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.

Comments

[William]

I was probably being too hasty. What's wrong with the contradictory: it is not the case that whenever there are some things, there is a whole they compose? I.e. sometimes there is a whole, sometimes there isn't?

[spencer]

Bill,

I am new to mereology, but I have been mulling over the possibility that there might be an even stronger argument against mereological nihilism than the one you present. If MN is true, then all of our ordinary beliefs about the compositions of wholes are false. So the merelogical nihilist must offer some sort of an error theory, but it's hard to see how this error theory would go without encountering a contradiction. For instance, suppose the error theory is that we evolved to see individuated objects to ensure our own survival. For this to be true don't "we" have to make up wholes rather than just parts? If so, than the MNist has run into a contradiction.

[Bill Vallicella]

William,

There is nothing wrong with the contradictory of universalism (mereological maximalism). That position has been labeled 'mereological moderatism' by Peter Simons. Intuitively, it is superior to both universalism and nihilism (mereological minimalism).

[Bill Vallicella]

Spencer: "For instance, suppose the error theory is that we evolved to see individuated objects to ensure our own survival."

I think you want 'composite' for 'individuated.'

I don't see the contradiction. Suppose we have evolved to see wholes where there are no wholes. There is no contradiction because the wholes we have evolved to see are not wholes in reality but wholes only relative to us and our interests and cognitive capacities.

Or perhaps your point is that WE have to be wholes in reality in order to see some things as composing a whole. If that is your point, then I think it is a good one.

Here is an even quicker argument adapted from van Inwagen. If there are no wholes, if there are only simples, then human beings don't exist. But surely at least one human being exists, ergo, etc.

Peter Unger won't accept this, though!

[John]

A couple of thoughts here.

First, while Bill is surely correct to note that "mereological moderatism" is "intuitively" superior to both universalism and nihilism, it faces a serious concern that neither universalism and nihilism face. That concern stems from an argument that some have dubbed "the Sider sorites". Very, very, roughly, the Sider sorites looks like this:

(1) Suppose that mereological moderatism is true.
(2) If moderatism is true, then composition only occurs some of the time.
(3) If composition only occurs some of the time, then there is a restriction on composition in virtue of which it occurs only some of the time.
(4) But any restriction on composition must necessarily be vague.
(5) If a restriction on composition is vague, then there are cases where it is vague as to whether or not composition has occurred.
(6) If it is vague as to whether or not composition has occurred, then it is vague as to whether or not a composite object exists.
(7) But existence is not vague.
(8) Therefore, mereological moderatism is false.

This argument, put more precisely, can be found in Sider's "Four-Dimensionalism". He has adapted it from some remarks of David Lewis, which I believe can be found in his "On the Plurality of Worlds". The only two positions regarding composition which survive this argument are nihilism and universalism. Mereological moderatism, the argument shows, entails ontic vagueness, that is, an account of vagueness according to which vagueness is in the world, as opposed to in our language or thought. And that, intuitively, looks bad.

This isn't to say that there are no responses to the argument. Mereological moderates typically have something to say in response. But this argument has certainly been important in the literature, and it shows that for all the intuitive support for moderatism, it looks (on the face of it) as though moderatism runs afoul of a very intuitive idea, namely, that the world itself is not vague.

Second, both so-called "quasi-nihilists" (e.g. Van Inwagen and Merricks), as well as genuine nihilists like Cian Dorr, have offered well-developed error theories to explain away our common sense judgments. As for Spencer's concern that we ourselves would have to be wholes in order to make the foregoing error theory work, I have a few things to say. First, the worry doesn't arise for either Van Inwagen or Merricks, both of whom admit that we exist and are composite. It would arise for Dorr. Second, the objection seems to depend on simply assuming (as, say, van Inwagen does) that human beings, if they exist, must be composite material objects. Dualists would reject this on the grounds that humans are not material objects and, so, presumably do not enter into mereological relations. But some thinkers (and I can't think of any names here, sadly) have suggested that perhaps humans are mereological simples. That is, perhaps human beings are objects which have no proper parts. Perhaps we are even EXTENDED simples, that is, objects without proper parts but which are nevertheless spatially extended. I believe van Inwagen at least mentions such a position in "Material Beings", though of course he rejects it. I don't recall his reasons. But on the face of it, this looks like a coherent position. And if it is, then the contradiction Spencer sees for the mereological nihilist doesn't arise. In general, my concern about the objection is just that it assumes a certain view about what sorts of objects persons are, and which nihilists would surely reject.

[Bill Vallicella]

John,

Thank you for an excellent and helpful contribution. I wonder about

>>(6) If it is vague as to whether or not composition has occurred, then it is vague as to whether or not a composite object exists.<<

This is very plausible if EPISTEMIC vagueness is at issue. But epistemic vagueness is compatible with ontic determinateness. (7) is false if epistemic vagueness is at issue. So it is at least arguable that the truth of (6) requires the falsity of (7) in which case the argument is unsound.

[Bill Vallicella]

John,

Studying further your version of the Sider sorites, I have a question about (4): "But any restriction on composition must necessarily be vague." It may be that any restriction must be arbitrary, but what could it mean to say that the restriction is vague?

Suppose I lay it down that 12 long-stemmed roses form a bunch only if the stems are close enough together to fit through a circular hole the diameter of which is 2" or less. That is an arbitrary (but not unreasonable) stipulation as to what shall count as a bunch. Though the stipulation is arbitrary, it is a perfectly definite stipulation: there is nothing vague about the stipulation.

[spencer]

Bill,

"Or perhaps your point is that WE have to be wholes in reality in order to see some things as composing a whole. If that is your point, then I think it is a good one."

That better expresses what I was trying to get across. I'll work on refining the argument I hope to present. But basically, I want to argue that the MNist encounters a contradiction, because in explicating the error theory (we are such to see things as composite wholes where there are none) we must already be wholes!

As for John's point that some philosophers think human beings are simple, that is true enough. Dave Barnett at U of Colorado is one such philosopher, argued in his paper "You are Simple" which is the first paper in Robert Koonz anthology "The Waning of Materialism." If Barnett or some similar view is right than there is no contradiction, but I suspect we have independently good arguments against them. For instance, how do you explain akrasia if we are simples and not composite wholes? How can there be tension within a simple?

[John]

Bill:

Both (6) and (7) are intended to be read as making claims about ontic vagueness. More precisely, the idea is supposed to be that (7) claims that ontic vagueness is false, but since the consequent of (6) says that there's going to be ontic vagueness (on the assumption that mereological moderatism is true), we ought to reject mereological moderatism. I gather from your remarks that you don't think (6) is particularly plausible if read as a claim about ontic vagueness. But I'm not sure I understand why.

As for (4), I think Sider's thought is something like this. Arbitrary restrictions on composition are implausible because, he thinks, they are somehow ontologically unmotivated. In the case of your example, he would want to know what it was about the 2" diameter that was special. Why couldn't the cutoff have been at 2.25"? Now, your case seems (in my view) to be a clear case where the question of what should count as a "bunch" of roses is simply a matter of convention. So in that sense, there just ISN'T anything special about the 2" cutoff other than that we happened to choose it. But I suspect that Sider, being what he calls an "ontological realist", would deny that composition in general is a matter of convention. So restrictions on composition, not being a matter of convention, cannot be arbitrary in the manner of your example, because arbitrary restrictions are ontologically unmotivated. That leaves non-arbitrary restrictions, and from what he says in "Four-Dimensionalism", he thinks any of those are going to turn out to be vague. Van Inwagen's preferred answer to the Special Composition Question would probably be cited as evidence in support of this claim; van Inwagen's restriction on composition is non-arbitrary, but admittedly vague.

Spencer:

There can be tension within a simple if that simple is extended (I remain agnostic as to whether non-extended simples can exhibit tension). An extended simple may exhibit localized spatiotemporal variability, and so there may be "tension", as you say, between various of its properties. Presumably, if we are simples, then akrasia would be an instance of just this sort of tension, though I'm certainly not qualified to formulate the details.

One might get the feeling that this story is just so much hand-waving. But, granting the assumption that extended simples are metaphysically possible, there seems to be nothing in the concept of "simple" or "extended simple" that requires homogeneity. Simples, especially extended simples, might very well be heterogeneous in the way described above (i.e. exhibit localized spatiotemporal variability). My sense is that objections to that view will simply assume that spatiotemporal variability requires divisibility into proper parts, which goes hand-in-hand with the idea that there's something in the concept of "simple" or "extended simple" that requires homogeneity.

[Spencer]

An extended simple? With inner tension? I'm much too simple to understand what that could possibly be.

[John]

Spencer:

There's a fairly robust literature on the nature of simples. Everyone agrees, of course, that they lack proper parts. But which objects (if any) are simples? Kris McDaniel has several good papers on the subject, most notably "Brutal Simples", in which he argues for the claim that there is no way to state necessary and sufficient conditions for being a simple that does not invoke mereological vocabulary. In the course of that paper, he surveys several leading views on what simples are, including Ned Markosian's view that they are maximally continuous objects.

In another paper, McDaniel defends the view that extended simples - that is, objects which lack proper parts but are nevertheless extended in space - are possible. See his "Extended Simples". He also has a paper, which I've not read, called "Extended Simples and Qualitative Heterogeneity".

Peter Simons also has a paper in which he discusses extended simples. I also think some of Dean Zimmerman's work deals with these issues.

Finally, monists of all stripes must believe in extended simples. For, presumably, the sole concrete object which monists posit would be extended in space, but (on pain of denying monism) must lack proper parts. So that object would be an extended simple. For a contemporary defense, see Terry Horgan and Matjaz Potrc's "Austere Realism".

Admittedly, citing a bunch of sources at you isn't particularly helpful. I'm fairly new to this literature myself. But I wasn't sure if your remarks were intended to be genuine questions, or whether they were veiled suggestions that the notion of an extended simple is incoherent. Either way, providing you with sources should help.

[Spencer]

Ah yes I met Matjaz Potrc in Slovenia while on leave. Austere realism is high on my reading list. So I'll be looking into it shortly.