Where else but in metaphysics could you get a sustained argument about holes?
Lewis was a physicalist and a nominalist, and holes constitute an obvious problem for someone who believes that only concrete material objects exist. After all, holes are not made of matter. Yet holes have many of the other properties of material objects: size, shape, location, as well as causal powers. Thus there is a strong case for their reality, as Lewis concluded, despite the not-being-made-of-matter thing.
Since I view the prospect of non-material things with equanimity, I’m perfectly happy with a world full of holes.
My only question concerns their nature.
My answer: Holes strongly nomologically supervene on matter.
A’s supervene on B’s if the presence of A’s is rendered possible only by the presence of B’s. There can be holes only if they are holes in something.
The supervenience relation is nomological because it depends on physical law. Only in worlds in which the physical laws allow matter to form aggregations, to ‘clump’, can there be masses of matter capable of having holes in them.
The supervenience is strong: in all such physically similar worlds matter will be hole-capable.
Holes are not guaranteed even in such worlds, though: in a world whose physical law permits matter but where for some reason the possibility is not realized, or in a world where matter fills every point of space, holes will be absent.
But barring such possibilities, if certain conditions are met, the presence of matter will necessitate the presence of holes. Any aggregation of matter that is not completely homogeneous either in its surface topology or in the volume it occupies will have holes in it. A solid perfect cube or sphere has no holes. Dice and golf balls, however, have holes. Indeed golf balls are covered with them. A tennis ball, not being solid, has a great big hole in the center. It’s mostly hole, actually, by volume.
Why should we accept the reality of holes? Couldn’t a physicalist just say instead that reference to nothings like holes is absurd. Just make reference to the something, without countenancing holes at all.
There are two problems with such a reductionist program; the problems are connected.
Problem 1: Causal Powers
I once opened a pint of Ben & Jerry’s. (Actually I have done that more than once, but this particular episode was especially memorable.) I was wondering why it felt a bit light. Scooping into it I discovered a big bubble. That caused it to have the weight it did. It also caused me to be Quite Put Out.
Golf balls have dimples on them because they cause the air just above the surface to rotate with the ball. As a result the smoother air is pulled a bit more into the ball’s wake, reducing drag. (You may recognize Aristotle’s explanation of projectile motion here.) The dimples also lower the air pressure on the top of the ball, producing lift much like an airplane’s wing. A smooth golf ball would travel only about half as far as one with dimples. (Scientific American, September 2005)
To the extent that holes have causal powers, they must be countenanced in any account of What Goes On.
Problem 2: Explanations
But we are forced to attribute causal powers to holes only if we are forced to make reference to them in our explanations.
Wouldn’t it be better to explain things by appeal only to the properties and powers of somethings?
In this case the properties would presumably be shape properties of masses of matter. So don’t explain my disappointing pint of Ben & Jerry’s by saying that “it had a bubble yay big in it” (for some value of yay). Instead give a description of the shape of the mass. Don’t mention ‘voids’, ‘absences’, ‘discontinuities’ either. If you’re going to cheat, cheat smart.
A mass of ice cream with two smaller bubbles with volumes equaling the single bubble in mine would be equally disappointing. Describe the differences in the two shapes of the ice cream yielding this same result. Then describe all possible shapes that would yield the same result. Grasping that many shape properties is beyond human cognitive powers.
But counting bubbles isn’t.
Try to give the explanation of why dimpled golf balls fly farther than smooth ones without mentioning the dimples. Such an explanation will appeal only to the shape of surface. How many possible shapes of surfaces would produce the same result? How could we grasp all those shapes? Several companies have experimented with hexagonal dimples instead of round ones. Describe the difference in the surface of a golf ball with hexagonal dimples instead of round ones without mentioning the dimples or their shape.
It would seem then, that holes function in explanations as natural kinds.
But if an entity is a natural kind possessing causal powers, it has an excellent claim to be real.
This admittedly rather silly example strikes me as instructive for physicalist programs of reduction.
Since the supervenience relation that brings holes into existence is ‘physicalistically kosher’, if you’re going to compile a complete list of the physical objects in the world you’re going to have to count the holes.
Do golf balls have their dimples as parts then?
Of course not. They’re supervenient objects, not constituent objects.
What would be a reasonable motive for avoiding this conclusion?
*This post is dedicated to my students in PHIL 181: Metaphysics this semester, who put up with a lot.
Department of Philosophy