Identity and Individuation – Page 5

Intentionality and Haecceity

Steven Nemes inquires:

Do you think that your stand on intentionality not requiring the existence of the intentional object is contradictory with your argument against haecceity properties (as non-qualitative thisnesses)? You say that an individual can have the property of searching after Atlantis, let's say, even if Atlantis doesn't exist. But your argument against haecceities is that identity-with-Socrates would be nonsense if Socrates didn't exist.

How would you solve the apparent contradiction?

Let's first note an ambiguity that infects 'intentional object.' Intentionality is object-directedness. So there is a clear sense in which every intentional mental state 'takes an accusative,' 'is of or about an object.' That object could be called the intentional object. Accordingly, whether I want a three-headed dog or a one-headed dog, my wanting has an intentional object. The nonexistence of three-headed dogs does not prejudice the object-directedness of my wanting a three-headed dog. It is equally important to note that the existence of one-headed dogs plays no role in making my wanting a one-headed dog object-directed. This is because object-directedness is an intrinsic feature of mental acts. To see this more clearly, suppose I want a one-headed dog that is distinct from every one-headed dog that presently exists. This mental state is object-directed, but its object-directedness does not derive from the present existence of any one-headed dog, or anything else.

But one could also use 'intentional object' to refer to the mind-independent entity, if there is one, that satisfies the description (definite or indefinite) that expresses the content of the intentional state. If we use the term in this second way, then my wanting a three-headed dog does not have an intentional object.

It is only in this second sense that intentionality does not require the existence of the intentional object. It is part of the very essence of wanting as an intentional mental state that it be a wanting of something (that is an objective genitive, by the way, not a subject genitive.) But it doesn't follow that the something exists. Similarly for perceiving, imagining, believing, etc.

As for the haecceity-property identity-with-Socrates, it is nothing at all at times and in worlds in which Socrates doesn't exist. I stick to that self-evident point pace Plantinga. (See A Difficulty With Haecceity Properties)

It seems to me that my line on haecceities is entirely consistent with my line on intentionality. Socrateity (identity-with-Socrates) essentially involves Socrates himself, that very individual, in a way in which seeking Atlantis (construed as a mental state, not as a physical action or actions) does not essentially involve Atlantis itself. And this is a good thing since there is no such island.

You seem to think that an intentional mental state acquires its object-directedness from without in virtue of the mind-independent existence of an entity that the state is directed to. It is this misconception that suggests to you that there is a contradiction in my affirming both

1. An haecceity H of x is nothing if x does not exist
and
2. It is not the case that a wanting W of x is nothing if x does not exist.

But note that 'H of x' is a subjective genitive whereas 'W of x' is an objective genitive. The haecceity or nonqualitative thisness of Atlantis is nothing at all because Atlantis does not exist. There is nothing for it to be the haecceity of. But a wanting of Atlantis is what it is whether or not Atlantis exists.

And similarly in other cases. An ancient Greek can be a Zeus-worshipper whether or not Zeus exists. But the same Greek cannot own a slave unless there exists some slave he owns. The instance of of ownership requires for its individuation the existence of both relata. But the instance of worshipping does not require the existence of both relata.

On Our Knowledge of Sameness

How ubiquitous, yet how strange, is sameness! A structure of reality so pervasive and fundamental that a world that did not exhibit it would be inconceivable.

How do I know that the tree I now see in my backyard is numerically the same as the one I saw there yesterday? Alvin Plantinga (Warrant and Proper Function, Oxford 1993, p. 124) says in a Reidian vein that one knows this "by induction." I take him to mean that the tree I now see resembles very closely the one I saw yesterday in the same place and that I therefore inductively infer that they are numerically the same. Thus the resemblance in respect of a very large number of properties provides overwhelming evidence of their identity.

But this answer seems open to objection. First of all, there is something instantaneous and immediate about my judgment of identity in a case like this: I don't compare the tree-perceived-yesterday, or my memory of the tree-perceived-yesterday, with the tree-perceived-today, property for property, to see how close they resemble in order to hazard the inference that they are identical. There is no 'hazarding' at all. Phenomenologically, there is no comparison and no inference. I just see that they are the same. But this 'seeing' is of course not with the eyes. For sameness is not an empirically detectable property or relation. I am just immediately aware — not mediately via inference — that they are the same. Greenness is empirically detectable, but sameness is not.

What is the nature of this awareness given that we do not come to it by inductive inference? And what exactly is the object of the awareness, identity itself?

A problem with Plantinga's answer is that it allows the possibility that the two objects are not strictly and numerically the same, but are merely exact duplicates or indiscernible twins. But I want to discuss this in terms of the problem of how we perceive or know or become aware of change. Change is linked to identity since for a thing to change is for one and the same thing to change.

Let's consider alterational (as opposed to existential) change. A thing alters iff it has incompatible properties at different times. Do we perceive alteration with the outer senses? A banana on my counter on Monday is yellow with a little green. On Wednesday the green is gone and the banana is wholly yellow. On Friday, a little brown is included in the color mix. We want to say that the banana, one and the same banana, has objectively changed in respect of color.

But what justifies our saying this? Do we literally see, see with the eyes, that the the banana has changed in color? That literal seeing would seem to require that I literally see that it is the same thing that has altered property-wise over ther time period. But how do I know that it is numerically the same banana present on Monday, Wednesday, and Friday? How do I know that someone hasn't arranged things so that there are three different bananas, indiscernible except for color, that I perceive on the three different days? On that extraordinary arrangement I could not be said to be perceiving alterational change. To perceive alterational change one must perceive identity over time. For there is change only if one and the same thing has different properties at different times. But I do not perceive the identity over time of the banana.

I perceive a banana on Monday and a banana on Wednesday; but I do not visually perceive that these are numerically the same banana. For it is consistent with what I perceive that there be two very similar bananas, call them the Monday banana and the Wednesday banana. I cannot tell from sense perception alone whether I am confronting numerically the same banana on two different occasions or two numerically different bananas on the two occasions. If you disagree with this, tell me what sameness looks like. Tell me how to empirically detect the property or relation of numerical sameness. Tell me what I have to look for.

Suppose I get wired up on methamphetamines and stare at the banana the whole week long. That still would not amount to the perception of alterational change. For it is consistent with what I sense-perceive that there be a series of momentary bananas coming in and out of existence so fast that I cannot tell that this is happening. (Think of what goes on when you go to the movies.) To perceive change, I must perceive diachronic identity, identity over time. I do not perceive the latter; so I do not perceive change. I don't know sameness by sense perception, and pace Plantinga I don't know it by induction. For no matter how close the resemblance between two objects, that is consistent with their being numerically distinct. And note that my judgment that the X I now perceive is the same as the X I perceived in the past has nothing tentative or shaky about it. I judge immediately and with assurance that it is the same tree, the same banana, the same car, the same woman. What then is the basis of this judgment? How do I know that this tree is the same as the one I saw in this spot yesterday? Or in the case of a moving object, how do I know that this girl who I now see on the street is the same as the one I saw a moment ago in the coffee house? Surely I don't know this by induction.

How then do I know it?

The Bundle Theory and the Identity of Indiscernibles

I have been defending the bundle-of-universals theory of concrete particulars (BT) against various weak objections over a series of posts, here, here, here, and here. Now I consider a very powerful objection, one that many will consider decisive. The objection can be cast in the mold of modus tollendo tollens: If BT is true, then the Identity of Indiscernibles is a necessary truth. But the Identity of Indiscernibles is not a necessary truth. Ergo, BT is not true.

1. The Identity of Indiscernibles (IdIn) is the converse of the Indiscernibility of Identicals (InId) and not to be confused with it. InId is well-nigh self-evident, while IdInis not. Roughly, the latter is the principle that if x and y share all properties, then x = y. It is a strictly ontological principle despite the epistemological flavor of 'indiscernible.' As just stated, it is more of a principle-schema than a principle. We will get different principles depending on what we count as a property. To arrive at a plausible nontrivial principle we must first rule out haecceity properties. If, for any x,there is a property of identity-with-x, then no two things could share all properties, and the principle would be trivially true due to the falsehood of the antecedent. Haecceity properties are creatures of darkness in any case as I argue elsewhere.

A plausible, nontrivial, principle results if we allow as properties all and only relational and nonrelational pure properties. A pure property is one that makes no reference to any specific individual. Being married would then be an example of a pure relational property: to be married is to be married to someone, but not to any specified individual. Being married to Xanthippe, however, is an impure relational property. Being obese would be an example of a nonrelational property. Here then is a plausible version of the Identity of Indiscernibles:

Necessarily, for any x, for any y, and for any relational or nonrelational pure property P, if (x has P iff y has P) then x = y.

2. It is obvious, I think, that BT entails IdIn in the above form. Consider a concrete particular, an iron sphere say, at a time. On BT it is nothing but a bundle of universals. This implies that it is not possible that there be a second iron sphere that shares with the first all relational and nonrelational pure properties. This is not possible on BT because on BT a concrete particular is nothing more than a bundle of universals. Thus there is no ontological ingredient in a concrete particular that could serve to differentiate it from another particular having all the same relational and nonrelational pure properties. And if it is not possible that there be two things that differ numerically without differing property-wise, then the Identity of Indiscernibles as above formulated is necessarily true.

I am assuming that BT, if true, is necessarily true. This is a special case of the assumption that the propositions of metaphysics, if true, are necessarily true. If this assumption is granted, then BT entails IdIn.

3. But is IdIn true? Since it is necessarily true if true, all it takes to refute it is a possible counterexample. Imagine a world consisting of two iron spheres and nothing else. (The thought experiment was proposed in a 1952 Mind article by Max Black.) They are the same size, shape, volume, chemical composition and so on. They agree in every nonrelational respect. But they also agree in every relational respect. Thus, each has the property of being ten meters from an iron sphere. What Black's example seems to show is that there can be numerical difference without property-difference. But then IdIn is false, whence it follows that BT is false.

4. This is a powerful objection, but is it fatal? Here are three ways to resist the argument, fit topics for further posts. He who has the will to blog will never be bereft of topics.

a. Maintain that BT is a contingent truth. If so, then BT does not entail IdIn as formulated above.

b. Grant that BT entails IdIn, but deny that scenarios such as Black's are really possible. Admit that they are conceivable, but deny that conceivability entails possibility.

c. An immanent universal can be wholly present at different places at once. So why can't a bundle of universals be wholly present in different places at once? Argue that Black's world can be interpreted, not as two particulars sharing all universals, but as one particular existing in two places at the same time. From that infer that Black's Gedankenexperiment does show that IdIn is false.

Any other paths of resistance?

A Closer Look at Material Composition and Modal Discernibility Arguments

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

Suppose God creates ex nihilo a bunch of TinkerToy 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)

The gist of the argument is that if x = y, then they are identical in every possible world in which both of them exist. But there are possible worlds in which TTS and TTH both exist but are not identical. (E.g., a world in which the pieces are assembled into a fort instead of a house.) Therefore, TTS andf TTH are not identical.

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.

Varzi, Sums, and Wholes

Achille C. Varzi, "The Extensionality of Parthood and Composition," The Philosophical Quarterly 58 (2008), p. 109:

Suppose we have a house made of Tinkertoy pieces. Then the house qualifies as a sum of those pieces: each piece is part of the house and each part of the house overlaps at least one of the pieces . . . . Are there other things that qualify as the sums of those pieces? UC says there aren't; the house is the only candidate: it is the sum of those pieces.

UC is Uniqueness of Composition:

UC If x and y are sums of the same things, then x = y,

where

(1) x is a sum of the zs =_df The zs are all parts of x and every part of x has a part in common with at least one ofthe zs.

Perhaps commenter John, who knows some mereology and the relevant literature on material composition, can help me understand this. What I don't understand is what entitles Varzi to assume that the Tinkertoy house — 'TTH' to give it a name — is identical to a classical mereological sum. I do not deny that there is a sum of the parts of TTH. And I do not doubt that this sum is unique. Let us name this sum 'TTS.' (I assume that names are Kripkean rigid designators.) What I do not understand is the justification of the assumption, made near the beginning of his paper, of the identity of TTH and TTS. TTH is of course a whole of parts. But it doesn't straightaway follow that TTH is a sum of parts.

Please note that 'sum' is a technical term, one whose meaning is exactly the meaning it derives from the definitions and axioms of classical mereology. 'Whole' is a term of ordinary language whose meaning depends on context. It seems to me that one cannot just assume that a given whole of parts is identical to a mereological sum of those same parts.

I am not denying that it might be useful for some purposes to think of material objects like TTH as sums, but by the same token it might be useful to think of material objects as (mathematical) sets of their parts. But surely it would be a mistake to identify TTH with a set of its parts. For one thing, sets are abstract while material objects are concrete. For another, proper parthood is transitive while set-theoretic elementhood is not transitive.

Of course, sums are not sets. A sum of concreta is itself concrete whereas a set of concreta is itself abstract. My point is that, just as we cannot assume that that TTH is identical to a set, we cannot assume that TTH is identical to a sum.

What is the 'dialectical situation' when it comes to the dispute between those who maintain that TTH = TTS and those who deny this identity?

It seems to me that the burden of proof rests on those who, like Varzi, identify material objects like TTH with sums especially given the arguments against the identity. Here is one argument. (a) Taking TTH apart would destroy it, (b) but would not destroy TTS. Therefore, (c) TTH is not identical to TTS. This argument relies on the wholly unproblematic Indiscernibility of Identicals as a tacit premise: If x = y, then whatever is true of x is true of y, and vice versa. Because something is true of TTH — namely, that taking it apart would destroy it — that is not true of TTS, TTH cannot be identical to TTS.

The simplicity and clarity of modal discernibility arguments like this one cast grave doubt on the opening assumption that TTH is a sum. I am not saying that Varzi and Co. have no response to the argument; they do. My point is that their response comes too late dialectically speaking. If you know what a sum is, you know that the identity is dubious from the outset: the discernibility arguments merely make the dubiousness explicit. Responding to these arguments strikes me as too little too late; what the identity theorist needs to do is justify his intitial assumption as soon as he makes it.

My main question, then, is this. What justifies the initial assumption that material particulars such as Tinkertoy houses are mereological sums? It cannot be that they are wholes of parts, for a whole needn't be a sum. TTH is a whole but it is not a sum. It is not a sum because a sum is a collection that is neutral with respect to the arrangement or interrelation of its parts, whereas it is essential to TTH that its parts be arranged house-wise.

Four-Dimensionalism to the Rescue?

Let us return to that impressive product of porcine ingenuity, Brick House. Brick House, whose completion by the Wise Pig occurred on Friday, is composed entirely of the 10,000 Tuesday Bricks. I grant that there is a sum, call it 'Brick Sum,' that is the classical mereological sum of the Tuesday Bricks. Brick Sum is 'generated' — if you care to put it that way — by Unrestricted Composition, the classical axiom which states that "Whenever there are some things, then there exists a fusion [sum] of those things." (D. Lewis, Parts of Classes, p. 74) I also grant that Brick Sum is unique by Uniqueness of Composition according to which "It never happens that the same things have two different fusions [sums]." (Ibid.) But I deny Lewis' Composition as Identity. Accordingly, Brick Sum cannot be identical to the Tuesday Bricks. After all, it is one while they are many.

Now the question I am debating with commenter John is whether Brick House is identical to Brick Sum. This ought not be confused with the question whether Brick House is identical to the Tuesday Bricks. This second question has an easy negative answer inasmuch as the former is one while the latter are many. Clearly, one thing cannot be many things.

The question, then, is whether Brick House is identical to Brick Sum. Here is a reason to think that they are not identical. Brick Sum exists regardless of the arrangement of its parts: they can be scattered throughout the land; they can be piled up in one place; they can be moving away from each other; they can be arranged to form a wall, or a corral, or a house, or whatever. All of this without prejudice to the existence and the identity of Brick Sum. Now suppose Hezbollah Wolf, a 'porcicide' bomber, enters Brick House and blows it and himself up at time t on Friday evening. At time t* later than t, Brick Sum still exists while Brick House does not. This shows that they cannot be identical; for if they were identical, then the destruction of Brick House would be the destruction of Brick Sum.

This argument, however, rests on an assumption, namely, that Brick Sum exists both at t and at t*. This won't be true if Four Dimensionalism is true. If bricks and houses are occurrents rather than continuants, if they are composed of temporal parts, then we cannot say, strictly and philosophically, that Brick Sum at t still exists at t*. And if we cannot say this, then the above argument fails.

But all is not lost since there remains a modal consideration. Brick House and Brick Sum both exist at time t in the actual world. But there are plenty of possible worlds in which, at t, the latter exists but not the former. Thus it might have been the case at t that the bricks were arranged corral-wise rather than house-wise. So Brick Sum has a property that Brick House lacks, namely, the modal property of being such that its parts could have been arranged in non-house-wise fashion. Therefore, by the Indiscernibility of Identicals, Brick House is not identical to Brick Sum.

So even if the historical discernibility argument fails on Four Dimensionalism, the modal discernibility argument seems to work even assuming Four Dimensionalism.

Please note that my thesis is not that Brick House is a sum that violates Uniqueness of Composition, but that Brick House is not a classical mereological sum. If Brick House were a sum, then it would be Brick Sum. But I have just argued that it cannot be Brick Sum. So it cannot identified with any classical sum. It is a whole of parts all right, but an unmereological whole. What does that mean? It means that it is a whole that cannot be adequately understood using only the resources of classical mereology.

Van Inwagen on Arbitrary Undetached Parts

In order to get clear about Dion-Theon and related identity puzzles we need to get clear about the Doctrine of Arbitrary Undetached Parts (DAUP) and see what bearing it has on the puzzles. Peter van Inwagen provides the following statement of DAUP:

For every material object M, if R is the region of space occupied by M at time t, and if sub-R is any occupiable sub-region of R whatever, there exists a material object that occupies the region sub-R at t. ("The Doctrine of Arbitrary Undetached Parts" in Ontology, Identity, and Modality, CUP, 2001, 75.)

Suppose I am smoking a cigar. DAUP implies that the middle two-thirds of the cigar is just as much a concrete material object as the whole cigar. This middle two-thirds is an undetached part of the cigar, but also an arbitrary undetached part since I could have arbitrarily selected uncountably many other lengths such as the middle three-fourths. Applied to Tibbles the cat, DAUP implies that Tibbles-minus-one-hair is just as full-fledged a material object as Tibbles. Van Inwagen maintains that DAUP is false.

I will reconstruct van Inwagen's argument for the falsity of DAUP as clearly as I can. Consider Descartes and his left leg L. To keep it simple, we make the unCartesian assumption that Descartes is just a live body. DAUP implies that L is a material object as much as Descartes himself. DAUP also implies that there is a material object we can call D-minus. This is Descartes-minus-L. It is obvious that Descartes and D-minus are not the same. (For one thing, they are differently shaped. For another, they are 'differently abled' in PC jargon.) At time t, D-minus and L are undetached nonoverlapping proper parts of Descartes, and both are just as much full-fledged material objects as Descartes himself is.

Now suppose a little later, at t*, L becomes detached from D-minus. In plain English, Descartes at t* loses his leg. (To avoid certain complications, we also assume that the leg is not only removed but also annihilated.) Does D-minus still exist after t*? Van Inwagen thinks it is obvious that D-minus does exist after the operation at t*. DAUP implies that the undetached parts of material objects are themselves material objects. So D-minus prior to t* is a material object. Its becoming detached from L does not affect D-minus or its parts, and if the separation of L from D-minus were to cause D-minus to cease to exist, then, van Inwagen claims, D-minus could not properly be called a material object. Descartes himself also exists after the operation at t*. Surely one can survive the loss of a leg. So after t* both D-minus and Descartes exist. But if they both exist, then they are identical. For otherwise there would be two material objects having exactly the same size, shape, position, mass, velocity, etc., and that is impossible.

In sum, at time t, D-minus and Descartes are not identical, while at the later time t* they are identical. The result is the following inconsistent tetrad:

D-minus before t* = D-minus after t*

D-minus after t* = Descartes after t*

Descartes after t* = Descartes before t*

It is not the case that D-minus before t* = Descartes before t*

The first three propositions entail the negation of the fourth. From this contradiction van Inwagen infers that there never was any such thing as D-minus. If so, then DAUP is false. But as van Inwagen realizes, his refutation of DAUP has a counterintuitive consequence, namely, that L does not exist either: there never was any such thing as Descartes' left leg. For it seems obvious that D-minus and L stand or fall together, to repeat van Inwagen's pun.

That is, D-minus exists if and only if L exists, and D-minus does not exist if and only if L does not exist. D-minus is an arbitrary undetached proper part of Descartes if and only if L is an arbitrary undetached proper part of Descartes. At this point, I think it becomes clear that van Inwagen's solution to the Dion/Theon or Descartes/D-minus puzzle is not compelling. He solves the puzzle by denying that there was ever any such material object as D-minus. But if there was no D-minus, then there was never any such material object as Descartes' left leg. It is obvious, however, that there was such a material object as Descartes' left leg L. So how could it be maintained that there was no such object as Descartes-minus? Van Inwagen makes it clear (p. 82, n. 12) that he does not deny that there are undetached parts. What I take him to be denying is that, for any P and O, where P is an undetached part of material object O, there is a complementary proper part of O, O-minus-P. So perhaps van Inwagen can say that L is a non-arbitrary undetached part of Descartes and that this is consistent with there being no D-minus. If so, he would have to reject the following supplementation principle of mereology which seems intuitively sound:

For any x, y, z, if x is a proper part of y, then there exists a z such that z is a part of y and z does not overlap x , where x overlaps y =df there exists a z such that z is a part of x and z is a part of y.

What the above supplementation principle says is that you cannot have a whole with only one proper part. Every whole having a proper part has a second proper part that supplements or complements the first so as to constitute a whole. Now Descartes' leg is a proper part of Descartes. So the existence of D-minus falls out of the supplementation principle.

It seems, then, that van Inwagen's rejection of DAUP issues in a dilemma. If there is no such object as Descartes minus his left leg, then there is no such object as Descartes' left leg, which is highly counterintuitive, to put it mildly. But if van Inwagen holds onto the left leg, then it seems his must reject the seemingly obvious supplementation principle lately mentioned.

My interim conclusion is that van Inwagen's solution to the Descartes/D-minus puzzle by rejection of DAUP is not compelling.

Can a Mereological Sum Change its Parts?

This post is an attempt to understand and evaluate Peter van Inwagen's "Can Mereological Sums Change Their Parts," J. Phil. (December 2006), 614-630. A preprint is available online here.

The Wise Pig and the Brick House: My Take

On Tuesday the Wise Pig takes delivery of 10,000 bricks. On the following Friday he completes construction of a house made of exactly these bricks and nothing else. Call the bricks in question the 'Tuesday bricks.' I would 'assay' the situation as follows. On Tuesday there are some unassembled bricks laying about the building site. By Unrestricted Composition, these bricks compose a classical mereological sum. Call this sum 'Brick Sum.' (To save keystrokes I will write 'sum' for 'classical mereological sum.' ) By Uniqueness of Composition, there is exactly one sum that the Tuesday bricks compose. On Friday, both the Tuesday bricks and their (unique) sum exist. But as I see it, the Brick House is identical neither to the Tuesday bricks nor to their sum. Thus I deny that the Brick House is identical to the sum of the things that compose it. I give two arguments for this non-identity.

Nonmodal 'Historical' Argument: Brick Sum has a property that Brick House does not have, namely the property of existing on Tuesday. Therefore, by the Indiscernibility of Identicals, Brick Sum is not identical to Brick House.

Modal Argument: Suppose that the actual world is such that Brick Sum and Brick House always existed, exist now, and always will exist: every time t is such that both exist at t. This does not alter the plain fact that the house depends for its existence on the bricks, while the bricks do not depend for their existence on the house. Thus there are possible worlds in which Brick Sum exists but Brick House does not. (Note that Brick Sum exists 'automatically' given the existence of the bricks.) These worlds are simply the worlds in which the bricks exist but in an unassembled state. So Brick Sum has a property that Brick House does not have, namely, the modal property of being possibly such as to exist without composing a house. Therefore, by the Indiscernibility of Identicals, Brick Sum is not identical to Brick House.

In sum (pardon the pun!), The Brick House is not a mereological sum. (If it were, it would have existed on Tuesday as a load of bricks, which is absurd.) This is not to say that there is no sum 'corresponding' to the Brick House: there is. It is just that this sum — Brick Sum — is not identical to Brick House. So what I am saying implies no rejection of Unrestricted Composition. The point is rather that a material artifact such as a house cannot be identified with the mereological sum of the things it is made of. This is because sums abstract or prescind from the mutual relations of parts in virtue of which parts form what we might call 'integral wholes' as opposed to a mere mereological sums. Unassembled bricks do not a brick house make: you have to assemble them properly. And the assembly, however you want to assay it, is an added ontological ingredient that escapes consideration by a general purely formal part-whole theory such as classical mereology.

I assume with van Inwagen that Brick House can lose a brick (or gain a brick) without prejudice to its identity. But, contra van Inwagen, I do not take this to imply that mereological sums can gain or lose parts. And this for the simple reason that Brick House and things like it are not identical to sums of the things that compose them. I would say, pace van Inwagen, that mereological sums can no more gain or lose parts than (mathematical) sets can gain or lose elements.

The Wise Pig and the Brick House: Van Inwagen's Take

I agree with van Inwagen that "The Tuesday bricks are all parts of the Brick House and every part of the Brick House overlaps at least one of the Tuesday bricks." (616-617) But he takes this obvious truth to imply that " . . . 'a merelogical sum' is the obvious thing to call something of which the Tuesday Bricks are all parts and each of whose parts overlaps at least one of the Tuesday Bricks." (617) Well, he can call it that but only if he uses 'mereological sum' in a way different that the way it is used in classical mereology.

Now if we acquiesce in van Inwagen's usage, and we grant that things like houses can change their parts, then it follows that mereological sums can change their parts. But why should we acquiesce in van Inwagen's usage of 'mereological sum'?

Is Everything a Mereological Sum?

As I use 'mereological sum,' not everything is such a sum. The Brick House is not a sum. It is no more a sum than it is a set. There are sums and there are sets, but not everything is a sum just as not everything is a set. There is a set consisting of the Tuesday Bricks, and there is a singleton set of the Brick House. But neither of these sets is identical to the Brick House. Neither of them has anything to fear from the pulmonary exertions of the Big Bad Wolf — not because they are so strong, but because they are abstract objects removed from the flux and shove of the causal order. Sums of concreta, unlike sets of concreta, are themselves concrete — but the Brick House is not a sum. Van Inwagen disagrees. For him, "Everything is a mereological sum." (618)

His argument for this surprising claim is roughly as follows. PvI's presentation is tedious and technical but I think I will not be misrepresenting him if I sum up the gist of it as follows:

1. Everything, whether simple or composite, has parts. (This is a consequence of the following definition: x is a part of y =_df x is a proper part of y or x = y. Because everything is self-identical, everything has itself as a part, an improper part to be sure, but a part nonetheless. Therefore:

2. Everything is a mereological sum of its parts. Therefore:

3. Everything is a mereological sum. Therefore:

4. ". . . mereological sums are not a special sort of object." (622) In this respect they are unlike sets."'Mereological sum' is not a useful stand-alone general term." (622) 'Set' is.

What's At Issue Here?

I confess to not being clear about what exactly is at issue here. One could of course use 'mereological sum' in the way that van Inwagen proposes, a way that implies that everything is a mereological sum, and that implies that there is no conceptual confusion in the notion of a mereological sum changing its parts. But why adopt this usage? How does it help us in the understanding of material composition?

What am I missing?

Van Inwagen Contra Lewis on Composition as Identity

Modifying an example employed by Donald Baxter and David Lewis, suppose I own a parcel of land A consisting of exactly two adjoining lots B and C. It would be an insane boast were I to claim to own three parcels of land, B, C, and A. That would be 'double-counting': I count A as if it is a parcel in addition to B and C, when in fact all the land in A is in B and C taken together. Lewis, rejecting 'double-counting,' will say that A = (B + C). Thus A is identical to what composes it. This is an instance of the thesis of composition as identity.

Or suppose there are some cats. Then, by Unrestricted Composition ("Whenever there are some things, then there exists a fusion [sum] of those things"), there exists a sum that the cats compose. But by Composition as Identity, this sum is identical to what compose it, taken collectively, not distributively. Thus the sum is the cats, and they are it. I agree with van Inwagen that this notion of Composition as Identity is very hard to make sense of, for reasons at the end of the above link. But Peter van Inwagen's argument against Composition as Identity strikes me as equally puzzling. Van Inwagen argues against it as follows:

Suppose that there exists nothing but my big parcel of land and such parts as it may have. And suppose it has no proper parts but the six small parcels. . . . Suppose that we have a bunch of sentences containing quantifiers, and that we want to determine their truth-values: 'ExEyEz(y is a part of x & z is a part of x & y is not the same size as z)'; that sort of thing. How many items in our domain of quantification? Seven, right? That is, there are seven objects, and not six objects or one object, that are possible values of our variables, and that we must take account of when we are determining the truth-value of our sentences. ("Composition as Identity," Philosophical Perspectives 8 (1994), p. 213)

In terms of my original example, Lewis is saying that A is identical to what composes it. Van Inwagen is denying this and saying that A is not identical to what composes it. His reason is that there must be at least three entities in the domain of quantification to make the relevant quantified sentences true. A is therefore a third entity in addition to B and C. It is this that I don't understand. Van Inwagen's argument strikes me as a non sequitur. Or perhaps I just don't understand it. Consider this obviously true quantified sentence:

1. For any x, there is a y such that x = y.

(1) features two distinct bound variables, 'x'and 'y.' But it does not follow that there must be two entities in the domain of quantification for (1) to be true. It might be that the domain consists of exactly one individual a. Applying Existential Instantiation to (1), we get

2. a = a.

Relative to a domain consisting of a alone, (1) and (2) are logically equivalent. From the fact that there are two variables in (1), it does not follow that there are two entities in the domain relative to which (1) is evaluated. Now consider

3. There is an x, y and z such that x is a proper part of z & y is a proper part of z.

(3) contains three distinct variables, but it does not follow that the domain of quantification must contain three distinct entities for (3) to be true. Suppose that Lewis is right, and that A = (B + C). It will then be possible to existentially instantiate (3) using only two entities, thus:

4. B is a proper part of (B + C) & C is a proper part of (B + C).

If van Inwagen thinks that a quantified sentence in n variables can be evaluated only relative to a domain containing n entities (or values), then I refute him using (1) above. If van Inwagen holds that (3) requires three entities for its evaluation, then I say he has simply begged the question against Lewis by assuming that (B + C) is not identical to A. It is important not to confuse the level of representation with the level of reality. That there are two different names for a thing does not imply that there are really two things. ('Hesperus' and 'Phosphorus' both name the same planet, Venus, to coin an example.) Likewise, the fact that there are two distinct bound variables at the level of linguistic representation does not entail that at the level of reality there are two distinct values. There might be or there might not be.

So I cannot see that van Inwagen has given me any reason to think that A is a third entity in addition to B and C. But it doesn't follow that I think that Lewis' thesis is correct. Both are wrong. Here is the problem. 'A = (B + C)' is the logical contradictory of '~ (A = (B + C)).' Thus one will be tempted to plump for one or the other limb of the contradiction. But there are reasons to reject both limbs.

Surely A is more than the mereological sum of B and C. This is because A involves a further ontological ingredient, namely, the connectedness or adjacency of B and C. To put it another way, A is a unity of its parts, not a pure manifold. The Lewis approach leaves out unity. Suppose B is in Arizona and C is in Ohio. Then the mereological sum (B + C) automatically exists, by Unrestricted Composition. But this scattered object is not identical to the object which is B-adjoining-C. On the latter I can build a house whose square footage is greater than that of B or C; on the scattered object I cannot. But A is not a third entity. It is obvious that A is not wholly distinct from B and C inasmuch as A is composed of B and C as its sole nonoverlapping proper parts. Analysis of A discloses nothing other than B and C. But neither is A identical to B + C.

In short, both limbs of the contradiction are unacceptable. How then are we to avoid the contradiction?

Perhaps we can say that A is identical, not to the sum B + C, but to B-adjoining-C, an unmereological whole. But this needs explaining, doesn't it?

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.

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 is 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 retelling:

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 beween 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.

A Difficulty With Haecceity Properties

By popular demand, here is revised version of a post that first appeared on the old blog in July of 2005.

Introduction. I find haecceity properties hard to accept, although I grant they they would do various useful jobs if they existed. ('Haecceity' from the Latin haecceitas, thisness.) In this post I explain one or two of my reasons for nonacceptance. If you know your Plantinga, you will know that he is my primary target in these notes. This post is not about Duns Scotus or any medieval.

Definition. Suppose we take on board for the space of this post the assumptions that (i) properties are abstract objects, that (ii) they can exist unexemplified, and that (iii) they are necessary beings. We may then define the subclass of haecceity properties as follows.

A haecceity is a property H of x such that: (i) H is essential to x; (ii) nothing distinct from x exemplifies H in the actual world; (iii) nothing distinct from x exemplifies H in any metaphysically possible world.

So if there is a property of Socrates that is his haecceity, then there is a property that individuates him, and indeed individuates him across all times and worlds at which he exists: it is a property that he must have, that nothing distinct from him has, and that nothing distinct from him could have. Call this property Socrateity. Being abstract and necessary, Socrateity is obviously distinct from Socrates, who is concrete and contingent. Socrateity exists in every world, but is exemplified (instantiated) in only some worlds. What's more, Socrateity exists at every time in every world that is temporally qualified, whereas Socrates exist in only some worlds and only at some times in the worlds in which he exists. Haecceity properties have various uses. I'll mention just one.

Use. Suppose I need to analyze 'Socrates might not have existed.' I start with the rewrite, 'Possibly, Socrates does not exist' which features a modal operator operating upon an unmodalized proposition. But 'Socrates does not exist,' being a negative existential proposition, gives rise to an ancient puzzle dating back to Plato. How is reference to the nonexistent possible? The sentence 'Socrates does not exist' is apparently about Socrates, but how so given that he does not exist? If the meaning of 'Socrates' is the name's referent, and nothing can be a referent of a term unless it exists, then Socrates must exist if he is to have nonexistence predicated of him. But the whole point of the sentence is to say that our man does not exist. How can one say of a thing that it does not exist without presupposing that it exists? Haecceities provide a solution. We can understand 'Socrates does not exist' to be about Socrateity rather than about Socrates, and to predicate of Socrateity the property of being exemplified. Recall that Socrateity, unlike Socrates, exists at every time and in every world. So this property, unlike Socrates, is always and necessarily available. Accordingly, we analyze 'Possibly, Socrates does not exist' as 'Possibly, Socrateity is not exemplified.' Socrates' possible nonexistence boils down to Socrateity's possible nonexemplification. It is a nice, elegant solution to the puzzle –assuming that there are haecceity properties.

Problem. One of the stumbling blocks for me, however, is the notion that the thisness of an individual could exist even if the individual whose thisness it is does not exist. Consider the time before Socrates existed. During that time, Socrateity existed. But what content could that property have during that time (or in those possible worlds) in which Socrates does not exist? Socrateity is identity-with-Socrates. Presumably, then, the property has two constituents: identity, a property had by everything, and Socrates. Now if Socrates is a constituent of identity-with-Socrates, then it seems quite obvious that Socrateity can exist only at those times and in those worlds at which Socrates exists. Socrateity would then be like Socrates' singleton, the set consisting of Socrates and Socrates alone: {Socrates}. Clearly, this set cannot exist unless Socrates exists. It is ontologically dependent on him. The same would be true of identity-with-Socrates if Socrates were a constituent of this property.

Problem Exacerbated. If, on the other hand, Socrates is not a constituent of Socrateity, then what gives identity-with-Socrates the individuating content that distinguishes it from identity-with-Plato and identity-with-Pegasus? Consider a possible world W in which Socrates, Plato, and Pegasus do not exist. In W, their haecceities exist since haecceities ex hypothesi exist in every world. What distinguishes these haecceities in W? Nothing that I can see. The only things that could distinguish them would be Socrates, Plato, and Pegasus; but these individuals do not exist in W. It might be said that haecceity properties are simple: identity-with-Socrates is not compounded of identity and Socrates, or of anything else. Different haecceities just differ and they have the content they do in an unanalyzable way. But on this suggestion haecceities seem wholly ungraspable or inconceivable or ineffable, and this militates against thinking of them as properties. I have no problem with the notion of a property that only one thing has, nor do I have a problem with a property that only one thing can have; but a property that I cannot grasp or understand or conceive or bring before my mind — such an item does not count as a property in my book. It would be more like a bare particular and inherit mutatis mutandis the unintelligibility of bare particulars.

Haecceities must be nonqualitative. Consider a conjunctive property the conjuncts of which are all the mutiply exemplifiable properties a thing has in the actual world. Such a property would individuate its possessor in the actual world: it would be a property that its possessor and only its possessor would have in the actual world. Such a property is graspable in that I can grasp its components (say, being barefooted, being snubnosed, being married, etc.) and I can grasp its construction inasmuch as I understand property conjunction. But the only way I can grasp Socrateity is by grasping is as a compound of identity and Socrates — which it cannot be for reasons given above.

Note that Socrateity is not equivalent to the big conjunctive property just mentioned. Take the conjunction of all of Socrates' properties in the actual world and call it K. In the actual world, Socrates has K. But there are possible worlds in which he exists but does not exemplify K. And there are possible worlds in which K is exemplified by someone distinct from him. So Socrateity and K are logically nonequivalent. What we need, then, if we are to construct a qualitative thisness or haecceity of Socrates is a monstrous disjunctive property D[soc] the disjuncts of which are all the K's Socrates has in all the possible worlds in which he exists. This monstrous disjunction of conjunctions is graspable, not in person so to speak, but via our grasp of the operations of conjunction and disjunction and in virtue of the fact that each component property is graspable. But D[soc] is not identical to Socrateity. The former is a qualitative thisness whereas the latter is a nonqualitative thisness. Unless the Identity of Indiscernibles is true, these two thisnesses are nonequivalent. And there are good reasons to think that the Identity of Indiscernibles is not true. (Max Black's iron spheres, etc.) So D[Soc] is not identical to Socrateity.

Conclusion. To compress my main point into one sentence: identity-with-Socrates is graspable only as a compound of identity and Socrates; but then this property cannot exist unexemplified. Hence haecceity properties as defined above do not exist.