Thursday, July 5, 2012

From ease to counterfactuals?

Consider the concept of how easy it is for a proposition to be made true, given how things are. It is by far easiest for propositions that are already true: nothing more needs to happen. It is hardest for self-contradictory propositions, like that Socrates is not Socrates: there is no way at all for it to happen. Contingently false propositions that require changes that go far back in time are going to be harder to be made true than ones that don't. And we can talk of the ease of p being made false as just the ease of not-p being made true. So, we can offer this account of counterfactuals:

  • pq holds if and only if it is easier for p to be made true than for the material conditional pq to be made false.

This yields the Lewis-Stalnaker account of counterfactuals provided that we stipulate that a is easier to be made true than b if and only if there is a world where a holds which is closer than every world where b holds.

But we need not make this stipulation. We might instead take the easier to be made true relation as more fundamental. (And while we might define a closeness relation in terms of it—say, by saying that w1 is closer than w2 iff <w1 is actual> is easier to be made true than <w2 is actual>—depending on which axioms easier to be made true satisfies, that might not yield an account equivalent to the Lewis-Stalnaker one.)

On some assumptions, this is a variant of the central idea in yesterday's post.


Heath White said...

What occurs to me is that it makes sense to ask "easier for who?" whereas there is no corresponding question about nearness.

I'm not sure what else to do with that observation or whether it is a plus or a minus for the theory.

Alexander R Pruss said...

That's true. And maybe "easier" makes no sense apart from a cause. So this approach may require something like my causal account of modality.