Monday, April 4, 2016

Holes as natural kinds

Metaphysical questions can sound profound and stupid at the same time.*  That’s why it’s difficult to know whether a sense of humor (or at least of irony) is a useful trait for a metaphysician, or a hindrance. David Lewis, a metaphysician of the first rank with a highly developed sense of both, once authored a witty little essay on holes.

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.

Thomas Pyne
Department of Philosophy
Sacramento State


  1. Shannon Paige FleenerApril 4, 2016 at 11:21 AM

    I appreciate the dedication, Dr. Pyne, but I think I should cede my portion of it to someone else. I fear I don't "put up with a lot" all that gracefully. I'll donate my percentage to the Foundation for Uncountenanced Holes.

    1. Paige,
      Poor uncountenanced holes...
      Did you have any particular ones in mind?

  2. Could it be that any non-material object must necessarily supervene on material objects? Even in the case of things that do not necessarily describe themselves by the material on which they supervene (as holes seem to).

    1. Stan,
      It depends on what non-material objects your thinking of. I seem in fact to have worked my way around to arguing that holes are physical objects after all, since they supervene on material things their supervenience relation is physicalistically kosher. They’re physical objects with no mass or energy! This might be an example of the utility of distinguishing between ‘material’ and ‘physical’, where ‘physical’ means ‘describable using the terms and concepts of physics’.
      Terry Horgan argues in several places that the supervenience relation holding between mental states and physical states is not so physicalistically ‘kosher’.
      David Lewis was open to the possibility that in some possible worlds mental states which are tokened physically in the actual world may still be realized, but not in anything physical.

  3. Tom, do you mean that all holes supervene on matter or only some of them? Isn't a torus a purely abstract object with a hole in it? It seems to me that your case for explanation is stronger if you characterize it as an indispensable formal kind of explanation, and this makes more sense to me if the existence of a hole is strictly a matter of form. Wouldn't that also fit a bit better with your advocacy of formal causes, too?

    1. You get the point about explanation via natural kinds. Quine treated natural kinds as a retrograde form of explanation, but they’ve undergone a massive revival since, of course. They seem to me indispensable epistemically and heuristically at the beginning of an explanatory project, as well as indispensable metaphysically at the end (though what kinds we ultimately end up countenancing can change as a result of the project).
      Wilfrid Sellars proposed the sentence “The Lion is tawny” as a statement about the kind The Lion.
      Suppose we go the Roundhouse. You buy a doughnut, and I buy a cookie.
      You say, (a) “The doughnut has a hole”.
      I respond, “Yes, that’s true.”
      You go on to say, (b) “The Doughnut has a hole”. That’s also true.
      (Philosophers don’t really talk this way.)
      How are occurrences of “hole” in those two propositions related?
      Sellars was no friend of abstract objects, as you know, so he proposed an elaborate semantical work-around for (b)-style occurrences.
      Here are two different accounts. In both accounts, the two occurrences are literal uses of “hole”.
      1. The truth of (a)-type occurrences controls the truth of (b)-type occurrences.
      2. The truth of (b)-type occurrences controls the truth of (a)-type occurrences.
      The supervenience theory of holes seems more consistent with (1). Just as individual holes are determined by the stuff of the individual doughnut, so The Doughnut Hole is fixed by the reality of doughnuts.
      Account (2) seems more like Aristotelian formal causes, since substance turns out to be substantial form in the end.
      Aristotle considers the two uses of “hole” a particular sort of equivocation. It’s not really ambiguity since the uses are so closely tied

    2. Tom, thanks, that all makes sense to me. Except that I would have expected you to be more attracted to account (2) based on your defense, on this blog, of formal causes. What do I miss? That you actually are but you are just showing that it follows either way? Or that you aren't, and your stance on formal clause doesn't require it?

    3. Randy,
      Good point!
      I hadn’t consciously thought about the difference, but I seemed instinctively to avoid the Aristotelian approach here.

      Holes might be real objects, and maybe even real physical objects despite not being made of matter.

      But treating them as primary substances would of course have driven Aristotle straight up the flue. There just seems to be something dependent about them in a way that a substance should be fundamental

  4. Gee, what a beautiful space this makes in the dance of reason. Kind of like square dancing, after you 'spin your partner round and round' and then you move away from each other…creating a hole between you.

    Which actually gives me an idea.

    Not all holes in the head supervene on physical matter.

    Some do, of course. Like the sort of hold referred to by "that there varmit is gonna get a hole in the head if he tries to steal any more of my hayseed."

    But not all do. A hole in one's consciousness may not always require matter.

    Type 1's may, of course: where a physical concussion produces a physical change, which produces a big noticeable gap in one's consciousness. As a former philosophy professor once told me, describing her post-concussive experience of trying to teach philosophy (and I paraphrase), "it was like I was going to the book of my memories, only to find huge pages simply gone. Ripped out of where they should be. With nothing there where it should have been." This was, entirely reasonably, frightening as can be.

    Type 2: if there are entities whose consciousness does not depend on physical matter, then perhaps they have holes too.

    God is not the first one to think of here. He's like the physical cube you mentioned: hole-less. (Though holy.)

    Perhaps Satan (or whatever angel is assigned to take care of Donald Trump's soul, since he or she is not doing such a great job right now) could have a hole where there is something that should be there but isn't. There's a privation where there should be a proposition. There's a hole. In the 'head.'

    And it's not physical. Right?

    1. Sorry, my last sentence should have read, "And it's not physical, or supervening on anything physical."

    2. True enough. Once you’re jiggy with holes, why boggle at other sorts of gaps, lacks, absences, and privations?
      At least some of your examples are non-literal uses of “hole” (at least as the term was being used in the blogpost) – but none the less worthy of consideration for that.
      Here’s another non-material hole somewhat different from your friend’s more frightening experience with concussion: That annoying gap between what you already think is true and what you want to have follow from it. That gap is often surprisingly difficult to fill!
      For the possibility of holes on non-material things, see the reply to Stan Lovelace.
      My own attitude toward gaps, lacks, absences (like the absence of Sartre’s friend Pierre in the cafe), is similar to Kyle’s toward aliens: Let ‘em in, so long as they’re prepared to work to pay their way.

  5. A reasonable response to my previous posts to Tom here might take the form of "well, sure, if you are going to admit those sorts of entities, why fuss over holes?"

    One reason is to show that an account of holes need not depend upon anything physical. Even if holes are in some sense metaphysical parasitic entities, they don't just feed on physical hosts.

    But there are others. Besides having a hole in my head.

    1. My reply to you should be here, obviously.