Rule-following as coordination: a game-theoretic approach

Abstract

Famously, Kripke has argued that the central portion of the Philosophical Investigations describes both a skeptical paradox and its skeptical solution. Solving the paradox involves the element of the community, which determines correctness conditions for rule-following behavior. What do such conditions precisely consist of? Is it accurate to say that there is no fact to the matter of rule following? How are the correctness conditions sustained in the community? My answers to these questions revolve around the idea (cf. P.I. § §198, 199) that a rule is followed insofar as a convention is in place. In particular, I consider the game-theoretic definition of convention offered by David Lewis and I show that it illuminates essential aspects of the communitarian understanding of rule-following.Make the following experiment: say "It's cold here" and mean "It's warm here". Can you do it?Ludwig Wittgenstein, Philosophical Investigations, 1953, §510.I can't say "it's cold here" and mean "it's warm here"-at least, not without a little help from my friends.David Lewis, Convention. Rule-following as coordination: A game-theoretic approach Giacomo Sillari University of PennsylvaniaMake the following experiment: say "It"s cold here" and mean "It"s warm here". Can you do it?Ludwig Wittgenstein, Philosophical Investigations, §510.I can"t say "it"s cold here" and mean "it"s warm here"-at least, not without a little help from my friends.David Lewis, Convention. AbstractFamously, Kripke has argued that the central portion of the Philosophical Investigations describes both a skeptical paradox and its skeptical solution. Solving the paradox involves the element of the community, which determines correctness conditions for rulefollowing behavior. What do such conditions precisely consist of? Is it accurate to say that there is no fact to the matter of rule following? How are the correctness conditions sustained in the community? My answers to these questions revolve around the idea (cf. P.I. § § 198, 199) that a rule is followed insofar as a convention is in place. In particular, I consider the game-theoretic definition of convention offered by David Lewis and I show that it illuminates important elements of the communitarian understanding of rulefollowing 1 .

Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals

“…The contribution of this paper is twofold: first, I suggest that CBR provides a useful and insightful perspective to formalize Schelling's account of focal points but also Saul Kripke's [6] "collectivist solution" to Wittgenstein's so-called rule-following paradox. The latter strengthens a claim already made by Giacomo Sillari [7]. Second, I argue that a formalization of CBR brings interesting insights over the issue of epistemic and causal (in)dependence in normal form games.…”

“…As he pointed out, the very possibility for a state of affairs to become common knowledge (or common belief) depends on "suitable ancillary premises regarding our rationality, inductive standards, and background information" (p. 53). Lewis' account also relies on the key notion of indication (see [2,7]) which broadly corresponds to the various forms of inductive standards that one may use. The inductive inference mentioned in step (d) can be understood in terms of Lewis' indication notion.…”

“…It can be seen as a list of true propositions about the strategies chosen by the players, what they know and believe, and so on. 7 Therefore, the actual state w* specifies how the game is actually played while all the other states w' indicate how the game would have been played or could have been played. C i : W S i is player i's decision function; it indicates what strategy i is playing in each possible world.…”

“…What I am tacitly assuming is that one cannot endorse community-based reasoning if he regards it as invalid. 7 In logic, it is usual to write explicitly as a counterpart to the semantic models a syntax, i.e., a list of propositions that are derived from a set of axioms on the basis of an alphabet. The semantics is derived from the syntax by building a state space on the basis of a truth value function that indicates for each state whether a given proposition is true or false.…”

“…This can be seen as a requirement that the players have a common understanding of the situation they are embedded in and which shares some similarities with Wittgenstein's notion of lebensform (forms of life) [7,26]. The precise nature of this condition has been left undefined as we do not have a full understanding of the cognitive mechanisms through which individuals are able to replicate others' reasoning.…”