Wednesday, March 12, 2014

A theory of contingency and an argument for a causal Principle of Sufficient Reason

Consider this theory, a modification of my causal power account of possibility:

  • A proposition p is contingent provided that something has a power for p and something has a power for not-p.
Here, I say that x has a power for p if and only if x has the power to bring p about, or x has the power to bring it about that something has the power to bring p about, or ....

It follows from this theory that every contingent true propositions has a causal explanation.

For suppose for reductio ad absurdum that p is contingently true and has no causal explanation. Let q be the conjunction of p with the claim that p has no causal explanation. Then q is true, and it is not necessarily true since p is not necessarily true, so q is contingent. It follows from our account of contingency that something has the power to ... bring q about (where the "..." is a possible chain of causal power claims). But that's absurd, since something that brings q about thereby also brings p about, and then p isn't bereft of causal explanation!


Heath White said...

I'm not seeing how the proof is supposed to go. My thought is that just because something has a power to bring about p, doesn't mean that it exercised that power. What is wrong with the conjunction of (a) p, (b) something has a power to bring about p, (c) something has a power to bring about not-p, and (d) nothing exercised its power to bring about p. Then by (a) p is true, by (b) and (c) it is contingent on your definition, but by (d) it has no causal explanation.

Alexander R Pruss said...

Yeah, but if it has that power, then it *can* exercise it.

As for your case, apply the account not to p, but to q: "p and p has no causal explanation".

vexingquestions said...

Dr. Pruss,

Clearly in supposing p is contingent, q is contingent. But your say that your account of contingency means that q has a causal explanation. If so, are you not begging the question that p has an explanation simply by stipulating a definition of "contingent" that entails some sort of causal-power explanation?



Alexander R Pruss said...

Questions of begging the question are tricky. Of course, like in any valid argument, the premises imply the conclusion. But notice that I don't say in the account of contingency that p has a causal explanation, only that *something* has the power to cause (a chain causing) p to be true. Prima facie (but not ultima facie) that's compatible with nothing actually causing p to be true.

William said...

Let's define a "holding back" as something with a power to prevent x from exercising its power that not p.

q is "p and p has no causal explanation".

Then a "holding back" for p can be one of the explanations for q.

So, because of the "holding back" causal explanation factor for q, "p and p has no causal explanation."

Of course, this is also compatible with the proposition

"(not p) and p has no causal explanation"

also. But you stipulated p as true already.

Alexander R Pruss said...

But if something explains a conjunction, it explains each conjunct. So the holding back will explain p, too.

William said...

I think the holding back explains only the proposition below without or prior to the stipulation that p is true:

( p and p has no causal explanation ) OR ( (not p) and p has no causal explanation )

and then since you stipulated p is true, it explains p, because of the stipulation otherwise not.

It confuses me, but I think maybe this means a universe where the above definition of contingency holds, everything has a causal explanation AFTER the fact, but there can be no causal necessity for something like

( p will be true and p has no causal explanation until it is true )

to allow valid predictions before the fact is stipulated.