There is a certain philosophical view, an adherent of which is Eli Hirsch in The Concept of Identity 1, about the persistence of ordinary, medium-sized dry goods that I am prone to find quite curious. The view is that when certain objects cease to be of a certain form, they cease to be. Here are three examples to illustrate this view.

(1) I own a copper coin, and decide to melt it down, so that all that remains is a lump of copper. At some point during the melting process, presumably the point at which the copper is no longer properly called 'coin-shaped', the coin ceases to exist. All that remains is a lump of copper that is not, and never was, strictly identical with any coin.

(2) There is an old car in a junkyard, which gets crushed into a block of scrap metal. When the car is crushed, it ceases to exist. All that remains is a block of scrap metal that is not, and never has been, strictly identical with any car.

(3) I knit a sweater that turns out to be, upon completion, an utter disaster. I decide to unravel the sweater and wind the yarn that the sweater was composed of into a skein. The sweater ceases to exist at some point during the unraveling, and the remaining skein of yarn is not, and never was, strictly identical with any sweater.

I find this view prima facie quite curious. I for one would say in each of these three cases that no physical object has ceased to exist, any more than I would if the coin were merely flattened by a train, the car rendered undriveable in an accident, or one of the sleeves of the sweater partly unraveled. Rather, I maintain that in each of these cases a physical object has undergone a rather radical alteration in form, somewhat more drastic than the coin's merely being flattened, etc., but nevertheless not sufficient to render an object non-existent. It seems to me perfectly literal and straightforward to say 'That lump of copper was once a coin', 'That block of scrap metal was once a car', and 'That skein of yarn was once a lousy excuse for a sweater'. My take on this matter, according to Hirsch, is "deviant," although a "nondrastic deviation" (26-27):

There may in fact be some considerable resistance to admitting that the car has to go out of existence just because it turns into a block of scrap metal.... When we soberly reflect on the case, however, and keep in mind that we are talking about the car, and not the material components that make it up, it becomes sufficiently clear, I think, that the car does go out of existence.... (51)

Hirsch's view, however, seems even more curious when we note that it is surely not the case that a lump of copper went out of or came into existence during the smelting process, or that a mass of metal went out of or came into existence when the car was crushed, or that a long strand of yarn went out of or came into existence during the unraveling process. It seems, on Hirsch's view, that when I unravel the sweater at time t, something, viz. the sweater, goes out of existence, while something else, viz. the strand of yarn, does not go out of existence. The sweater has the property ceasing to exist at time t; the strand of yarn does not have this property. So by Leibniz' Law of the indiscernability of identicals, we may conclude that the sweater is not strictly identical with the strand of yarn. Prior to t, however, the volume occupied by the sweater was identical to the volume occupied by the strand of yarn. So prior to t, there were two different objects, the sweater and the strand of yarn, that occupied exactly the same volume at the same time. Furthermore, if at sometime during the sweater's existence I put the sweater in a box, there would seem to be two physical objects in the box. And had I decided to give the sweater to my mother for Christmas, I would have given her two Christmas presents. " 'Curiouser and curiouser!' cried Alice. . . ."

Hirsch solves this problem by appealing to a notion of "constitutive identity," which is not the same relation as strict identity, and to which Leibniz' Law does not apply. "We might define 'x is constitutively identical with y' (or 'x and y constitute each other') as meaning 'x and y occupy [exactly] the same place' " (59). Immediately prior to the unraveling, the sweater is constitutively identical with the strand of yarn, i. e. it occupies the same volume as the strand of yarn (59), but it is not strictly identical with it. And presumably, it is this relation of constitutive identity that I am "counting by," rather than the relation of strict identity, when I maintain that there would only be one physical object in the box (discounting numerous molecules of air), and that I only gave my mother one Christmas present.

I wish to challenge Hirsch's view in this paper, and instead maintain that ordinary artifacts are strictly identical with the masses of matter of which they are composed. 2 My attack will be three-pronged. First, after briefly describing Hirsch's sortal analysis of the persistence of ordinary physical objects, I will show that Hirsch's notion of constitutive identity, as he uses it, is so flexible that it admits of deviant uses that run contrary to some of Hirsch's own examples. Second, I will show that any attempted sortal analysis of the persistence of an object in terms of an artifact sortal (such as 'car', 'coin', or 'sweater') is doomed to be hopelessly circular and hence unilluminating, just as would an attempted sortal analysis of the unity of an object through space. Third, I will present a thought experiment that I hope will clearly show that the mere altering of the shape of a mass of matter, with or without an intention to "create" an artifact, cannot bring any new physical object into existence.

Hirsch's Sortal Analysis of Persistence Hirsch's sortal analysis of persistence may be summed up in the following two principles (from chapter 2):

The Sortal Rule: Two object stages, X and Y, are stages of the same persisting physical object if there exists a succession S of object stages such that (1) X and Y are stages of S, (2) S is moderately spatiotemporally continuous (except at its endpoints), (3) S is weakly qualitatively continuous (except at its endpoints), and (4) there is a sortal term F that applies to each stage of F. 3

The Sortal Rule Addendum: Where F is a sortal and S is a continuous 4 succession of F-stages, the beginning and end of S correspond to the coming into and going out of existence (respectively) of an F-thing iff S is not a segment of a longer continuous succession of G-stages, where G is a sortal to which F is subordinate.

The notion of an object stage, an instantaneous temporal part of an object, is taken as a primitive. A succession of object stages is the "sum" of a set of object stages such that no two stages occur at the same instant of time. A succession of object stages is moderately spatiotemporally continuous if and only if around every object stage O in the succession there is an interval of time such that every object stage of the succession in that interval overlaps O by at least fifty percent. A succession of object stages is weakly qualitatively continuous if and only if for every object stage O of the succession there is an interval of time around O such that all object stages of the succession in the interval are "very similar" to O in respects other than their spatial location. A sortal is a term F of English such that it is a conceptual (or "analytic") truth that any continuous succession of F-stages (i. e. object stages to which F applies) corresponds to stages of a single persisting F-thing. For example, the term 'car' is a sortal in virtue of the fact that it is a conceptual truth that any continuous succession of car-stages corresponds to stages of a single persisting car.

A sortal F is subordinate to a sortal term G if and only if F's being truly predicable of an object stage O conceptually (or "analytically") implies that G is truly predicable of O. For example, the sortal term 'brown table' is subordinate to the sortal term 'table', since is it conceptually true that all brown tables are tables. The sortal term 'puppy' is subordinate to the sortal term 'dog', since it is conceptually true that all puppies are dogs. (This implies, as a degenerate case, that every sortal term is subordinate to itself.) The effect of the sortal rule addendum is to prevent his theory from yielding the incorrect judgment that when one paints a brown table green, something, viz. a brown table, has gone out of existence, or that when a puppy grows up and becomes an adult dog, something, viz. a puppy, has gone out of existence. For the continuous succession of brown- table-stages will be a part of a longer continuous succession of table stages, and 'brown table' is subordinate to 'table'. Thus, the end of the continuous succession of brown-table-stages does not correspond to the going out of existence of a persisting physical object, and the beginning of the continuous succession of green-table-stages does not correspond to the coming into existence of a physical object. Similarly, the end of the continuous succession of puppy-stages does not correspond to the going out of existence of a physical object, nor does the beginning of the succession of adult-dog-stages correspond to the coming into existence of a physical object, since each continuous succession is a part of a longer continuous succession of dog stages, and 'puppy' and 'adult dog' are both subordinate to the sortal term 'dog'.

Trouble for the Sortal Rule Addendum Consider the sortal term 'copper coin'. This term, it seems, is subordinate to the term 'lump of copper', for it seems analytically true that any copper coin is a lump of copper. Thus, according to the Sortal Rule Addendum, the copper coin discussed in case (1) at the beginning of this paper does not go out of existence, for the continuous succession S of copper-coin-stages is a part of longer continuous succession T of lump-of-copper- stages that has parts after the time at which the coin is melted down. Hirsch, however, would like to say that when the copper coin is melted down into a lump of copper, some physical thing, viz. the copper coin, goes out of existence. 5 Furthermore, if we trace the succession S under the sortal 'coin', the Sortal Rule Addendum tells us that the end of the succession of coin-stages does correspond to the going out of existence of a physical thing, for there does not appear to be a sortal term G to which 'coin' is subordinate and such that S is a part of a longer continuous succession of G-stages 6, for it is not analytically true that all coins are lumps of copper, as some coins are lumps of silver, and others lumps of aluminum. The Sortal Rule Addendum tells us that a coin goes out of existence, but a copper coin does not, which seems completely absurd.

One route out of this problem for Hirsch would be to deny that 'copper coin' is subordinate to 'lump of copper' by denying the analytic truth of 'Every copper coin is a lump of copper'. This is where the notion of constitutive identity comes in. Hirsch might say that it is false that the copper coin is (i. e. is strictly identical with) a lump of copper, but it is true (indeed analytically true) that the copper coin is constitutively identical with a lump of copper. Hirsch must also add, to make this way out the problem work, that 'thing constitutively identical with a lump of copper' is not a sortal term, for surely it is an analytic truth (if anything is) that all copper coins are constitutively identical with a lump of copper. Thus, the continuous succession S of copper-coin-stages is not a part of any longer continuous succession of G-stages, where 'copper coin' is subordinate to G.

If this seems like a cheating way out, well it is. For if it is open to Hirsch to deny that the copper coin is (strictly identical with) a lump of copper, but rather is merely constitutively identical with a lump of copper, it would seem open, depending on how seriously one takes intuitions about analyticity, for someone to deny in the case of the table that the brown table is strictly identical with a table. Rather, someone might maintain, every brown table is merely constitutively identical with a table. And this would account for the unreflective affirmative answer one might get to the question 'Did a brown table go out of existence?', asked after the table was painted. 7 A brown table went out of existence, and a green table came into existence, although there was a table simpliciter (that was first green and then brown) that persisted through the painting. There were two tables in the room the whole time, just as when I held the coin in my hand I had two things (strictly speaking, or "counting by strict identity") in my hand: a coin and a lump of copper.

It is of course absurd and completely contrary to our ordinary concept of identity (which is what Hirsch purports to be analyzing) to say there are two tables, one that persists through the painting and one that goes out of existence. But I can see no principled way, given the slipperiness of our intuitions about analyticity, to disallow the judgment that the brown table goes out of existence when it is painted but permit the judgment that the coin goes out of existence when it is melted down. It seems that this mysterious notion of constitutive identity is entirely too strong for Hirsch's purposes; but without it, Hirsch has no way to account for the judgment that the coin is a lump of copper and the lump of copper is (prior to the melting process) a coin.

A Circularity Problem for the Sortal Rule In chapter 3, in the course of analyzing our notion of unity through space, i. e. answering the question 'What is an object stage?' (a notion he took as primitive in chapter 2), Hirsch points out that there cannot be an illuminating, non-circular analysis of unity though space that is analogous to the sortal rule for persistence through time. Such an attempted analysis might look something like the following (100): Two parts, X and Y, are parts of the same physical object iff X and Y are both parts of a spatially continuous succession of F-parts, where F is a sortal term. But as Hirsch correctly points out, this analysis is so blatantly circular as to be unilluminating, for quite often a part is an F-part (where F is some sortal) solely in virtue of its relations to other parts, together with which it constitutes a whole F-thing. Parts that are only F-parts in virtue of there relations to other parts Hirsch labels non-intrinsic. For example, any given square inch of steel on the hood of my car is non-intrinsically a car-part, for it is only a car-part in virtue of its relationship to the other parts of my car. Any given square inch of steel on the hood of my car might have been part of a building, or part of an airplane, or part of a ship, instead of part of a car. 8 Thus any attempted sortal analysis of unity through space, especially one that takes mereological atoms as primitive parts analogous to instantaneous object stages (for atoms, I take it, are never intrinsic parts of any macroscopic physical objects), is doomed to be circular, and thus unilluminating. 9

Hirsch recognizes that this circularity problem holds for some sortal terms that might be used in analysis of persistence through time, such as 'car which is in the process of moving from New York to California', for a car-which-is-in-the-process-of- moving-from-New-York-to-California-stage is such a stage only in virtue of being suitably related to other object stages (103). Hirsch, however, thinks this is an unusual case, i. e. that for the most sortals F, all F-stages are intrinsic F stages. He quotes Anthony Quinton approvingly (101-102):

The temporal parts of an enduring thing would have been a perfectly good thing of that kind if they had existed on their own, without the other phases which in fact preceded and followed them, while this is very seldom true in the analogous spatial case: the spatial parts of a thing, conceived as existing in spatial disconnection from one another, are not things of the same kind. 10 I wish to maintain, on the other hand, that whenever a sortal F is a artifact-term, such as 'coin', 'car', or 'sweater', most instantaneous F-stages (except those stages that are cotemporal with the initial intention that the object be an artifact of type F) are not intrinsically F-stages. Suppose that somewhere out in the asteroid belt there is a small, coin-shaped, lump of copper, perhaps even having a remarkable likeness of Lincoln on one side and a remarkable likeness of the Lincoln memorial on the other. This lump of copper, despite its shape, is not a coin. A thing is a coin only if it is minted with the intention that it be a coin. That very lump of copper could have been a coin, had it been shaped with the intention that it be used as currency, but given its origin, and the fact that it has never been in the possession of any sentient being, it is not a coin, nor are any of its stages coin-stages. A coin-stage is a coin stage only in virtue of its being related to an initial coin-stage, toward which an intention that it be used as currency is directed. Noam Chomsky makes a similar point (albeit for a somewhat different purpose, I believe):

Is a knife . . . an object of such and such physical properties, or an object that is used for such and such purposes. . . ? How would we in fact identify an object looking exactly like a knife but used for some totally different purpose in some other culture? 11 It follows that a sortal analysis of persistence through time utilizing an artifact-sortal is doomed to be no more illuminating than a sortal analysis of unity through space. My conclusion in this section is a hypothetical one: if there is to be an illuminating, non-circular account of the persistence through time of artifacts, it will have to be in terms of sortals such as 'lump of copper' or 'strand of yarn', which will make the analysis judge that nothing goes out of existence when the coin is melted, the car is crushed, or the sweater is unraveled. 11 A Parable about Persistence Marian is a sculptor. In her studio, she has a fist-sized lump of aluminum that she calls 'Al', which she uses to practice her sculpting talents upon. At one time, Al was spherical, at another time egg-shaped, at another time cubical. Marian has never regarded Al as a statue, merely as a lump of aluminum that she uses for practice. It certainly seems that Al persists through the changes that she makes in "him." One day, Marian decides that she needs an ashtray, so she flattens out Al on one side so that he may sit steadily on her desk, and makes an indentation in the other side to hold cigarette butts. Hirsch, I believe, would hold that a new object, viz. an ashtray, call it 'Ash', has come into existence. Ash, on Hirsch's view, is not strictly identical with Al, for there is a time t before which Al existed but Ash did not. Furthermore, when once again Marian needs to practice her sculpting talents and once again forms Al into a spherical shape, Ash ceases to exist, but Al does not. Ash, during the entirety of his existence, is merely constitutively identical with Al. There are, strictly speaking and counting by strict identity, two objects sitting on Marian's desk: Ash, an ashtray; and Al, a lump of aluminum.

Suppose, however, that the following scenario occurred. Marian, without any intention of making an ashtray, flattens Al on one side and makes an indentation on the other. Al is not an ashtray. Al sits around in this shape for about a week on her desk, until one day, having misplaced her ashtray, Marian realizes that Al, in his current shape, would be a great ashtray, and she begins to dispose of her cigarette butts in Al's indentation. There is now an ashtray that is at least constitutively identical with Al, in existence. Has a new physical object, viz. Ash, now come into existence? Ash certainly does not exist prior to Marian's using Al as an ashtray. The mere shaping of Al into his current shape does not make Al into an ashtray, nor does it bring an ashtray into existence. But it would seem strange to say that Marian has brought a new object into existence merely by intending to dispose of her cigarette butts in Al's indentation. No one can bring a physical object into existence with a mere intention. So in this scenario it seems that there is only one object on the desk, viz. Al, and Al is an ashtray.

The only difference, however, between this second scenario and the first was the order in which the reshaping of Al and Marian's intention to dispose of her cigarette butts in Al's indentation occurred. But how could this difference be relevant to the question of whether a new physical object has come into existence? I conclude that in the first case, as in the second, no new object came into existence: Ash is strictly identical with Al. Furthermore, no object will go out of existence when Marian reshapes Al into a sphere. Al (as well as Ash, for Ash = Al) will cease to be an ashtray, but nothing will cease to be.

And I think that the moral we should draw from this thought experiment will hold for all artifacts, since it is at least conceivable that the mass of matter that makes up any artifact was first shaped, without any intention to put the newly shaped mass of matter to any particular use, then later it was decided that the mass of matter would be useful. Thus, nothing ceases to exist when the coin is melted down, for the coin is strictly identical with the lump of copper, and the lump of copper continues to exist. The same will hold for the car and the sweater. Artifacts are strictly identical with the spatially continuous masses of matter of which they are composed; nothing is essentially an artifact. There may be some tendency to say that a coin goes out of existence when it is melted down, but this is not, I believe, a sufficiently reflective judgment, any more than would be the judgment that a brown table goes out of existence when it is painted green.

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1. New York: Oxford University Press, 1982. All parenthetical citations herein are to this work.

2. This view is intended to apply solely to artifacts. I am certain that persons are not strictly identical with the masses of matter of which they are composed, nor, I think, are other living things of which we may properly predicate psychological or intentional states. I am not sure about natural objects such as trees. I will not herein deal with the paradoxes of undetached parts, as raised by Peter van Inwagen in "The Doctrine of Arbitrary Undetached Parts" (Pacific Philosophical Quarterly 62, 123-137). I will deal herein only with those cases in which one object is (on Hirsch's view) constitutively identical with another for the entirety of its existence.

3. The Sortal Rule only gives sufficient criteria for X and Y to be two stages of the same persisting physical object, as Hirsch wishes to allow for objects to go out of and come back into existence, such as a watch which is taken apart and put back together. He allows for this by addition to his theory of the Compositional Criterion, which does not here concern me.

4. I. e. moderately spatiotemporally (except at its endpoints) and weakly qualitatively (except at its endpoints) continuous.

5. To be fair to Hirsch, it should be said that he does not actually discuss the copper coin case. He says very similar things, however, about the case of the car being crushed and the sweater being unraveled, and I am extrapolating his opinion on the copper coin case from his claims about these other two cases. I feel the copper coin case best illustrates the problem, but analogous problems could be brought up concerning the car and the sweater.

6. Unless the sortal term is 'mass of matter', which would be even better for my view, for it seems analytically true (to me, anyway) that all artifacts are masses of matter.

7. "This reductio ad absurdum [i. e. that the brown table goes out of existence when it is painted green] is not, I have found, always immediately appreciated" (49). After all, it is no longer the case that a brown table is there, so it might seem prior to reflection that a brown table must have gone out of existence.

8. In contrast, the whole of my car (given the standard axiom that everything is a part of itself) and the portion of my car between the bumpers are intrinsic car-parts, as they are car parts regardless of their relations to other parts.

9. There is a further problem with the attempted sortal analysis of unity through space, viz. that whenever two distinct F-things, A and B, are attached together, the given analysis will incorrectly judge that the parts of A and the parts of B are parts of one physical object, e. g. if one car was attached to another for the purpose of towing (101). A similar problem may arise for the sortal analysis of persistence through time, if there is a case of "immaculate replacement." See Chris Swoyer, "Causation and Identity." Midwest Studies in Philosophy IX, 593-622.

10. The Nature of Things. Boston: Routledge, 1973, p. 77.

11. "Quine's Empirical Assumptions," Synthese 19, 53-69, p. 63.

Copyright © 1997 Carl Brock Sides. Permission granted to distribute in any medium, commercial or non-commercial, provided all copyright notices remain intact.