Tuesday, March 13, 2012

Lewis on bias and analogy in Convention (1969)

David K. Lewis' short book Convention: A Philosophical Study (1969) is an attempt to explain meaning in terms of equilibria in coordination games. The concepts that do the most of the heavy lifting are precedent, analogy, and salience.

The Ambiguity of Precedent
Lewis is aware that no two situations are ever alike, and that agent thus have to engage in some kind of extrapolation:
Suppose not that we are given the original problem again, but rather that we are given a new coordination problem analogous somehow to the original one. Guided by whatever analogy we notice, we tend to follow precedent by trying for a coordination equilibrium in the new problem which uniquely corresponds to the one we reached before. (p. 37)
A consequence of this is ambiguity. He immediately continues:
There might be alternative analogies. If  so, there is room for ambiguity about what would be following precedent and doing what we did before. Suppose that yesterday I called you on the telephone and I called back when we were cut off. We have a precedent in which I called back and a precedent—the same one—in which the original caller called back. But this time you are the original caller. No matter what I do this time, I do something analogous to what we did before. Our ambiguous precedent does not help us. (p. 37)
Or, that is exactly the big question: Whether and when precedent decides or even strictly determines what a construction means in some new situation.

Finding A Relevant Precedent
We then have a two-dimensional similarity space (me/you differences and caller/receiver differences). If these dimensions have the same weight, then both analogies yield the same average fit:

The big question is then how convention is possible at all, if everything is similar to everything else in some respects. Some sense of immediate similarity must be picked up along the way or have been there all along.

Lewis doesn't seem to have any psychological theory of salience or of similarity between new and old situations. However, one could construct a similarity measure based on possible courses of action, so that situations are similar when their elements can be handled in a similar way.

For instance, electricity can be much like water because many of our intuitions about how it behaves are reliable. Thus source elements such as "source," "direction," "pressure," etc. can be paired with certain target elements without needing much behavioral adjustment.

Similarly, source elements as "front" and "back" can be paired with the screen-side and the wall-side of a television in either of two ways. These pairings will on average require less behavioral adjustment than, say, pairing "head" and "feet" with screen-side and wall-side. A few candidate analogies are thus consistent with our prior knowledge, although no single analogy takes absolute priority.

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