## 1. Issues raised by convention




In everyday usage, "convention" has various meanings, as
suggested by the following list: Republican Party Convention; Geneva
Convention; terminological conventions; conventional wisdom; flouting
societal convention; conventional medicine; conventional weapons;
conventions of the horror genre. As Nelson Goodman observes:



> 
> 
> The terms "convention" and "conventional" are
> flagrantly and intricately ambiguous. On the one hand, the
> conventional is the ordinary, the usual, the traditional, the orthodox
> as against the novel, the deviant, the unexpected, the heterodox. On
> the other hand, the conventional is the artificial, the invented, the
> optional, as against the natural, the fundamental, the mandatory.
> (1989, p. 80)




Adding to the confusion, "convention" frequently serves
as jargon within economics, anthropology, and sociology. Even within
philosophy, "convention" plays so many roles that we must
ask whether a uniform notion is at work. Generally speaking,
philosophical usage emphasizes the second of Goodman's
disambiguations. A common thread linking most treatments is that
conventions are "up to us," undetermined by human nature or
by intrinsic features of the non-human world. We *choose* our
conventions, either explicitly or implicitly.


### 1.1 Social convention




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




Two putative social conventions commonly cited by philosophers are
*money* and *language*. Aristotle mentions the former
example in the *Nicomachean Ethics* (V.5.II33a):



> 
> 
> Money has become by convention a sort of representative of demand; and
> this is why it has the name "money"
> ("*nomisma*")--because it exists not by nature
> but by law (*nomos*) and it is in our power to change it and
> make it useless,




and the latter example in *De Interpretatione* (16a.20-28):



> 
> 
> A name is a spoken sound significant by convention... I say
> "by convention" because no name is a name naturally but
> only when it has become a symbol.




David Hume mentions both examples in the *Treatise of Human
Nature* (p. 490):



> 
> 
> [L]anguages [are] gradually establish'd by human conventions
> without any explicit promise. In like manner do gold and silver become
> the common measures of exchange, and are esteem'd sufficient
> payment for what is of a hundred times their value.




Although Hume analyzed money at some length in the 1752 "Of
Money," it now receives systematic attention mainly from
economists rather than
 philosophers.[1]
 In contrast, philosophers still lavish great attention upon the
extent, if any, to which language rests upon convention. David Lewis
offers a theory of linguistic conventions, while Noam Chomsky and
Donald Davidson argue that convention sheds no light upon
language. See section 7,
 Conventions of language.




For many philosophers, a central philosophical task is to elucidate how
we succeed in "creating facts" through our conventions. For
instance, how does convention succeed in conferring value upon money or
meaning upon linguistic items? Ideally, a satisfying answer to these
questions would include both an analysis of what social conventions
*are* and a description of the particular conventions underlying
some range of "conventional" facts. Hume's theory of
property and Lewis's theory of linguistic meaning serve as
paradigms here.




What are social conventions? A natural first thought is that they are
*explicit agreements*, such as promises or contracts, enacted
either by parties to the convention or by people suitably related to
those parties (such as their ancestors). This conception underwrites at
least one famous conventionalist account: Thomas Hobbes's theory
of government as resulting from a *social contract*, into which
agents enter so as to leave the *state of nature*. However, it
seems clear that the vast majority of interesting social phenomena,
including government, involve no explicit historical act of agreement.
Social conventions can arise and persist without overt convening.




Partly in response to such worries, John Locke emphasized the notion
of a *tacit* agreement. A tacit agreement obtains if there has
been no explicit agreement but matters are otherwise *as if* an
explicit agreement occurred. A principal challenge here is explaining
the precise respects in which matters are just as if an explicit
agreement occurred. Moreover, many philosophers argue that appeal even
to "as if" agreements cannot explain linguistic meaning.
What language would participants in such an agreement employ when
conducting their deliberations? Bertrand Russell observes that
"[w]e can hardly suppose a parliament of hitherto speechless
elders meeting together and agreeing to call a cow a cow and a wolf a
wolf" (1921, p. 190). As W. V. Quine asks, then, "What is
convention when there can be no thought of convening?" (1969, p.
xi). Some philosophers take this argument to show that language does
not rest upon convention. Others, such as Lewis, take it as impetus to
develop a theory of convention that invokes neither explicit nor tacit
agreement.


### 1.2 Conventionalism




Conventionalism about some phenomenon is the doctrine that, perhaps
despite appearances to the contrary, the phenomenon arises from or is
determined by convention. Conventionalism surfaces in virtually every
area of philosophy, with respect to such topics as property (Hume's
*Treatise of Human Nature*), justice (Hume's *Treatise*
again), morality (Gilbert Harman (1996), Graham Oddie (1999), Bruno Verbeek (2008)),
geometry (Henri Poincare (1902), Hans Reichenbach (1922), Adolf
Grunbaum (1962)), Lawrence Sklar (1977)), pictorial
representation (Nelson Goodman (1976)), personal identity (Derek
Parfit (1984)), ontology (Rudolf Carnap (1937), Nelson Goodman (1978),
Hilary Putnam (1987)), arithmetic and mathematical analysis (Rudolf
Carnap (1937)), necessity (A. J. Ayer (1936)), Alan Sidelle (1989)),
and almost any other topic one can imagine. Conventionalism arises in
so many different forms that one can say little of substance about it
as a general matter. However, a distinctive thesis shared by most
conventionalist theories is that there exist *alternative*
conventions that are in some sense equally good. Our choice of a
convention from among alternatives is undetermined by the nature of
things, by general rational considerations, or by universal features
of human physiology, perception, or cognition. This element of free
choice distinguishes conventionalism from doctrines such as
projectivism, transcendental idealism, and constructivism about
mathematics, all of which hold that, in one way or another, certain
phenomena are "due to us."




A particularly important species of conventionalism, especially within
metaphysics and epistemology, holds that some phenomenon is partly due
to our conventions about the meaning or proper use of words. For
instance, Henri Poincare argues that "*the axioms of
geometry are merely disguised definitions*," concluding
that:



> 
> 
> The *axioms of geometry therefore are neither synthetic* a
> priori *judgments nor experimental facts*. They are
> *conventions*; our choice among all possible conventions is
> *guided* by experimental facts; but it remains *free* and
> is limited only by the necessity of avoiding all contradiction. (1902,
> p. 65)




Poincare holds that, in practice, we will always find it more
convenient to choose Euclidean over non-Euclidean geometry. But he
insists that, in principle, we could equally well choose non-Euclidean
axioms. This position greatly influenced the logical positivists,
including Rudolf Carnap, Moritz Schlick, and Hans Reichenbach, who
generalized it to other aspects of science.




Beginning with *Logical Syntax of Language* (1937/2002), Carnap
developed a particularly thoroughgoing version of linguistic
conventionalism. Carnap invites us to propose various linguistic
frameworks for scientific inquiry. Which framework we choose
determines fundamental aspects of our logic, mathematics, and
ontology. For instance, we might choose a framework yielding either
classical or intuitionistic logic; we might choose a framework
quantifying over numbers or one that eschews numbers; we might choose
a framework that takes sense data as primitive or one that takes
physical objects as primitive. Questions about logic, mathematics, and
ontology make no sense outside a linguistic framework, since only by
choosing a framework do we settle upon the ground rules through which
we can rationally assess such questions. There is no theoretical basis
for deciding between any two linguistic frameworks. It is just a
matter for conventional stipulation based upon pragmatic factors like
convenience.




Conventionalist theories differ along several dimensions. The most
obvious concerns the underlying understanding of conventions
themselves. In many cases, such as Hume's theory of property and
justice, the conventions are *social*. In other cases, however,
convention lacks any intrinsically social element. For example, both
Poincare and Carnap seem to regard conventional stipulation as
something that a lone cognitive agent could in principle achieve.




Another important difference between conventionalist theories
concerns what the "conventional" is contrasted with.
Options include: the natural; the mind-independent; the objective; the
universal; the factual; and the truth-evaluable.




Poincare's geometric conventionalism contrasts the
conventional with the truth-evaluable. According to Poincare,
there is no underlying fact of the matter about the geometry of
physical space, so geometric axioms are not evaluable as true or false.
Rather, the choice of an axiom system is akin to the choice of a
measuring standard, such as the metric system. In many conventionalist
theories, however, the idea is that our conventions somehow
*make* 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 that property
rights and monetary value are due largely to convention. Yet few
philosophers would hold that claims about property rights or monetary
value are
 non-truth-evaluable.[2]
As this example illustrates, conventionalism
need not reflect an "anti-realist" or
"deflationary" stance towards some subject matter.




Conventionalism often entrains *relativism*. A particularly
clear 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 infanticide as horrific, while
another may regard it as routine and necessary. Moral statements are
true only relative to a conventional standard. On the other hand, as
the example of property rights illustrates, one can accept that some
fact is due to social convention while denying that it is relative or
non-universal. For instance, one might urge, the conventions of my
society make it the case that I own my house, but this fact is then
true *simpliciter*, without relativization to a particular
societal convention.




A final division among conventionalist theories concerns whether the
putative conventions inform pre-existing practice. Hume's theory
of property purports to unveil actual conventions at work in actual
human societies. But some conventionalists instead urge that we must
*adopt* a convention. Carnap's conventionalist treatment
of logic, mathematics, and ontology illustrates this approach. Carnap
exhorts us to replace unformalized natural language with conventionally
chosen formal languages. Carnap has no interest in describing
pre-existing practice. Instead, he offers a "rational
reconstruction" of that practice.


## 2. Truth by convention




Carnap's conventionalism was the culmination of the logical
positivists' efforts to accommodate logic and
mathematics within an empiricist setting. Rejecting the Kantian
synthetic *a priori*, the positivists held that logic and
mathematics were analytic. Kant had explained the
 analytic-synthetic distinction
 in terms of concept-containment, which struck the positivists as
psychologistic and hence "unscientific." The positivists
instead treated analyticity as "truth by virtue of
meaning." Specifically, they treated it as the product of
linguistic convention. For instance, we can adopt the stipulative
convention that "bachelor" means "unmarried
man." "All bachelors are unmarried men" is true by
virtue of this convention. The positivists sought to extend this
analysis to far less trivial examples, most notably mathematical and
logical truth. In this regard, they were heavily influenced by Gottlob
Frege's logicism and also by Ludwig Wittgenstein's conception,
developed in the *Tractatus 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 conventionalism in
logical positivism.




Although initially attracted to Carnap's conventionalism, W.V.
Quine eventually launched a sustained attack on it in "Truth by
Convention" (1935) and "Carnap and Logical Truth"
(1963). Quine's anti-conventionalist arguments, in conjunction
with his attack upon the analytic-synthetic distinction, profoundly
impacted metaphysics and epistemology, casting conventionalist theories
of logic, mathematics, and ontology into general disrepute.




One of the Quine's most widely cited arguments (1936),
directed against a crude conventionalism about logic, traces back to
Lewis Carroll. There are infinitely many logical truths. Human beings
are finite, so we can explicitly stipulate only a finite number of
statements. Thus, in generating all the logical truths we must
eventually apply rules of inference to finitely many conventionally
stipulated statements. But then we are employing logic to derive logic
from convention, generating a vicious regress. Quine's point here
is not just that logic did not *in fact* come into existence
through conventional truth assignment. His point is that it *could
not* have thus come into existence.




To avoid the Quinean regress, one might propose that we
conventionally stipulate a finite number of axioms *and* a
finite number of inferences rules, thereby fixing an infinite number of
logical truths. The question here is what it means to
"stipulate" an inference rule. We can conventionally
stipulate that we will henceforth obey a certain inference rule. But
that stipulation does not entail that we are *entitled* to
reason in accord with the inference rule. Mere conventional stipulation
that we will henceforth obey a inference rule does not ensure that the
rule carries truths into truths. What if we stipulate that the
inference rule carries truths into truths? Then our stipulation is
merely another axiom. So we require a new inference rule to draw any
consequences from it, and the regress continues.




While it is doubtful that Carnap or the other positivists held the
crude form of conventionalism attacked by Quine's argument, the
argument suggests that conventionalism about logic requires an account
of "tacit" conventions. If logic is indeed "true by
convention," then some of the relevant conventions must
apparently be "implicit" in our practice, rather than the
results of explicit stipulation. So we require an account of what an
"implicit" convention amounts to. Carnap offers no such
account. Jared Warren (2017) attempts to meet the challenge by developing an account of "implicit" inference rules.




Another Quinean argument holds that "truth by
convention" offers no explanatory or predictive advantage over
the far less exciting thesis that certain statements are true due to
obvious features of extra-linguistic reality. For instance, we can all
agree that linguistic convention makes it the case that
"Everything is identical to itself" means what it does. But
why should we furthermore hold that the *truth* of this sentence
is due to linguistic convention, rather than to the fact that
everything is indeed self-identical? According to Quine, Carnap has
offered no reason for thinking that such truths are somehow vacuous as
opposed to merely obvious.




A final notable Quinean argument centers on the role of
"conventional stipulation" in scientific theorizing.
Consider a scientist introducing a new theoretical term by
definitional stipulation. The new term is embroiled in an evolving
body of scientific doctrine. As this body of doctrine develops, the
original legislated definition occupies no privileged status. We may
reject it in light of new empirical developments. Thus,
"conventionality is a passing trait, significant at the moving
front of science but useless in classifying the sentences behind the
lines" (1954, p. 119). Hilary Putnam (1962) further develops
this argument, offering the example of "kinetic energy
\(= \bfrac{1}{2} mv^{2}\)". Although that identity began
as a stipulative definition in Newtonian mechanics, Einsteinian
mechanics deems it false. Inspired by such examples, Quine rejects as
untenable any distinction between statements "true by
convention" or otherwise.




Quine therefore rejects Carnap's picture of science as a
two-stage process: the first stage in which we conventionally stipulate
constitutive aspects of our scientific language (such as its ontology
or logic) based solely upon pragmatic, non-rational factors; the second
in which we deploy our language by subjecting non-conventional theories
to rational scrutiny. For Quine, this two-stage picture does not
describe even idealized scientific inquiry. There is no clear
separation between those aspects of theory choice that are solely
"pragmatic" and those that are rational.




These and other Quinean arguments proved extremely influential.
Ultimately, many philosophers became convinced that Carnap's
conventionalist program was fundamentally
 flawed.[3]
This reaction dovetailed with
additional developments inimical to conventionalism. For instance,
Hilary Putnam (1963, 1974) and various later philosophers, such as
Michael Friedman (1983), vigorously attacked
geometric
 conventionalism.[4]




On the other hand, conventionalism still finds defenders. Lawrence
Sklar (1977) advocates a refurbished version of geometric
conventionalism. Alan Sidelle (1989) advocates conventionalism about
necessary truth. Michael Dummett (1991), Christopher Peacocke (1987),
and Dag Prawitz (1977) follow Gerhard Gentzen in treating certain
fundamental inferences as "implicit definitions" of the
logical connectives, a theory somewhat reminiscent of Carnap's
conventionalism about logic. Jared Warren (2015) invokes implicit definition to elucidate arithmetical vocabulary, defending on that basis a conventionalist treatment of arithmetical truth. Thus, the issues raised by Quine remain
unresolved. Still, it seems safe to say that philosophers nowadays
regard conventionalist solutions within metaphysics and epistemology
more warily than philosophers from the pre-Quinean
 era.[5]


## 3. Analyzing social convention




Although philosophers have always been interested in social
conventions, Hume's *Treatise* *of Human Nature*
offered the first systematic analysis of what they *are*. The
topic then lay dormant until Lewis revived it in *Convention*,
providing an analysis heavily influenced by Hume's but far more
detailed and rigorous. Lewis's analysis continues to shape the
contemporary discussion. In this section, we briefly discuss Hume and
then discuss Lewis in detail. Henceforth, "convention"
means "social convention."


### 3.1 Hume




Hume's analysis of convention, while compressed, has proved
remarkably fertile. As Hume puts it in the *Enquiry*
*Concerning Human Understanding*, a convention is



> 
> 
> a sense of common interest; which sense each man feels in his own
> breast, which he remarks in his fellows, and which carries him, in
> concurrence 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 each
member of the population plays his part in some system of actions
because he perceives that it is in his interest to do so, given that
others perceive it is in their interests to do so. Several features of
this definition deserve emphasis. First, a convention contributes to
the mutual benefit of its participants. Second, a convention need not
result from explicit promise or agreement. Third, each participant
believes that other participants obey the convention. Fourth, given
this belief, each participant has reason to obey the convention
herself. This fourth point emerges even more sharply in the
*Treatise*: "the actions of each of us have a reference to
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 two men
sitting in a row-boat. In order to move at all, they must synchronize
their rowing, which they do without any explicit agreement.




Having clarified convention, Hume deploys it to illuminate property,
justice, promising, and government. In each case, Hume offers a
broadly conventionalist account (see the entry on Hume's moral
philosophy for details). For instance, property emerges from the state
of nature through a social convention "to bestow stability on
the possession of those external goods, and leave every one in the
peaceable enjoyment of what he may acquire by his fortune and
industry" (*Treatise*, p. 489). This convention makes it
the 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 is intelligible
only with reference to convention that, when one employs a certain
"form of words" (e.g., "I promise to
\(j\)"), one thereby expresses a resolution to \(j\)
and subjects oneself to penalty if one does not \(j\).




In both the *Treatise* and "Of the Original
Contract," Hume rejects a Hobbesian conception of government as
arising from the state of nature through a social contract. Hume offers
various criticisms, but a particularly fundamental objection is that
Hobbes adopts a misguided order of explanation. Hobbes explains
government as the result of phenomena, such as *promising* or
*contracting*, that themselves rest upon convention and hence
could not arise in a pure state of nature. Hume contends that promising
and government arise independently, albeit in the same basic way and
from the same basic source:
 convention.[6]




Perhaps the most notable feature of Hume's account is that it
provides a detailed model of how social order can arise from rational
decisions made by individual agents, without any need for either
explicit covenant or supervision by a centralized authority. In this
respect, Hume's discussion prefigures Adam Smith's
"invisible hand" analysis of the marketplace.


### 3.2 Lewis




Lewis develops a broadly Humean perspective by employing game
theory, the mathematical theory of strategic interaction among
instrumentally rational agents. Drawing inspiration from Thomas
Schelling's *The Strategy of Conflict* (1960), Lewis
centers his account around the notion of a *coordination
problem*, i.e., a situation in which there are several ways agents
may coordinate their actions for mutual benefit.




Suppose \(A\) and \(B\) want to meet for dinner. They can
choose between two restaurants, Luigi's and
Fabio's. Each agent is indifferent between the two
restaurants, and each agent prefers meeting the other one to not
meeting. We represent this situation through a *payoff
matrix*:





|  |  |  |
| --- | --- | --- |
|  | Luigi's | Fabio's |
| Luigi's | 1, 1 | 0, 0 |
| Fabio's | 0, 0 | 1, 1 |


Restaurant Rendezvous Payoff Matrix





The rows (respectively, columns) represent \(A\)'s
(respectively, \(B\)'s) possible *strategies*: in
this case, their two restaurant options. Each cell contains the
respective *payoffs* for \(A\) and \(B\) for a given
strategy combination. Since there are two incompatible ways that
\(A\) and \(B\) might achieve a mutually desirable result,
the two "players" must coordinate their actions.




In several respects, Restaurant Rendezvous is an unrepresentative
coordination problem. First, \(A\) and \(B\) must perform the
*same* action in order to achieve the desired result. Second,
\(A\) and \(B\) achieve identical payoffs in each circumstance.
The following payoff matrix represents a coordination problem lacking
these two properties:





|  |  |  |
| --- | --- | --- |
|  | Call back | Wait |
| Call back | 0, 0 | 1, 2 |
| Wait | 2, 1 | 0, 0 |


Telephone Tag Payoff Matrix





As an intuitive interpretation, imagine that \(A\) and
\(B\) are speaking on the phone but that they are disconnected.
Who should call back? Each would prefer that the other call back, so as
to avoid paying for the call. However, each prefers paying for the call
to not talking at all. If both try to call back, then both will receive
a busy signal. The payoff matrix summarizes this situation. This kind
of case is sometimes called an *impure coordination problem*,
since it enshrines a partial conflict of interest between players.




Coordination problems pervade social interaction. Drivers must
coordinate so as to avoid collisions. Economics agents eliminate the
need for barter by coordinating upon a common monetary currency. In
many such cases, there is no way to communicate in advance, and there
is no centralized authority to impose order. For instance, prisoners in
POW camps converge without any centralized guidance upon a single
medium of exchange, such as cigarettes.




Lewis analyzes convention as an arbitrary, self-perpetuating
solution to a recurring coordination problem. It is self-perpetuating
because no one has reason to deviate from it, given that others
conform. For example, if everyone else drives on the right, I have
reason to as well, since otherwise I will cause a collision.
Lewis's analysis runs as follows (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 if and 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 all
> possible combinations of actions;
> 
> 
> 
> 
> (4) everyone prefers that everyone conform to \(R\), on
> condition that at least all but one conform to \(R\);
> 
> 
> 
> 
> (5) everyone would prefer that everyone conform to \(R'\),
> on condition 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 \(S\) among members of \(P\) could conform both
> to \(R'\) and to \(R\).
> 
> 




Lewis finally settles upon a modified analysis that allows
occasional exceptions to conventions. The literature spawned by
Lewis's discussion tends to focus on the exceptionless
characterization given above.




Lewisian convention is a special case of *Nash equilibrium*, the
central idea behind modern game theory. An assignment of strategies to
players is a Nash equilibrium iff no agent can improve his payoff by
deviating unilaterally from it. An equilibrium is *strict* iff
each agent *decreases* his payoff by deviating unilaterally from
it. Intuitively, a Nash equilibrium is a "steady state",
since each player behaves optimally, given how other players behave. In
this sense, Nash equilibrium "solves" the strategic problem
posed by a game, so it is sometimes called a "solution
concept". However, Lewisian convention goes well beyond Nash
equilibrium. In a Lewisian convention, everyone prefers that
*everyone else* conform if at least all but one conform.
Equilibria with this property are sometimes called *coordination
equilibria*.




By classifying \(R\) as a convention only if there is some
alternative regularity \(R'\) that could serve as a
convention, Lewis codifies the intuitive idea that conventions are
*arbitrary*. This was one of the most widely heralded features
of Lewis's definition, emphasized by both Quine (1969) and Putnam
(1981).




Notably, Lewis introduces the concept of *common knowledge*.
Roughly, \(p\) is common knowledge iff everyone knows \(p\),
everyone knows that everyone knows \(p\), everyone knows that
everyone knows that everyone knows that \(p\), etc. The subsequent
game-theoretic and philosophical literature offers several different
ways of formalizing this intuitive idea, due to researchers such as
Robert Aumann (1976) and Stephen Schiffer (1972). Recently, some
controversy has arisen concerning the precise relation between these
later formalizations and Lewis's own informal remarks. Robin
Cubitt and Robert Sugden (2003) argue that Lewis's conception of
common knowledge is radically different from the later formalizations,
while Peter Vanderschraaf (1998) and Giacomo Sillari (2005) downplay
the differences. 
See the entry on
 common knowledge
 for discussion of this controversy and of how common knowledge informs both
game theory and the philosophical study of convention.




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 starting point,
if only as a foil for motivating some alternative. Many philosophers
simply help themselves to Lewis's account without modifying it. On the
other hand, virtually every element of Lewis's account has attracted
criticism during the past few decades. For instance, Ken Binmore
(2008) and Richard Moore (2013) attack the "common
knowledge" condition in Lewis's analysis. In this section, we
will review some prominent criticisms of Lewis's account.


### 4.1 Regularities *de facto* and *de jure*




Lewis's definition of convention demands complete or
near-complete conformity. Many commentators object that this is too
strict, excluding conventions "more honored in the breach than
the observance." To take Margaret Gilbert's example (1989),
there might be a convention in my social circle of sending thank-you
notes after a dinner party, even though few people actually observe
this convention anymore. Lewis must deny that sending thank-you notes
is a convention, a verdict which Gilbert and other commentators find
unintuitive. Wayne Davis (2003) and Ruth Millikan (2005) develop
similar objections.




This objection sometimes accompanies another: that Lewis overlooks the
essentially *normative* character of conventions. The idea is
that conventions concern not just how people actually behave but also
how they *should* behave. In other words, conventions are
regularities not (merely) *de facto*, but *de jure*. For
instance, if there is a convention that people stand a certain distance
from one another when conversing, then it seems natural to say that
people *should* stand that distance when conversing. It is not
obvious that Lewis can honor these intuitions, since his conceptual
analysis does not mention normative notions. On this basis, Margaret
Gilbert (1989) and Andrei Marmor (1996) conclude that Lewis has not
provided sufficient conditions for a convention to prevail among some
group.




A closely related idea is that violations of convention elicit some
kind of *sanction*, such as tangible punishment or, more
commonly, negative reactive attitudes. Lewis emphasizes the
*self-perpetuating* character of convention: one conforms
because it is in one's interest to conform, given that others
conform. But, the argument goes, this emphasis overlooks a distinct
enforcement mechanism: non-conformity elicits some kind of sanction
from other people.




Lewis (1969, pp. 97-100) anticipates such objections and attempts to
forestall them. He argues that conventions will tend to become norms.
Once a convention prevails in some population, any member of the
population will recognize that others expect him to conform to it and
that they prefer he do so. He will also recognize that conforming
answers to his own preferences. It follow that he *ought* to
conform, since, other things being equal, one ought to do what answers
both to one's own preferences and to those of other people.
Moreover, if people see that he fails to conform, then they will tend
to sanction him through punishment, reproach, or distrust, since they
will see that he acts contrary both to his own preferences and to
theirs. To some extent, this argument recalls Hume's argument in
the *Treatise* that 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 show
that conventions have a tendency to *acquire* normative force,
they do not show that normativity is essential to convention.
Theoretically, it seems possible for rational agents to instantiate a
Lewisian convention without regarding it as a norm and without making
any effort to enforce the convention through sanctions. Thus, Gilbert
concludes, Lewis's account does not preserve the intrinsic link
between convention and normativity.




Even if one sympathizes with this objection, how to elucidate more
systematically the normativity of convention remains unclear. It does
not seem to be the normativity of morality, since someone who violates
some convention of, say, etiquette or fashion need not thereby act
immorally. Nor is it straightforwardly reducible to the normativity of
instrumental rationality: many philosophers want to say that, other
things being equal, one should conform to convention quite
independently of whatever one's beliefs and desires happen to be.
("You really ought to send a thank-you note.") What is this
mysterious brand of normativity, which apparently derives from neither
morality nor instrumental rationality? That question is still a focus
of active philosophical research.


### 4.2 Alternative conventions?




Seumas Miller (2001) deploys an example of Jean-Jacques Rousseau to
question whether a convention must have a conventional alternative. In
Rousseau's example, agents stationed throughout a forest must
decide whether to hunt stag or hunt hares. Hunting stag yields a higher
pay-off for everyone, but only if all other players hunt stag as well.
We can represent a two-person stag hunt through the following pay-off
matrix:





|  |  |  |
| --- | --- | --- |
|  | Hunt Stag | Hunt Hare |
| Hunt Stag | 2, 2 | 0, 1 |
| Hunt Hare | 1, 0 | 1, 1 |


The Stag Hunt Payoff 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 the other
player do likewise. Miller argues that this result accords with
intuition. He furthermore argues that hunting stag \(is\),
intuitively speaking, a possible convention. He concludes that Lewis errs by
requiring convention to have a conventional alternative.




Tyler Burge (1975) develops a related but distinct worry. He agrees
with Lewis that convention must have a conventional alternative, but he
denies that participants must *know* of such an alternative.
Burge offers as an example a primitive, isolated society with a single
language. Members of this society believe, as a matter of religious
principle, 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 that
credits participants in convention with far more rational
self-understanding than they necessarily possess. While Burge agrees
with Lewis that conventions are arbitrary, he thinks that "the
arbitrariness of conventions resides somehow in the 'logic of the
situation' rather than in the participants' psychological
life" (p. 253). For Burge, the arbitrariness of a convention
consists in the following facts: the conventions operative within a
society emerge due to historical accident, not biological,
psychological or sociological law; and, with effort comparable to that
expended in learning the original convention, parties to the convention
*could have* instead learned an incompatible convention that
would have served roughly the same social purpose.


### 4.3 Which equilibrium concept?




The game-theoretic literature contains numerous solution concepts that
either generalize or refine Nash equilibrium. Various commentators
suggest that a proper analysis of convention requires one of these
alternate 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 they have an additional stability property: once established, they
can resist invasion by deviant agents trying to establish a new
convention. Sugden argues that this approach illuminates a wide range
of social phenomena, including familiar examples such as money and
property.




Another widely discussed solution concept is *correlated
equilibrium*, introduced by Robert Aumann (1974, 1987). To
illustrate this generalized concept, consider a modified version of
Restaurant Rendezvous. In the new version (sometimes called
"Battle of the Sexes"), each agent prefers a different
restaurant, although both agents prefer meeting to not meeting. We
represent this situation with the following payoff matrix:





|  |  |  |
| --- | --- | --- |
|  | Luigi's | Fabio's |
| Luigi's | 2, 1 | 0, 0 |
| Fabio's | 0, 0 | 1, 2 |


Battle of the Sexes Payoff Matrix





This game has two "pure" Nash equilibria: one in which
both players go to Luigi's, the other in which both go to
Fabio's. Intuitively, neither equilibrium is fair, since one
player achieves a higher payoff than the other. The game also has a
"mixed-strategy" Nash equilibrium: that is, an equilibrium
in which each agent chooses his strategy based upon the outcome of a
randomizing device. Specifically, the game has a mixed-strategy
equilibrium 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 equilibrium is given as
follows, where "\(Prob(x, y)\)"
denotes the probability that \(A\) goes to \(x\) and
\(B\) goes to \(y\):



\[\begin{align}
A\text{'s expected payoff} &= Prob(\text{Luigi's, Luigi's})\times 2 \\
 &\quad + Prob(\text{Luigi's, Fabio's})\times 0 \\ 
 &\quad + Prob(\text{Fabio's, Luigi's})\times 0 \\ 
 &\quad + Prob(\text{Fabio's, Fabio's})\times 1 \\ 
 &= \bfrac{2}{9}\times 2 + \bfrac{2}{9} \times 0 + \bfrac{2}{9} \times 0 + \bfrac{2}{9} \times 1 \\
 &= \bfrac{2}{3}.
\end{align}\]



Similarly, \(B\)'s expected payoff
is \(\bfrac{2}{3}\). Neither player can improve upon this
payoff by deviating from the mixed-strategy equilibrium, given that
the other player is playing her end of the equilibrium. This
equilibrium is fair, in that it yields the same expected payoff for
both players. But it also yields a lower expected payoff for each
player than either pure equilibrium, since there is a decent chance
that the players' separate randomizing devices will lead to them to
different restaurants.




If the players can contrive to correlate their actions with a
*common* randomizing device, they can achieve a new equilibrium
that is fair and that Pareto dominates the old mixed-strategy
equilibrium. More specifically, suppose that there is a
*single* coin toss: each player goes to Luigi's if the toss is
heads, Fabio's if the toss is tails. The resulting strategy
combination yields an expected payoff of \(\bfrac{3}{2}\) for
each player. Intuitively, this strategy combination is an
equilibrium, since no player has reason to deviate unilaterally from
it. But the strategy combination does not count as a *Nash*
equilibrium of the original game, since in mixed Nash equilibria
players' actions must be probabilistically independent. Aumann calls
this strategy combination a *correlated equilibrium*, since
players' actions are probabilistically correlated. He develops this
intuitive idea in great formal detail, without reliance upon explicit
pre-game communication between players.




Building upon Aumann's formal treatment, Brian Skyrms (1996) and
Peter Vanderschraaf (1998b, 2001) argue that we should treat convention
as a kind of correlated equilibrium. For example, consider the
convention that drivers at traffic intersections correlate their
actions with the color of the traffic signal. As the restaurant and
traffic examples illustrate, correlated equilibria often provide far
more satisfactory solutions to coordination problems than one could
otherwise achieve.


### 4.4 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 that
conventions need not be coordination equilibria. For instance, Davis
claims that fashion conventions do not solve coordination problems,
since we do not usually care how other people dress.




To develop this objection, Sugden introduces *conventions of
property* and *conventions of reciprocity*, neither of which
solves coordination problems. He illustrates the former with the
Hawk-Dove game (also sometimes called "Chicken"):





|  |  |  |
| --- | --- | --- |
|  | Dove | Hawk |
| Dove | 1, 1 | 0, 2 |
| Hawk | 2, 0 | \(\bfrac{1}{2},\) \(\bfrac{1}{2}\) |


Hawk-Dove Payoff Matrix





The intuitive interpretation here is that two people faced with an
item 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 and
the other Dove, then the Hawk gets the entire good. If they both play
Hawk, then they again split it, but its value is reduced by half to
reflect the cost of fighting. This game has no coordination
equilibrium. However, consider the following strategy for recurring
instances of the game: "If you are already in possession of the
relevant item, then play *Hawk*; otherwise, play
*Dove*." It is an equilibrium for both players to play
this strategy. (More technically, following Skyrms (1996), we might
regard this strategy combination as a correlated equilibrium.) Sugden
argues that such an equilibrium might emerge as a convention among
agents who repeatedly play Hawk-Dove. But the equilibrium is not a
convention according to Lewis's definition. If I play my end of
it, I do not prefer that other people do likewise. I prefer that others
play Dove. Thus, the equilibrium lacks one of the main characteristics
emphasized by Lewis: a preference for general conformity over
slight-less-than-general conformity.




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





|  |  |  |
| --- | --- | --- |
|  | Cooperate | Defect |
| Cooperate | 2, 2 | 0, 3 |
| Defect | 3, 0 | 0, 0 |


Prisoner's Dilemma Payoff Matrix





The original intuitive interpretation of this payoff matrix is that
the police are separately interrogating two prisoners, each of whom
must decide whether to cooperate with the other prisoner by remaining
silent or whether to "defect" by confessing. If both
cooperate, then both receive very light sentences. If both defect, then
both receive very harsh sentences. If one defects and the other
cooperates, then the defector goes free while the cooperator receives a
harsh sentence. Although this scenario may seem rather contrived, we
can model many common social interactions as instances of
Prisoner's Dilemma. Sugden offers as an example two academics who
exchange houses for their sabbaticals. Each academic must decide
whether to maintain the other's house in good condition, even
though leaving it a mess would be easier.




Prisoner's Dilemma has no coordination equilibrium. Yet Sugden
argues that the following "tit-for-tat" strategy might
emerge as a convention when players repeatedly play Prisoner's
Dilemma over some indefinite period (e.g., two academics with a
standing arrangement to exchange houses every summer): co-operate as
long as your opponent cooperates; if your opponent defects, then defect
for some prescribed number of rounds \(r\) as retaliation before
cooperating again; if your opponent cooperates but you defect by
mistake, then accept your opponent's punishment in the next
\(r\) rounds without retaliating. This equilibrium is not a
convention in Lewis's sense, since one always prefers that
one's opponent cooperate rather than defect.




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




Marmor (2009) also questions Lewis's focus on coordination
problems. Marmor emphasizes actual games, such as chess, rather than
the "games" primarily studied by game theorists, such as Prisoner's
Dilemma. According to Marmor, the rules of chess are conventions that
do not solve a coordination problem. Chess playing activity does not
involve coordinating one's actions with those of other players, in
anything like the sense that driving on the right side of the road
(rather than the left) involves coordination among agents. Drawing on
John Searle's (1969) discussion of "constitutive rules," Marmor argues
that Lewis has overlooked an important class of conventions, which
Marmor calls "constitutive conventions," modeled after the rules of a
game. Roughly, a constitutive convention helps "constitute" a social
practice, in the sense that it helps define what the practice is and
how to engage in it correctly. Marmor offers a generalized analysis
designed to accommodate both Lewisian conventions and constitutive
conventions. The analysis resembles Lewis's, but it makes no mention
of coordination problems, and it contains no reference to common
knowledge.


## 5. Equilibrium selection




Lewis requires that a convention be one among several possible
alternatives. Even if one follows Miller in rejecting that requirement,
it seems clear that there are many cases, such as the choice of
monetary currency, where we must select from among numerous candidate
conventions. This raises the question of how we select a particular
candidate. An analogous question arises for game theory more generally,
since a game may have many Nash equilibria. It is rational to play my
part in a Nash equilibrium, *if I believe that other agents will
play their parts*. But why should I believe that others will play
their parts in this particular equilibrium? If we assume that players
cannot engage in pre-game communication, three basic answers suggest
themselves: players converge upon a unique equilibrium through rational
reflection on the logic of their strategic situation; or they are
guided by psychological factors outside the ambit of purely rational
analysis; or they learn from prior experience which equilibrium to
choose. One might also combine these 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 players about the game's payoff structure and their own
rationality, then, through relatively *a priori* reasoning,
they can successfully predict which equilibrium others will select. An
early example of this explanatory tradition is the method of backwards
induction, introduced by Ernst Zermelo (1913). The tradition
culminates in John Harsanyi and Reinhard Selten's *A General Theory
of Equilibrium Selection* (1988). However, few researchers still
champion this tradition. Its basic flaw is already apparent from our
simplest coordination problem, Restaurant Rendezvous. Nothing
intrinsic either to rationality or to the logic of the situation
favors one equilibrium over the other. Indeed, Harsanyi and Selten's
theory dictates that each player choose a mixed-strategy randomizing
over Luigi's and Fabio's. Clearly, then, Harsanyi and Selten cannot
explain how, in a wide variety of cases, people converge upon a
unique, non-randomized solution. Nor does it seem likely that we can
overcome this difficulty by emending our analysis of rationality or
refining our solution concept. Apparently, breaking the tie between
otherwise symmetrical equilibria requires us to supplement the austere
viewpoint of pure rational analysis with some additional input, either
from human psychology or else from experience.


### 5.1 Salience




Following Thomas Schelling (1960), who introduced the notion of a
*focal point*, Lewis argues that agents will select the
*salient* convention. A convention is salient (it is a focal
point) if it "stands out" from the other choices. A
candidate convention might acquire salience through precedent, explicit
agreement, or its own intrinsic properties. Schelling conducted a
famous experiment to illustrate the concept of salience. He asked
subjects to choose a time and place to meet a friend on a given day in
New York City, without any possibility of prior communication about
where or when to meet. Most respondents chose noon at Grand Central
Station. Somehow, then, this choice stands out as the most conspicuous.
As Schelling's example illustrates, salience is a
"subjective" psychological trait that does not follow in
any obvious way from the rational structure of the strategic situation.
Hume already anticipated a role for subjective psychological traits,
noting that our choice of convention often depends upon "the
imagination, or the more frivolous properties of our thought and
conception" (*Treatise*, p. 504, note 1).




Salience plays two distinct roles in Lewis's account,
corresponding to the following two questions: *How do conventions
arise?* and *Why do people conform to convention*? The
former question concerns dynamics (i.e., the factors governing how
conventions originate and evolve over time), while the latter concerns
statics (specifically, the rational structure that sustains a
convention at a given moment). Lewis's answer to the first
question is that agents initially select some equilibrium either by
chance, agreement, or intrinsic salience. The equilibrium gradually
becomes more salient through precedent, until eventually it becomes a
convention. Lewis's answer to the second question is that a
pre-existing convention is so overwhelmingly salient that agents expect
one another to abide by it, an expectation which furnishes reason to
conform.




Philosophers have heavily criticized Lewis's reliance upon
salience, arguing that the notion of salience is obscure, or that there
is often no salient option among candidate conventions, or that
precedence does not confer salience, or that Lewis fails to integrate
salience into the formal game-theoretic framework that otherwise shapes
his discussion. Margaret Gilbert (1989) argues that salience cannot
provide a reason for action: merely observing that some possible
convention is salient tells us nothing, because we cannot assume that
others will abide by the most salient convention. In a similar vein,
Brian Skyrms (1996) asks how it comes to be common knowledge that
others will choose the salient equilibrium over the alternatives.




Despite these criticisms, many authors over the intervening decades,
such as Robert Sugden (1986/2004, 2011) and Ken Binmore and Larry Samuelson
(2006), have argued that a satisfactory theory of equilibrium selection
requires something like Lewis's notion of salience. Note also
that, even if the foregoing criticisms are legitimate, they do not
impugn Lewis's analysis of what conventions *are*. They
only show that Lewis has not offered a complete theory of how
conventions are chosen, how they evolve, and how they sustain
themselves.


### 5.2 Dynamical models




For the past decade, the most popular approach to equilibrium
selection has been broadly *dynamical*. The dynamical approach,
a branch of evolutionary game theory, develops formal models of how
strategy choice evolves in a population whose members repeatedly play
some game against each another. In contrast with "static"
game theory (i.e., the study of equilibria), dynamical models
incorporate an explicitly temporal parameter. The basic goal is to
study the conditions under which dynamical models with various
properties tend to converge to static equilibria with various
properties.




Dynamical models of equilibrium selection differ along several
dimensions. Does the model depict learning by individual players or
aggregate trends in the population as a whole? How much rationality
does the model attribute to players? Is the model deterministic or
stochastic? Do players have limited or unlimited memory of past events?
How much common knowledge do players have about the game's payoff
structure? Can players learn about the results of interactions in which
they do not participate? Do the same players participate in each round
of play, or are the players repeatedly drawn anew from a larger
population? Is that larger population modeled as finite or infinite? An
overview of the burgeoning and forbiddingly technical literature on
these questions falls beyond the scope of this article. We confine
attention here to three developments: replicator dynamics; fictitious
play; and sophisticated Bayesian learning. Interested readers should
consult the detailed surveys offered by Drew Fudenberg and David Levine
(1998) and H. Peyton Young (2004).



*Replicator dynamics*: In this deterministic model,
introduced by Peter Taylor and Leo Jonker (1978), the proportion of
players choosing some strategy grows proportionally to the difference
between that strategy's mean payoff and the mean payoff for the
population as a whole. The model does not describe how the behavior of
individual players changes over time. Rather, the model describes
aggregate trends in the population as a whole.




A *stable steady state* of a dynamical system is a state
\(s\) with the following two features: once the system enters
\(s\), it never leaves it; and once the system approaches
"close enough" to \(s\), then it always remains near
\(s\). The *basin of attraction* of \(s\) is the set
of states such that, if the dynamical system begins in one of those
states, then it will eventually converge towards \(s\). In many
cases, the best way to understand a dynamical system is to construct a
"phase portrait" diagramming its steady states and their
basins of attraction. In the case of interest to us here, the
"state" of a dynamical system is simply the proportion of
players choosing each strategy.




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




Replicator dynamics originated within evolutionary biology.
Subsequently, game theorists such as Larry Samuelson (1997) have argued
that it illuminates social interaction among humans. Within philosophy,
Brian Skyrms (1996, 1998) argues that replicator dynamics shows how
conventions of property and linguistic meaning could evolve without any
need for Lewisian "salience." He places particular emphasis
upon *signaling games*, that is, games in which a sender wishes
to communicate a message to a receiver, a message determining which
action from among a fixed repertoire the receiver will perform. (See
 section 7.1 
 for more detail on signaling games.) For
certain signaling games, replicator dynamics almost always converges to
an evolutionarily stable signaling convention. Which convention emerges
depends solely upon chance facts about players' initial
propensities to adopt various strategies (i.e., the basin of attraction
from which the system happens to begin). As Skyrms puts it,
"*[w]hich signaling system is selected is a matter of chance,
not of salience*" (1996, p. 93).




Despite the popularity of replicator dynamics, critics such as H.
Peyton Young (1998) remain skeptical. The most natural motivation for
replicator dynamics is biological. We conceptualize players as animals
genetically programmed to exhibit certain behaviors. Creatures who
achieve higher payoffs have higher reproductive fitness, and they pass
their strategy choices along to their progeny. Natural selection
therefore causes certain behaviors to become more prevalent. Under
these assumptions, replicator dynamics seems plausible. But it is not
clear that a comparable rationale applies to human interaction, since
humans generally act not based solely upon their genetic programming
but rather upon their beliefs and desires. Why should the choices of
individual human agents yield the pattern described by replicator
dynamics?




In response to this worry, theorists try to derive replicator dynamics
from models of individual adaptive behavior. Some models posit that
people tend to imitate the behavior of others, based either on how
popular or how successful that behavior seems. Other models posit some
kind of reinforcement mechanism. Neither approach accords very well
with the traditional preference among both philosophers and economists
for *rational* explanations. Samuelson (1997, p. 23) responds
that such approaches may nevertheless be appropriate "if we are
interested in people, rather than ideally rational agents." But
it is hardly obvious that our best cognitive science of actual human
psychology will eschew rational explanation in favor of the
psychological mechanisms currently being invoked to underwrite
replicator dynamics.



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




The literature explores many different variations on this theme. One
can restrict how many past trials the player remembers or how much
weight the player places upon older trials. One can embed the player
in a large population and restrict how much a player knows about
interactions within that population. One can introduce a
"neighborhood structure," so that players interact only
with their neighbors. One can introduce a stochastic element. For
instance, 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 conventions
evolve in which each player chooses a "best reply" with
probability \(1-\varepsilon\) and some random strategy with
probability \(\varepsilon\). One can also generalize the fictitious play
framework to accommodate correlated equilibrium. Peter Vanderschraaf
(2001) explores a variant of fictitious play in which a player frames
hypotheses about correlations between her opponents' strategies and
external events. Applying this framework to convention, he argues that
we can treat the emergence of correlated equilibrium conventions as an
instance of rational belief-fixation through inductive
deliberation.




Fictitious play does not attribute knowledge of other people's
payoffs or their rationality. It does not depict players as reasoning
about the reasoning of others. Instead, it depicts players as
performing a mechanical statistical inference that converts an
action's observed historical frequency into a prediction about
its future probability of recurrence. For this reason, critics such as
Ehud Kalai and Ehud Lehrer (1993) contend that fictitious play
attributes to players insufficient recognition that they are engaged in
*strategic* interaction. For instance, a player who reasons in
accord with fictitious play implicitly assumes that each opponent plays
some stationary (either pure or mixed) strategy. This assumption
overlooks that her opponents are themselves updating their beliefs and
actions based upon prior interaction. It also prevents players from
detecting patterns in the data (such as an opponent who plays one
strategy in odd-numbered trials and another strategy in even-numbered
trials). Moreover, fictitious play instructs a player to maximize her
expected payoff for the *current* round of play. This
"myopic" approach precludes maximizing one's future
expected payoff at the price of lowering one's current payoff
(e.g., playing Hawk rather than Dove even if I expect my opponent to do
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
by Paul Milgrom and John Robert (1991), replaces the rather crude
statistical inference posited by fictitious play with a more refined
conception of inductive deliberation. Specifically, it abandons the
questionable assumption that one faces stationary strategies from
one's opponents. Ehud Kalai and Ehud Lehrer (1993) offer a widely
discussed model of sophisticated Bayesian learning. Players engaged in
an infinitely repeated game constantly update probability distributions
defined over the set of possible strategies played by their opponents,
where a strategy is a function from the set of possible histories to
the set of possible actions. At each stage, a player chooses an action
that maximizes the expected value of her payoffs for the
*entire* future sequence of trials, not just for the present
trial. This approach allows a player to discern patterns in her
opponents' behavior, including patterns that depend upon her own
actions. It also allows her to sacrifice current payoff for a higher
expected long-term payoff. Kalai and Lehrer prove that their procedure
almost always converges to something approximating Nash equilibrium,
under the crucial assumption (the "grain of truth"
assumption) that each player begins by assigning positive probability
to all strategies that actually occur.




Critics such as John Nachbar (1997) and Dean Foster and H. Peyton Young
(2001) argue that there is no reason to accept the "grain of
truth" assumption. From this perspective, Kalai and Lehrer merely
push the problem back to explaining how players converge upon a
suitable set of prior probabilities satisfying the "grain of
truth" assumption. Although Kalai and Lehrer's proof
actually requires only a somewhat weakened version of this assumption,
the problem persists: sophisticated Bayesian learning converges to Nash
equilibrium only under special assumptions about players' prior
coordinated expectations, assumptions that players might well fail to
satisfy.




Sanjeev Goyal and Maarten Janssen (1996) develop this criticism,
connecting it with the philosophical problem of induction, especially
Nelson Goodman's grue problem. Robert Sugden (1998, 2011) further develops
the criticism, targeting not just sophisticated Bayesian learning but
virtually every other learning model found in the current
literature. As the grue problem highlights, there are many different
way of extrapolating past observations into predictions about the
future. In philosophy of science, the traditional solution to this
difficulty is that only certain predicates are
"projectible." But Sugden argues that the difficulty is
more acute for strategic interaction, since successful coordination
requires shared standards of projectibility. For instance, suppose
that I repeatedly play a coordination game with an opponent who has
two 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 my opponent will
henceforth play \(s\_{1}\). But I might instead project a
"grueified" pattern, such as: "play
\(s\_{1}\) until time \(t\), and then play
\(s\_{2}\)." Which inductive inference I make
depends upon which predicates I regard as projectible. There is no
guarantee that my opponent shares my standards of projectibility. In
effect, then, convergence through inductive deliberation requires me
and my opponent to solve a new coordination problem: coordinating our
standards of projectibility. According to Sugden, existing dynamical models implicitly assume
that players have already solved this new coordination problem. Sugden
concludes that a full explanation of equilibrium selection requires
something like Lewis's notion of salience. In particular, it
requires shared psychological standards regarding which patterns are
projectible and which are not. Sugden urges, contra Skyrms, that
dynamical models of convention cannot displace salience from its
central role in understanding convention.




As the foregoing discussion indicates, the dynamical study of
equilibrium selection is a diverse, fast-growing area of 
research.[7]
Moreover, it raises difficult questions on the boundary between
economics and philosophy, such as how to analyze inductive reasoning,
how much rationality to attribute to social agents, and so on. It is
undeniable that, in a wide variety of circumstances, people
successfully converge upon a single unique convention amidst a range of
alternatives. It seems equally undeniable that we do not yet fully
understand the social and psychological mechanisms that accomplish this
deceptively simple feat.


## 6. Alternative treatments of convention




We now survey some alternative theories of convention proposed in the
past few decades. Unlike the rival proposals discussed in section 4,
which accept Lewis's basic perspective while emending various
details, the theories discussed below reject Lewis's entire
approach.


### 6.1 Gilbert: plural subjects




Eschewing Lewis's game-theoretic orientation, Margaret Gilbert
(1989) instead draws inspiration from sociology, specifically from
Georg Simmel's theory of "social groups" (1908). The
basic idea is that individual agents can "join forces" to
achieve some common end, thereby uniting themselves into a collective
entity. To develop this idea, Gilbert provides a complex account of how agents
bind themselves into a "plural subject" of belief and
action. A plural subject is a set of agents who regard themselves as
jointly committed to promoting some goal, sharing some belief, or
operating under some principle of action. By virtue of their common
knowledge of this joint commitment, members of the plural subject
regard themselves as "we". They thereby regard one another
as responsible for promoting the group's goals and principles.
For instance, two traveling companions make manifest their commitment
to keep track of one another, whereas two people who happen to share a
seat on a train do not. The traveling companions form a plural subject.
The unaffiliated travelers do not. The traveling companions regard each
other as responsible for helping if one person falls behind, for not
losing one another in a crowd, and so on.




Gilbert proposes that "our everyday concept of a social
convention is that of a jointly accepted principle of action, a group
fiat with respect to how one is to act in certain situations" (p.
377). Members of a population *jointly accept a fiat* when it is
common knowledge that they have made manifest their willingness to
accept and promote that fiat as a basis for action. By Gilbert's
definition, participants in a convention constitute a plural subject.
For they jointly accept the common goal of promoting some fiat.
Moreover, members of the social group regard the fiat as exerting
normative force simply by virtue of the fact that they jointly accept
it. Note that not all plural subjects instantiate conventions. For
instance, depending on the details of the case, the traveling
companions from the previous paragraph might not. A convention arises
only when individual members of a plural subject jointly accept some
fiat.




Gilbert's account differs from Lewis's in both
*ontology* and *ideology*. Ontologically, Gilbert
isolates a *sui generis* entity, the plural subject, that
Lewis's "individualistic" approach does not
countenance. Gilbert argues that a population could instantiate a
Lewisian convention without giving rise to a plural subject.
Participants in a Lewisian convention may *prefer* that other
participants conform to it, given that almost everyone does. But they
need not regard themselves as *responsible* for enforcing it or
for helping others conform. They would so regard themselves if they
viewed themselves as belonging to a plural subject. Thus, a Lewisian
convention does not ensure that its adherents constitute a plural
subject.




Regarding *ideology*, Gilbert's account attributes to
convention an intrinsically normative element that Lewis rejects. For
Gilbert, adopting a convention is making manifest a willingness to
promote a certain fiat. Parties to a convention therefore accept that
they *ought* to act in accord with the fiat. In contrast, as we
saw in section 4.2, Lewis's account does not recognize any
normative elements as intrinsic to convention.




The contrast between Gilbert and Lewis instantiates a more general
debate over *Homo economicus*: a conception of agents as
self-interested and instrumentally rational. Lewis attempts to analyze
social 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 on
her self-identification as a member of a social group constituted by
various norms. Elizabeth Anderson (2000) analyzes how the clash between
these two conceptions relates to convention and normativity.




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


### 6.2 Miller: collective ends




Seumas Miller (2001) introduces the notion of a "collective
end." A collective end is an end that is shared by a group of
agents and that can be achieved only through action by all of those
agents; moreover, these facts are mutually believed by the agents. A
convention to \(j\) in some recurring situation \(s\) prevails among
some agents iff it is mutually believed by the agents that each one has
a standing intention to \(j\) in \(s\), as long as others perform \(j\) in
\(s\), so as to realize some shared collective end \(e\). For
instance, the collective end corresponding to the convention of driving
on the right side of the road is avoiding collisions.




In many respects, Miller's account is more similar to
Lewis's than to Gilbert's. Miller shares Lewis's
"reductionist" perspective, analyzing social convention as
a pattern of interaction between rational agents, without any
irreducibly "social" element. In particular, Miller rejects
*sui generis* social entities, such as plural subjects, and he
does not invoke specialized norms of convention beyond those engendered
by morality and rationality.




One objection to Miller's account is that, in many cases, there
is no clear "collective end" subserved by convention. For
instance, what collective end must participants in a monetary practice
share? It seems that each agent might care only about his own
individual 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 the *definition* of
convention? As Burge observes, "parties to a convention are
frequently confused about the relevant ends (the social functions of
their practice); they are often brought up achieving them and do not
know the origins of their means" (1975, p. 252). Thus, it might
seem that Miller attributes too much self-understanding to participants
in a convention.


### 6.3 Millikan: patterns sustained by weight of precedent




Ruth Millikan (2005) offers a radical alternative to the views surveyed
so far. She draws inspiration not from economics or sociology but from
biology. On her view, a convention is a pattern of behavior
*reproduced* within a population due largely to weight of
precedent. To say that an instance of some pattern
"reproduces" previous instances is to say that, if the
previous instance had been different, the current instance would be
correspondingly different. Many patterns of behavior are
"reproduced" in this sense, such as the propensity to greet
one another by shaking hands in a certain way. However, not all
reproduced patterns are conventions. For instance, we learn from our
parents to open stuck jars by immersing them in hot water, but our
reproduction of this pattern is not a convention. To count as a
convention, 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 different
populations, in contrast with a pattern such as immersing stuck jars in
hot water.




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




Perhaps the most striking aspect of Millikan's discussion is
that it assigns no essential role to rationality in sustaining
conventions. For instance, a society in which people maintain a
convention simply from unreflective conformism would satisfy
Millikan's definition. The tradition established by Hume and
continued by Lewis seeks to explain how social order emerges from the
rational decisions of individual agents. Millikan rejects that
tradition. To some extent, Burge also departs from the tradition,
writing that "the stability of conventions is safeguarded not
only by enlightened self-interest, but by inertia, superstition, and
ignorance" (p. 253). However, Millikan's position is more
extreme than Burge's, since she assigns reason no role in
sustaining convention. In other words, whereas Burge apparently thinks
that convention rests upon both rational and irrational underpinnings,
Millikan does not acknowledge any rational underpinnings.


## 7. Conventions of language




Plato's *Cratylus* offers a notable early discussion of
linguistic convention. Hermogenes defends a broadly conventionalist
view of linguistic meaning:



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




while Cratylus advocates a rather obscure anti-conventionalist
alternative:



> 
> 
> A thing's name isn't whatever people agree to call it
> --some bit of their native language that applies to it--but there
> is a natural correctness of names, which is the same for everyone,
> Greek or foreigner. (383a-b)




Nowadays, virtually all philosophers side with Hermogenes. Barring a
few possible exceptions such as onomatopoeia, the association between a
word and its referent is not grounded in the intrinsic nature of either
the word or the referent. Rather, the association is
*arbitrary*. In this weak sense, everyone agrees that language
is conventional. However, disagreement persists about whether social
convention plays a useful role in illuminating the workings of
language.


### 7.1 Conventional theories of meaning




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




Lewis begins by studying *signaling problems*. A
*communicator* has privileged information differentiating among
states \(s\_{1},\ldots, s\_{m}\).
*Audience members* can choose among responses
\(F(s\_{1}), \ldots, F(s\_{m})\). Everyone prefers that audience
members do \(F(s\_{i})\) if
\(s\_{i}\) obtains. There is a set of signals
\(x\_{1},\ldots,x\_{n}\), \(m \le n\), that the communicator can pass to the audience. In
Lewis's example, the sexton knows whether the redcoats are staying
home, coming by land, or coming by sea. By placing either zero, one,
or two lanterns in the belfry, he signals Paul Revere whether to go
home, warn people that redcoats are coming by land, or warn people
that the redcoats are coming by sea. A signaling problem is a
coordination problem, because communicator and audience must
coordinate so that the communicator's signal elicits the mutually
desired action. Building on Lewis's discussion, Skyrms (2010) offers
an intensive analysis of signaling problems, with applications to
diverse biological cases studies ranging from bacteria to apes.




In comparison with normal linguistic interaction, signaling problems
are very specialized. A fundamental difference is that people normally
need not agree upon which action(s) would be desirable, given some
state of affairs. When we search for an audience reaction canonically
associated with an assertion that \(p\), the most natural
candidate is something like *believing* that \(p\) (or
perhaps believing that the speaker believes \(p)\). Yet coming to
believe a proposition is not an action, and Lewis's definition of
convention presupposes 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, he
eventually concluded that we should alter the analysis of convention.
In "Languages and Language" (1975/1983), he broadened the
analysis so that regularities of action *and belief* could serve
as conventions. Clause (4) of Lewis's definition entails that
everyone prefers to conform to the convention given that everyone else
does. Preferences regarding one's own beliefs are dubiously
relevant to ordinary conversation. Thus, in his revised analysis, Lewis
substitutes a new clause:



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




The "reason" in question might be either a
*practical* reason, in the case of action, or an
*epistemic* reason, in the case of belief.




Lewis defines a *language* as a function that assigns
truth-conditions to sentences. More precisely, and ignoring
complications such as vagueness and indexicality, a language \(L\)
is a mapping that assigns each sentence \(s\) a set of possible
worlds \(L(s)\). A sentence \(s\) is "true in
\(L\)" iff the actual world belongs to
\(L(s)\). There are infinitely many possible languages.
We must explain what it is for a given group of agents to use a given
language. In other words, what is the "actual language"
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 an interest in communication,




where a speaker is "truthful in \(L\)" iff she
tries to avoid uttering sentences not true in \(L\), and a speaker
is "trusting in \(L\)" iff she believes that sentences
uttered by other speakers are true in \(L\). Given that this
convention prevails, speakers who want to communicate have reason to
conform to it, which in turn perpetuates the convention. Note that
Lewis's account avoids the Russell-Quine regress argument from
 section 1.1, since Lewisian convention does not
presuppose explicit agreement between participants.




In many respects, Lewis's account descends from Grice's theory of
speaker-meaning. A simplified version of Grice's account runs as
follows: a speaker *speaker*-*means* that \(p\) iff
she performs an action with an intention of inducing the belief that
\(p\) in her audience by means of their recognition of that very
intention. Although Lewis does not explicitly build speaker-meaning
into his analysis of the "actual language" relation, a
broadly Gricean communicative mechanism informs his discussion. Like
Grice, Lewis emphasizes how meaning emerges from coordination between
the speaker's communicative intentions and the hearer's communicative
expectations. Grice does not provide a very compelling account of how
speakers and hearers coordinate their communicative intentions and
expectations by exploiting a *pre-existing* practice. Lewis
fills this lacuna by citing a standing convention of truthfulness and
trust.




Stephen Schiffer (1972) and Jonathan Bennett (1976) offer alternative
"neo-Gricean" accounts that combine Lewisian convention
with more explicit appeal to Gricean speaker-meaning. In effect, both
theories are sophisticated variants upon the following:



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




Thus, both accounts analyze sentence meaning as the result of a
convention that certain sentences are used to communicate certain
propositions.




 A fundamental question for philosophy of language is how meaning
arises from use. How do we confer significance upon inherently
meaningless linguistic expressions by employing them in linguistic
practice? Neo-Gricean accounts such as Lewis's, Schiffer's, and
Bennett's provide detailed answers to this question. For instance,
Lewis isolates a self-perpetuating communicative mechanism that
systematically associates sentences with propositional contents. He
reduces social convention to the propositional attitudes of individual
speakers, and he then uses social convention to explain how meaning
arises from use. He thereby depicts linguistic expressions as
inheriting content from antecedently contentful propositional
attitudes. On this approach, thought is the primary locus of
intentionality, and language enjoys intentional content merely in a
derivative way, through its employment in communicative
transactions. That general view of the relation between language and
thought goes back at least to Book III of Locke's *Essay on Human
Understanding*. It is currently quite popular. Much of its
popularity stems from the widespread perception that Lewis's account,
or some other such account, successfully explains how language
inherits content from thought.


### 7.2 Objections to conventional theories




Conventional theories of linguistic meaning attract several different
types of criticism. We may distinguish four especially important
criticisms: denial that the putative conventions prevail in actual
practice; denial that convention can determine linguistic meaning;
denial that convention is necessary for linguistic meaning; and denial
that convention-based accounts employ the proper order of
explanation.


#### 7.2.1 Do the putative conventions prevail?




This criticism surfaces repeatedly throughout the literature. For
instance, Grice's analysis of speaker-meaning generated a
mini-industry of counter-example and revised analysis. The gist of the
counter-examples is that there are many perfectly normal linguistic
interactions in which speakers lack the communicative intentions and
expectations cited by Grice. Thus, it is difficult to see how our
practice could instantiate a convention that crucially involves those
intentions and expectations. One might respond to this argument in
various ways, such as classifying certain linguistic interactions as
"paradigmatic" and others as "derivative." But
at least one prominent Gricean, Stephen Schiffer (1987), eventually
concluded, partly from such counter-examples, that the program of
explicating linguistic meaning through Lewisian convention and Gricean
speaker-meaning was hopeless.




Regarding Lewis's account, critics such as Wayne Davis (2003),
Max Kolbel (1998), Stephen Laurence (1996), and Bernard Williams
(2002) question whether there is a convention of truthfulness and
trust. As Davis and Williams urge, it is hardly obvious that speakers
generally speak the truth or generally trust one another, despite
frequent claims by diverse philosophers to the contrary. Even if we
grant that people generally speak the truth and generally trust one
another, does this give me reason to speak truthfully? It does, *if
I want other people to believe the truth*. But if I want them to
believe falsehoods, then I have reason to lie rather than speak the
truth. Thus, one might object, a regularity of truthfulness and trust
is not self-perpetuating in the way that Lewisian convention requires.
Expectation of conformity does not provide reason for conformity. In
contrast, consider the convention of driving on the right. That
convention likewise provides reason for conformity only given an
appropriate desire: namely, desire to avoid a collision. The difference
is that virtually everyone seeks to avoid a collision, while deception
is a normal feature of ordinary linguistic interaction.




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


#### 7.2.2 Can convention determine linguistic meaning?




The most serious version of this objection, advanced by Stephen
Schiffer (1993, 2006), John Hawthorne (1990, 1993), and many other
philosophers, focuses on the *productivity* of language. We can
understand a potential infinity of meaningful sentences. Yet we can
hardly master infinitely many linguistic conventions, one for each
meaningful sentence. How, then, can convention fix the meanings of
these infinitely many sentences?




This general worry arises in a particularly acute way for Lewis's
theory. Consider some sentence \(S\) that we would never normally
use, perhaps because it is too long or too grammatically
complex. Suppose that some speaker nevertheless utters \(S\). As
Lewis acknowledges, we would not normally believe that the speaker was
thereby attempting to speak truthfully. Instead, we would suspect that
the speaker was acting for some deviant reason, such as trying to
annoy, or settling a bet, and so on. We would not normally trust the
speaker. But then Lewis cannot use his convention of truthfulness and
trust to underwrite a unique truth-condition for \(S\).




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




Lewis's account is not alone in encountering difficulties with
productivity. Most contemporary conventionalist theories encounter
similar difficulties, because most such theories, heeding Frege's
context principle (only the context of a sentence do words have
meaning), focus attention upon the link between sentences and
propositions rather than the link between words and their meanings.
One might hope to supplement convention-based accounts with the
Chomsky-inspired thesis, advocated by James Higginbotham (1986) and
Richard Larson and Gabriel Segal (1995), that speakers have tacit
knowledge of a compositional semantic theory. However, as Martin
Davies observes (2003), no one seems to have worked out this
supplementary strategy in any detail, and it is not obvious how
important a role the resulting account would assign to convention, let
alone the Gricean communicative mechanism.




Ultimately, the force of these worries remains unclear. For instance,
Wayne Davis (2003) develops a conventionalist account that harkens back
to the pre-Fregean tradition. In simplified form, Davis's Lockean
proposal is that a word is meaningful because we conventionally use it
to express a certain "idea". The meaning of a sentence is then determined by the meanings of its component words, along with the (conventionally determined) semantic import of the syntactic structure in which those words are arranged. Evidently, these issues
connect with vexed questions about compositionality, linguistic
understanding, the unity of the proposition, and the role played by
formal semantic theories in the study of natural language.


#### 7.2.3 Is convention necessary for linguistic meaning?




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




Chomsky regards language as a system of grammatical rules
"tacitly known" by a speaker. Linguistics, which Chomsky
treats as a branch of cognitive psychology, studies the grammatical
competence of individual speakers. It should not posit a mysterious and
unscientific "communal language" shared by speakers, but
should instead focus upon "idiolects." Thus, language has
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 Chomskian perspective.
The basic idea behind both accounts is that a linguistic item as used
by some speaker is associated with certain semantic properties just in
case the association between the linguistic item and the semantic
property figures in the psychological processes through which the
speaker assigns meanings (or truth-conditions) to sentences.




Davidson elaborates a model of communication that takes as its paradigm
"radical interpretation." During radical interpretation,
one tries to assign truth-conditions to utterances in a completely
unfamiliar tongue. To do so, one detects patterns concerning which
sentences the speaker "holds true," and one tries to make
rational sense of those patterns, guided by general maxims such as the 
*principle of charity* (roughly, maximize true beliefs on the
part of the speaker). Davidson admits that, in everyday life, we tend
as a default to interpret one another "homophonically." But
there is no principled reason why we must embrace this homophonic
default, and we readily deviate from it whenever seems appropriate, as
illustrated by cases of idiosyncratic usage, malapropism, and so on. In
a sense, then, all linguistic understanding rests upon radical
interpretation. So shared linguistic conventions are inessential to
linguistic communication:



> 
> 
> Knowledge of the conventions of language is thus a practical crutch to
> interpretation, a crutch we cannot in practice afford to do
> without--but a crutch which, under optimum conditions for
> communication, we can in the end throw away, and could in theory have
> done without from the start. (1984, p. 279)




Davidson concludes that theories of meaning and understanding should
not 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 broader
Lockean strategy of explaining language in terms of thought. According
to this objection, which is espoused by philosophers such as Robert
Brandom (1994), Donald Davidson (1984), and Michael Dummett (1993),
language does not inherit content from thought. Rather, thought and
language are on a par, acquiring content through their mutual
interrelations. (One might also claim that language is the primary
locus of intentionality and that thought inherits content from
language. However, few if any contemporary philosophers espouse this
viewpoint.) Thus, we should not analyze linguistic meaning as the
product of convention, so long as conventions are understood as
Lewisian systems of intentions, preferences, and expectations. Those
propositional attitudes are themselves intelligible only through their
relations to language. As Davidson puts it, "philosophers who
make convention a necessary element in language have the matter
backwards. The truth is rather that language is a condition for having
conventions" (1984, p. 280).




Two main difficulties face this approach. First, although philosophers
have offered various arguments for the thesis that thought is not
explanatorily prior to language, none of the arguments commands
widespread assent. Christopher Peacocke (1998) forcefully criticizes
many of the most well-known arguments. As things stand, the objection
constitutes not so much a *problem* for conventional theories
as a prospectus for a rival research program. The second and more
serious difficulty is that, so far, the rival research program has not
yielded results nearly as precise or systematic as existing
conventional theories. Perhaps the two most commanding theories within
the rival research program are Davidson's (1984) and Brandom's
(1994). Many contemporary philosophers feel that both theories
enshrine an overly "anti-realist" conception of mental
content. Moreover, neither theory yields detailed necessary and
sufficient conditions for linguistic meaning analogous to those
provided by Lewis.