Online Papers - Brian Weatherson

David Lewis 70
Instead of ranking collections of truths by two measures, strength and simplicity,
we will rank them by three, strength, simplicity and fit. A collection of truths that
entails that what does happen has (at earlier times) a higher chance of happening
has better fit than a collection that entails that what happens had a lower chance of
happening. The laws are those generalisations in the collection of truths that do the
best by these three measures of strength, simplicity and fit. The collection will entail
various ‘history-to-chance’ conditionals. These are conditionals of the form If H t then
P t (A) = x, where H t is a proposition about the history of the world to t, and P t is the
function from propositions to their chance at t. The chance of A at t in w is x iff there
is some such conditional If H t then P t (A) = x, where H t is the history of w to t.
The position that I’ve sketched here is the position that Lewis says that he originally
was drawn towards in 1975, and that he endorsed in print in 1994. (The dates are
from his own description of the evolution of his views in (1994a).) But in between, in
both (1980c) and Postscript C to its reprinting in (1986c), he rejected this position because
he thought it conflicted with a non-negotiable conceptual truth about chance.
This truth was what he called the “Principal Principle”.
The Principal Principle says that a rational agent conforms their credences to the
chances. More precisely, it says the following is true. Assume we have a number x,
proposition A, time t, rational agent whose evidence is entirely about times up to and
including t, and a proposition E that (a) is about times up to and including t and (b)
entails that the chance of A at t is x. In any such case, the agent’s credence in A given
E is x.
An agent who knows what happens after t need not be guided by chances at t. If
I’ve seen the coin land heads, that its chance of landing heads was 0.5 at some earlier
time is no reason to have my credence in heads be 0.5. Conversely, if all I know is
that the chance is 0.5, that’s no reason for my conditional credence in heads to be 0.5
conditional on anything at all. Conditional on it landing heads, my credence in heads
is 1, for instance. But given these two restrictions, the Principal Principle seems like
a good constraint. Lewis calls evidence about times after t ‘inadmissible’, which lets
us give a slightly more concise summary of what the Principal Principle says. For
agents with no inadmissible evidence, the rational credence in A, conditional on the
chance of A being x, combined with any admissible evidence, is x.
The problem Lewis faced in the 1980s papers is that the best systems account
of chance makes the Principal Principle either useless or false. Here is a somewhat
stylised example. (I make no claims about the physical plausibility of this setup;
more plausible examples would be more complicated, but would make much the
same point.) Let t be some time before any particle has decayed. Let A be the proposition
that every radioactive particle will decay before it reaches its actual half-life.
At t, A has a positive chance of occurring. Indeed, its chance is 1 in 2 n , where n is
the number of radioactive particles in the world. (Assume, again for the sake of our
stylised example, that n is finite.) But if A occurred, the best system of the world
would be different from how it actually is. It would improve fit, for instance, to say
that the chance of decay within the actual half-life would be 1. So someone who
knows that the chance of A is 1 in 2 n knows that A won’t happen.