Monday, June 14, 2010

Mumford's "Ungrounded Argument"

Mumford's argument for dispositions not grounded in non-dispositional properties is:

  1. Some subatomic particles are simple.
  2. Simples have "no lower-level components or properties".
  3. All properties of subatomic particles are dispositional.
  4. If x has a grounded dispositional property, the ground of that property is "among the lower-level components or properties" of x.
Here is one problem. A proton is supposed to be composed of two up quarks and one down quark, and this is a compositional, and not a dispositional, property of the proton. Maybe it is charitable, however, to restrict 3 to simple particles.

However, even after this modification, it seems that 3 is dubious. For instance, suppose an up quark is simple. But then, isn't simplicity a property, and a non-dispositional one at that, so that the up quark has a non-dispositional property?

Perhaps, then, we need to have a sparse view of properties. But simplicity seems sufficiently natural to qualify as a property even on sparse views. A different way to save 3 would be to restrict to intrinsic properties, and have a very narrow view of intrinsic properties: having an intrinsic property does not depend on an entity's relations to other entities or the lack of such relations. But being simple depends on not standing in a whole-to-part relation to anything else. In fact, the same restriction lets us not worry about the proton counterexample to 3, since being composed of quarks is not an intrinsic property, then. Note, however, that such a notion of intrinsic properties is narrow enough—for instance, squareness might not be an intrinsic property, since maybe an object is a square only because its parts are arranged a certain way.

But let us continue with such a narrow sense of intrinsicness. Is 3 true? Maybe not. Bill the Up Quark seems to have all sorts of non-dispositional properties: being identical with Bill, being u seconds old, having a worldline that is shaped in such-and-such a way, etc. Maybe some of these don't count as properties on a sufficiently austere sparse account of properties. But all that needs significant argument.

Actually, I am not completely sure about 4, or more precisely the conjunction of 3 and 4. Suppose Occasionalism is true. Then properties like "charge" are grounded in God's dispositions to move particles around. In such a case, we might keep 4 but deny that anything other than God has dispositional properties, or else we might keep 3, but allow that the particles' dispositions are grounded in God's dispositions. Now, Occasionalism is false. But the same issue comes up if one thinks that laws of nature are grounded in global entities—say, fields—that push particles around. Now, in such a case, we can try to ask about the entities that push particles around—don't they have dispositional properties, and aren't they simple? And quite possibly the answer is positive. But a lot more work is needed here.


Derrick said...

I don't see why a believer in sparse properties has to allow for the existence of the property of simplicity. It seems that all simplicity would be a negative property, i.e. the lacking of parts. Given that sparse theories of properties reject the notion of a negative property, it seems that there is no reason for a sparse theorist to reify simplicity. Am I missing something?

Derrick said...

Whoops. I meant to say "...seems that simplicity would be a negative property..."

Alexander R Pruss said...

Maybe then instead of talking of simplicity, I should talk of fundamentality?

Derrick said...

Could you elaborate on that? I'm not seeing how that is different from talking about simplicity.

Alexander R Pruss said...

Fundamentality seems pretty fundamental, and fundamental properties seem to me to be natural.

Derrick said...

My worry for that move was that it seems that we can give a similar analysis for fundamentality that we can for simplicity, e.g. lacking proper parts and lacking structural properties. If that is the case, then fundamentality need not be countenanced for those like myself that accept a sparse theory of properties. Is there something in the notion of being fundamental that I'm leaving out?