perspective while emending variousdetails, the theories discussed below reject Lewis’s entireapproach.

6.1 Gilbert: plural subjects

Eschewing Lewis’s game-theoretic orientation, Margaret Gilbert(1989) instead draws inspiration from sociology, specifically fromGeorg Simmel’s theory of “social groups” (1908). Thebasic idea is that individual agents can “join forces” toachieve some common end, thereby uniting themselves into a collectiveentity. To develop this idea, Gilbert provides a complex account ofhow agents bind themselves into a “plural subject” ofbelief and action. A plural subject is a set of agents who regardthemselves as jointly committed to promoting some goal, sharing somebelief, or operating under some principle of action. By virtue oftheir common knowledge of this joint commitment, members of the pluralsubject regard themselves as “we”. They thereby regard oneanother as responsible for promoting the group’s goals andprinciples. For instance, two traveling companions make manifest theircommitment to keep track of one another, whereas two people who happento share a seat on a train do not. The traveling companions form aplural subject. The unaffiliated travelers do not. The travelingcompanions regard each other as responsible for helping if one personfalls behind, for not losing one another in a crowd, and so on.

Gilbert proposes that “our everyday concept of a socialconvention is that of a jointly accepted principle of action, a groupfiat with respect to how one is to act in certain situations”(p. 377). Members of a populationjointly accept a fiat whenit is common knowledge that they have made manifest their willingnessto accept and promote that fiat as a basis for action. ByGilbert’s definition, participants in a convention constitute aplural subject. For they jointly accept the common goal of promotingsome fiat. Moreover, members of the social group regard the fiat asexerting normative force simply by virtue of the fact that theyjointly accept it. Note that not all plural subjects instantiateconventions. For instance, depending on the details of the case, thetraveling companions from the previous paragraph might not. Aconvention arises only when individual members of a plural subjectjointly accept some fiat.

Gilbert’s account differs from Lewis’s in bothontology andideology. Ontologically, Gilbertisolates asui generis entity, the plural subject, thatLewis’s “individualistic” approach does notcountenance. Gilbert argues that a population could instantiate aLewisian convention without giving rise to a plural subject.Participants in a Lewisian convention mayprefer that otherparticipants conform to it, given that almost everyone does. But theyneed not regard themselves asresponsible for enforcing it orfor helping others conform. They would so regard themselves if theyviewed themselves as belonging to a plural subject. Thus, a Lewisianconvention does not ensure that its adherents constitute a pluralsubject.

Regardingideology, Gilbert’s account attributes toconvention an intrinsically normative element that Lewis rejects. ForGilbert, adopting a convention is making manifest a willingness topromote a certain fiat. Parties to a convention therefore accept thattheyought to act in accord with the fiat. In contrast, as wesaw in section 4.2, Lewis’s account does not recognize anynormative elements as intrinsic to convention.

The contrast between Gilbert and Lewis instantiates a more generaldebate overHomo economicus: a conception of agents asself-interested and instrumentally rational. Lewis attempts to analyzesocial phenomena reductively within that framework. In contrast,Gilbert rejects the rational choice conception, opting for a picture,Homo sociologicus, according to which an agent acts based onher self-identification as a member of a social group constituted byvarious norms. Elizabeth Anderson (2000) analyzes how the clashbetween these two conceptions relates to convention andnormativity.

In her later work, Gilbert (2008) adopts a more concessive stancetowards Lewis’s analysis of convention. She maintains that heranalysis handles many important social phenomena that Lewis’saccount overlooks, but she grants that there may be other socialphenomena that Lewis’s account handles well.

6.2 Miller: collective ends

Seumas Miller (2001) introduces the notion of a “collectiveend.” A collective end is an end that is shared by a group ofagents and that can be achieved only through action by all of thoseagents; moreover, these facts are mutually believed by the agents. Aconvention to \(j\) in some recurring situation \(s\) prevails amongsome agents iff it is mutually believed by the agents that each onehas a standing intention to \(j\) in \(s\), as long as others perform\(j\) in \(s\), so as to realize some shared collective end \(e\). Forinstance, the collective end corresponding to the convention ofdriving on the right side of the road is avoiding collisions.

In many respects, Miller’s account is more similar toLewis’s than to Gilbert’s. Miller shares Lewis’s“reductionist” perspective, analyzing social convention asa pattern of interaction between rational agents, without anyirreducibly “social” element. In particular, Millerrejectssui generis social entities, such as plural subjects,and he does not invoke specialized norms of convention beyond thoseengendered by morality and rationality.

One objection to Miller’s account is that, in many cases, thereis no clear “collective end” subserved by convention. Forinstance, what collective end must participants in a monetary practiceshare? It seems that each agent might care only about his ownindividual welfare, without concern for some more general social end.Even where there is a clear collective end served by some convention,should we really build this fact into thedefinition ofconvention? As Burge observes, “parties to a convention arefrequently confused about the relevant ends (the social functions oftheir practice); they are often brought up achieving them and do notknow the origins of their means” (1975, p. 252). Thus, it mightseem that Miller attributes too much self-understanding toparticipants in a convention.

6.3 Millikan: patterns sustained by weight of precedent

Ruth Millikan (2005) offers a radical alternative to the viewssurveyed so far. She draws inspiration not from economics or sociologybut from biology. On her view, a convention is a pattern of behaviorreproduced within a population due largely to weight ofprecedent. To say that an instance of some pattern“reproduces” previous instances is to say that, if theprevious instance had been different, the current instance would becorrespondingly different. Many patterns of behavior are“reproduced” in this sense, such as the propensity togreet one another by shaking hands in a certain way. However, not allreproduced patterns are conventions. For instance, we learn from ourparents to open stuck jars by immersing them in hot water, but ourreproduction of this pattern is not a convention. To count as aconvention, a reproduced pattern must be reproduced, in large part,simply because it is a precedent, not because of its intrinsic merits.Thus, a convention is unlikely to emerge independently in differentpopulations, in contrast with a pattern such as immersing stuck jarsin hot water.

Through what mechanisms does convention spread “by weight ofprecedent”? Millikan mentions several ideas: lack ofimagination, desire to conform, playing it safe by sticking with whathas worked. The use of chopsticks in the East and forks in the Westillustrates how obeying precedent is often the most practical policy,since these respective implements are more readily available in therespective locations.

Perhaps the most striking aspect of Millikan’s discussion isthat it assigns no essential role to rationality in sustainingconventions. For instance, a society in which people maintain aconvention simply from unreflective conformism would satisfyMillikan’s definition. The tradition established by Hume andcontinued by Lewis seeks to explain how social order emerges from therational decisions of individual agents. Millikan rejects thattradition. To some extent, Burge also departs from the tradition,writing that “the stability of conventions is safeguarded notonly by enlightened self-interest, but by inertia, superstition, andignorance” (p. 253). However, Millikan’s position is moreextreme than Burge’s, since she assigns reason no role insustaining convention. In other words, whereas Burge apparently thinksthat convention rests upon both rational and irrational underpinnings,Millikan does not acknowledge any rational underpinnings.

7. Conventions of language

Plato’sCratylus offers a notable early discussion oflinguistic convention. Hermogenes defends a broadly conventionalistview of linguistic meaning:

[N]o one is able to persuade me that the correctness of names isdetermined by anything besides convention… No name belongs to aparticular thing by nature, but only because of the rules and usagesof those who establish the usage and call it by that name, (384c-d)

while Cratylus advocates a rather obscure anti-conventionalistalternative:

A thing’s name isn’t whatever people agree to call it—some bit of their native language that applies to it—butthere is a natural correctness of names, which is the same foreveryone, Greek or foreigner (383a-b).

Nowadays, virtually all philosophers side with Hermogenes. Barring afew possible exceptions such as onomatopoeia, the association betweena word and its referent is not grounded in the intrinsic nature ofeither the word or the referent. Rather, the association isarbitrary. In this weak sense, everyone agrees that languageis conventional. However, disagreement persists about whether socialconvention plays a useful role in illuminating the workings oflanguage.

7.1 Conventional theories of meaning

David Lewis (1969) provides the first systematic theory of how socialconvention generates linguistic meaning. Subsequent philosophers tooffer convention-based accounts include Jonathan Bennett (1976), SimonBlackburn (1984), Wayne Davis (2003), Ernie Lepore and Matthew Stone(2015), Brian Loar (1976), and Stephen Schiffer (1972).

Lewis begins by studyingsignaling problems. Acommunicator has privileged information differentiating amongstates \(s_{1},\ldots, s_{m}\).Audience members can chooseamong responses \(F(s_{1}), \ldots, F(s_{m})\). Everyone prefers thataudience members do \(F(s_{i})\) if \(s_{i}\) obtains. There is a setof signals \(x_{1},\ldots,x_{n}\), \(m \le n\), that the communicatorcan pass to the audience. In Lewis’s example, the sexton knowswhether the redcoats are staying home, coming by land, or coming bysea. By placing either zero, one, or two lanterns in the belfry, hesignals Paul Revere whether to go home, warn people that redcoats arecoming by land, or warn people that the redcoats are coming by sea. Asignaling problem is a coordination problem, because communicator andaudience must coordinate so that the communicator’s signalelicits the mutually desired action. Building on Lewis’sdiscussion, Skyrms (2010) offers an intensive analysis of signalingproblems, with applications to diverse biological cases studiesranging from bacteria to apes.

In comparison with normal linguistic interaction, signaling problemsare very specialized. A fundamental difference is that people normallyneed not agree upon which action(s) would be desirable, given somestate of affairs. When we search for an audience reaction canonicallyassociated with an assertion that \(p\), the most natural candidate issomething likebelieving that \(p\) (or perhaps believingthat the speaker believes \(p)\). Yet coming to believe a propositionis not an action, and Lewis’s definition of conventionpresupposes that conventions are regularities of action. Hence,believing what people say cannot be part of a Lewisian convention.

Although Lewis explored various ways around this difficulty, heeventually concluded that we should alter the analysis of convention.In “Languages and Language” (1975/1983), he broadened theanalysis so that regularities of actionand belief couldserve as conventions. Clause (4) of Lewis’s definition entailsthat everyone prefers to conform to the convention given that everyoneelse does. Preferences regarding one’s own beliefs are dubiouslyrelevant to ordinary conversation. Thus, in his revised analysis,Lewis substitutes a new clause:

The expectation of conformity to the convention gives everyone a goodreason why he himself should conform. (p. 167)

The “reason” in question might be either apractical reason, in the case of action, or anepistemic reason, in the case of belief.

Lewis defines alanguage as a function that assignstruth-conditions to sentences. More precisely, and ignoringcomplications such as vagueness and indexicality, a language \(L\) isa mapping that assigns each sentence \(s\) a set of possible worlds\(L(s)\). A sentence \(s\) is “true in \(L\)” iff theactual world belongs to \(L(s)\). There are infinitely many possiblelanguages. We must explain what it is for a given group of agents touse a given language. In other words, what is the “actuallanguage” relation? Lewis proposes:

A language \(L\) is used by a population \(G\) iff there prevails in\(G\) a convention of truthfulness and trust in \(L\), sustained by aninterest in communication,

where a speaker is “truthful in \(L\)” iff she tries toavoid uttering sentences not true in \(L\), and a speaker is“trusting in \(L\)” iff she believes that sentencesuttered by other speakers are true in \(L\). Given that thisconvention prevails, speakers who want to communicate have reason toconform to it, which in turn perpetuates the convention. Note thatLewis’s account avoids the Russell-Quine regress argument fromsection 1.1, since Lewisian convention does not presuppose explicit agreementbetween participants.

In many respects, Lewis’s account descends from Grice’stheory of speaker-meaning. A simplified version of Grice’saccount runs as follows: a speakerspeaker-meansthat \(p\) iff she performs an action with an intention of inducingthe belief that \(p\) in her audience by means of their recognition ofthat very intention. Although Lewis does not explicitly buildspeaker-meaning into his analysis of the “actual language”relation, a broadly Gricean communicative mechanism informs hisdiscussion. Like Grice, Lewis emphasizes how meaning emerges fromcoordination between the speaker’s communicative intentions andthe hearer’s communicative expectations. Grice does not providea very compelling account of how speakers and hearers coordinate theircommunicative intentions and expectations by exploiting apre-existing practice. Lewis fills this lacuna by citing astanding convention of truthfulness and trust.

Stephen Schiffer (1972) and Jonathan Bennett (1976) offer alternative“neo-Gricean” accounts that combine Lewisian conventionwith more explicit appeal to Gricean speaker-meaning. In effect, boththeories are sophisticated variants upon the following:

Sentence \(s\) means that \(p\) as used by population \(G\) iff thereprevails in \(G\) a convention to use utterances of \(s\) so as tospeaker-mean that \(p\).

Thus, both accounts analyze sentence meaning as the result of aconvention that certain sentences are used to communicate certainpropositions.

A fundamental question for philosophy of language is how meaningarises from use. How do we confer significance upon inherentlymeaningless linguistic expressions by employing them in linguisticpractice? Neo-Gricean accounts such as Lewis’s,Schiffer’s, and Bennett’s provide detailed answers to thisquestion. For instance, Lewis isolates a self-perpetuatingcommunicative mechanism that systematically associates sentences withpropositional contents. He reduces social convention to thepropositional attitudes of individual speakers, and he then usessocial convention to explain how meaning arises from use. He therebydepicts linguistic expressions as inheriting content from antecedentlycontentful propositional attitudes. On this approach, thought is theprimary locus of intentionality, and language enjoys intentionalcontent merely in a derivative way, through its employment incommunicative transactions. That general view of the relation betweenlanguage and thought goes back at least to Book III of Locke’sEssay on Human Understanding. It is currently quite popular.Much of its popularity stems from the widespread perception thatLewis’s account, or some other such account, successfullyexplains how language inherits content from thought.

7.2 Objections to conventional theories

Conventional theories of linguistic meaning attract several differenttypes of criticism. We may distinguish four especially importantcriticisms: denial that the putative conventions prevail in actualpractice; denial that convention can determine linguistic meaning;denial that convention is necessary for linguistic meaning; and denialthat convention-based accounts employ the proper order ofexplanation.

7.2.1 Do the putative conventions prevail?

This criticism surfaces repeatedly throughout the literature. Forinstance, Grice’s analysis of speaker-meaning generated amini-industry of counter-example and revised analysis. The gist of thecounter-examples is that there are many perfectly normal linguisticinteractions in which speakers lack the communicative intentions andexpectations cited by Grice. Thus, it is difficult to see how ourpractice could instantiate a convention that crucially involves thoseintentions and expectations. One might respond to this argument invarious ways, such as classifying certain linguistic interactions as“paradigmatic” and others as “derivative.” Butat least one prominent Gricean, Stephen Schiffer (1987), eventuallyconcluded, partly from such counter-examples, that the program ofexplicating linguistic meaning through Lewisian convention and Griceanspeaker-meaning was hopeless.

Regarding Lewis’s account, critics such as Wayne Davis (2003),Max Kölbel (1998), Stephen Laurence (1996), and Bernard Williams(2002) question whether there is a convention of truthfulness andtrust. As Davis and Williams urge, it is hardly obvious that speakersgenerally speak the truth or generally trust one another, despitefrequent claims by diverse philosophers to the contrary. Even if wegrant that people generally speak the truth and generally trust oneanother, does this give me reason to speak truthfully? It does,ifI want other people to believe the truth. But if I want them tobelieve falsehoods, then I have reason to lie rather than speak thetruth. Thus, one might object, a regularity of truthfulness and trustis not self-perpetuating in the way that Lewisian convention requires.Expectation of conformity does not provide reason for conformity. Incontrast, consider the convention of driving on the right. Thatconvention likewise provides reason for conformity only given anappropriate desire: namely, desire to avoid a collision. Thedifference is that virtually everyone seeks to avoid a collision,while deception is a normal feature of ordinary linguisticinteraction.

Inevitably, such objections focus on details of particular theories.Thus, they cannot show that conventionalist theoriesingeneral are mistaken.

7.2.2 Can convention determine linguistic meaning?

The most serious version of this objection, advanced by StephenSchiffer (1993, 2006), John Hawthorne (1990, 1993), and many otherphilosophers, focuses on theproductivity of language. We canunderstand a potential infinity of meaningful sentences. Yet we canhardly master infinitely many linguistic conventions, one for eachmeaningful sentence. How, then, can convention fix the meanings ofthese infinitely many sentences?

This general worry arises in a particularly acute way forLewis’s theory. Consider some sentence \(S\) that we would nevernormally use, perhaps because it is too long or too grammaticallycomplex. Suppose that some speaker nevertheless utters \(S\). As Lewisacknowledges, we would not normally believe that the speaker wasthereby attempting to speak truthfully. Instead, we would suspect thatthe speaker was acting for some deviant reason, such as trying toannoy, or settling a bet, and so on. We would not normally trust thespeaker. But then Lewis cannot use his convention of truthfulness andtrust to underwrite a unique truth-condition for \(S\).

The most natural diagnosis here is that the sentence’s meaningis determined by the meanings of its parts. We understand it becausewe understand its component words and because we understand thecompositional mechanisms through which words combine to formmeaningful sentences. Of course, word meanings may themselves be fixedby convention. But then what the conventionalist should explicate isthe conventional link between words and their meanings, not just theconventional link between sentences and their truth-conditions. Lewisexplicates the latter, not the former. Although Lewis (1992) attemptsto circumvent these worries, Hawthorne (1993) and Schiffer (2006)argue that his response is inadequate.

Lewis’s account is not alone in encountering difficulties withproductivity. Most contemporary conventionalist theories encountersimilar difficulties, because most such theories, heedingFrege’s context principle (only the context of a sentence dowords have meaning), focus attention upon the link between sentencesand propositions rather than the link between words and theirmeanings. One might hope to supplement convention-based accounts withthe Chomsky-inspired thesis, advocated by James Higginbotham (1986)and Richard Larson and Gabriel Segal (1995), that speakers have tacitknowledge of a compositional semantic theory. However, as MartinDavies observes (2003), no one seems to have worked out thissupplementary strategy in any detail, and it is not obvious howimportant a role the resulting account would assign to convention, letalone the Gricean communicative mechanism.

Ultimately, the force of these worries remains unclear. For instance,Wayne Davis (2003) develops a conventionalist account that harkensback to the pre-Fregean tradition. In simplified form, Davis’sLockean proposal is that a word is meaningful because weconventionally use it to express a certain “idea”. Themeaning of a sentence is then determined by the meanings of itscomponent words, along with the (conventionally determined) semanticimport of the syntactic structure in which those words are arranged.Evidently, these issues connect with vexed questions aboutcompositionality, linguistic understanding, the unity of theproposition, and the role played by formal semantic theories in thestudy of natural language.

7.2.3 Is convention necessary for linguistic meaning?

Noam Chomsky (1980) and Donald Davidson (1984) acknowledge that thereare linguistic conventions while denying that they are fundamental tothe nature of language.

Chomsky regards language as a system of grammatical rules“tacitly known” by a speaker. Linguistics, which Chomskytreats as a branch of cognitive psychology, studies the grammaticalcompetence of individual speakers. It should not posit a mysteriousand unscientific “communal language” shared by speakers,but should instead focus upon “idiolects.” Thus, languagehas no special ties to social interaction or communication.Specifically, it has no special ties to convention. Stephen Laurence(1996) and Stephen Schiffer (2006) develop theories of the“actual language” relation informed by a broadly Chomskianperspective. The basic idea behind both accounts is that a linguisticitem as used by some speaker is associated with certain semanticproperties just in case the association between the linguistic itemand the semantic property figures in the psychological processesthrough which the speaker assigns meanings (or truth-conditions) tosentences.

Davidson elaborates a model of communication that takes as itsparadigm “radical interpretation.” During radicalinterpretation, one tries to assign truth-conditions to utterances ina completely unfamiliar tongue. To do so, one detects patternsconcerning which sentences the speaker “holds true,” andone tries to make rational sense of those patterns, guided by generalmaxims such as theprinciple of charity (roughly, maximizetrue beliefs on the part of the speaker). Davidson admits that, ineveryday life, we tend as a default to interpret one another“homophonically.” But there is no principled reason why wemust embrace this homophonic default, and we readily deviate from itwhenever seems appropriate, as illustrated by cases of idiosyncraticusage, malapropism, and so on. In a sense, then, all linguisticunderstanding rests upon radical interpretation. So shared linguisticconventions are inessential to linguistic communication:

Knowledge of the conventions of language is thus a practical crutch tointerpretation, a crutch we cannot in practice afford to dowithout—but a crutch which, under optimum conditions forcommunication, we can in the end throw away, and could in theory havedone without from the start. (1984, p. 279)

Davidson concludes that theories of meaning and understanding shouldnot assign convention a foundational role.

7.2.4 Do convention-based accounts employ the proper order of explanation?

A final objection to convention-based theories targets the broaderLockean strategy of explaining language in terms of thought. Accordingto this objection, which is espoused by philosophers such as RobertBrandom (1994), Donald Davidson (1984), and Michael Dummett (1993),language does not inherit content from thought. Rather, thought andlanguage are on a par, acquiring content through their mutualinterrelations. (One might also claim that language is the primarylocus of intentionality and that thought inherits content fromlanguage. However, few if any contemporary philosophers espouse thisviewpoint.) Thus, we should not analyze linguistic meaning as theproduct of convention, so long as conventions are understood asLewisian systems of intentions, preferences, and expectations. Thosepropositional attitudes are themselves intelligible only through theirrelations to language. As Davidson puts it, “philosophers whomake convention a necessary element in language have the matterbackwards. The truth is rather that language is a condition for havingconventions” (1984, p. 280).

Two main difficulties face this approach. First, although philosophershave offered various arguments for the thesis that thought is notexplanatorily prior to language, none of the arguments commandswidespread assent. Christopher Peacocke (1998) forcefully criticizesmany of the most well-known arguments. As things stand, the objectionconstitutes not so much aproblem for conventional theoriesas a prospectus for a rival research program. The second and moreserious difficulty is that, so far, the rival research program has notyielded results nearly as precise or systematic as existingconventional theories. Perhaps the two most commanding theories withinthe rival research program are Davidson’s (1984) andBrandom’s (1994). Many contemporary philosophers feel that boththeories enshrine an overly “anti-realist” conception ofmental content. Moreover, neither theory yields detailed necessary andsufficient conditions for linguistic meaning analogous to thoseprovided by Lewis.

Bibliography

• Alston, William, 2000.Illocutionary Acts and SentenceMeaning, Ithaca: Cornell University Press.
• Anderson, Elizabeth, 2000. “BeyondHomo Economicus:New Developments in Theories of Social Norms,”Philosophyand Public Affairs, 29: 170–200.
• Aristotle, 1980.Nicomachean Ethics, trans. David Ross.Rev. trans. J. L. Ackrill and J. O. Urmson. Oxford: Oxford UniversityPress.
• –––, 1984.De Interpretatione, inThe Complete Works of Aristotle, ed. Jonathan Barnes,Princeton: Princeton University Press.
• Aumann, Robert, 1974. “Subjectivity and Correlation inRandomized Strategies,”Journal of MathematicalEconomics, 1: 67–96.
• –––, 1976. “Agreeing to Disagree,”Annals of Statistics, 4: 1236–1239.
• –––, 1987. “Correlated Equilibrium as anExpression of Bayesian Rationality,”Econometrica, 55:1–18.
• Avramides, Anita, 1997. “Intention and Convention,” inA Companion to the Philosophy of Language, ed. Bob Hale andCrispin Wright, Malden: Blackwell.
• Ayer, A. J., 1936/1952.Language, Truth, and Logic, 2nded., New York: Dover.
• Axelrod, Robert, 1984.The Evolution of Cooperation, NewYork: Basic Books.
• Ben-Menahem, Yemima, 2006.Conventionalism, Cambridge:Cambridge University Press.
• Bennett, Jonathan, 1976.Linguistic Behavior, Cambridge:Cambridge University Press.
• Bicchieri, Cristina, 2006.The Grammar of Society,Cambridge: Cambridge University Press.
• –––, 2016.Norms in the Wild: How toDiagnose, Measure, and Change Social Norms, Oxford: OxfordUniversity Press.
• Binmore, Ken, 2008. “Do Conventions Need to be CommonKnowledge?”Topoi, 27:17–27.
• Binmore, Ken and Samuelson, Larry, 2006. “The Evolution ofFocal Points,”Games and Economic Behavior, 55:21–42.
• Blackburn, Simon, 1984.Spreading the Word, Oxford:Clarendon Press.
• Blume, Andreas, DeJong, Douglas, Kim, Yong Gwan, and Sprinkle,Geoffrey, 1998. “Experimental Evidence on the Evolution ofMeaning of Messages in Sender-Receiver Games,”The AmericanEconomic Review, 88: 1323–1340.
• Brandom, Robert, 1994.Making it Explicit, Cambridge:Harvard University Press.
• Brown, George, 1951. “Iterative Solutions to Games byFictitious Play,” inActivity Analysis of Production andAllocation, ed. T. C. Koopmans, New York: Wiley.
• Bruner, Justin, O’Connor, Cailin, Rubin, Hannah, andHuttegger, Simon, 2018. “David Lewis in the Lab: ExperimentalResults on the Emergence of Meaning,”Synthese, 195:603–621.
• Bunzl, Martin and Kreuter, Richard, 2003. “Conventions Madetoo Simple?”.Philosophy of the Social Sciences 33:417–426.
• Burge, Tyler, 1975. “On Knowledge and Convention,”Philosophical Review, 84: 249–255.
• Carnap, Rudolf, 1937/2002.The Logical Syntax ofLanguage, trans. Amethe Smeaton. Chicago: Open Court Press.
• Chomsky, Noam, 1980.Rules and Representations, New York:Columbia University Press.
• Cochran, Calvin, and Barrett, Jeffrey, 2021. “How SignalingConventions Are Established,”Synthese, 199:4367–4391.
• Coffa, Alberto, 1993.The Semantic Tradition from Kant toCarnap, Cambridge: Cambridge University Press.
• Cubitt, Robin, and Sugden, Robert, 2003. “Common Knowledge,Salience, and Convention: A Reconstruction of David Lewis’s GameTheory,”Economics and Philosophy, 19:175–210.
• Davidson, Donald, 1984. “Convention andCommunication,” inInquiries into Truth andInterpretation, Oxford: Oxford University Press.
• Davies, Martin, 2003. “Philosophy of Language,” inThe Blackwell Companion to Philosophy, ed. Nicholas Bunninand E. P. Tsui-James, Malden: Blackwell.
• Davis, Wayne, 2003.Meaning, Expression, and Thought,Cambridge: Cambridge University Press.
• DiSalle, Robert, 2002. “Conventionalism and Modern Physics:A Reassessment,”Noûs, 36: 169–200.
• Dummett, Michael, 1991.The Logical Basis of Metaphysics,Cambridge: Harvard University Press.
• –––, 1993.The Seas of Language,Oxford: Oxford University Press.
• Einheuser, Iris, 2006. “CounterconventionalConditionals,”Philosophical Studies, 127:459–482.
• Foster, Dean and Young, H. Peyton, 2001. “On theImpossibility of Predicting the Behavior of Rational Agents,”Proceedings of the National Academy of Sciences, 98:12848–12853.
• –––, 2003. “Learning, Hypothesis Testing,and Nash equilibrium,”Games and Economics Behavior,45: 73–96.
• –––, 2006. “Regret Testing: Learning toPlay Nash Equilibrium Without Knowing that You Have anOpponent,”Theoretical Economics, 1:341–367.
• Franssen, Maarten, 2004. “Review of PeterVanderschraaf’s Learning,and Coordination: InductiveDeliberation, Equilibrium, and Convention,”Economicsand Philosophy, 20: 375–416.
• Friedlin, M. I., and Wentzell, A. D., 1984.Randomperturbations of dynamical systems, New York: Springer.
• Friedman, Michael, 1983.Foundations of Space-TimeTheories, Princeton: Princeton University Press.
• –––, 1999.Reconsidering LogicalPositivism, Cambridge: Cambridge University Press.
• Fudenberg, Drew and Levine, David, 1998.The Theory ofLearning in Games, Cambridge, MA: MIT Press.
• Gauthier, David, 1979. “David Hume: Contractarian,”Philosophical Review, 88: 3–38.
• Gilbert, Margaret, 1981. “Game Theory andConvention,”Synthese, 46: 41–93.
• –––, 1983. “Agreements, Conventions, andLanguage,”Synthese, 54: 375–407.
• –––, 1983. “Notes on the Concept of SocialConvention,”New Literary History, 14:225–251.
• –––, 1989.On Social Facts, New York:Routledge.
• –––, 1990. “Rationality, Coordination, andConvention,”Synthese, 84: 1–21.
• –––, 2008. “Social ConventionRevisited,”Topoi, 27: 5–16.
• Gödel, Kurt, 1995. “Is Mathematics Syntax ofLanguage?”. InKurt Gödel: Collected Works, vol.3., ed. Solomon Feferman, John Dawson, Warren Goldfarb, CharlesParsons, and Robert Solovay, Oxford: Oxford University Press.
• Goldfarb, Warren, 1995. “Introductory Note to [Gödel1995],” inKurt Gödel: Collected Works, vol. 3.ed. Solomon Feferman, John Dawson, Warren Goldfarb, Charles Parsons,and Robert Solovay, Oxford: Oxford University Press.
• –––, 1997. “Semantics in Carnap: ARejoinder to Coffa,”Philosophical Topics, 25:51–66.
• Goldfarb, Warren and Ricketts, Thomas, 1992. “Carnap and thePhilosophy of Mathematics,” inScience andSubjectivity, ed. David Bell and Wilhelm Vossenkuhl, Berlin:Akademie.
• Goodman, Nelson, 1976.Languages of Art, Indianapolis:Hackett.
• –––, 1978.Ways of Worldmaking,Indianapolis: Hackett.
• –––, 1989. “Just the Facts,Ma’am!,” InRelativism: Interpretation andConfrontation, ed. Michael Krausz, Notre Dame: University ofNotre Dame Press.
• Goyal, Sanjeev, and Janssen, Maarten, 1996. “Can WeRationally Learn to Coordinate?,”Theory and Decision,40: 29–49.
• Grandy, Richard, 1977. “A Review of Lewis’sConvention: A Philosophy Study,”Journal ofPhilosophy, 74: 129–139.
• Grünbaum, Adolf, 1962. “Geometry, Chronometry, andEmpiricism,” inMinnesota Studies in the Philosophy ofScience, vol. 3. Eds. Herbert Feigl and Grover Maxwell.Minneapolis: University of Minnesota Press.
• Harman, Gilbert, 1996. “Moral Relativism,” inMoral Relativism and Moral Objectivity, ed. Gilbert Harmanand J.J. Thompson, Cambridge: Blackwell.
• Harsanyi, John, and Selten, Reinhard, 1988.A General Theoryof Equilibrium Selection, Cambridge, MA: MIT Press.
• Hawkins, Robert, Franke, Michael, Frank, Michael C., Goldberg,Adele, Smith, Kenny, Griffiths, Thomas, and Goodman, Noah, 2023.“From Partners to Populations: A Hierarchical Bayesian Accountof Coordination and Convention,”Psychological Review,130: 977–1016.
• Hawthorne, John, 1990. “A Note on ‘Languages andLanguage,’”Australasian Journal of Philosophy,68: 116–118.
• –––, 1993. “Meaning and Evidence: A Replyto Lewis,”Australasian Journal of Philosophy, 71:206–211.
• Higginbotham, James, 1986. “Linguistic Theory andDavidson’s Program in Semantics,” inTruth andInterpretation, ed. Ernest Lepore. New York: Blackwell.
• Hume, David, 1740/1976.A Treatise of Human Nature, ed.L. A. Selby-Brigge, revised 3^rd edn., ed. P. H. Nidditch,Oxford: Clarendon Press.
• –––, 1777/ 1975.Enquiries Concerning HumanUnderstanding and Concerning the Principles of Morals, ed. by L.A. Selby-Brigge, revised 3^rd edn., ed. P. H. Nidditch,Oxford: Clarendon Press.
• –––, 1741–2/1985. “Of the OriginalContract,” inEssays Moral, Political, and Literary,ed. Eugene Miller, New York: Liberty Press.
• –––, 1752/1994. “Of Money,” inHume: Political Essays, ed. Knud Haakonssen, Cambridge:Cambridge University Press.
• Huttegger, Simon, 2014. “How Much Rationality Do We Need toExplain Conventions?,”Philosophy Compass, 9:11–21.
• Jamieson, Dale, 1975. “David Lewis on Convention,”Canadian Journal of Philosophy, 5: 73–81.
• Kalai, Ehud, and Lehrer, Ehud, 1993. “Rational LearningLeads to Nash Equilibrium,”Econometrica, 61:1019–45.
• Kandori, Michihiro, Mailath, George, and Rob, Rafael, 1993.“Learning, Mutation, and Long-Run Equilibria in Games,”Econometrica, 61: 29–56.
• Kölbel, Max, 1998. “Lewis, Language, Lust, andLies,”Inquiry, 41: 301–315.
• Larson, Richard and Segal, Gabriel, 1995.Knowledge ofMeaning, Cambridge, MA: MIT Press.
• Laurence, Stephen, 1996. “A Chomskian Alternative toConvention-Based Semantics,”Mind, 105:269–301.
• Lepore, Ernie, and Stone, Matthew, 2015.Imagination andConvention, Oxford: Oxford University Press.
• Lewis, David, 1969.Convention, Cambridge: HarvardUniversity Press.
• –––, 1975/1983. “Languages andLanguage,” Reprinted inPhilosophical Papers, vol. 1.Oxford: Oxford University Press.
• –––, 1976/2000. “Convention: Reply toJamieson,” Reprinted inPapers in Ethics and SocialPhilosophy, Cambridge: Cambridge University Press.
• –––, 1992/2000. “Meaning Without Use:Reply to Hawthorne,” Reprinted inPapers in Ethics andSocial Philosophy, Cambridge: Cambridge University Press.
• Loar, Brian, 1976. “Two Theories of Meaning,” inTruth and Meaning, ed. Gareth Evans and John McDowell,Oxford: Oxford University Press.
• Locke, John, 1689/1975.An Essay Concerning the HumanUnderstanding, ed. Peter Nidditch, Oxford: Clarendon Press.
• –––, 1689/1988.Two Treatises ofGovernment, ed. Peter Laslett, Cambridge: Cambridge UniversityPress.
• Marmor, Andrei, 1996. “On Convention,”Synthese, 107: 349–371.
• –––, 2007. “Deep Conventions. ”Philosophy and Phenomenological Research, 74:586–610.
• –––, 2009.Social Conventions,Princeton: Princeton University Press.
• Maynard Smith, John, and Price, George, 1973. “The Logic ofAnimal Conflicts,”Nature, 146: 15–18.
• Milgrom, Paul, and Robert, John, 1991. “Adaptive andSophisticated Learning in Normal Form Games,”Games andEconomics Behavior, 3: 82–100.
• Miller, Seumas, 1986a. “Truthtelling and the Actual LanguageRelation,”Philosophical Studies, 49:281–94.
• –––, 1986b. “Conventions, Interdependenceof Action, and Collective Ends,”Nous, 20:117–140.
• –––, 1990. “RationalizingConventions,”Synthese, 84: 23–41.
• –––, 2001.Social Action: A TeleologicalAccount. Cambridge: Cambridge University Press.
• Millikan, Ruth, 2005.Language: A Biological Model,Oxford: Clarendon Press.
• –––, 2008. “A Difference of SomeConsequence Between Conventions and Rules,”Topoi, 27:87–99.
• Moore, Richard, 2013. “Imitation and ConventionalCommunication,”Biology and Philosophy, 28:481–500.
• Murphy, Liam and Nagel, Thomas, 2002.The Myth ofOwnership, Oxford: Oxford University Press.
• Nachbar, John, 1997. “Prediction, Optimization, and Learningin Repeated Games,”Econometrica, 65:275–309.
• O’Connor, Cailin, 2021. “MeasuringConventionality,”Australasian Journal of Philosophy,99: 579–596.
• Oddie, Graham, 1999. “Moral Realism, Moral Relativism, andMoral Rules,”Synthese, 117: 251–274.
• Parfit, Derek, 1984.Reasons and Persons, Oxford: OxfordUniversity Press.
• Peacocke, Christopher, 1987. “Understanding LogicalConstants: A Realist’s Account,”Proceedings of theBritish Academy, 73: 153–200.
• –––, 1998. “Concepts Without Words,”inLanguage, Thought, and Logic:Essays in Honor ofMichael Dummett, ed. Richard Heck, Oxford: Oxford UniversityPress.
• Plato, “Cratylus,” trans. C. D. C. Reeve. InComplete Works, ed. John Cooper, Indianapolis: Hackett,1997.
• Poincaré, Henri, 1902/1905.Science andHypothesis. InThe Foundations of Science, trans. GeorgeHalsted, New York: The Science Press.
• Prawitz, Dag, 1977. “Meaning and Proofs: On the ConflictBetween Classical and Intuitionistic Logic,”Theoria,43: 2–40.
• Putnam, Hilary, 1962/1985. “The Analytic and theSynthetic,” Reprinted inPhilosophical Papers, vol. 2.Cambridge: Cambridge University Press.
• –––, 1962/1975. “An Examination ofGrünbaum’s Philosophy of Geometry,” Reprinted inPhilosophical Papers, vol. 1. Cambridge: Cambridge UniversityPress.
• –––, 1974/1985. “The Refutation ofConventionalism,” Reprinted inPhilosophical Papers,vol. 2. Cambridge: Cambridge University Press.
• –––, 1981. “Convention: A Theme inPhilosophy,”New Literary History, 13: 1–14.
• –––, 1987.The Many Faces of Realism,LaSalle: Open Court.
• Quine, W. V., 1936/1976. “Truth by Convention,”reprinted inThe Ways of Paradox, 2nd ed., Cambridge: HarvardUniversity Press.
• –––, 1963/1975. “Carnap and LogicalTruth,” ReprintedThe Ways of Paradox, 2nd ed.,Cambridge: Harvard University Press.
• –––, 1969. “Foreword,” in Lewis,1969.
• Rawls, John, 1955. “Two Concepts of Rules,”Philosophical Review, 63: 3–32.
• Reichenbach, Hans, 1922/1978. “The Present State of theDiscussion on Relativity,” trans. M. Reichenbach. InHansReichenbach: Selected Writings, 1909–1953, vol. 2,Dordrecht: Reidel.
• Russell, Bertrand, 1921.The Analysis of Mind, London:Unwin Brothers Ltd.
• Samuelson, Larry, 1997.Evolutionary Games and EquilibriumSelection, Cambridge, MA: MIT Press.
• Schelling, Thomas, 1960.The Strategy of Conflict,Cambridge: Harvard University Press.
• Schiffer, Stephen, 1972.Meaning, Oxford: OxfordUniversity Press.
• –––, 1987.Remnants of Meaning,Cambridge, MA: MIT Press.
• –––, 1993. “Actual-LanguageRelations,”Philosophical Perspectives, 7:231–258.
• –––, 2006. “Two Perspectives on Knowledgeof Language,”Philosophical Issues, 16:275–287.
• –––, 2017. “Intention and Convention inthe Theory of Meaning,” in B. Hale, C. Wright, and A. Miller(eds.),A Companion to the Philosophy of Language, 2ndedition, Malden, MA: Wiley.
• Schlick, Moritz, 1917/1920.Space and Time in ContemporaryPhysics, trans. H. L. Brose. Oxford: Oxford UniversityPress.
• –––, 1953.“Are Natural LawsConventions?,” trans. Herbert Feigl and May Brodbeck. InReadings in the Philosophy of Science, ed. Feigl andBrodbeck, New York: Appleton-Century-Crofts.
• Schotter, Andrew, 1981.The Economic Theory of SocialInstitutions, Cambridge: Cambridge University Press.
• Searle, John, 1969.Speech Acts, Cambridge: CambridgeUniversity Press.
• –––, 1995.The Construction of SocialReality, New York: Free Press.
• –––, 2001.Rationality in Action,Cambridge, MA: MIT Press.
• Sellars, Wilfrid, 1963. “Some Reflections on LanguageGames,” Reprinted inScience, Perception, and Reality,New York: Routledge and Kegan Paul.
• Shapley, Lloyd, 1964. “Some Topics in Two-personGames,”Advances in Game Theory: Annals of MathematicalStudies, 5: 1–28.
• Shin, Hyun Song and Williamson, Timothy, 1996. “How MuchCommon Belief is Necessary for Convention?,”Games andEconomic Behavior, 13: 252–268.
• Sidelle, Alan, 1989.Necessity, Essence, and Individuation: ADefense of Conventionalism, Cornell: Cornell UniversityPress.
• Sider, Theodore, 2003. “Reductive Theories ofModality,” inThe Oxford Handbook of Metaphysics, ed.Michael Loux and Dean Zimmerman, Oxford: Oxford University Press.
• Sillari, Giacomo, 2005. “A Logical Framework forConvention,”Synthese, 147: 379–400.
• –––, 2008. “Common Knowledge andConvention,”Topoi, 27: 29–39.
• Simmel, Georg, 1908/1971. “How is Society Possible?,”Reprinted inGeorge Simmel: On Individuality and SocialForms, ed. Donald Levine, Chicago: University of ChicagoPress.
• Simons, Mandy, and Zollman, Kevin, 2019. “NaturalConventions and Indirect Speech Acts,”Philosophers’Imprint, 19: 1–26.
• Sklar, Lawrence, 1977.Space, Time, and Spacetime.Berkeley: University of California Press.
• Skyrms, Brian, 1996.Evolution of the Social Contract,Cambridge: Cambridge University Press.
• –––, 1998. “Salience and Symmetry-Breakingin the Evolution of Convention,”Law and Philosophy,17: 411–418.
• –––, 2010.Signals: Evolution, Learning, andCommunication, Oxford: Oxford University Press.
• –––, 2023. “Quasi-Conventions,”Synthese, 201: 1–16.
• Snare, Francis, 1991.Moral, Motivation, and Convention.Cambridge: Cambridge University Press.
• Sugden, Robert, 1986/2004.The Economics of Rights,Co-operation, and Welfare, 2nd ed., New York: PalgraveMacmillan.
• –––, 1998. “The Role of InductiveReasoning in the Evolution of Conventions,”Law andPhilosophy, 17: 377–410.
• –––, 2011. “Salience, Inductive Reasoning,and the Emergence of Conventions,”Journal of EconomicBehavior and Organization, 79: 35–47.
• Syverson, Paul, 2003.Logic, Convention, and Common Knowledge:A Conventionalist Account of Logic, Stanford: CSLIPublications.
• Taylor, Peter and Jonker, Leo, 1978. “Evolutionarily StableStrategies and Game Dynamics,”MathematicalBiosciences, 40: 145–156.
• Ullmann-Margalit, Edna, 1977.The Emergence of Norms,Oxford: Clarendon Press.
• Vanderschraaf, Peter, 1995. “Convention as CorrelatedEquilibrium,”Erkenntnis, 42: 65–87.
• –––, 1998a. “The Informal Game Theory inHume’s Account of Convention,”Economics andPhilosophy, 14: 215–247.
• –––, 1998b. “Knowledge, Equilibrium, andConvention,”Erkenntnis, 49: 337–369.
• –––, 2001.Learning and Coordination:Inductive Deliberation, Equilibrium, and Convention, London:Routledge.
• –––, 2019.Strategic Justice: Convention andProblems of Balancing Divergent Interests, Oxford: OxfordUniversity Press.
• Verbeek, Bruno, 2008. “Conventions and Moral Norms: TheLegacy of Lewis,”Topoi, 27: 73–86.
• Warren, Jared, 2015. “Conventionalism, Consistency, andConsistency Sentences,”Synthese, 192:1351–1371.
• –––, 2017. “Revisiting Quine on Truth byConvention,”Journal of Philosophical Logic, 46:119–139.
• –––, 2020.Shadows of Syntax, Oxford:Oxford University Press.
• Williams, Bernard, 2002.Truth and Truthfulness,Princeton: Princeton University Press.
• Williamson, Timothy, 2000.Knowledge and its Limits,Oxford: Oxford University Press.
• Young, H. Peyton, 1993. “The Evolution ofConventions,”Econometrica, 61: 57–84.
• –––, 1996. “The Economics ofConvention,”Journal of Economic Perspectives, 10:105–122.
• –––, 1998.Individual Strategy and SocialStructure, Princeton: Princeton University Press.
• –––, 2004.Strategic Learning and itsLimits, Oxford: Oxford University Press.
• Zermelo, Ernst, 1913. “Über eine Anwendung derMengenlehre auf die theorie des Schachspiels,”Proceedingsof the Fifth International Congress of Mathematicians, 2:501–4.

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