Wholes and Parts – Page 3 – Maverick Philosopher

Mereological Nihilism

I put to William the following question:

Are you prepared to assert the following? It is never the case that whenever there are some things, there is a whole with those things as parts. Equivalently: For any xs, if the xs are two or more, there is no y such that the xs compose y.

To which he replied: "Agreed, if you are using xs as a plural quantifier, and by implication y as a singular quantifier."

I think William was too hasty in agreeing since his agreement makes him a mereological nihilist, or nihilist for short. Nihilism is the logical contrary, not contradictory, of mereological universalism, or universalism for short. Universalism is what is expressed by Unrestricted Composition:

UC. Whenever there are some things, then there exists a fusion [sum] of those things. (David Lewis, Parts of Classes, Basil Blackwell 1991, p. 74)

Given Extensionality — no two wholes have the same parts — (UC) says that whenever there are some individuals, no matter what their character or category, there is a unique individual that they compose. This is their mereological sum. Universalism is hard to swallow. I do not balk at the sum of the books in my house. But I balk at the sum of : the books in my house, William's last heartbeat, Peter's left foot, and the planet Mercury. But if, recoiling from Universalism, one embraces Nihilism, then one is committed to the proposition that there are no composite objects, there are only simples. And surely William does not want to be committed to that.

Mereological Innocence and Composition as Identity

This is the third in a series. Part I, Part II. What follows is a 10th example of eliminativist/reductivist ambiguity.

One of the axioms of mereology is Unrestricted Composition. Here is David Lewis' formulation (Parts of Classes, Basil Blackwell 1991, p. 74):

Unrestricted Composition: Whenever there are some things, then there exists a fusion of those things.

A fusion is a mereological sum, so I'll use 'sum.' The axiom assures us that, for example, if there are some cats, then there exists a sum of those cats. The cats are many but the sum is one. So it is not unreasonable to think that if there are five cats that compose the sum, the sum is a sixth thing. One could argue as follows: (a) The sum is distinct from each of the cats. (b)There are five cats, each of which exists, and by UC the sum also exists. Therefore, (c) at least six things exist.

But consider this example, adapted from Donald Baxter. You proceed with six bottles of beer to the supermarket 'six items or fewer' checkout line. The attendant protests your use of the line on the ground that you have seven items: six bottles of beer plus one mereological sum. This would be an outrage, of course. The example suggests that the argument to (c) above has gone wrong.

Lewis avoids the mistake — assuming it is one — by pleading that "Mereology is ontologically innocent." (PC 81) That means that a commitment to a cat-sum is not a further commitment over and above the commitment to the cats that compose the sum. The cat-sum just is the cats, and they are it. This is the thesis of Composition as Identity. The xs compose the y by being identical to the y. As Lewis says,

Take them together or take them separately, the cats are the same portion of Reality either way. Commit yourself to their existence all together or one at a time, it's the same commitment either way. If you draw up an inventory of Reality according to your scheme of things, it would be double counting to list the cats and also list their fusion. In general, if you are already committed to some things, you incur no further commitment when you affirm the existence of their fusion. (PC 81-82)

I'm sorry, but this doesn't make much sense. Glance back at Unrestricted Composition. It is not a tautology. It does not say that whenever there are some things, then there are some things. It says that whenever there are some things, then there exists a fusion or sum of those things. Now if the sum of the xs is just the xs, then UC is a tautology. But if UC is not a tautology, then Composition as Identity is false. How can Unrestricted Composition and Composition as Identity both be true?

The problem is already present at the purely syntactic level. 'Y is identical to the xs' is unproblematic if the xs are identical to one another. For then the open sentence collapses into 'y is identical to x.' But if the xs are distinct from each other, then 'y is identical to the xs' is syntactically malformed. How can one thing be identical to many things? If one thing is identical to many things, then it is not one thing but many things. A contradiction ensues: the one thing is one thing and not one thing because it is many things. The gaps in the predicate '. . . is identical to ____' must either be both filled with singular terms or both filled with plural terms.

And now we come back to our main theme, eliminativist/reductivist ambiguity. Lewis wants to say that there is the sum of the xs (by Unrestricted Composition) but that the the sum of the xs is identical to the xs. So he seems to be making a reductionist claim: sums reduce to their members. But I say the thesis is unstable and topples over into eliminativism: there are no mereological sums. For if the sum is just its members, then all that exists is the members so that the sum does not exist!

Fist and Hand, Statue and Lump: The Aporetics of Composition

1. Some maintain that a hand, and that same hand made into a fist, are identical. And there are those who would say the same about a piece of bronze and the statue made out of it, namely, that they are identical at every time at which both exist. This is not an unreasonable thing to say. After all, fist and hand, statue and bronze, are spatially coincident and neither has a physical part the other doesn't have. A fist is just a certain familiar arrangement of hand-parts. There is no part of the fist that is not part of the hand, and vice versa. So at looks as if first and hand are identical. But we need to be clear as to what identity is.

2. Identity is standardly taken to be an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals (InId) and the Necessity of Identity (NecId). The first principle says that, if two items are numerically identical, then they share all properties. The second says that if two items are numerically identical, then this is necessarily the case. Both principles strike me as beyond epistemic reproach. 'Identity' is short for 'numerical identity.'

3. Despite the considerations of #1, it looks as if fist and hand, statue and hunk of bronze, cannot be identical since they differ in their persistence conditions. The hunk of bronze can, while the statue cannot, survive being melted down and recast in some other form. The hand can, while the fist cannot, survive adoption of a different 'posture.' In both cases, something is true of the one that is not true of the other. So even at the times at which the fist is the hand, and the bronze is the statue, the two are not identical: the 'is' is not the 'is' of identity. It is the 'is' of composition and what you have are two things, not one.

What I have just given is a modal discernibility argument. Let me spell it out. Consider a time t at which the hand is in the shape of a fist. At t, the hand, but not the fist, has the modal property of being possibly such as to to be unfisted. So the hand cannot be identical to the fist given that, for any x, y, if x = y, then x, y share all properties.

But there is also this nonmodal discernibility argument. The hunk of bronze existed long before the statue came into existence, and the hunk of bronze exists while the form of a statue. So the hunk of bronze exists at more times that the statues does, which implies the the hunk of bronze is not identical to the statue.

There is also this consideration. Identity is symmetrical. So we can say either fist = hand or hand = fist. But is it the fist or the hand that both are? Intuitively, it is the hand. The hand is the fundamental reality here, not the fist. So how can fist and hand be identical? It seems that fist and hand are numerically distinct, albeit spatially coincident, concrete individuals.

4. The Law of Excluded Middle seems very secure indeed, especially in application to presently existing things. So either the fist is identical to the hand, and there is just one thing, a fisted hand, or the fist is not identical to the hand and there are two spatially coincident things, a fist and a hand. So which is it?

5. If you say that the fist = the hand, then when you make a fist nothing new comes into existence, and when the potter makes a pot out of clay, nothing new comes into existence. And when a mason makes a wall out of stones, nothing new comes into existence. He started with some stones and he ended with some stones. Given that the stones exist, and that the mason's work did not cause anything new to come into existence, must we not say that the single composite entity, the wall, does not exist? (For if it did exist, then there would be an existent in addition to the stones.) But it sounds crazy to say that the wall the mason has just finished constructing does not exist.

6. If, on the other hand, you say that the fist is not identical to the hand, then you can say that the making of a fist causes a new thing to come into existence, the fist. And similarly with the statue and the wall. After the mason stacks n stones into a wall, he has as a result of his efforts n +1 objects, the original n stones and the wall.

But this is also counterintuitive. Consider the potter at his wheel. As the lump of clay spins, the potter shapes the lump into a series of many (continuum-many?) intermediate shapes before he stops with one that satisfies him. Thus we have a series of objects (proto-pots) each of which is a concrete individual numericallt distinct from the clay yet (i) spatially conicident with it, and (ii) sharing with it every momentary property. And that is hard to swallow, is it not?

7. We appear to be at an impasse. We cannot comfortably say that the fist = the hand, nor can we comfortably say that the fist is not identical to the hand. Nor can we comfortably give up LEM. If there are no fists, statues, walls, artifacts generally, then there cannot be any puzzles about their composition. But we cannot comfortably say that there are no such things either.

Do we have here an example of a problem that is both genuine but insoluble?

Peter van Inwagen, Artifacts, and Moorean Rebuttals

Two commenters in an earlier van Inwagen thread, the illustrious William the Nominalist and the noble Philoponus of Terravita, have raised Moore-style objections to an implication of PvI's claim that "every physical thing is either a living organism or a simple" (MB 98), namely, the implication that "there are no tables or chairs or any other visible objects except living organisms." (MB 1) The claim that there are no inanimate objects, no tables, chairs, ships and stars will strike many as so patently absurd as to be not worth discussing. Arguments to such a conclusion, no matter how clever, will be dismissed as unsound without evaluation on the simple ground that the conclusion to which they lead is preposterous. This is the essence of a Moorean objection. If someone says that time is unreal, you say, 'I ate breakfast an hour ago.' If someone denies the external world, you hold up your hands. If someone denies that there are chairs, you point out that he is sitting on one. And then you clinch your little speech by adding, 'The points I have just made are more worthy of credence than any premises you can marshall in support of their negations.'

I myself have never been impressed with Moorean rebuttals. To my mind they signal on the part of those who make them a failure to understand the nature of philosophical (in particular, metaphysical) claims. See, e.g., Can One See that One is not a Brain in a Vat?

Though I disagree with van Inwagen's denial of artifacts, I think he can be quite easily defended against the charge of maintaining something 'mad' or something refutable by a facile Moorean rejoinder.

Chapter 10 of Material Beings deals with the Moorean objection. Van Inwagen does not deny that we utter such true sentences as 'There is a wall that separates my property from my neighbor's.' But whereas most of us would infer from this that walls exist, and thus that composite non-living things exist, van Inwagen refuses to draw this inference maintaining instead that the truth of 'There is a wall that separates my property from my neighbor's' is consistent with there being no walls.

This is not as crazy as it sounds. For suppose that what the vulgar call a wall is (speaking with the learned) just some stacked stones, some stones arranged wall-wise. And to simplify the discussion, suppose the stones are simples. Then the denial that there is a wall is a denial that there is one single thing that the stones compose. But this is consistent with the existence of the stones. Accordingly, the sentence 'There is a wall that separates my property from my neighbor's' is true in virtue of the existence of the stones despite the fact that there is no wall as a whole composed of these stony parts.

Or consider the house built by the Wise Pig years ago out of 10, 000 blocks (which for present purposes we may consider to be honorary simples.) (The tail tale of the Wise Pig is recounted on p. 130 of Material Beings.) At the completion of construction, did something new come into existence? I would say 'yes.' Van Inwagen would say 'no.' All that has happened on PvI's account is that some blocks have been arranged house-wise. His denial then, is that there is a y such that the xs compose y. He is not denying the xs (the blocks construed as simples); he is denying that there is a whole that they compose. And because there is no whole that they compose, the house does not exist.

Furthermore, because the house does not exist, there can be no question whether the house built by the Wise Pig years ago, and kept in good repair by him and his descendants by replacement of defective blocks, is the same as or is not the same as the one that his descendants live in today. The standard puzzles about diachronic artifact identity lapse if there are no artifacts.

Does this fly in the face of Moorean common sense? If madman Mel were to say that there are no houses he would not mean what the metaphysican means when he says that there are no houses. If Mel is right, then it cannot be true that I have been living in the same house for the last ten years. But the truth of 'I have been living in the same house for the last ten years' is consistent with, or at least not obviously inconsistent with, PvI's denial of houses (which is of course not a special denial, but a consequence of his denial of artifacts in general). This is because PvI is not denying the existence of the simples which we mistakenly construe as parts of a nonexistent whole.

But then how are we to understand a sentence like, 'The very same house that stands here now has stood here for three hundred years'? Van Inwagen proposes the following paraphrase:

There are bricks (or, more generally, objects) arranged housewise here now, and these bricks are the current objects of a history of maintenance that began three hundred years ago; and at no time in that period were the then-current objects of that history arranged housewise anywhere but here. (133)

I am not endorsing PvI's denial of artifacts, I am merely pointing out that it cannot be dismissed Moore-style.

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.