David Lewis, answered from the texts and cited to the page.
A regularity R in the behavior of a population P is a convention if and only if: (1) almost everyone conforms to R; (2) almost everyone expects almost everyone else to conform to R; (3) almost everyone prefers to conform to R on the condition that almost everyone else does; (4) almost everyone would prefer that almost everyone conform to some R' rather than to no regularity (so the regularity is sustaining itself by mutual expectation, not by force or coincidence); (5) the conditions just listed are matters of common knowledge in P; and (6) there is at least one alternative regularity R' that would have served almost as well and that would have been similarly stable had it arisen instead (the arbitrariness condition that distinguishes a convention from a forced response).123
This analysis treats conventions as solutions to coordination problems sustained by mutual expectations, without any requirement of explicit agreement or a moment of founding or any other historical fiction. The extension to language in "Languages and Language" (1975) treats a language L as a function from sentences in contexts to truth-conditions; a population uses L just in case there is in P a convention of truthfulness in L (one tries to utter sentences of L only when they are true-in-L-in-context) and trust in L (one expects others to be truthful in L, and on that basis relies on their utterances as evidence for what they believe to be true).4
The conventions of truthfulness and trust together explain what it is for a population to speak a given language — without invoking either an inner grasp of meaning or a public agreement that semantics somehow ratifies.5
More precisely: a regularity R, in action or in action and belief, is a convention > Languages and Language > 16$ in a population P if and only if, within P, the following six conditions hold. (Or at least they almost hold.Part 3: Philosophy of Language, p. 165
There is at least one alternative R' such that the belief that the others conformed to R' would give everyone a good and decisive practical or epistemic reason to conform to R' likewise; such that there is a general preference for general conformity to R' rather than slightly-less-than-general conformity to R'∙, and such that there is nor mally no way of conforming to R and R' both.Part 3: Philosophy of Language, pp. 165–166
Then the regularity of truthfulness and trust in £z is an alternative to the prevailing regularity of truthfulness and trust in £. For the alternative regularity, as for the actual one, general conformity by the others would give one a reason to conform; and general conformity would be gen erally preferred over slightly-less-than-general conformity.Part 3: Philosophy of Language, pp. 168–169
To be truthful in L is to avoid uttering any sentence of L unless it is true in L; to be trusting in L is to expect others to be truthful in L. We (or any population) use L iff, by convention, we are truthful and trusting in L. (A convention is a regularity in the population that is sustained, in a certain way, by expectation of others' conformity.12 Meaning without use: Reply to Hawthorne, pp. 146–147
It has a certain meaning in P if and only if it has that meaning in some language £ which is used in P. It is true in P at a world w if and only is it is true at w in some language £ which is used in P. It is true in P if and only if it is true in some language £ which is used in P.Part 3: Philosophy of Language, pp. 169–170
Convention (1969) founded the contemporary philosophical literature on convention and remains the standard reference; the 1975 extension to language is the foundational Lewisian alternative to the Gricean speaker-meaning-first program and the Davidsonian radical- interpretation program. The principal contemporary alternatives are Margaret Gilbert's plural-subject account (On Social Facts 1989 and subsequent work), which holds that genuine social facts require joint commitment of a kind Lewisian mutual expectations cannot capture; Bratman's shared-intention framework; the Gricean speaker-meaning tradition; and the contemporary game- theoretic descendants in economics and political science (Sugden, Young, Skyrms). The common-knowledge condition has been weakened by Sillari, Vanderschraaf, and others on grounds that the iterated-knowledge requirement is too strong for the conventions ordinary speakers actually sustain.