Mereology Map

Recently, my colleague David Faraci posted a "flowchart" for metaethics on PeaSoup, and he impressed on me how much useful feedback he received. Not long ago, I composed something analogous for mereology, and was hoping to get feedback as well. (I realize my "road map" is incomplete, e.g., it does not address growing block theories, though I am hoping to revise it in the near future.)

The document is at: http://www.unc.edu/~tparent/Identitymap.pdf

Taking Statues of Clay With a Pinch of Salt

The puzzle of the statue and the clay is so well-known that it hardly needs any introduction. On Monday, a sculptor buys a piece of clay. On Tuesday, she moulds it into a statue. The statue and the piece of clay, the argument goes, cannot be identical because there are predicates that are satisfied by the one but not by the other. For instance, the piece of clay existed on Monday while the statue did not or, to take another example, the piece of clay would survive being squashed into a ball but the statue wouldn't. (These argument is often put in terms of properties rather than predicates, but I take it that anyone who accepts a reasonably sparse conception of properties would deny that any properties correspond to predicates such as 'x exists on Monday' or 'x would survive being squashed into a ball'.)

Slightly more formally, the arguments look more or less like this:

A:
(A1) The piece of clay existed on Monday
(A2) The statue did not exist on Monday
(A3) If the piece of clay and the statue are identical, then the piece of clay existed on Monday iff the statue existed on Monday
(AC) The piece of clay and the statue are not identical

B:
(B1) The piece of clay would survive being squashed into a ball
(B2) The statue would not survive being squashed into a ball
(B3) If the piece of clay and the statue are identical, then the piece of clay would survive being squashed into a ball iff the statue would survive being squashed into a ball.
(BC) The piece of clay and the statue are not identical

To my mind, the most surprising feature of this puzzle is that it has mislead so many good philosophers into embracing the view that material constitution is a relation between distinct objects with all its implausible consequences despite the fact that a much more simple and plausible solution to the puzzle has been around for decades (as far as I can see the position I have in mind is the one developed and defended by Roderick Chisholm in the 1970s). So, I was wondering if readers could help me see what's wrong with the Chisholmian solution or explain why it is almost completely ignored in the literature (in fact I cannot even think of anyone truly engaging with it in the literature).

Let me start by putting aside my mereological nihilist sympathies (as I assume few would embrace mereological nihilism with its seemingly implausible consequences just for the sake of solving that puzzle) and assume that there are pieces of clay and statues. For the sake of simplicity, let me also assume that the one made on Tuesday is the only statue there is, was, and will ever be in the whole wide world. Given these assumptions, it seems that one could truly affirm that

(A1*) On Monday, there was a piece of clay (i.e. On Monday, there is an x such that x is a piece of clay),

and that

(A2*) On Monday, there was no a statue (i.e. On Monday, there is no y such that y is a statue).

It is our inclination to accept something like (A2*), I suspect, that can be exploited to mislead us into assenting to (A2). However, accepting (A2*) does not amount to accepting anything like (A2), as one can easily concede that there was no statue on Monday and that there was one on Tuesday while denying that something new has come into existence between Monday and Tuesday (contrary to what (A2) surreptitiously suggests). One can do so simply by maintaining that, whereas our piece of clay (call it 'Clay') was not yet a statue on Monday, it became one on Tuesday, when the artist turned it into one. So, while there was no statue on Monday and there is one on Tuesday, the thing that became a statue on Tuesday (i.e. Clay) already existed on Monday, although on Monday it was not yet a statue, as it did not meet the conditions for satisfying 'x is a statue' (whatever these may be).

Consider now Argument B. Sure enough, if Clay were to be squashed into a ball, something would still be a piece of clay and nothing would be a statue. However, this does not imply that something would go out of existence in the process. It is simply that, under these counterfactual circumstances, Clay would no longer meet the conditions for satisfying 'x is a statue' (whatever these may be), while it would still meet the ones for satisfying 'x is a piece of clay'. So, one could truly affirm that:

(B1*) If Clay were to be squashed into a ball, there would still be something that is a piece of clay (i.e. there would be an x such that x is a piece of clay).

and that

(B2*) If Clay were to be squashed into a ball, there would no longer be be something that is a statue (i.e. there would be no y such that y is a statue).

And that, I think, is all we really mean to assent to when we assent to (B1) and (B2).

Consider now a third variation on our puzzle.

C:
(C1) The piece of clay would not survive the loss of any of its proper parts
(C2) The statue would survive the loss of some of its proper parts
(C3) If the piece of clay and the statue are identical, then the piece of clay would not survive the loss of any of its proper parts iff the statue would not survive the loss of any of its proper parts.
(CC) The piece of clay and the statue are not identical

Consider, for example, a piece of Clay that is neither too big nor too small--e.g. the piece that forms the nose of the statue (call it 'Nosy'). Here, the underlying intuition seems to be that, if Nosy came to be detached, the statue would remain the same statue as before (although deprived of its nose) but the piece of clay wouldn't be any longer the same. All this argument seems to show, however, is that the conditions for satisfying 'x is the same statue as y' are different from those for satisfying 'x is the same piece of clay as y'. Let's grant that, if Nosy were to be detached from Clay, Clay would cease to exist. In its place, we would have two smaller pieces of clay: Nosy and the rest of Clay (call it 'Clay Jr'). Each of them used to be a proper part of Clay and, so each of them, is partially identical with it (in the sense that part of each is identical with part of Clay) although not (wholly) identical with it. More importantly, one of them (i.e. Clay Jr) still meets the conditions for satisfying 'x is a statue'. So, after Clay ceases to exist, there still is a statue.

But what of the intuition that this statue is the same statue as the one that was there before? Since Clay and Clay Jr are not identical, how can the statue that Clay Jr is be the same statue as the one that Clay used to be? I think the answer should be that, despite the appearances, 'x is the same statue as y' (nor 'x is the same piece of clay as y' for that matter) expresses an identity relation. (Note that this position differs from the one (in)famously put forward by Peter Geach, as it maintains that Clay and Clay Jr are absolutely distinct, whether or note we take them to satisfy 'x is the same statue as y' or 'x is the same piece of clay as y'.) In other words, in order for Clay and Clay Jr to satisfy 'x is the same statue as y' (or 'x is the same piece of clay as y'), Clay and Clay Jr need not be identical. In order to satisfy 'x is the same statue as y' or 'x is the same piece of clay as y', Clay Jr would only have to meet some set of weaker (and vaguer) conditions, which, in the case of 'x is the same statue as y', may include its overlapping significantly with Clay and retaining its shape (and, in the case of 'x is the same piece of clay as y', may include its overlapping (almost) completely with Clay even without retaining its shape).

Constitution and Strong Coincidence

I was rereading Ryan Wasserman's 'The Standard Objection to the Standard Account' for a seminar on material constitution that I'm teaching this term. In it, Wasserman considers a number of "mereological" solutions to the "standard objection" (i.e. since Lump and David share all of their microphysical parts, there is nothing to explain their difference in kind and de re modal and temporal properties). Wasserman considers three responses to that objection: the no coincidence response (Lump and David share no parts), the weak coincidence response (Lump and David weakly coincide, which essentially boils down to the fact that all parts of Lump are parts of David but some parts of David (e.g. its arm) are not part of Lump), and the strong coincidence response (Lump and David strongly coincide share all their (material) parts at every time they both exist). While I think Wasserman's case against the first two views is strong, I'm not persuaded by his case for the third view. (In fact, I'm not even sure I understand what his proposal exactly is.)

The strong coincidence response (SCR) seems to be committed to the following claims:

1. For any time t, if Lump and David exist at t, they wholly exist at t.
2. For any time t, if Lump and David exist at t, they strongly materially coincide at t (i.e. every (material?) part of Lump at t is a part of David at t and every part of David at t is a (material?) part of Lump at t.)
3. For any time t, if Lump and David exist at t, they spatially coincide at t (i.e. every spatial part of Lump at t is a part of David at t and every spatial part of David at t is a part of Lump at t.)

So, one could wonder (at least I do) how can David and Lump differ in their parts given (1)-(3)? Since I'm not quite sure I understand Wasserman's answer, I'll let him do the talking now (I only divide the different claims and label them for the sake of the discussion):

[(a)][Both the defender of the standard account and the defender of the doctrine of temporal parts] will agree that David is a temporal part of Lump during the interval from t2 [when David came into existence] to t3 [when David and Lump ceased to exist]. For David exists only during that interval, David is a part of Lump during that interval and David overlaps during that interval everything that is a part of Lump during that interval.

[(b)] Moreover, both parties will agree that David is a proper temporal part of Lump during the interval in question since David is not identical to Lump.

[(c)]The two parties will not agree on everything, of course. Most importantly, the temporal parts theorist will assert, and the proponent of the standard account will deny, that Lump has temporal parts (during the interval from t1 [when Lump came into existence] to t2) that David lacks.

[(d)] Still, given that David is a proper temporal part of Lump, there must be some sense in which these two objects differ in parts.

[(e)] Indeed there is: Lump has spatial parts during the interval from t1 to t2 that David lacks.

I find it very hard to see how (a) and (even harder) (b) can be true. In fact, I can't see any good reason for the constitutionalist qua endurantist to hold that David is a temporal part of Lump between t2 and t3 let alone a proper temporal part of it. If one believes that Lump and David wholly exist at every time at which they exist, they would seem to have to believe that, at most, David and Lump can only have improper temporal parts at every time at which they exist (At t, if Lump exists, it is its only temporal part) but I can't see any plausible way to think that one can be a proper temporal part of the other (David can be a proper temporal part of Lump only if there are temporal parts of Lump that are not temporal parts of David, but since, given (1), it would seem that neither Lump nor David has (proper) temporal parts, I can't see how the latter can be a proper temporal part of the former).

I find it even harder to see how (b) can be true given (c). If the constitutionalist qua endurantist denies that Lump has temporal parts David lacks how can the latter be a proper temporal part of the former? According to Wasserman's (e), it would seem it can be so by virtue of Lump's having spatial parts between t1 and t2 that David does not have (after all, David doesn't exist during that period!).

Okay, so, suppose that you and Wasserman are standing in front of Lump and David and you ask 'But how can Lump and David have different kind, de re temporal and de re modal properties right now even if right now they are sharing all of their parts and their only parts are parts that exist right now?' I guess Wasserman's answer would be: 'Well, they do because they did not share all of their parts yesterday when David did not exist' But, at most this can explain why bakc then it was posssible for them to have different properties but not how it's possible now when the two share all of their parts (according to (2)).

I guess I'm missing something terribly obvious. Can anyone help me see what that something is?

(Let me mention a few other things Wasserman says that I find very puzzling:

Wasserman suggests that the standard objection applies not only to constitutionalism but also to fourdimensionalism and to the view that my hand is a spatial part of myself. But how can that be the case if the standard objection is predicated on the two objects sharing all of their parts? (of course the part of me that spatially coincides with my hand shares all of the parts with my hand (it is my hand after all!) but I don't)

And even if the standard objection applies to those views as well wouldn't that be a reason for those who hold those views to worry rather than a reason for the constitutionalist to feel relieved given that there are other views (most notably, nihilism) that are immune to that objection?

Finally, Wasserman seems to assume that a difference in temporal or spatial parts can explain a difference in kind, but I don't see any good reason to think so. There seems to be plenty of objects that differ in spatial and temporal parts without differing in kind and the reason why I am a human being and my hand is not is presumably not that I don't spatially coincide with my hands (althugh presumably it is a necessary condition for my being human).)

Bennett on The Ideological Price of "Low" Ontologies (Part I: Constitution)

I'm reading Karen Bennett's 'Composition, Colocation, and Metaontology' (which is published in this book). In it, Bennett draws a number of interesting metaontological morals by considering two ontological disputes--the one about composition and the one about constitution. In each dispute, she identifies a "low-ontology" side and a "high-ontology" side and at a certain point she argues that, in each dispute, what the low-ontologist gains in terms of ontological simplicity may be lost in terms of ideological simplicity. However, I'm not completely convinced by the specific cases she makes. In this post, I will focus on her case against for the ideological costs of the low-ontology side when it comes to constitution and focus on the composition case in another post.

As an example of the low-ontologist side in the constitution case, Bennett considers the Lewisian position that (let me over simplify here) even, if Statue and the Lump are identical, we can truly say that Statue would not survive being squashed into a ball while Lump would not by appealing to the different counterpart relations in which Lump/Statue stands with otherworldly things.

Bennett complains:

The heart of this strategy is to say that the relatively straightforward predicate 'being possibly squashed' in fact hides a multiplicity of more complex predicates that pack in some reference to the kind. (Lewis, of course, will invoke counterpart-theoretical properties like having a squashed counterpart under the lump-counterpart relation) Perhaps this require that the one-thinger [i.e. the one who takes the low-ontologist side in the constitution dispute] postulate a different complicated modal property for each object the multi-thinger [i.e. the one who takes the high-ontology side in the constitution dispute] countenances. Perhaps it just requires that she employ a different complicated modal predicate for each such object. That depends on the broader question about the viability of nominalism. What matters for my purposes is that the multi-thinger need not do either. (p.28)

In other words, what the low-ontologists saves on the cost of her ontology comes at the price of her ideology. Now, I have no sympathy for Lewis' modal realism or his counterpart theory, but Bennett's interpretation of the Lewisian position does not seem to be particularly charitable to me. Let me put aside the issue of nominalism and that of conceptual vs. ontological simplicity and focus on Bennett's interpretation of the Lewisian use of the counterpart relation in this case.

As far as I can see, the Lewisian's reply to Bennett should be that he does not need the complex predicates or the corresponding properties. When saying that 'Lump would survive being squashed' is true and 'Statue would survive being squashed' is not even if 'Lump' and 'Statue' refer to one and only one thing, the Lewisian would not directly appeal to the fact that the same thing has two different modal properties but to the fact that in different contexts the same thing can have different counterparts because the different contexts make different respects of similarirty with otherworldly things relevant. So, for example, when talking of Lump/Statue as 'Lump', we are making the material is made of, its mass, etc. salient, while when talking of it as 'Statue', we are making also its shape and history salient. So, there are things that are counteraprts of Lump/Statue qua lump of clay that are not counterparts of it qua statue (things that resemble it in being made of clay and having a certain mass, etc. but not in having a certain shape etc.) and some of this things are temporal parts of things whose other temporal parts were counterparts of Lump/Statue qua statue but are no longer counterparts of it because they no longer bear the right sort of resemblance to Lump/Statue qua statue because they have been squashed. So, the Lewisian really only needs the property having been squashed and claim that some counterparts of Lump/Staute qua lump of clay have it while some counterparts of it qua statue do not have it. It is only in virute of its counterparts having or not having the property having been squashed that Lump/Statue has or has not (derivatively) the modal property of being possibly squashed. Of course, Bennett could claim that the counterpart theory already comes at too high an ideological cost (I would just say that it is false, but I won't argue for that here), but Lewis and the Lewisians would claim it's a cost worth paying because of the benefit that it brings with it and, in any case, the Lewisian does not seem to need the strange predicates Bennett wants to saddle them with. Am I being too charitable to the Lewisian position or unfair to Bennett's objection?