Convention: A Philosophical Study

What is the role of rationality in understanding the nature of conventions? Prior to Lewis, philosophers mostly considered conventions to be determined by "agreement," and thereby consigned their study to game theory. For David Lewis, conventions are social regularities, and hence do not reduce to issues in pure interactive epistemology. This shocking, anti-methodological individualist conclusion, is shared by Thomas Schelling, whose key notion of "salience" and "focal point" equilibria, inspired Lewis's emphasis on precedence.The idea that I conform to a social practice because I believe everyone else will, and I believe everyone else will because everyone else did so last time around, or even since time immemorial, is prima facie highly plausible, but it suffers from the same problem as inductive inference, which surely works in the real world, but does not follow from some principle of logic or rational inference. There just happen to be "natural kinds" in the universe, such as solid bodies, for which inductive inference works, while other entities that we can freely construct in our mind but do not exist, violate the principle of inductive inference (such, for instance, as Nelson Goodman's famous concept of the color `grue').It is striking that Lewis's basic explanation of conventions in terms of precedence is meant to apply only to pure coordination problems, but in fact almost never does Lewis use any property of a pure coordination game other than the fact that an equilibrium is a strict Nash equilibrium (Nash is not cited in the Index). Informally, Lewis discusses additional properties of coordination problems, including the notion that a shift of strategy by a single player makes all worse off, and the notion that agents are close to indifferent as to which of several equilibria is actually chosen. But, as far as I can see, Lewis' remarks apply to the far wider class of games with multiple strict Nash equilibria. Lewis think that the absence of "substantial conflict of interest" is important in his analysis, but in fact, there is no point at which this assumption is formally deployed to achieve some conclusion.Lewis's genius, and there is no doubt but this book is a work of genius, lies in his success in linking the non-individualist concept of "precedent" with standard game theory and interactive epistemology by exploring the following argument. Suppose each agent is rational and hence takes an action only if there are grounds for believing this is the best action to take. Then, I cannot expect that everyone else will do x simply because each argues that that's what everyone else did the last time the occasion arose. Rather, everyone else will seek rational grounds for doing x. My rational grounds for doing x is that this is optimal for me providing I expect everyone else will expect everyone else to do x as well. This type of reasoning of course leads to an infinite spiral of i believes j believes k believes l believes, and so on, for all finite sequences i,j,k,l,...Lewis concludes, for conventions to work with rational agents, it must be "commonknowledge" that people are rational and have rational grounds for doing x. Lewis's task in the middle section of this book is to explain how common knowledge, which is a naturally infinitary concept, could possibly come about in real life. Lewis also supplies an answer, or at least a sketch of an answer.It is crucial that Lewis does not attempt to describe how a convention (or any other Nash equilibrium) might come about, but only why a rational agent would obey a convention (or a Nash equilibrium) once it has been attained. The issue of how social regularities are instituted in society is a deep and unanswered question, going far beyond the issues dealt with in this book. I believe we need gene-culture coevolutionary theory to answer this question, but that is another story.It is interesting that game theorists generally acknowledge Lewis as the first to study the concept of common knowledge, but completely ignore his theory of how a state of affairs, call it A, could become common knowledge. The Achilles heel of classical game theory is precisely that it is totally dependent on the concept of common knowledge, but gives absolutely no conditions under which a state of affairs A might become common knowledge. Lewis provides an answer, but this too goes beyond methodological individualism, and depends upon non-rational properties of being human.When is an event common knowledge? For concreteness, suppose Ann and Bob are sipping tea and Carl runs in the room, hand dripping in blood, and exclaims "I've cut myself.'' If Ann and Bob are of normal intelligence and in possession of their five senses, the event A, that Carl has claimed to have cut himself, is common knowledge for Ann and Bob. Ann knows it. Bob knows it. Ann knows that Bob knows it because she saw Bob in the room looking at Carl and listening to him. For similar reasons, Bob knows that Ann knows that Bob knows it, because Bob saw her looking at him when Carl made his announcement. And so on.Lewis' argument is on p. 52, and goes like this. What is it about A that explains the generation of these higher-order expectations? (1) Ann and Bob have reason to believe that A holds; (2) A indicates to Ann and Bob that they each have reason to believe that A holds; and (3) A indicates to Ann and Bob that Carl claims he cut his hand. Lewis shows in some detail how these three statements imply common knowledge of Carl's claim A. Lewis' argument is laid out in detail and with great clarity in a brilliant paper by Cubitt and Sugden, published in Economics and Philosophy (1993). These authors conform to Lewis' limitation of his argument to games of pure coordination, but there is nothing in their argument that limits its application to such games. All strict Nash equilibria of repeated games could be analyzed similarly.Ultimately, the "reason to believe" in (2) cannot be explained in purely individualist or rationalist terms, but rather requires that humans recognize certain basic symmetries of the form "if I have rational grounds for believing x, then so do you." This fundamental symmetry lies in the realm of human nature and human psychology, is probably lacking in many other species, and is itself the product of gene-culture coevolution is humans. The bottom line is that Lewis (and Cubitt and Sugden) begin to give us a handle on linking human rationality with human sociality, which is a quite different thing.

clarifies lot of things.

As important as any work of philosophy published in English since "Philosophical Investigations". Nobody ever assigned me this book when I was studying philosophy, and yet if you haven't read it carefully at least three times you won't really know anything about what actually happened after "Two Dogmas of Empiricism", or what's going on now.The comment by Gintis about pure coordination games seems whiggish - you have to read the book in the context of what was happening in game theory then, what Schelling himself was saying. Of course things have been tidied up now, and the definitions are all more precise, but you can't criticize Lewis for not predicting the future in 1969. I'm not sure he ever actually says the theory is only supposed to apply to pure coordination games. As Gintis himself points out, none of the examples he used support that theory.In fact. if we do want to read whiggishly, a much more interesting claim can be extracted from the book. It's clear from what Lewis says about the way conventions can function as traps that not all of them are in the Core... Which would make no sense if all of them are equilibriums in games of pure coordination.

This book does what it purports to do, analyse convention. It is writtin the the spirit of Quine and Carnap's style of philisophical analysis, and is a fantastic book if you are familiar with thier work (especially Carnap's "Meaning and Necessity" and Quines "Word and Object" and "From a Logical Point of View" all of which are avialable). There is a significant amount of game theoretical explanation in the first part of the book and would be a great as an example of what game theory is capable of doing (besides the usual economic and biological examples). A great book by a great philosopher and a great writer.