Thursday, July 9, 2009

Laws of nature

It is a really interesting question for someone who believes in lower level laws (e.g., Aristotelian laws grounded in the natures of substances, or in separate laws of nature governing different kinds--electrical, gravitational, etc.--of interaction) how higher level laws like the law of conservation of mass-energy which depend on the appropriate coordination of lower level laws (e.g., in the Aristotelian case, that no entity can increase its mass-energy without some other entity decreasing its mass-energy at the same time) get to be explanatory. One answer is that the higher level laws entail the lower level ones and are ontologically more basic. Aristotelians will deny this, though, and I am not sure we have reason to think so. Certainly, the law of conservation of mass-energy does not by itself entail various electromagnetic laws--other assumptions need to be added. It seems at least possible, and I think plausible, that the lower level laws are in fact ontologically more basic, and the higher level ones supervene on them.

I wonder whether the right answer to that question isn't Leibnizian. The lower level laws (perhaps combined with certain boundary conditions) entail the higher level ones. The explanation of the coordination of lower level laws to produce certain cool results like conservation of mass-energy is that it is good that the lower level laws be such as to result in these higher level laws (which have various positive axiological features, such as elegance), and God does what is good.

There may also be a nice teleological answer, if one can make sense of a teleological dependence between laws. In fact, the theistic answer might have two takes: a more voluntarist one and a more teleological one.

7 comments:

Huume said...

Alex, this is not on topic of your post so forgive me.

Is their any possible reality where truth does not exist?
It could be as simple as a yes or no answer.

You have such wonderful blog posts!

enigMan said...

Hi Alex,

I've been thinking about this question myself lately; not very deeply, but because it is connected to deep questions (e.g. what supertasks could tell us about infinity).

Some clay can become a lump, and a statue, and then bits of a statue, and dust, because it's the same stuff changing. That is, if there are to be things that change, then there has to be something substantial staying the same over time, for the thing to be the same thing before and after its change. A conservation law is a lot like that, I think. The mass/energy is conserved because energy is the substance that is changing its form. If so then the lower laws govern such changes of form (like the physical chemistry of clay), while the higher laws express something more metaphysical (and hence are implicit in the more specific laws).

But not only is that very simple, I got stuck with the conservation of momentum. Momentum doesn't seem like a substance, to be passed around during collisions (although maybe it is a substantial aspect of the space in which the collisions take place).

Alexander R Pruss said...

enigMan:

That's an interesting suggestion. I think one difficulty is that it is not clear that mass-energy can be numerically identified as a particular. Consider a case where photons A and B collide to produce electron C and positron D. Where did A's mass-energy go? Into C? Into D? Half into C and half into D?

Mass-energy seems more like Aristotle's prime matter, identifiable only under a form.

Huume:

If God necessarily exists, then, no, because in every possible world, every one of God's beliefs is true.

If God does not exist, the answer to the question hinges on what the bearers of truth are. If they are propositions, then the proposition that 2+2=4 is true in every possible world. If they are sentence types relative to an abstractly characterized language, then the sentence "2+2=4" is true in every possible world relative to English. If they are sentence tokens or beliefs, then if there were a world with no speakers and no believers, there would be no truths.

Matt said...

Alex, you write If they are sentence tokens or beliefs, then if there were a world with no speakers and no believers, there would be no truths.

I am not sure this last option is coherent. Would it be true that in such a world there are no truths?

It would also seem to lead to the counter intuitive conclusion that there are no necessary truths.

(and is this latter claim also incoherent, after all if there are no necessary truths, the claim that there are none itself must be a contingent truth, which would suggest that in some worlds there are necessary truths, in which case there are necessary truths)

The reason I ask is that I wonder if there is a theistic argument lurking here somewhere, a kind of inference from the idea that truth is a property of beliefs to the necessary existence of beliefs, to the necessary existence of a mind.

Alexander R Pruss said...

Matt:

I've wondered about the possibility of such a theistic argument, too. There might be one.

But about necessary truth, that is very interesting. There are two ways of analyzing the necessary truth of a sentence.

(1) s is necessarily true = necessarily(s is true)
(2) s is necessarily true = s has the property of necessary-truth

If (1) is correct, then your argument works. Necessary truths must themselves necessarily exist. But if (2) is the right rendering, then "necessary-truth" might turn out to be a basic property not to be analyzed further (think of what Platonists like Plantinga might say of the necessity of propositions), and (2) simply attributes that property to s.

Let's explore whether (2) could work. We want necessary-truth to have some formal properties. For instance, necessarily (if s has necessary-truth, then s has truth). Perhaps, but perhaps not (because the meaning of a sentence might vary between worlds), we want to say that if s has necessary-truth, then having necessary-truth is an essential property of s.

It may be a little puzzling why it is that necessary-truth entails truth if the former and the latter are basic, further indefinable properties.

But on some concrete takes on necessary-truth this is less puzzling. Suppose we confine ourselves to a first order language L. We then say that a sentence token is a necessary-truth if and only if it is a tautology. Then (a) necessary-truth entails truth, and (b) necessary-truth is always had essentially (relative to L). So that satisfies our formal conditions.

So far, (2) seems at least somewhat viable. What do you think?

Matt said...

Alex: That’s an interesting response, Plantinga (the Platonists you cite) actually gives arguments similar to mine (albeit in a much more rigorous fashion) in Warrant and Proper Function chapter 6 and responds to something like what you are suggesting. Basically he contends that if one understands necessary truth as an essential property of a sentence then various problems arise.

I am note sure how this would apply to the account of necessity you tentatively suggest.

What would the modal status of the sentence “language exists” be on this account?

Alexander R Pruss said...

"Language exists" would be contingent.

Compare Robert Adams' distinction between a proposition being true in a world and its being true at a world. p is true in w iff it is the case at w that p has the property of truth. It follows from p's being true in w that p exists in w. On the other hand, p is true at w iff p correctly describes w (or something like that). Propositions that make direct reference to particulars exist only in those worlds where those particulars exist. Consequently, if p is the proposition that Socrates does not exist, then p is true at world without Socrates, but p is not true in them because p doesn't, according to Adams, exist in them.

Anyway, if we have Adams' view in mind, then there will be necessarily true propositions--in the sense of propositions that are true at every world--even though the propositions themselves will be contingent beings. Thus, the proposition that Socrates exists or Socrates does not exist is true at every world but exists only in those worlds in which Socrates exists.