Language-games (Wittgenstein, Waismann)
A language, and its usage / context expressed as a game. We understand the former by seeing it through the lens of the latter.
Questions that can be asked: wherefore this language construct? How do we arrive at agreement on a given usage?
Wittgenstein (note: where? we need this original source) created the concept of a language game, or a tiny language whose creation, purpose and nature was entirely captured by its usage. The example he gave, now famous, is the four-word "builder-assistant" language. A builder asks an assistant for blocks, pillars, slabs, or beams, who then fetches them. To achieve this, only four signals need be agreed upon. Their meaning is sensibly spoken of only with the full context of their use: speakers, listeners, and situations.
Lewis (1969) Lewis argues that such signals need not be iteratively established, or set by an authority, but arise from exploiting the spontaneous and inevitable regularities across situations, each as an instance of the coordination game.
Language games were, among other things, an exploration of the rule-following paradox (in simple terms, the lack of incentive to adhere to a rule that has been thus far followed), Kripke interprets Wittgenstein as redefining a rule as a property that arises from regular behaviour as opposed to inciting it, and regular behaviour itself as incentivized by the community of participants in the game, as a whole.
Lewis' extension of that concept explains language as convention, or a set of sentences that are each the result of a coordination game in a population of players, 2where every sentence is agreed to mean something particular by most speakers and listeners, most of the time. Truth is an important part of this formulation: truthful speech in a language is useful, and a given listener's trust in a given speaker's intent to communicate truthfully is the basis upon which the speaker's uuternance can be agreed to mean something. There are two complementary pitfalls to this particular aspect of Lewisian convention:
Lack of justification for new sentences: Hawthorne(1990) Hawthorne argued that Lewis' system cannot explain the intuitive meaning of very long sentences; when sentences are taken as the primary way to comprise a language, and the strength of the language as a convention rests on the truthfulness of the speakers, the status of a potential sentence cannot be endorsed, and every new sentence must be a new coordination game.
see Clark - "what's wrong with that? every new sentence can be a new coordination game. we just need to provide a good account for its shape within the rules of this game."
Lack of endorsement for rules: If rules are abstractions that arise from the primary, rather than the primary themselves, then there is no difference between a rule and a possible rule in practice. The number of possible rules for a given sentence is infinitely high, and clearly nonsensical in almost all cases (since we want to concern ourselves with almost none of the possible rules).
if you have a protocol to communicate in, you can (somehow) communicate about additions to the protocol. see ramanujam and parikh Parikh & Ramanujam, apparently.
The effort is to reconcile the need for a normative rule system with the assertion that any normative rule is philosophically unjustifiable.
This is only the case if "normative" is taken to mean "universally wise", or even largely so. A rule, as an abstraction, can see edits. Lewis (2002) proposes a rewrite rule that introduces a new word to a theory, by expressing the theory as a single sentence and attempting to substitute a term for any unique variable in the theory. Success indicates that the term denotes the variable.
Such simple edits to a language are readily conceivable. However, their occurrence as an operation of the users of the language is less well explored, and interesting.
Potential consequences, ie. if the means to edit a language's rules were expressible in that language such that players could successfully propose and carry out edits, then:
a given set of rules can be motivated by individual or coalition incentives, rather than an aggregate measure of efficiency (which measures as if it dropped players into their places without relevant histories)
the transition from one set of rules to another, and its costs, can be modeled.
In the earlier four-word example, if a builder fashions a new tool for himself - say a trowel - the addition of one more word to the language consists of making any vocalization that is not one of the four already established words, perhaps pointing or otherwise calling attention to the trowel. Both the builder and the assistant can perform this edit successfully. Regularities in the shared environment have been exploited, but they come from three distinct areas of interest: the shared environment to which the language is meant to apply (the trowel); a shared basis for action that is not the language (attention, the expectation that the other player also has attention that can be directed); and the existent language (not using a sound already in the lexicon).