## Monday, March 3, 2014

### Explaining the contingent via the necessary

It has been claimed that contingent truths cannot be explained by necessary ones. Indeed, Peter van Inwagen has contended that this shows that the Principle of Sufficient Reason is false. But it seems that here is a case of a necessary truth explaining a contingent one: That it's extremely unlikely that 30 fair die throws would be all sixes explains why nobody has tossed 30 sixes in a row with a fair die.

lukebarnes said...

Just a thought ... don't you have to add to this explanation the fact that the total number of dice throws that have ever happened is much smaller than 6^30?

Alexander R Pruss said...

Fair enough.

Revised version: The probability fact explains why the first 30 die tosses that have occurred weren't all sixes.

tblogardus said...
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tblogardus said...

Part of the explanation of why the first 30 die tosses that have occurred weren't all sixes, it seems to me, is that the dice were fair dice. (If they weren't fair dice, that probability fact you mention concerning fair dice would hardly explain the phenomenon!) And that they were fair dice is a contingent fact. So the full explanation is a conjunction of a necessary probability fact and that contingent fact. So the full explanation is really a contingent fact.

Objection: you (originally) designed the explanandum so that it entails that the dice were fair. So that can't figure into the explanans (or at least it need not). Response: that p is entailed by the explanandum is no barrier to p's figuring into the explanans, or even to p's *needing* to figure into the explanans. Suppose I want to know why the window broke in a funny star shape. I'm pretty sure any good explanation will have to mention the window's breaking, or at least that there was a window, or at least that there's something.

Alexander R Pruss said...

Yeah, I forgot to add "fair" in my modified version.

You can add to the explanation, if you like, that either there were no 30 first fair die tosses or there were 30 first fair die tosses. A necessary truth.

Mike Almeida said...

But PvI says that because he assumes that explanation goes by entailment. If P entails Q and P is necessary, then Q is necessary (not contingent).

Mike Almeida said...
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Alexander R Pruss said...

Actually, I've convinced PvI that explanation doesn't require entailment, but he still held that the contingent cannot explain the necessary.

tblogardus said...

You can add to the explanation, if you like, that either there were no 30 first fair die tosses or there were 30 first fair die tosses. A necessary truth.

For simplicity:

p = it's extremely unlikely that the first 30 fair die throws would be all sixes
q = there were 30 first fair die tosses
r = the first 30 die tosses that have occurred weren't all sixes

p&(q or ~q) explains r. After all, p&(q or ~q) entails that there is an explanation of r, like so:

1. p & (q or ~q)
2. So, (p & q) or (p & ~q)
3. If (p & q), then there is an explanation of r.
4. If (p & ~q), then there is an explanation of r.
5. Therefore, there is an explanation of r.

I think that's right: p&(q or ~q) entails that there's an explanation of r. But it doesn't follow that p&(q or ~q) explains r! For in the consequent of 3, the explanation of r would crucially involve q, a contingent truth. And in the consequent of 4, the explanation would crucially involve ~q, another contingent truth. Two different explanations in each case, both crucially involving contingent truths. In neither case does p&(q or ~q)--that necessary truth--do the explanatory work. In both cases it's a contingent truth doing the explaining.

It's like this case. We see a broken window and wonder what explains it. We learn that Timmy was playing outside, and he threw either a brick or a baseball through the window. THAT information doesn't explain why the window broke--we still don't know why it broke! But that information does entail that there is an explanation, and it's either that Timmy was playing outside and threw a brick at the window, OR that Timmy was playing outside and threw a baseball at the window. It's possible for some proposition to entail that there is an explanation of a phenomenon, without that proposition itself explaining that phenomenon. That, I think, is what's happening with the proposition p&(q or ~q) and the phenomenon r.

Alexander R Pruss said...

Maybe the fact that there were 30 first fair die tosses shouldn't figure in the explanation because it makes the explanandum *more* likely?

tblogardus said...

Maybe the fact that there were 30 first fair die tosses shouldn't figure in the explanation because it makes the explanandum *more* likely?

I didn't understand this. Could you elaborate? Why shouldn't an explanation raise the probability of an explanandum? Sometimes good explanations raise the probability of their explananda (indeed, if explanation requires entailment, this always happens).

Alexander R Pruss said...

Sorry, I meant to say that it makes the negation of the explanandum more likely. :-)

tblogardus said...

So it sounds like you're saying that if p raises the probability of ~q, then p cannot/shouldn't figure into an explanation of q.

But...

This dead bird is on the ground here (q) because he was shot while he was flying overhead.

That he was flying overhead (p) raises the probability of ~q. Yet p can (and should) still figure into the explanation of q.

Alexander R Pruss said...

I think that the bird was flying overhead does raise the probability that it is now on the ground. After all, it tells you that the bird was in the vicinity.

But there may be a similar kind of counterexample to the general claim that we don't include in the explanans things that lower the probability of the explanandum. For instance, suppose that the house burnt down because (a) the house caught on fire from a candle, and (b) when the fire truck was on its way, it got a flat tire. It seems that the explanation could include the fact that the fire truck was on its way.

Could but perhaps doesn't have to. Maybe a better explanation is: (a) the house caught on fire from a candle and (b) no fire truck made it. Then the explanation of (b) is the flat tire.

tblogardus said...

I think that the bird was flying overhead does raise the probability that it is now on the ground. After all, it tells you that the bird was in the vicinity.

I don't think I'm with you on that one, but we could change the proposition to just that the bird was flying. That doesn't tell you the bird was in the vicinity, and it sure seems like it doesn't raise the probability that it's now on the ground here.

This dead bird is on the ground here (q) because he was shot while he was flying overhead.

That he was flying (p) raises the probability of ~q. Yet p can (and should) still figure into the explanation of q.