Online Papers - Brian Weatherson

David Lewis 54
that, and it is common knowledge in P that, in almost any instance of S
among members of P,
1. almost everyone conforms to R;
2. almost everyone expects everyone else to conform to R;
3. almost everyone has approximately the same preferences regarding
all possible combinations of actions;
4. almost everyone prefers that any one more conform to R, on condition
that almost everyone conform to R;
5. almost everyone would prefer that any one more conform to R ′ , on
condition that almost everyone conform to R ′ ,
where R ′ is some possible regularity in the behaviour of members of P in
S, such that almost no one in almost any instance of S among members
of P could conform to both R ′ and to R. (Lewis, 1969a, 78)
This is clearly a vague definition, with many ‘almost’s scattered throughout. But
Lewis, characteristically, thought this was a feature not a bug of the view. Our intuitive
notion of a convention is vague, and any analysis of it should capture the vagueness.
The idea that analyses of imprecise folk concepts should be imprecise recurs
throughout Lewis’s career.
The notion of ‘common knowledge’ that Lewis is working with here is not the
standard modern notion. Lewis does not require that everyone know that everyone
know etc., that all of these conditions hold. Rather, when Lewis says that it is common
knowledge that p, he means that everyone has a reason to believe that p, and
everyone has a reason to believe everyone has a reason to believe that p, and everyone
has a reason to believe that everyone has a reason to believe everyone has a reason to
believe that p, and so on. That people act on these reasons, or are known to act on
these reasons, to form beliefs is unnecessary. And that the beliefs people would get if
they acted on their reasons are true is also not part of the view. Hence it is necessary
to specify truth as well as common belief in the definition.
Lewis argues that this definition captures many of our ordinary conventions, such
as the convention of driving on the right side of the road in the United States, the
convention of taking certain pieces of paper as payments for debts, and, most importantly,
the conventions governing the use of language.
2.2 Conventions of Language
In the final chapter of Convention, Lewis gives his theory of what it is for a community
to speak a language (see the section on conventional theories of meaning in the
entry on convention), i.e., for a community to have adopted one language as their
language by convention. Lewis individuates languages largely by the truth conditions
they assign to sentences. And his account of truth conditions is given in terms
of possible worlds. So the truth condition of an indicative sentence is the set of possible
worlds in which it is true. Somewhat more abnormally, Lewis takes the truth
condition for an imperative to be the set of possible worlds in which the imperative