Material Composition and Modal Discernibility

(For David Brightly, whom I hope either to convince or argue to a standoff.)

Suppose God creates ex nihilo a bunch of Tinker Toy pieces at time t suitable for assembly into various (toy) artifacts such as a house and a fort. A unique classical mereological sum -- call it 'TTS' -- comes into existence 'automatically' at the instant of the creation ex nihilo of the TT pieces. (God doesn't have to do anything in addition to creating the TT pieces to bring TTS into existence.) Suppose further that God at t assembles the TT pieces (adding nothing and subtracting nothing) into a house. Call this object 'TTH.' So far we have: the pieces, their sum, and the house. Now suppose that at t* (later than t) God annihilates all of the TT pieces. This of course annihilates TTS and TTH. During the interval from t to t* God maintains TTH in existence.

I set up the problem this way so as to exclude 'historical' and nonmodal considerations and thus to make the challenge tougher for my side. Note that TTH and TTS are spatially coincident, temporally coincident, and such that every nonmodal property of the one is also a nonmodal property of the other.  Thus they have the same size, the same shape, the same weight, etc. Surely the pressure is on to say that TTH = TTS? Surely my opponents will come at me with their battle-cry, 'No difference without a difference-maker!' There is no constituent of TTH that is not also a constituent of TTS. So what could distinguish them?

Here is an argument that TTH and TTS are not identical:

1. NecId: If x = y, then necessarily, x = y.

2. If it is possible that ~(x = y), then ~(x = y). (From 1 by Contraposition)

3. If it is possible that TTS is not TTH, then TTS is not TTH. (From 2, by Universal Instantiation)

4. It is possible that TTS is not TTH. (God might have assembled the parts into a fort instead of a house or might have left them unassembled.)

5. TTS is not TTH. (From 3, 4 by Modus Ponens)

If you are inclined to reject the argument, you must tell me which premise you reject. Will it be (1)? Or will it be (4)?

Your move, David.

Comments

[David Brightly]

Thank you Bill,

To remain germane to the present discussion I think we must interpret the equality sign to mean 'is the same individual as.' But then I think the move from (2) to (3) fails because 'TTS' does not name an individual as I understand this term. The TT pieces (presumably more than one) are in general a scattered, not a connected body. But if there is just one TT piece then (4) is false.

The Piranha brothers notoriously cowed their underworld victims into submission by the use of ghastly devices like Litotes. Bill 'the Maverick' Vallicella has a different method. I now know what to be 'modally challenged' really means!

[john]

Off-topic but if you’re interested, philosophical powerhouse Sam Harris interviews cosmologist Lawrence Kraus re his latest book: A Universe from Nothing -- Why There Is Something Rather Than Nothing
Everything and nothing: an interview with Lawrence M. Kraus:
http://www.samharris.org/blog/item/everything-and-nothing/

excerpt:
"Modern science has made the something-from-nothing debate irrelevant. It has changed completely our conception of the very words “something” and “nothing”."

[David Brightly]

Morning Bill,

Just a summary of my thoughts after shutting down last night: if there is just one piece then the house is the same individual as the piece(s). Otherwise, there is more than one piece and the house is not the same individual as the pieces. It is one and they are many. This follows immediately from one's understanding of is the same individual as. Either way, after time t we can say that the pieces comprise an individual and this individual is the same individual as the house. I've tried to indicate where I think your argument goes wrong in failing to make this distinction. I hope this is consistent with what I've said earlier.

[John]

This has been bothering me all night, Mr. Vallicella. The argument you provide for the distinctness of TTS and TTH is, of course, common in the literature on material objects. It's most frequently used to demonstrate the distinctness of an object and the matter of which it is constituted (e.g., a statue and a lump of clay). Correct me if I'm wrong, but you seem to be using the argument in a slightly different way, because TTH is not supposed to be an object whose constituting matter is TTS. Instead, your argument seems to be a sort of criticism of classical extensional mereology, to the extent that the existence of TTH (and its distinctness from TTS) implies that classical extensional mereology does not provide us with the tools to recognize all of the objects in the world. For of course, from the point of view of the classical extensional mereologist, TTH and TTS are identical because the arrangement of a thing's parts is irrelevant to the thing's identity.

I am no fan of classical extensional mereology, but I worry that your argument defeats the view too easily. I suspect that the classical extensional mereologist will deny premise 4. Here is how I think they will try to do this. They will begin by following David Lewis in supposing that our only understanding of the concept of parthood is provided by classical extensional mereology. The axioms of classical extensional mereology, they'll say, are constitutive of our understanding of what it is for some object to be a *part* of something else. Having established this, they'll go on to claim that if this is the case, then it is not possible for TTS and TTH to be distinct. This is not possible, the argument will go, because it requires there to be a notion of parthood that is *distinct* from the notion of parthood governed by the axioms of classical extensional mereology, such that TTS is governed by the latter while TTH is governed by the former. For, they will say, if you admit that TTH is governed by the notion of parthood at work in classical extensional mereology, then you cannot say that the manner of arrangement of the Tinker Toys brought anything new (namely, TTH) into existence from TTS. So there must be some notion of parthood governing TTH that is distinct from that found in classical extensional mereology. But, having already established that there is no such notion of parthood, they'll conclude that TTH could not possibly be distinct from TTS. Thus, premise 4 is false.

I'm curious what you think of this kind of argument, because I really was troubled (and fascinated) by your use of a very common argument in a new way against the classical extensional mereologist.

[P.S. You often receive emails from readers, but I have been unable to locate your email address. Could you possibly direct me to it?]

[Leo Carton Mollica]

Mr. Brightly,

Perhaps our disagreement boil down to this: we are inclined to say of the statue that it is essentially a statue, whereas you wish to say that the statue is but accidentally a statue. The lump "becomes" the statue the same way Cardinal Ratzinger became the Vicar of Christ: by acquiring a new and wholly contingent feature. Does this seem a good characterisation of our (near-)impasse?

[Bill Vallicella]

Leo,

I think you've put your finger on the problem. David is thinking in terms of a bare particular x which exists selfsame through an interval of time and is first a mere lump, then a lump and a statue, and then a mere lump again. This implies that the bare particular is only accidentally related to its properties, whether these be lump properties or statue properties or both. For you and me, however, the statue is essentially a statue whereas the lump is not essentially a statue which implies, first, that statue and lump are distinct, and second, that there is no bare partocular at the ontological core of the statue/lump.

[Bill Vallicella]

John,

Thanks for the comment, and I hope you didn't lose too much sleep. I should have stuck with the statue/lump example and not have muddied the waters by using the TTH vs. TTS example. As Brightly points out, TTS is not an individual in exactly the same sense in which a lump of clay is. If I understood what he was saying, the parts of the latter are well-connected in the topological sense but the parts of the former are not.

And as you seem to be saying, the constituting matter of TTH is not TTS but the extension of this mereological sum, i.e., the TT pieces.

My e-mail address can be found via the right sidebar. Near the top, click on About.

[Bill Vallicella]

John,

As for classical mereology, if it implies that TTH and TTS are identical, then so much the worse for classical mereology. After all, it is obvious that they are not identical. The one is a house essentially, the other (the mere sum) is not a house even if the parts are arranged house-wise.

The house has causal properties that the disconnected parts lack. That suffices to show that the house and sum of its parts cannot be identical.

Why should anyone think that the only notion of 'part' is supplied by classical mereology?

[Account Deleted]

Bill,

Premise (1) is problematical as it stands, unless you put some restrictions on 'x' and 'y'; for instance that they must be rigid. O/w consider (1)* as an instance of (1):

(1)* If (the morning star = the evening star), then necessarily (the morning star = the evening star).

(2)* If it is possible ~(the morning star = the evening star), then ~(the morning star = the evening star).

(3)* It is possible ~(the morning star = the evening star)

Therefore,

(4) ~(the morning star = the evening star).

So you have just proved an astronomical fact that the morning star is not identical to the evening star based upon logic alone.

[David Brightly]

Bill, Leo,

I can't quite go with Leo's diagnosis as I'd be reluctant to characterise an object's possession of a property as essential versus accidental. I'm not sure I can make sense of the usual modal understanding of this distinction. An object that is square is necessarily equi-sided, though, but this seems more a relation between concepts than between objects and concepts.

Bill is perhaps closer, but what is conserved throughout all these transformations seems to me to be a certain quantity of matter, say bronze, which takes on different shapes as a result of melting and casting, or hammering, say, but since this has chemical properties I find it hard to see it as a bare particular.

I struggle with the perhaps technical use of individual that you both make. To say that several numerically distinct physical objects can co-occupy a region of space seems to stretch the ordinary notion of physical object too far. It seems simpler and more familiar to think of one thing falling under different concepts as change occurs: I was successively baby, child, adult, but all along a human, for example. If we say that the person existed before the adult, I think we are guilty of treating temporal slices as if they were objects. We must keep a static four-dimensional view of the world well-separated from the ordinary spatial and temporal view. Importing from one to the other creates paradox.

So we have lots of differences. What interests me is Bill's remark

For you and me, however, the statue is essentially a statue whereas the lump is not essentially a statue which implies, first, that statue and lump are distinct, and second, that there is no bare particular at the ontological core of the statue/lump.

This suggests that you are inferring what individuals there are from an analysis of properties and an application of principles such as Indiscernibility of Identicals and Necessity of Identity, which I put to Leo earlier. Does this amount to another methodological difference between us?

[Edward Ockham]

Happy New Year from London. I'm sorry I missed this series of posts. The issues resembles the one we discussed last year, re Van Inwagen, no?

[Leo Carton Mollica]

Mr. Brightly,

What do you find confusing about the "usual [albeit impoverished] modal understanding" of the accidental/essential distinction? a is essentially F on such an interpretation of the terms iff, necessarily, a exists if and only if a is F, merely accidentally F otherwise. What is obscure about this?

"To say that several numerically distinct physical objects can co-occupy a region of space seems to stretch the ordinary notion of physical object too far. It seems simpler and more familiar to think of one thing falling under different concepts as change occurs: I was successively baby, child, adult, but all along a human, for example. If we say that the person existed before the adult, I think we are guilty of treating temporal slices as if they were objects."

I quite agree, but I think neither I nor Dr. Vallicella would say that some new individual comes into being at every change. The Pope, for example, has not existed only since 2005, when he was declared Sovereign Pontiff: he has existed since 1927, when Joseph Ratzinger was born (or conceived, or whatever). What motivates my calling the statue a new individual, at least, is our ordinary ways of considering and speaking of a statue: we say without a second thought that it was made or manufacturedby a sculptor, that it did not exist so-and-so many years ago (even when the relevant marble did), that it would be destroyed were a hammer taken to it, that it might never have existed had its author not sculpted it, etc. Taken at face value, all of these locutions (quite systematically) suggest we should attribute to the statue properties the marble hunk simply does not have. None of this is true of the Pope or young adult Leo.

(This, of course, raises the question of what sorts of properties elevate something to the status of a distinct individual. I am inclined to say that it is (something like) what Aristotle called a substantial form, but my thoughts on this matter are too ill-developed to be of much interest in discussion.)

Incidentally, I adhere to neither four-dimensionalism or eternalism, so I can assure you that my failing to "keep a static four-dimensional view of the world well-separated from the ordinary spatial and temporal view."

[Bill Vallicella]

Happy New Year, Ed.

Yes, we've been over this ground before. The point of entry was a bit different this time, however: the question whether the reduction of one particular to another is a coherent notion.

Read an article on transubstatiation this morning by one D. C. Cassidy (REL STUD June 1994: "Is Transubstantiation without Substance?") Cassidy defends the coherence of the doctrine drawing on Barry Miller and your teacher C J F Williams. Interesting logical questions. Curious to see Frege put to work in this area.

[Edward Ockham]

>>The Pope, for example, has not existed only since 2005, when he was declared Sovereign Pontiff: he has existed since 1927,

A scholastic would leap in here in a flash, armed with a pile of nested syllogisms, and say something like, the Pope, insofar as he is Pope has only existed since 2005, but the Pope, insofar as he is a person, has existed since 1927.

Ockham has something useful here, let me go and find it.

[Edward Ockham]

Ockham's presentation of reduplicative propositions is here. Brandon also has a nice explanation of the idea. I'm wondering if this could be a solution. This lump of stone, qua lump of stone, has existed for a million years. But this this lump of stone, qua statue, has only existed for ten years. The objection to your argument would then be on similar lines to David's above.