Wednesday, March 7, 2012

Of chocolates and laws

According to David Lewis, the fundamental laws of nature are those propositions that collectively optimize a balance of the twin desiderata of informativeness and simplicity. (You can get maximal informativeness by listing all the facts about the world, at the expense of maximal complexity of description, and you can get maximal simplicity by saying nothing, at the expense of minimal informativeness.) And laws are what follows from the fundamental laws.

But laws are explanatory. While Lewis's laws aren't.

Imagine a finite world w1 which contains a powerful contingent magical being who creates a very large number N of golden boxes, and places a chocolate in each one, to fulfill some aesthetic goal—chocolate goes well with gold. No other explanation of the chocolate content of the boxes exists at w1.

We can ask at w1 why the third golden box contains a chocolate. And the answer is that the magical being put a chocolate in every golden box.

Now imagine a world w2 just like w1 but where the magical being doesn't exist and the boxes and chocolates come into existence ex nihilo. Nothing gets added to w2 that wasn't there in w1. Plainly at w2 there just is no explanation of why the third golden box contains a chocolate.

If the number of boxes N is large enough, the proposition that every box contains a chocolate will be informative enough that it'll be included in the system that maximizes informativeness and simplicity (as N increases, the informativeness of the proposition increases but its simplicity stays constant).

But then if Lewis's account of laws is correct, then at w2 it will be a law that all golden boxes contain chocolates. But laws are explanatory. So at w2 we'll be able to explain why the third golden box contains a chocolate. But we said that at w2 there is no explanation of this!

So the Lewisian account of laws is wrong.

Options: (1) Deny that laws are explanatory. (2) Abandon the Lewisian account of laws. (3) Deny that it is possible to have uncaused chocolates.

I think that (3) by itself won't do, because we can run the argument on a counterpossible. And (1) is unattractive. That leaves (2).

In summary, I think "Lewisian laws" aren't explanatory, and hence aren't laws.


Heath White said...

I don’t know a great deal about laws, but here is a line I find tempting: deny the coherence of the counterexample.

Let’s say that at w3 every golden box starts out containing a chocolate, and every chocolate starts out in a golden box, and this state of affairs comes about ex nihilo. I think the denizens of w3 will be very tempted to say (once they form the concept) “it’s a natural law that chocolates come in golden boxes.” And I am not clear what we need to add to the situation to make this belief true (or false).

This is not vastly different from the situation in our world where electrons always come with a charge of 1 eV. The “explanation” of this fact is: it’s a natural law! But we could also say: it just is.

Alexander R Pruss said...

I agree that the denizens of w3 would want to say that it's a law of nature, and would want to offer this as an explanation. But it seems clear to me that they're wrong about the latter, and hence about the former. We've removed the explanation from the story by removing the magical being. We haven't put anything new in its place that would do the explaining that the magical being did.

If the electrons of our world are exactly parallel, then "This is an electron, hence it has a charge of 1eV" is a pseudo-explanation.

Heath White said...

I think if you push this line of reasoning, you will have an argument that explanations in terms of law cannot be explanatory in a fundamental way. I.e. fundamental explanations in terms of law will be indistinguishable from universal generalizations, and “for all x, Px implies Qx” gains no explanatory power from the prefix “It is a natural law that…”.

A nearby conclusion is that all fundamental explanations are teleological or intentional, as in the one invoking a magical being.

Whether that would be persuasive, and to whom, I don’t know. I am inclined to think that the best “real definition” of metaphysical naturalism is the claim that no fundamental explanations are teleological or intentional.

Alexander R Pruss said...

I don't think so. My argument is compatible with natural necessity accounts of laws, on which what makes a universal generalization into a law is that it has natural necessity.

Heath White said...

Take a generalization P (perhaps about chocolate in boxes, perhaps about electrons). You claim that it has natural necessity and I claim that it does not. What is at stake here?

(Or: why is "natural necessity" not grade-A prime metaphysical mumbo jumbo?)

Alexander R Pruss said...

It's not my theory of laws. :-) My current theory of laws is Lewis+theism.

But let's see what I can say. One thing one can say is that "All Fs are Gs" shouldn't be expected to support counterfactuals, but "Naturally necessary: All Fs are Gs" does. Also, from non-modal claim, I can't infer that I am unable to make an F be a non-G. But from the modal claim, I can infer that, barring miracles, I can't make an F be a non-G.