Maverick Philosopher: Strictly Philosophical

Holes and Their Mode of Being

Written 1 August 2012; edited and reviewed 19 March 2021. 

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Consider a particular hole H in a piece of Swiss cheese.  H is not nothing.  It has properties.  It has, for example, a shape: it is circular.  The circular hole has a definite radius, diameter, and circumference.  It has a definite area equal to pi times the radius squared: A=πr²  If the piece of cheese is 1/16th of an inch thick, then the hole is a disk having a definite volume.  H has a definite location relative to the edges of the piece of cheese and relative to the other holes.  H has causal properties: it affects the texture and flexibility of the cheese and its resistance to the tooth.  H is perceivable by the senses: you can see it and touch it. You touch a hole by putting a finger or other appendage into it and experiencing no resistance.

Now if anything has properties, then it exists.  H has properties; so H exists. 

The foregoing was set-up for the question. H exists and the piece of cheese exists.  Do they exist in the same way?  Not by my lights.  The hole depends for its existence on the piece of cheese; the latter does not depend for its existence on the former.  H is a particular, well-defined, indeed wholly determinate absence of cheese.  It is a particular, existing absence.  As an absence of cheese it depends for its existence on the cheese in which it is one of the holes.

So I say the hole exists in a different way than the piece of cheese.  It has a dependent mode of existence whereas the piece of cheese has a relatively independent mode of existence.

On the basis of this and other examples I maintain that there are modes of being or existence. (I am using 'being' and 'existence' interchangeably.)  To be precise, I maintain that it is intelligible that there be modes of being.  This puts me at odds with those, like Peter van Inwagen, who consider the idea unintelligible and rooted in an elementary mistake:

. . . the thick conception of being is founded on the mistake of transferring what properly belongs to the nature of a chair -- or of a human being or of a universal or of God -- to the being of the chair. (Ontology, Identity, and Modality, Cambridge 2001, p. 4)

Did I make a mistake above, the mistake van Inwagen imputes to thick theorists?  Did I mistakenly transfer what properly belongs to the nature of the hole -- its dependence on the piece of cheese -- to the being (existence) of the hole?

I plead innocent.  Perhaps it is true that it is the nature of holes in general that they depend for their existence on the things in which they are holes.  But H is a particular, spatiotemporally localizable, hole in a particular piece of cheese.  Since H is a particular existing hole, it cannot be part of H's multiply exemplifiable nature that it depend for its existence on the particular piece of cheese it is a hole in.  The dependence of H on its host is due to H's mode of existence, not to its nature.

Suppose there are ten quidditatively indiscernible holes in the piece of cheese: H1, H2, . . . H10.  Each exists.  Each has its own existence.  But each has the very same nature.  How then can this common nature be the factor responsible for making H1 or H2 or H3, etc., dependent on the particular piece of cheese?  The dependence of each hole on its host is assignable not to the nature common to all ten holes but to each hole's existence as a mode of its existence.

Now of course this will not convince any thin theorist.  But then that is not my goal.  My goal is to show that the thick theory is rationally defensible and not sired by any obvious 'mistake.'  If any 'mistakes' are assignable then I 'd say they are assignable with greater justice to the partisans of the thin theory.

Metaphilosophical Coda

Talk of 'mistakes,' though, is out of place in serious philosophy.  For apart from clear-cut logical blunders such as affirming the consequent, quantifier shift fallacies, etc. any alleged 'mistakes' will rest on debatable substantive commitments.

The Aporetics of Artifacts: Puzzling Over Van Inwagen's Denial of Artifacts

This post is a sequel to Van Inwagen on the Ship of Theseus.  Peter van Inwagen, Material Beings (Cornell UP, 1990), p. 31, writes: 

The question 'In virtue of what do these n blocks compose this house of blocks?' is a question about n + 1 objects, one of them radically different from the others. But the question 'What could we do to get these n blocks to compose something? is a question about n rather similar objects. . . . . questions of the former sort turn our minds to various metaphysical and linguistic questions about the "special" n + 1st [read: n + 1th] object and our words for it: What are the identity conditions for houses of blocks?

Why does van Inwagen think that a house of blocks is an object radically different from the blocks that compose it? And why does he think that if there are, say, 1000 blocks, then in the place where the house is, there are 1001 objects? Not only do I find these notions repugnant to my philosophical sense, I suspect that it is their extremism that motivates van Inwagen to recoil from them and embrace something equally absurd, namely, that there are no such things as houses of blocks or inanimate concrete partite entities generally. 

In other words, if one begins by assuming that if a house of blocks, for example, is a whole of parts, then it is an object radically different from the objects that compose it, an object numerically additional to the objects that compose it; then, recoiling from these extreme positions, one will be tempted to embrace an equal but opposite extremism according to which there are no such inanimate partite entities as houses of blocks. What then should we say about a house of blocks?

First off, it is not identical to any one of its proper parts. Second, it is not identical to the mereological sum of its parts: the parts exist whether or not the house exists. From this it follows that there is a sense in which the house is 'something more' than its parts. But surely it is not an object "radically different" from, or numerically additional to, its proper parts. If there is a house of 1000 blocks in a place, there are not 1001 objects or entities in that place. After all, the house is composed of the blocks, and of nothing else.

So on the one hand the house is 'something more' than its constituent blocks, while on the other hand it is not a "radically different" object above and beyond them. Think of how absurd it would be for me to demand that you show me your house after you have shown me every part of it. "You've shown me every single part of your house, but where is the bloody house?"

The house, thought not identical to the blocks that compose it,  is not wholly diverse from the blocks that compose it .  The house is the blocks arranged housewise. The house is not the blocks, and the house is not some further entity "radically different" from the blocks. The house is just the blocks in a certain familiar arrangement. Should we conclude that the house exists or that it does not exist? I say it exists: the house is the blocks arranged housewise, and the existence of the house is the housewise unity of the blocks. Van Inwagen seems to think that there is no house, there are just the blocks. (Of course, he doesn't believe in the blocks either since they too are inanimate partite entities; but to keep the discussion simple, we may assume that the blocks are simples.)  

Now if it is allowed that the house exists, it seems clear that the house does not exist in the way the blocks do. But this does not strike me as a good reason for saying that the house does not exist at all. What is wrong with saying that the house is a dependent existent? And what is wrong with saying that about partite entities generally? They exist, but they do not exist in addition to their parts, but as the unity or connectedness of their parts. Saying this, we avoid van Inwagen's absurd thesis that inanimate partite entities do not exist. Of course, this commits me to saying that there are at least two modes of existence, a dependent mode and an independent mode. I suspect van Inwagen would find such a distinction incoherent. But that is a topic for a separate post.

The problem can be set forth as an aporetic pentad:

1. The house is not identical to the blocks that compose it.

2. The house is not wholly diverse from the blocks that compose it; it is not an object numerically additional to the blocks that compose it:  given that the house is composed of n blocks, the house itself is not an n + 1th object.

3. The house exists.

4. The constituent blocks exist.

5.  'Exists' is univocal as between wholes and parts: wholes and their parts exist in the same sense.

Each limb has a strong claim on our acceptance.  But they cannot all be true.  Any four of the propositions, taken together, entails the negation of the remaining one.  For example, if the first four are all true, then the fifth must be false.  To solve the problem, one of the limbs must be rejected.  But which one? 

To me it seems obvious that the first four are all true.  So I reject (5).  Rejecting (5), I can say that the house exists as the connectedness of the blocks.  Thus the mode of existence of the whole is different from the mode of existence of its simple parts.  But this solution requires us to believe in modes of existence, which is sure to inspire opposition among analytic philosophers.  Van Inwagen, if I understand him, denies (2) and (3) while accepting the others.

But van I's solution is just crazy, is it not?  Mine is less crazy.  But perhaps you, dear reader, have a better suggestion.

Van Inwagen on the Ship of Theseus

Peter van Inwagen's Material Beings (Cornell UP, 1990) is a very strange book, but he is a brilliant man, so one can expect to learn something from it. A central claim is that artifacts such as tables and chairs and ships do not exist. One can appreciate  that if there are no ships then the ancient puzzle about identity known as the Ship of Theseus has a very quick (dis)solution. 

The Ship of Theseus is a puzzle about diachronic artifact identity. Here is one version. You have a ship, or a rowboat, or any object, composed entirely of wooden planks. You remove one of the planks and replace it with an aluminum plank of the same size. The wooden plank is placed in a warehouse. After this minor replacement, you have a ship and indeed numerically the same ship as the one you started with. It is not a numerically different ship. Now replace a second wooden plank with an aluminum plank, and place the second wooden plank in the warehouse. Again, the numerical identity of the original ship has been preserved. Continue the replacement process until all of the wooden planks have been replaced with aluminum planks. You now have a wholly aluminum ship that is presumably numerically identical to the original wholly wooden ship despite the fact that none of the original matter is to be found in the aluminum ship. After all, the aluminum ship 'grew out of' the original wooden ship by minor changes each of which was identity-preserving.

Now take the wooden planks from the warehouse and assemble them in the form of a ship and in such a way that the planks bear the same relations to one another as the planks in the original wooden ship bore to one another. You now have two ships, a wooden one and an aluminum one. The question is: which of these ships is identical to the original wooden one?

Suppose the two ships collide on the high seas, and suppose the captain of the original ship had taken a solemn vow to go down with his ship. Where does his duty lie? With the wooden ship or with the aluminum one? Is the original ship identical to the resultant aluminum ship? One will be tempted to say 'yes' since the aluminum ship 'grew out' of the original wooden ship by minor transformations each of which was identity-preserving. Or is the original ship identical to the wooden ship that resulted from the re-assembly of the wooden planks? After all, it consists of the original matter arranged in the original way. Since the resultant wooden and aluminum ships are numerically distinct, they cannot both be identical to the original ship.

Van Inwagen makes short work of the puzzle: "There are no ships, and hence there are no puzzles about the identities of ships." (128) One way van Inwagen supports this bizarre solution is by re-telling the story in language that does not make even apparent reference to ships. Here is his re-telling:

Once upon a time, there were certain planks that were arranged shipwise. Call then the First Planks. . . . One of the First Planks was removed from the others and placed in a field. Then it was replaced by a new plank; that is, a carpenter caused the new plank and the remaining First Planks to be arranged shipwise, and in just such a way that the new plank was in contact with the same planks that the removed planks had been in contact with, and at exactly the same points. Call the planks that were then arranged shipwise the Second Planks. A plank that was both one of the First Planks and one of the Second Planks was removed from the others and placed in the field and replaced (according to the procedure laid down above), with the consequence that certain planks, the Third Planks, were arranged shipwise. Then a plank that was one of the First Planks and one of the Second Planks and one of the Third Planks . . . . This process was repeated till all the First Planks were in the field. Then the First Planks were caused to be arranged shipwise, and in just such a way that each of them was in contact with the same planks it had been in contact with when the First Planks had last been arranged shipwise, and was in contact with them at just the same points. (128-129)

If I understand what van Inwagen is claiming here, it is that there is nothing in the standard telling of the story, a version of which I presented above, that is not captured in his re-telling. But since there is no mention of any ships in the re-telling, no puzzle about ship-identity can arise. Perhaps van Inwagen's point could be put by saying that the puzzle about identity is an 'artifact' of a certain way of talking that can be paraphased away. Instead of talking about ships, we can talk about shipwise arrangements of planks. The planks do not then compose a ship, he thinks, and so there is no whole of which they are proper parts, and consequently no question about how this whole maintains its diachronic identity under replacement of its parts.

What are we to say about van Inwagen's dissolution of the puzzle? What I find dubious is van Inwagen's claim that ". . . at no time do two or more of these planks compose anything, and no plank is a proper part of anything." (129) This strikes me as plainly false. If the First Planks are arranged shipwise, then there is a distinction between the First Planks and their shipwise arrangement. The latter is the whole ship and the former are its proper parts. So how can van Inwagen claim that the planks do not compose a ship?

Van Inwagen seems to think that if the planks were parts of a whole, and there were n planks, then the whole would be an n + 1 th entity. Rejecting this extreme, he goes to the other extreme: there is no whole of parts. If there were ships, they would be wholes of parts, but there are no artifactual wholes of parts, so there are no ships. The idea seems to be that when we build an artifact like a ship we are not causing something new to come into existence; we are merely re-arranging what already exists. If so, then although a ship's planks exist, the ship does not exist. Consider what van Inwagen says on p. 35:

If I bring two cubes into contact so that the face of one is conterminous with the face of the other, have I thereby brought into existence a solid that is twice as long as it is wide? Or have I merely rearranged the furniture of the earth without adding to it?

Van Inwagen seems to be saying that when it comes to artifacts, there is only rearrangement, no 'addition to existence.' As a general thesis, this strikes me as false. A ship is more than its planks, and van Inwagen seems to concede as much with his talk of a shipwise arrangement of planks; but this shipwise arrangement brings something new into being, namely, a thing that has causal powers that its constituents do not have. For example, a boat made of metal planks properly arranged will float, while the planks themselves will not float.