Mereological Essentialism Restricted

Do wholes have their parts essentially? If y is ever a part of x, is the property of having y as one of its parts then essential to x, so that y will necessarily be a part of x as long as x exists? To answer affirmatively is to accept what has been called mereological essentialism. (ME) Familiar cases immediately come to mind suggesting that ME must be false, but outstanding thinkers have held that it is true.

Chisholm's Puzzle

Roderick Chisholm presents ME as a basic principle in the theory of whole and part.1 What he actually discusses, however, is not the theory of whole and part in complete generality, but only of a certain subclass of wholes, containing "such familiar things as ships, trees, houses, chairs and cars." (PO 145) The famous ship of Theseus case, where over time every part of the ship was hypothetically replaced with a new part, has been used to question the nature and the fact of identity in these entities. Such wholes as these are wholes that exist at and through continuous sequences of space/time points. That is, they are what we would ordinarily characterize as physical substances.2 It might seem, accordingly, that we could formulate Chisholm's position more precisely as: "Physical substances have their parts (pieces) essentially." In fact he does not discuss physical substances merely insofar as they might be illustrative of wholes in general. But in what follows we shall, for convenience sake, continue to speak simply of "wholes," always meaning thereby (except where otherwise indicated) physical substances such as "ships, trees, houses, chairs and cars" or certain of their temporal segments.

Other refinements need to be noted. When Chisholm speaks of "part" he means what is often referred to as a "proper" part. In this sense of "part," if a is part of b then it follows that b is not part of a. But much more importantly, when Chisholm speaks of "part" he refers to an entity that can exist in separation from that of which it is a part. (PO 146, & 151f) Parts to which wholes are essential do not concern him. Every distinct part is separable, and all composites of the kinds of parts he recognizes have only contingent existence. He thus uses "part" to refer to what a more subtle account might call a "fragment" or "piece," retaining "part" to designate any constituent or element in the makeup of an entity. The petals of a rose, for example, are parts of the rose, in Chisholm's sense, but their configuration in the rose and the rose's color are not.3

So what, in his discussions, Chisholm rather misleadingly calls "mereological essentialism" is really a claim about ordinary physical substances. It seems--contrary to what later emerges--to be the claim that such entities lose their identity if one of the pieces belonging to them is replaced by a different piece. When, for example, you have a heart or kidney transplant, you do not just get another heart or kidney, you also get another body. Of course you also get another body if a cell in some bodily tissue is replaced by another cell, or if one electron in one atom in your body is replaced by another.

Such cases make ME, as Chisholm at first seems to take it, about as counter-intuitive and puzzling as any view could be. His awareness of this may be what prompts him to say in a later publication that "It would take courage to defend this thesis before nonphilosophers." He continues on to say, nevertheless, "I am convinced, all the same, that it is true." (RMC, 228) He is not only convinced that ME is true, but that it is obvious. He commented in first writing on the subject in 1973 that "the principle of mereological essentialism may seem to be obvious. Indeed, I would say that it ought to seem to be obvious." (OM 67; PO 147)

In that initial paper, he presented ME as one wing of a set of apparently conflicting intuitions. The other wing was, to take a familiar case, the claim that my automobile has had and could have parts, e.g., tires, other than those it now has. (Ibid.) It seems intuitively obvious that I still have the same car though I have changed its tires, and even that I could have bought still other tires than I did without thereby creating another car than the one I now have. Chisholm's treatment is not to dismiss one of the two presumed intuitions, but, by splitting the senses of "part" and "whole," to show, or at least suggest, that the intuitions do not really conflict, because they are intuitions about different types of parts and wholes.

But of course we might have intuitions that do not conflict and one or both be false. Chisholm does not, I think, attempt to offer an argument for the truth of ME, either as a thesis about parts and wholes in complete generality, or about physical substances and their pieces. And he doesn't try to refer his intuition of the truth of ME to an immediate insight into the essence of part or whole. He does introduce, only to reject, a position that he calls "complete, unbridled mereological inessentialism." (CUMI) "This is the view that, for any whole w, w could be made up of any two things whatever." (OM 68f; PO 147f) The existence and identity of the whole for this position has no dependence at all upon what is substituted for its parts. Such a view is ridiculous, as Chisholm easily makes clear. But the truth of ME does not follow from the falsity of CUMI. ME and CUMI are not contradictories, and both can be, as I think they are, false.

The discussion of CUMI in this context appears to be something of a red herring, though the acceptance of ME might recommend itself as protection against CUMI, for both cannot be true. Indeed, Chisholm says that "the consequences of extreme mereological inessentialism may suggest to us that some version of mereological essentialsim must be true." (OM 69) But it is hard to see why they would do so. Rather, they only suggest that some--perhaps many--wholes of certain types cannot continue to exist if some of their parts are 'replaced' by entities of a type other than that of the part removed. Or perhaps we should say that "replacement" just makes no sense in such cases. It makes a certain sense to replace a heart with a mechanical pump, or even with the heart of a baboon. But not with a lung. Contrary to CUMI, not every entity can 'replace' any part in any whole, and we do not need, like Chisholm, to construct elaborate scenarios of its consequences to show that. It does seem intuitively plausible that for every whole w and every part p of w there is something x that cannot replace p in w, and we shall later see why. But to fend off CUMI all that is required is that there be one whole which does not permit arbitrary substitution for one of its part.

Now I think that Chisholm is in fact presupposing something like a replacement restriction on possible parts in his stories of ships, tables and cars. For example, in the ship-of-Theseus stories, a plank or panel replaces a plank or panel in the ship until all of the original ones have been replaced. In Chisholm's preferred cases, a leg or top replaces a leg or top in the table, a tire a tire on the car. He never contemplates replacing a leg of a table with another top, much less with a feather, nor a tire with a carburetor, much less with a leaf from a tree or his left foot. It is, I think, the obvious structure of replacement, never dealt with in his account, that founds a restricted and sound version of mereological essentialism. That structure depends upon the fact that the whole/part relation is never ultimate, but is founded or supervenient upon the specific relations between the part and other parts and the whole, which in turn depend for their obtaining upon the intrinsic natures, the non-relational characteristics, of the part and of the whole and of its other parts. The 'non-fragment' (non-separable) constituents of the whole and of its parts are, accordingly, ontologically prior to whole/part relations between the fragment parts ('pieces') within the respective entity, and determine their possible range of replacement. But we must return to this later.

A few other observations about how Chisholm sets up the, to him, intuitive plausibility of ME need to be made before proceeding to his resolution of the apparent conflict of his intuitions.

First, there is an ambiguity in talk of a whole losing a part. Chisholm quotes Leibniz to the effect that "we cannot say...that the same whole is preserved when a part is lost." (OM 66; PO 145) If a part is simply lost, and not replaced, there is indeed a certain intuitive force to saying that the whole is not whole, hence not a whole, hence not the same whole. In the current discussion we shall not discuss the loss of a part, but the replacement of a part, which is clearly the main intent of Chisholm's treatment. By this we do not, however, mean to accept the view that ME is automatically true of loss without replacement. A car that loses a wheel, or certainly a motor, is not a whole car, and, perhaps we must therefore add, not the same car. But a fleck of paint? Or a fender? And what of a centerpede that loses a leg. The differences obviously make a difference from case to case.

Secondly, the originating parts of physical substances do not play the same role in the identity of an object as do parts that enter "along the way." Chisholm does not always seem to keep this in mind. He says of "a very simple table, improvised from a stump and a board," that "the only way of constructing precisely that table is to use that particular stump and that particular board. It would seem, therefore, that that particular table is necessarily made up of that particular stump and that particular board." (OM 66; PO 146) But the conclusion cited does not follow. Let us grant the premiss to be true. That table cannot have come into being except with the precise parts it incorporated at the moment of its origin. They establish the 'line of succession' within which any subsequent replacement must occur. But matters of essence touching parts of origin do not carry over automatically to parts of continuation. We need to keep in mind that origin and continuation are distinct, though by no means separable, issues.

A final observation concerns the two cases Chisholm discusses to introduce the principle of ME as something that "ought to seem obvious," or something that is intuitively right. Alvin Plantinga has suggested that the initial plausibility Chisholm finds in ME may be tied to the examples he selects,4 and I think this is quite right. These two cases present us with highly problematic entities. The first, borrowing from G. E. Moore, is "a visual sense datum," a "colored patch half of which is red and half yellow." (OM p.66; PO p. 145f) This 'patch' is represented as having two 'patches' as parts. Moore claimed that the whole patch could not have existed without having the red patch for a part, though "the red patch might perfectly well have existed without being part of that particular whole." (Ibid.) After quoting Moore at length on the yellow and red 'patch', Chisholm immediately turns away from it without comment to "consider physical things." (OM p. 66; PO 146) But exactly what was the point of introducing this case in the first place? I believe it provides a context for the 'intuition' of ME in a way I shall explain after noticing his second introductory case. This is his case, already mentioned, of a "very simple table, improvised from a stump and a board." But what should be noted here is that we hardly have a table at all. An improvised table is, precisely, not a table, but something arranged to serve as a table in given circumstance. Exactly how the board and stump are united to form a whole is not indicated. Is the board fastened to the stump or only placed upon it. If fastened, how? With a nail? Or Glue? With a string wrapped around the board or a rock laid on top of it? And so forth for the details of the union of the parts to form a whole, this 'table'.

Now I think that these types of cases are very important in framing the context for an 'intuition' of the truth of ME. It is after his introduction of the two cases, and then a brief dismissal of dedicto necessity as irrelevant here, that Chisholm states: "Considered in the abstract and considered in application to such simple examples as these, the principle of mereological essentialism may seem obvious. Indeed, I would say that it ought to seem obvious." (OM 67; PO 147) But these cases make ME seem plausible precisely because they involve wholes where the parts are 'together' in an extremely weak, obscure and dubious sense. In the case of the 'patch' it is merely a matter of one part (the red) being "joined" with the other (the yellow). But what does "joining" mean as applied to sense data? The precise nature of sense data, and therefore their existence, has never been determined. (Are they thick? How thick? What, exactly, does "joining" mean for things that have no thinkness?) What 'stuff' these 'patches' are made of, how it functions in the context of their existence, and the laws of its behavior, are all completely obscure.

It is not the entirely the same, of course, in the case of the improvised table. We know the stuff of the stump and the board and why it will 'do' for a table--which, though a "very simple" table, still is not made of an amoeba and a moose--and in what context of facts, purposes and actions a table is improvised. But the improvised table as Chisholm describes it remains more of an aggregate or heap of objects, its 'parts', than an actual table. And that, I think, is the heart of the matter. For heaps or groups of two entities arguably, if not intuitively, do not remain the same aggregate or heap when one of their members is removed or replaced. That is obvious or intuitively clear. And if we think of wholes as aggregates, then one can see how the principle of ME itself might seem obvious. For there is little or nothing to the whole, then, other than the pieces that are grouped, and nothing that could provide a continuing identity while and when the 'parts' are changed. But actual, not provisional, tables--consisting of many, not just two, parts--are wholes of a type different from aggregates, heaps, groups or collocations. There is much more to them than parts in spatial arrangement or collected in an act of enumeration as for a list.5 And it is this fact, one might surmise, that both makes ME as Chisholm formulates it false and at the same time rules out CUMI. How, we shall see.

Chisholm's Solution

Now let us consider the way Chisholm resolves what he takes to be the apparent conflict between ME and the claim, for example, that my car has had tires other than the ones it now has, and could have had other tires than the ones it actually has. He wants to allow that both ME and the claim about my car are true. Yet they certainly seem to contradict each other. If my car continues to exist after a tire is replaced, then the property of having the old tire as part is not essential to it and ME must be false. So some difference of meaning must be found to relieve the contradiction.

In order to bring out an appropriate difference of meaning, Chisholm proposes an analysis of "what happens when...a thing such as a table undergoes a change of parts." (OM 71) He starts from an idealized story about our very simple table:

"Consider the history of a very simple table. On Monday it came into being when a certain thing A was joined with a certain other thing B. On Tuesday A was detached from B and C was joined to B, these things occuring in such a way that B remained throughout as a part of a table. And on Wednesday B was detached from C and D was joined with C, these things occurring in such a way that C remained throughout as a part of a table. Let us suppose that no other separating and joining occurred."(OM p. 70)







Here Chisholm finds two types of wholes, with corresponding types of parts. He also finds a special relationship between wholes. There is the whole AB, for example, which is our table on Monday. The parts are A and B, and they are parts of AB in "the strict and philosophical sense," as he calls it, which makes them his "S-parts.""S-part of" designates a relation that is transitive, asymmetrical, and essential to any relatum it attaches to. Schematically,

If A is S-part of AB, then it is of ABC.

If A is S-part of AB, AB is not S-part of A.

If A is S-part of AB, AB cannot exist without A.6

These three axioms are Chisholm's "attempt to explicate 'S-part'." (OM 73; PO 154) Thus symbolically expressed, the axioms seem clearly true. Whether there actually are parts and wholes in this strict and philosophical sense, and, if so, which ones they are, is another matter.

The other type of whole that shows up in this story is the succession:

{AB > BC > CD}

Here, for example, is our table, as an object that persists through time and admits of replacement of parts. These wholes are ordinary material objects, and Chisholm refers to them as "ordinary things" and as "non-primary objects." The table is also said to be a "successive being" or "ens successivum" (PO 101, 154ff, 188); and, perhaps most significantly, he calls such objects "modes,""entia per alio" and "ontological parasites," not substances. (OM 81; PO 103f; RMC 66-68)

Wholes such as AB are then said by Chisholm to constitute wholes such as {AB > BC > CD} at or during a time. This is his special relationship between wholes. AB constitutes the table on Monday, as BC and CD do on the other days. At the time when AB constitutes the table, the table consists of just A and B in union. Formally, x constitutes y, for Chisholm, provided that there is a certain place such that x occupies that place at t and y occupies exactly the same place at t. (OM 70) This will be the case of the non-primary object, the table, and the primary object AB, on Monday. They then constitute each other at that time, and obviously every whole of either kind constitutes itself.

Now what is mainly of interest about non-primary objects, such as tables, ships and cars, is not just that they stand in this relation of constitution, but also that they admit of parts other than S-parts. Something x is a part of a non-primary object y in "the loose and popular sense," or is an "L-part," provided that it is an S-part of something that constituted y at some time. Thus A is a part of the table {AB > BC > CD} in the loose and popular sense in that it is an S-part of AB and AB constituted the table on Monday. Only non-primary objects, such as our ordinary physical things, have L-parts. (PO 154)

Having now explained that there are two types of wholes and two types of corresponding parts that are involved in ordinary physical things and their pieces, Chisholm can now proceed to dispel the appearance of conflict between the alleged intuitions about wholes and parts. ME is itself to be understood as a thesis about S-parts, while the claims about the tires my car did have or could have will be reformulated, utilizing the above distinctions, in such a way that those claims will not be inconsistent with what ME says about S-parts and their corresponding wholes.

I.     1. My car had parts (certain tires) last week that it no longer has.

        2. But if ME is true, then nothing ever lacks parts it ever has.

        So: ME is false.

Chisholm's reply is that in 2 "part" means "S-part" as explicated by the three axioms above. But in 1 "part" means "L-part" as explained, where something y can have x as an L-part if x is an S-part of something that constitutes y at a given time. The tires on my car last week were S-parts of the totality of parts that constituted my car then.

II.     1. My car could have tires it does not now have. (I might have chosen others for it.)

        2. But if ME is true, the parts a whole actually has are the only parts it could have.

        So: ME is false.

Chisholm's reply is the same for 2 as in the first case. As for 1, when we say that our present car could have had tires it doesn't have, we are saying, according to him, that something which constitutes an S-part of my automobile now--namely, all of it but the tires it now has--could be joined to the unchosen tires to form a whole that does not now exist or perhaps ever will. The statement which seems to be about what could happen to the whole, my present and enduring auto, is actually a statement about one of its current S-parts and some other objects, the unchosen tires, that are no part of that S-part in any sense. ME is a claim about what cannot happen with wholes. It does not confine parts, even S-parts, to wholes, but wholes to S-parts. "The unrealised possibilities of entia successiva may be reformulated more precisely in terms of the unrealized possibilities of genuine individuals" (PO 157), the S-Parts and their wholes that enter into entia successiva.

With the resolution of the apparent conflict of intuitions now completed--and happily in possession, we might suppose, of both ME and what we thought we knew about our car and its past, present and possible tires--we survey where Chisholm has brought us. Surprisingly, we find that ME has simply been surrendered with reference to what we initially took it to describe: ordinary physical objects such as tables, trees and ships. These, we now find, can continue to exist without parts they once had, and so ME is false of them. Exactly why, we may ask, does this not seem to matter very much to Chisholm? The answer is that these sorts of things have been ontologically demoted by Chisholm to the status of "modes" (OM 81), or the status of what modes have ever been, "ontological parasites." (RMC 104) He makes the assumption widely shared through the history of ontology, that whatever is derivative in its being is "not really," and need not conform to basic principles of identity and existence such as ME.

But what is it, on Chisholms view, that does conform to these principles? That is, what are the real physical substances for him? In what, so far as I know, is his final statement on ME, which he himself describes in 1986 as the correct version of it (RMC 228), he states ME directly as a principle of substances, not of wholes. A substance is said to be any contingent thing that is not a mode. But he adds that any entity is a substance only if it conforms to ME. (RMC, 67) That about the table which meets this condition, the substrate or substance of the table (tree, ship, etc.) at a given time, is the aggregate or heap of its L-parts at the time. Tables, etc.--ontologically flighty things that they are now revealed to be--can have different parts at different times, and can even be modes of different substances at different times, but the substances thus conceived never change their parts.

Chisholm asks us to:

"Consider a whole W that persists through time--taking on new parts and shedding off old ones during the course of its existence:

Monday: X Y Z ABC      
Tuesday: X Y   ABZ C
Wednesday:  X AYZ B C
Thursday: XYZ A B C

  W could be the Ship of Theseus." (RMC 68)

The ship W, then, cannot be a substance (genuine whole), for it has different parts on different days. But then where, Chisholm asks, "are we to find an instance of our concept of substance?" (Ibid.) He finds the answer by considering "the relation that W bears at any time to the aggregate, or heap, of its parts that exist at the time (say, the relation it bears on the third day to the aggregate AYZ)." These "aggregates" do indeed hold their parts throughout the time indicated. Indeed Chisholm's view is that the aggregate ABCXYZ and all of its proper parts persist from Monday through Thursday. Thus: "The aggregate XYZ didn't come into being on Thursday. It was there all along--but prior to Thursday it wasn't a ship (it didn't have a ship as a mode) and it was more widely scattered than it was on Thursday." (Ibid.) Being 'in' an aggregate is not a matter of spatial location. Y and Z could have been in Siberia and South Africa respectively on Monday and still be a 'part' of the aggregate XYZ existing on Monday and constituting the ship on Thursday. This point is of considerable importance in understanding what Chisholm takes an aggregate to be. Clearly it is not a heap in any ordinary sense of that word, and the only condition which A must meet to be in the aggregate AB etc. is that it exist. Aggregates are not eternal beings, and they do cease to exist whenever one or more members do.

But clearly also, for ABC to be an aggregate is not enough for it to make ("constitute") a ship (table, tree, etc.). As Chisholm says, "XYZ...was there all along--but prior to Thursday it wasn't a ship." The aggregate (substance) can exist without being (constituting) a ship, but a ship cannot exist except as a mode of an aggregate. In sum: "If the ship W is a mode and not a substance, we need not hesitate to say that it changes its parts from one day to the next. But the various aggregates that the situation involves never change their parts. For they are substances." (Ibid.)



Chisholm's account of modes (physical things) and substances (true wholes=aggregates) obviously differs greatly from the accounts of mode and substance familiar from the Western philosophical tradition. Traditionally, modes could not transfer from substance to substance, and the unity of a substance was much more than that found in an aggregrate or 'set'. But there are problems facing his account that are more serious than non-conformity with tradition. These may suggest that we should look for another way of dealing with the problem that is actually driving Chisholm: the well-know puzzles about the persistence of physical objects such as Theseus' ship.

1. The 'Reformulations': To begin with, consider his attempted 'reformulations' of ME and of our claims about the car and its tires. ME initially seemed to be about such things as the car. That is what made it both interesting and shocking. Now we learn that it is only about aggregates. But how did we learn that it is only about aggregates? So far as I can tell, the only reason for saying that it is really about aggregates is that it comes out true when so read, and can be worked into a certain proposed solution to the persistence puzzles. But whether or not it is true was the initial questions, and its truth therefore should not be used to force a reading of its sense. The reformulations given by Chisholm have no more to recommend them than that they resolve the alleged conflict of intuitions.

Accordingly, if the alleged conflict can be resolved in other ways, the reformulations are unnecessary, and perhaps unfounded. One way of resolving it is simply to insist that ME in its general formulation is not intuitively plausible, or even true, and that it becomes or seems so only when we think of wholes from the outset as mere aggregates. The aggregate ABC is not the aggregate DBC, and no longer exists if you 'replace'A in it with D. Indeed, the whole idea of replacing a member of an aggregate with another is nonsense from the outset. If you take A out (destroy it) there is no 'place' left to 'insert'D, for ABC has just ceased to exist. This is, of course, strikingly unlike replacing a part in a physical object: a leg on a table or a tire on a car. ME is intuitively plausible if it is restricted to aggregates and their elements, but then it is no intuition about wholes and parts generally, nor about physical things in particular. This is because, to put it crudely, when some parts of these latter are removed, the other parts often remain in their interrelationships, preserving a continuous context of replacement. They preserve a 'place' for a new part to be inserted, sustaining wholeness and retaining identity.

If this does not happen, the whole ceases to exist and the part removed is thereby shown to be essential to its whole. Replacement either cannot occur or yields a new whole. As Alvin Plantinga observes: "If I replace a tire on my automobile, we think the same automobile persists through the change, acquiring a new part. But if I replace the automobile on my tire, then the whole that contains my tire is not the whole I began with."7 I think this is true because we now have in the latter case a different context of replacement, and the context of replacement is what provides the continuing identity of the physical object through suitable changes of its parts and properties.

So we take the position that Chisholm's "conflict of intuitions" is resolved by understanding that ME as a general principle of wholes and parts that would contradict the claims about the tire, etc. is not intuitively plausible, and indeed is not true. The conflict is a genuine contradiction, but it is not a conflict of intutions. A restricted mereological essentialism remains true, however. There are some wholes with parts that are essential to them, and among such wholes are aggregates. The truth of Mereological Essentialism is that there are parts the loss of which destroys the corresponding whole, and such parts are, of course, essential to their wholes.

2. Aggregates Not Sufficient To Constitute Physical Objects: Aggregates do not merely as such constitute a physical object. There must be a modification of the aggregate before it becomes the substance or substrata of an ordinary object. The parts that compose the aggregate must interrelate in specific ways that constitute a ship, table, or house. We emphasized from Chisholm's exposition above that, according to him, the aggregate XYZ existed on Monday through Wednesday--and for all we know long before that--but it did not constitute the ship until Thursday. Something happened to the members of the aggregate XYZ--When? At midnight Wednesday?--that made them into a ship. So Chisholm says that before Thursday the aggregate "was more widely scattered than it was on Wednesday." Now I am not sure that the aggregate is even the sort of thing that can be more or less 'scattered'. I think not. And in any case it was not just more widely scattered, as if before Thursday Z, Y, and X were all one hundred miles apart and on Thursday they were within a radius of a few feet. Being scattered more or less widely is not the point. The point is that before Thursday they were not organized into an entity such as a ship or table. They were not in the pertinent relationships to one another. And this is not a matter of being less "scattered." In fact, it is conceivable that the pieces of the ship or table could be less widely scattered than they are when they actually constitute or make up the ship or table. For example, they could be arranged together to occupy less space, or to encompass less empty space, than they do when they actually constitute a ship or table.

But in any case there is a very great and obvious difference between a mere aggregate, and a group of things that make up a physical object at a time. The aggregate can exist without the object. Chisholm recognizes this. But he has no account of the difference when the aggregate is a physical object, and seems to neglect its importance in the process of aggregates becoming ordinary physical objects, which he explicitly admits they do. Thus, after telling the story about the "very simple table" he says: "And so we have described one possible way of looking upon what happens when, as we would ordinarily put it, a thing such as a table undergoes a change of parts." (OM 71) Our reply must be that he has described no such thing. He has said nothing at all about "what happens when...a thing such as a table undergoes a change of parts." We are presented with a static picture of times at which a thing (the table) has had parts replaced. But if he had ever seriously considered what happens when the table undergoes a change of parts he would, I think, never have given Complete Unbridled Mereological Inessentialism (CUMI) a thought. He would never have considered that this table might have Grand Central Station and his left foot (OM 68), or the number 36 and the property blue (PO 147), as parts, for he would have seen the impossibility or just the senselessness of replacing the stump or the board with Grand Central Station, the property blue, etc., etc.

The possibility of replacement is, however, the heart of the matter, so far as the essentiality or non-essentiality of the pieces of a physical object to that object is concerned. In the usual case the physical object has a very large number of pieces. (The simpleness of Chisholm's preferred cases and models is, we have suggested, prejudicial in favor of his conclusions.) These many pieces have specific relationships to one another, and in many if not most cases the relationships continue to hold between the parts even when one or a fiew of them are lost from the object. If you remove the tire from the car or the leg from an ordinary table, the other parts in the whole remain, at least for a significant time, in their customary relations. Greater lengths of time are a different matter, for the relations between the remaing parts have various dependencies upon the parts that are missing. Everyone knows that the tendency of a car without a tire or a table without a leg is toward total dissolution, though unusual circumstances--e.g. they are in a museum or in storage--can make a difference. The other parts are related in ways that cannot be indefinitely sustained unless the tire or leg is there and the whole can function as intended. A deciduous tree drops its leaves in the fall and replaces them in the spring. But if, for any reason, the leaves are prevented from returning in a certain cyle, the tree dies and disintegrates.

The parts which sustain their interrelations while other parts are absent from the object provide a context or framework or structure of replacement. Once that framework is gone, however, replacement becomes impossible and the whole ceases, more or less quickly, to exist. The difference between an aggregate XYZ and the type of whole that might constitute a ship or table is that the latter provides, precisely, a framework of replacement, while the mere aggregate provides none at all--which explains the intuitive plausibility of ME as applied to aggregates. The aggregate satisfies ME in virtue of the fact that its wholeness is its elements, and when an element is gone (ceases to exist) so is the whole.

We stand by our point, then, that ME has no intuitive plausibility for wholes in general, and that therefore there is no conflict of intuitions in the sense proposed by Chisholm. On the other hand, Chisholm's effort to find wholes that both satisfy ME and constitute physical objects at a time fails; for while his aggregates satisfy ME, they do not, as such, constitute physical objects, even though it is always possible to consider the parts (pieces) of a physical object at a time simply as an aggregate.

The force of the ship of Theseus puzzle derives from the assumption that there is nothing the same about the ship when all of its parts are replaced by others. But that is because of the prior commitment that all there is to the ship is the pieces, the removeable parts, that enter into it. This is simply false. It is still a ship, and the ship which originated from specific individual parts at a time, which parts were then followed by specific individual others in a specific sequence within a continuing, overall, integrative order. If we make another ship of all the old parts laid aside, as Thomas Hobbes suggested, there is no reason to suppose it might be the ship that resulted from the replacement process in the original ship. It cannot be the same ship as the earlier one, because it came into existence at a different time. It will not be the same even though its originating and present parts, we may assume, are the same as those of the earlier ship at its origination. The individualized structure of replacement is different in the two cases with respect to both the space and the time of its elements or stages.

2. Puzzles of Persistence: Chisholm says (PO 151) that three things count in favor of ME.

(1). ME has a certain intuitive plausibility. I hope that we have dealt with and successfully dismissed this claim, so far as ME is taken as a claim about wholes and parts in general.

(2) ME has the support of an impressive philosophical tradition. This, I think, is less so than Chisholm suggests. In particular his attempt to associate his views with Hume is not very promising. In fact, Hume cannot allow anything like what Chisholm counts as an aggregate; and, on the other hand, Chisholm does not seem prepared, as is Hume, to treat the ens successiva that physical objects are supposed by him to be as fictions. Modes and entia per alio are not for him fictions, as Hume takes enduring physical objects to be, nor are they mental, even "transcendental," constructions, as for Kant. If ME entails or can be supported only on Chisholm's account of substance as aggregate and physical objects as modes that can skip from one substance to another, then philosophical tradition is at least as much against it as for it. Indeed, much more against it.

(3). The fact that ME enables us to deal with what otherwise would be insolvable philosophical puzzles. These have to do, no doubt, with the identity of physical objects such as Theseus' ship, given the replacement of all its parts, as well as with how the same thing can have different properties at different times, e.g., the short boy and the tall man or the piece of metal which at one time is a statue and at another time a vase or just a lump or bar. (RMC 65) Now I do not think that I can here attempt a solution to these puzzles, but I would like to build on what has already been said about the structures or contexts of replacement to suggest a way of understanding the identity of physical objects that persist through time and change of parts.

First a comment about the relevance of the indiscernability of identicals, or the claim that if x and y are identical, then they have all properties in common. Clearly, if this principle is true, and physical objects at different times--with different parts and properties--are to be identical, then parts and properties must be temporally indexed. Here I am going to assume that this can be done,8 and accordingly that the indiscernability of identicals by itself offers no obstacle to the persistence of the self-same physical or other temporally enduring object through change. The short boy at T1 is the tall man of time T2. One entity has both properties: the property of being-short-at-T1 and the property of being-tall-at-T2. This can be extended to the properties of having parts and their replacements.

The indiscernability of identicals aside, however, we still need a better idea or model of the enduring structure or context of replacement that remains throughout the career of the physical object and constitutes its sameness even given some replacement of parts. To assist in this connection we reflect briefly on some aspects of the philosophical tradition, and specifically upon views of Hermann Lotze and Edmund Husserl.

Anti-Atomist Tradition

Chisholm claims to be standing in the atomist and constructivist traditions that is perhaps most clearly associated with Hume, but also, for physical objects at least, with Kant--not to mention more recent thinkers such as Bertrand Russell (in some of his moments), A. J. Ayer and Nelson Goodman, in their different ways. There is much that is right about his claim, with reservations already voiced. But there is also a very strong anti-atomist tradition, certainly including Aristotle and subsequent Aristotelians, the classical Rationalist philosophers, and the Nineteenth and Twentieth Century Idealists, as well as realists such as Hermann Lotze, Edmund Husserl and Alfred North Whitehead. Among contemporary Anglo-American philosophers, P. F. Strawson and Baruch Brody hold for the ontological priority of ordinary physical objects over their basic constituents.9 We conclude this paper by explaining some contributions made by Lotze and Husserl to the understanding of the structure of replacement characteristic of physical objects, and how their views might provide conceptual content to the thesis of a restricted mereological essentialism.

The Thing As The Law Of Its States. Lotze's work is especially relevant to understanding the relations of ordinary objects to their parts and properties. For him the first task of metaphysics is to understand what it is about the ordinary object--"The Thing," a phrase of special emphasis for him--that makes it a Thing. (MP 22)10 Simply put, he finds that to be a Thing is to be a process of change. "It is impossible for that to be unchangeable which we treat as a Thing." (MP 168) The Thing is never static. Its states, with the parts and properties involved in them, are always in transit to some degree, either within itself or in the context of its existence, and so it must be viewed "as a continual becoming." (MP 168, 174) Yet this change is never a mere succession of different entities, but one thing, as common experience finds, with aspects that replace one another within a determinate range and order. "The conception of a Thing which we adopt" involves, he says, "the union of oneness of essential being with multiplicity of so-called states." (MP 165) The difficulty is to express what the 'sameness' is that makes the process one.

Lotze dismisses two familiar accounts of this sameness. One treats it as deriving from a constantly present quality or essence in the Thing's states, and the other treats it as due to the constant presence at all states of a special kind of individual: a unit of "matter," or else a "bare particular" or totally non-qualitative element. In chapters 2 and 3 of Book I of his Metaphysics Lotze goes into great detail to explain why neither of these options can succeed in accounting for the peculiar type of sameness with difference that characterizes the Thing. Positively, he concludes that "the essence is not a dead point behind the activity but is identical with that activity." (MP 75) It is not "a rigid real nucleus" (MP 76) that can be grasped in one perception. (MP 60, 67) Rather, "that which makes a Thing what it is consists only in...a certain regularity with which it changes to and fro within a limited circle of states whether spontaneously or under visible external conditions, without passing out of this circle, and without even having an existence on its own account and apart from any one of the forms which within this circle it can assume." (MP 58) This view is succinctly expressed by equating the Thing--table, ship, tree, etc.--with the law of its states. "The real Thing is nothing but the realized individual law of its procedure." (MP 72) "The Thing is an individual law." (MP 71)

But "how could a law be that which, if simply endowed with reality, would constitute a Thing?" (MP 67) How are we to understand this difficult conception of the thing as law?

First, we must be clear that by "law" is not here meant something abstract or propositional, but the actual ordered sequence in the career of the given Thing. It is the law as real-ized or made concrete and individual. Individualization of the law is a matter of there being actual 'career' stages of physical objects, individuated to space/time coordinates, that are emerging from and passing over into others stages in the career cycle as is appropriate to the kind of object in question. The law itself is not, Lotze holds, a separate structure that forces or causes the states of the physical object to occur as they do (MP 113), and "conformity to law on the part of a Thing would be nothing else than the proper being and behavior of the Thing itself." (MP 71) There is nothing involved in such 'conformity' but the states (with parts and properties) of the Thing passing over in determinate ways into other states of the Thing, up to the point where it ceases to exist.

Now the states do not, for Lotze, merely succeed or accompany one another. There is no "naked coming into being" (MP 78), and no mere existential association. Rather, the states of the object each have inherent tendencies to exist with those that accompany them (and to exclude others) and to give rise to certain others and to them alone. He reclaims (MP 81) the Aristotelian doctrine of potential being as a way of uniting and excluding states that must or cannot enter jointly into the careers that make up physical objects.

In the abstract the career apple tree would be the same for apple tree A and apple tree B. But A and B will be different careers--different "individual laws" or "realized laws"--even though they are of the same abstract type. From the point where they begin to their end, different concrete states enter into them. Once the given tree exists, these states arise out of the previous states in virtue of the determinate potentialities or powers that they contain. The individualized order is what is present, in virtue of the interrelated potentialities and actualities involved at any point, to unify the many states into one entity, this Thing. (MP 149) It is the sameness in and of the Thing.

Lotze invokes the case of music and melody to clarify his view. (MP 69, 73, 146) The melody is present in each of its tones as the ground of it being when and where--and, to a degree, what--it is. This, he thinks, is illustrative of the physical object: of "that permanent yet changeable essence of a Thing." (MP 70)

He did not think, however, that merely by inspecting or philosophically analyzing physical objects themselves we can know that such a unity actually pervades them. (MP 168) Rather, what we know is only that if ships, trees, etc., are Things, they have the kind of unity in difference described. Only an immediate perception, Lotze supposes, could show that this unity actually occurs, and such a perception we have only in the case of our own self and its states. We experience the relation of our states to the identity that runs through them--somewhat as the one melody is present in each of its tones--and makes them the states of the same thing. "It is only through the fact that our attention, bringing events into relation, comprehends past and present in memory, while at the same time there arises the idea of the persistent Ego to which both past and present belong, that we become aware what is meant by Unity of Being throughout a change of manifold states, and that such unity is possible." (MP 169)

If we assume such careers for physical objects as is suggested by Lotze's analysis, then the limits imposed by the structure of replacement relevant to such objects and their pieces, with its inherent possibilities and limitations, may be understood as follows: Pieces whose replacement, in an appropriate manner, does not destroy the cycle, are not essential to their wholes. If replacement does destroy the cycle, they are essential to their wholes.

The line between essential and non-essential parts of a whole may be hard to draw in many cases. But there also are clear cases of essential and of non-essential parts. A leg can be replaced on an ordinary table, a tire on a car. It is the understanding of what the 'career' of the object is that guides us to the objective context or structure of replacement, where we may interact to sustain the ongoing life of a whole, or else write it off as finished. The entire table top (not just its surface or a part of it) cannot be removed and the same table restored from the legs only. A melody might omit a note, or flat or sharp several, while remaining the same melody. But "Variations on a Theme by Paganini" is not the theme by Paganini, nor conversely.

A Structure Resting On Ideal Laws. The views of Lotze are helpful in bringing some clarification to what the structure of replacement that determines the essential and unessential pieces of the physical object might be. The basic idea of the Thing as having a determinate career within the confines of law is adopted by Husserl. But the interweaving potencies that generate the unity of the physical object for Lotze are in effect taken by him as ultimates, not to be further conceptualized. This seems to me a mistake, in view of the fact that these potencies are obviously a function of the universals or properties that qualify the states of the object or even the object as a whole. Lotze rightly sees that "abstract" entities in themselves do not give rise to change. But he does not do justice to the fact that, when exemplified, they achieve a certain dynamism: they account for the determinate character of the potentialities of interrelation that the stages and parts of physical objects have. We turn to Husserl for a more precise account of the ontological structure of the physical object and its various kinds of parts.

Husserl begins his official treatment of part and whole from a discussion of "sense contents" or sense data; but what interests him is not, in the first instance, their pieces or fragments, as we saw in G. E. Moore and Chisholm. Rather, he is interested in the existential dependence between aspects or "moments" of sense contents, such as extension (or spatiality) and color in a visual sense content, or the pitch and intensity of an auditory sense content (a tone). (LI 440f)11 Husserl observes that these "moments" often exhibit a characteristic type of inseparability, such that, for example, if extension is taken away the color does not remain, and conversely. Such 'parts' cannot exist outside of the whole that they constitute, nor does the whole survive their disunion. Other sense contents, such as those famously introduced by Berkeley corresponding to the head of a horse (LI 438f), are separably presentable and capable of existing continuously through a complete variation of the sense contents surrounding them. (LI 443) This is true with respect to "every phenomenal thing and piece of a thing." (LI 439)

But Husserl does not find here a mere brute fact of dependence on independence of sense contents. Rather, the existential dependence (or lack thereof) is derivative from the essence or nature of the contents concerned, from the properties constitutive of what they are. Pitch, in a tone, has a certain character that requires intensity also to be present in its instances. The same is true for color and extension. But not for the horse-head image and its surroundings in the sense field. And this is the crucial step beyond Lotze that we find in Husserl's account. It is no longer 'blind' potentialities that move and structure the process of change, but rather the connections (Ideal Laws) and lack thereof between the properties inherent in entities and their states. Pitch is not just factually dependent upon intensity--as if the next pitch we find might very well be without any degree of loudness. It is essentially so, and, Husserl is sure, can be seen to be so. Similarly for the cases of independence: "A thing or a piece of a thing can be presented by itself, meaning that it would be what it is even if everything outside it were annhilated." (LI 445) This independence also is a matter of the essence and Ideal Laws involved in the case, and remains so even though, factually, things and their pieces, as well as the corresponding sense contents, exist only under certain conditions imposed by nature, and hence in some sense are dependent.

Although such distinctions were originally drawn by Husserl (following Carl Stumpf) in a study of sense contents, he points out that the difference between the dependent (or "abstract") and the independent (or "concrete") involves no essential connection with the mental. (LI 444) It is a completely general ontological distinction, applying to all types of entities: the Ideal or universal (LI 448) and the real ("Things"), as well as the psychical. The dependencies in question are "objectively-ideal necessities of an inability to be otherwise....given in our consciousness of apodictic self-evidence." (LI 446) The dependent object has an "essence, its pure species, which predestines it to partial being.... In the case of independent objects such a law is lacking: they may, but need not, enter into more comprehensive wholes." (LI 44f; cf. 454f)

Since the necessities and possibilities of dependence and independence that show up between parts and parts, and wholes and parts, are conditioned upon the specific qualities of those wholes and parts, they are not analytic or formal necessities and possibilities, but synthetic ones. Thus, "all the laws or necessities governing different sorts of non-independent items fall into the spheres of the synthetic a priori." (LI 456ff)

This synthetic a priori character carries over to the general laws of foundation, and of wholes and parts, which Husserl formulates in Chapter 2 of the IIIrd "Logical Investigation." If a law or connection of essence dictates that A, whatever entity it may be, cannot exist except in a whole unifying it with another thing M, then, Husserl says, "an A as such requires foundation by an M," or "an A as such needs to be supplemented by an M." (LI 463) Moreover, if the existence of A requires M, then "a whole including an A but no M cannot satisfy A's need for supplementation and must share it." (LI 464) In other words, whatever founds a necessary part of a whole founds the whole.

From these beginnings Husserl elaborates a subtle and intrinsically interesting theory of whole and part. In general, this theory, correctly I believe, takes the relation of whole and part to be definable in terms of his "foundation" relation (see LI 475), and foundation to be a matter of the Ideal Laws of--the inherent connections and disconnections between--properties or essences that constitute the natures of the wholes and parts in question. "The only true unifying factors, we may firmly state, are relations of 'foundation'. The unity even of independent objects is in consequence brought about by 'foundation'. Since they are not, as independent objects, 'founded' on one another, it remains their lot to 'found' new contents themselves,..." (LI 478) And this last point applies specifically to physical objects and their pieces.

For our purposes here, on Husserl's theory the pieces of physical objects, such as Chisholm has considered, have the interplay they do in their wholes only through the moments that make them up and through the laws that govern those moments and, thereby, the pieces in relation to their relevant wholes---ships, tables and trees. (See LI 482-488) This then opens the way for "modified Ideas of empirical'foundation', of empirical wholes, and empirical independence and non-independence." (LI 486), which go beyond strict laws of essence. "Nature with all its physical laws is a fact that could well have been otherwise." (Ibid.) The case of the dependence of the tree upon its leaves, discussed above, is not a matter of essence, but of natural law. A theory of whole and part in terms of the 'foundation' relation will therefore require an extension if it is to be adequate to physical objects as we know them. Husserl achieves this extension by allowing us to "treat natural laws, without regard to their infection with contingency, as true laws, and to apply to them all the pure concepts we have formed." (LI 486)

* * * * *

Now we cannot here defend the views of Lotze and Husserl relevant to physical objects and their parts, nor do we suggest that they are on the whole defensible. Indeed, they obviously pose serious philosophical problems in their own right--though I do regard Husserl's account as one of the better possibilities. Our aim has been to present them as serious possible accounts of what the structure of replacement, permitting a restricted version of mereological essentialism, might look like. At least we can cite them as illustrations of how such a structure might be interpreted.

But we can also say with assurance that mereological essentialism depends, even for its intelligibility as a claim, upon making sense of the idea of replacing parts. ME may be applied to aggregates as a limiting case. An aggregate is essentially the type of 'entity' which does not admit of replacement of parts. But this is simply because it provides no structure of replacement at all. 'Replacement' of a member of an aggregate cannot leave the same group of interrelated things because the aggregate is straightforwardly identical with its elements. Such wholes as physical objects sharply contrast with this. When some of their parts, though certainly not all, are removed, a structure of replacement remains--at least for a time--that may permit replacement of parts and the restoration of the whole. It is this enduring or continuous structure of replacement that constitutes the identity of the physical object through the replacement--and sometimes even the enduring lack--of some of its parts. Lotze and Husserl helpfully comment on how this structure might be understood.



  1. Chisholm's first essay on this topic was his "Parts as Essential to Their Wholes," Review of Metaphysics, XXV, (1973), 581-603. In this article I have referred to the slightly modified version of this essay reprinted in 1989. I utilize the following symbolisms to refer to Chisholm's writings:
    OM = "Parts as Essential to Their Wholes," in On Metaphysics (Minneapolis: University of Minnesota Press, 1989), pp. 65-82.
    PO = Person and Object: A Metaphysical Study (La Salle, IL.: Open Court Publishing Co., 1976), especially chapter III and Appendix B.
    RMC = Roderick M. Chisholm, edited by Radu J. Bogdan (Dordrecht: De. Reidel, 1986), especially pp. 65-71 & 228.

    See also Chisholm's "Mereological Essentialism: Some Further Considerations," Review of Metaphysics, XXVII (1975), 477-484, which is a reply to Alvin Plantinga's "On Mereological Essentialism," pp. 468-476 of that same volume.  Return to text.

  2. In has last statement on the subject, in RMC, he states ME directly as a truth about substances and not about wholes. See his "(BA1)" on page 67.  Return to text.

  3. For a discussion of these distinctions and others relevant to a theory of whole and part in general, See Husserl, IIIrd "Logical Investigation," in his Logical Investigations, translated by J. N. Findlay, (New York: Humanities Press, 1970), pp. 435-489. Also Peter M. Simons, Parts. A Study in Ontology, (Oxford: Clarendon Press, 1987), and his "Three Essays in Formal Ontology," in Parts and Moments: Studies in

Article Tags is co-sponsored by the family of Dallas Willard, Dallas Willard Ministries, and FiveStone.