Online Papers - Brian Weatherson

David Lewis 69
5.1 Laws and Chances
Lewis’s reductionist project starts with laws of nature. Building on some scattered
remarks by Ramsey and Mill, Lewis proposed a version of the ‘best-system’ theory
of laws of nature. There is no paper devoted to this view, but it is discussed in section
3.3 of Counterfactuals, in “New Work For a Theory of Universals”, extensively in
Postscript C to the reprint of “A Subjectivist’s Guide to Objective Chance” in (1986c),
and in “Humean Supervenience Debugged” (1994a).
The simple version of the theory is that the laws are the winners of a ‘competition’
among all collections of truths. Some truths are simple, e.g. the truth that
this table is brown. Some truths are strong; they tell us a lot about the world. For
example, the conjunction of every truth in this Encyclopedia rules out a large chunk
of modal space. Typically, these are exclusive categories; simple truths are not strong,
and strong truths are not simple. But there are some exceptions. The truth that any
two objects are attracted to one another, with a force proportional to the product of
their masses and inversely proportional to the distance between them, is relatively
simple, but also quite strong in that it tells us a lot about the forces between many
distinct objects. The laws, says Lewis, are these simple but strong truths.
Two qualifications are needed before we get to Lewis’s 1973 view of laws. It is
collections of truths, not individual truths, that are measured and compared for simplicity
and strength. And it is not every truth in the winning collection (or best
system), but only the generalisations within it, that are laws. So even if the best system
includes particular facts about the Big Bang or its immediate aftermath, e.g. that
the early universe was a low entropy state, those facts are not laws on Lewis’s view.
In “New Work For a Theory of Universals”, Lewis notes another restriction that
is needed. If we measure the simplicity of some truths by the length of their statement
in an arbitrarily chosen language, then any truth at all can be made simple. Let
Fx be true iff x is in a world where every truth in this Encyclopedia is true. Then Everything
is F is simply stateable in a language containing F, and is presumably strong.
So Everything is F will be a law. But this kind of construction would clearly trivialise
the theory of laws. Lewis’s solution is to say that we measure the simplicity of a claim
by how easily stateable it is in a language where all predicates denote perfectly natural
properties. He notes that this move requires that the natural properties are specified
prior to specifying the laws, which means that we can’t reductively specify naturalness
in terms of laws. (In any case, since Lewis holds that laws are contingent (1986b,
91) but which properties are natural is not contingent (1986b, 60n), this approach
would not be open to Lewis.)
In “Humean Supervenience Debugged”, Lewis notes how to extend this theory
to indeterministic worlds. Some laws don’t say what will happen, but what will have
a chance of happening. If the chances of events could be determined antecedently
to the laws being determined, we could let facts about chances be treated more or
less like any other fact for the purposes of our ‘competition’. But, as we’ll see, Lewis
doesn’t think the prospects for doing this are very promising. So instead he aims to
reduce laws and chances simultaneously to distributions of properties.