Abstract
The Standard View is that, other things equal, speakers’ judgments about the meanings of sentences of their language are correct. After all, we make the meanings, so how wrong can we be about them? The Standard View underlies the Elicitation Method, a typical method in semantic fieldwork, according to which we should work out the truth-conditions of a sentence by eliciting speakers’ judgments about its truth-value in different situations. I put pressure on the Standard View and therefore on the Elicitation Method: for quite straightforward reasons, speakers can be radically mistaken about meanings. Lewis (Convention: A Philosophical Study, Harvard University Press, Cambridge, 1969) gave a theory of convention in a game-theoretic framework. He showed how conventions could arise from repeated coordination games, and, as a special case, how meanings could arise from repeated signaling games. I put pressure on the Standard View by building on Lewis’s framework. I construct coordination games in which the players can be wrong about their conventions, and signaling games in which the players can be wrong about their messages’ meanings. The key idea is straightforward: knowing your own strategy and payoff needn’t determine what the others do, so leaves room for false beliefs about the convention and meanings. The examples are simple, explicit, new in kind, and based on an independently plausible meta-semantic story.
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Notes
Thanks to Alex Byrne, Thomas Byrne, Nilanjan Das, Kevin Dorst, Justin Khoo, Vann McGee, Milo Phillips-Brown, Daniel Rothschild, Kieran Setiya, Robert Stalnaker, and two anonymous referees for helpful comments.
Perhaps we learn more than this. You learn that I learn that you played U; I learn that you learn that I played R. And so on, up the hierarchy.
Thanks to an anonymous referee for pressing this point and supplying the example.
All orphan page numbers refer to Lewis (1969).
I give the actions different labels: ‘U’ or ‘D’ for Rowena, ‘L’ or ‘R’ for Colin, ‘W’ or ‘E’ for Mattea. That makes things easier to follow. But different labels needn’t mean different actions. For example, U, L, and W can all be the same action. See Sect. 4.3 for an example. Thanks to an anonymous referee for pressing me to clarify this.
A warning. After the players make their moves, each gets a payoff—lunch, for example. The numbers in the matrices—utilities—represent the players’ preferences over the payoffs. Utilities are coarser-grained than payoffs: if a player is indifferent between two payoffs (chicken and beef, say), then those payoffs have the same utility, even though the player may be able to tell apart the outcome in which they get the one (chicken) from the outcome in which they get the other (beef). Now, for the games in this paper, it matters which outcomes the players can tell apart. So the payoffs matter, not just the utilities. Therefore—and this is the key point—in all the games interpret the utilities in the matrices as normal, as representing the players’ preferences over the payoffs, except also assume that where the utilities are the same, the payoffs are the same too.
The Nature Game is known as a Bayesian game, because Roland and Col have incomplete information about the payoffs.
The situation includes the initial choice by Nature. The game is either the West Game or East Game. The structure of the game is not common knowledge, since the players don’t know which game Nature chooses. The structure of the situation is common knowledge.
Daniel Rothschild suggested this kind of example, but I don’t mean to imply that he agrees with what I say about it.
Suppose, for example, that there are eight players, each with two actions, 0 or 1. If an even number of players choose 1, all get lunch; else, nothing. Suppose they all eventually play 0, getting lunch every time, but, for one reason or another, two believe that they both play 0 and the other six play 1, while the six believe that those two play 1 and they all play 0.
The belief that Colin and Mattea will either play UR or LW won’t lead Rowena to a false belief about the convention. I mention it just to point out that a player may have correlated beliefs about her opponents’ actions. In other games, correlated beliefs may lead to false beliefs about the convention.
See Stalnaker (1998, pp. 43–44) for discussion of this point. To borrow one of his examples, suppose my partner and I are in our voting booths on election day. How she votes is causally independent of how I vote. You may have no idea how either of us will vote, but still be confident (and justifiably so) that, however we vote, we’ll vote the same way.
Thanks to an anonymous referee for pressing me on this point.
Gilbert (1981) pointed out that the term ‘proper coordination equilibrium’ is ambiguous, and Lewis didn’t make clear which he intended. Gilbert reports that Lewis clarified in private communication that this is what he had in mind.
p. 42.
p. 78.
He describes a further qualification, too, involving Abelard’s distinction between beliefs and expectations in sensu composito and in sensu diviso. See pp. 64–68.
Or perhaps \(m_1\) means the first coin landed heads and \(m_2\) means the second coin landed heads, and so on. We needn’t decide the matter here.
Note that the matrices don’t represent the games in strategic form; rather, they represent the payoffs for each state-act pair, from which the strategic forms may be derived, given a probability distribution over the states.
Isn’t it obvious what the players should do, namely, send \(m_i\) in \(s_i\) and do \(r_i\) given \(s_i\)? No. That confuses a property of our representation (how we label the states, messages and responses) with a property of what we’re representing.
Thanks to an anonymous referee for pressing this point.
For the ABC Game, things are not completely straightforward, because we don’t know what Sienna will do as a receiver. But if we suppose that she behaves the same way no matter which receiver she swaps with, then things will go wrong.
Lewis suggests when we should interpret them as indicatives and when as imperatives. See pp. 143–147. See also Millikan (1995).
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Grant, C. Mistakes About Conventions and Meanings. Topoi 40, 71–85 (2021). https://doi.org/10.1007/s11245-019-09656-3
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DOI: https://doi.org/10.1007/s11245-019-09656-3