Axiomathes

, Volume 21, Issue 4, pp 491–505

Metametaphysics and Substance: Two Case Studies

Authors

Invited Paper

DOI: 10.1007/s10516-010-9123-y

Cite this article as:
Hoffman, J. Axiomathes (2011) 21: 491. doi:10.1007/s10516-010-9123-y
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Abstract

This paper examines an often-ignored aspect of the evaluation of metaphysical analyses, namely, their ontological commitments. Such evaluations are part of metaphysical methodology, and reflection on this methodology is itself part of metametaphysics. I will develop a theory for assessing what these commitments are, and then I will apply it to an important historical and an important contemporary metaphysical analysis of the concept of an individual substance (i.e., an object, or thing). I claim that in evaluating metaphysical analyses, we should not only rule out counterexamples, but also compare them with respect to their ontological commitments, and we should hold that if they are comparable in other respects, then an analysis with fewer such commitments is preferable to one with more (There is, of course, a connection between counterexamples and ontological commitments. If the existence or possible existence of something one is committed to the existence or possible existence of is incompatible with an analysis, then one should reject that analysis as inadequate to the data. On the other hand, if one is uncertain about the existence or possible existence of something that is incompatible with an analysis, then while this does not refute the analysis for one, it raises doubts about it. The fewer such doubts are raised by an analysis, the better it is.).

Keywords

AristotleSubstanceMetametaphysicsOntologyOntological commitmentsE. J. LOWEPhilosophical analysis

1 Some Assumptions and Definitions

I shall make certain assumptions in this paper. First, I assume that there are universals (properties and relations), and they are the subjects of philosophical analysis. Second, I assume that there are philosophical or Socratic analyses of at least some metaphysical properties, and that seeking such analyses is an important part of the methodology of metaphysics. Third, I assume that there can be more than one analysis of the same metaphysical property. I know of no good argument to the contrary, and there seem to be examples of this sort in mathematics and elsewhere. Fourth, I assume the now widely accepted view that many metaphysical propositions are both necessary and synthetic a posteriori. Indeed, one can argue that this is one of the salient discoveries of twentieth century analytic philosophy.1

By a philosophical analysis of a property, being F, I mean a necessary equivalence between something’s being F and something’s being G (where being G is the analysis of being F), such that something’s being G explains something’s being F. The latter condition (the explanatory condition) rules out circularity in the analysans of the analysis—for instance, the concept of being F cannot appear in the analysans.

By an individual substance, I mean what in common parlance is thought of as an object or thing. Purported examples may include a quark, a cat, a rock, a pencil, and a (Cartesian) soul—or true atomic particles, organisms, inanimate compounds, artifacts, and purely spiritual beings, respectively. Of course, metaphysicians dispute which, if any, of these items or kinds of items truly are or could be substances. Aristotle, for example, rejects the possibility of substantial atomic substances, and seems to reject the possibility of substantial artifacts, while (closer to home) Peter van Inwagen rejects at least the actual existence of artifacts and other inanimate compounds, while admitting that there are atomic particles and organisms.2 This is, in fact, one way in which an analysis of substance may have more (or fewer) ontological commitments than another, as we shall see. For example, if analysis #1 implies that souls (or purely spiritual substances) are impossible, while analysis #2 does not imply either that souls are or are not impossible, then, other things being equal, analysis #2 has fewer ontological commitments than does analysis #1—analysis #1 is committed to the impossibility of souls, while analysis #2 is not. Absent a good argument showing that souls are impossible (which a number of philosophers have indeed tried to provide3), this would be a defect in analysis #1.

There is another notion of substance, namely, that of a kind of stuff. Water, steel, and air are substances in this sense. If I use the term ‘substance’ is this paper, then unless otherwise indicated, I am using it in the thing or object sense, rather than in the stuff sense. As some would say, the term ‘substance’ in the first sense is a count noun, while the term ‘substance’ in the second sense is a mass term.

2 Ontological Categories

At this point, it is useful to introduce and explicate the notion of an ontological category.4 Roughly speaking, an ontological category is a highly general kind, and figures in any basic metaphysical description of reality. Ontological categories are either more general, less general, or at the same level of generality as other such categories, so that they can be arranged in a hierarchy according to their level of generality and their logical relations to one another.They are such that if anything falls under an ontological category, then it is of that kind essentially. The universal category is that of being an existent or being an entity; everything falls under this category. Let us say that this category is at the highest level, or Level A. At the next level, which I call Level B, there are the contradictories, being abstract and being concrete.5 Everything is either abstract or concrete, but nothing is both abstract and concrete. The third level of generality, Level C, consists of a number of contraries, as the following diagram illustrates:https://static-content.springer.com/image/art%3A10.1007%2Fs10516-010-9123-y/MediaObjects/10516_2010_9123_Figa_HTML.gif Some examples help to understand what the categories at Level C are. I have already provided examples of subtances. Events are entities such as the baseball game or the sunset. Times are entities such as today and this minute. Places include where the earth is and where the apple is.6 Tropes are concrete, non-repeatable attributes such as the particular shape of the tree or the particular size of the rock. Boundaries are things like the surface of the table, or the edge of the ruler. Absences are entities like the hole in the doughnut or the shadow on the wall. Collections are things like the sum of the forks in the drawer or the sum of the coins in my pocket. The null set and the unit set are examples of sets. Five and pi are examples of numbers. Being square and being happy are examples of abstract properties. Being between and being taller than are examples of abstract relations. That today is Tuesday and that Caesar crossed the Rubicon are examples of propositions.

This scheme of categories is meant to be maximally ontologically neutral, by including as many categories as seem to be possibly instantiated. The intention is to leave it open both whether or not there are other categories at Level C, and whether or not some of the categories at Level C are either eliminable (not really possibly instantiated) or reducible (not really at Level C). For example, if substances are really collections of tropes (as some have held), then the category of being a substance belongs not at Level C, but at a lower level, under the category of collection (or perhaps under the category of being a trope). On the other hand, if, as others have held, substances are impossible, then the category of substance does not belong on the table of categories at all. There are levels of (less general) ontological categories, Level D, Level E, and so forth. At what level of specificity one no longer is dealing with an ontological category but with some other, less significant kind is a very interesting and difficult question, one that I do not need to grapple with here.7

There are obvious logical relations between ontological categories. For example, as mentioned above, the two categories at Level B are contradictories, and any two categories at Level C are contraries (assuming that they really belong at Level C, and not at some other level). Furthermore, any category at a given level, L, is a (logical) species of every category that is at both at a higher level than L and on the same side of the table of categories as L. For example, it is necessarily true that an organism is also a substance, a concretum, and an entity. It is also necessarily true that a rational number is a number, an abstractum, and an entity. Finally, it is a necessary truth that nothing is both an organism and a real number, or a trope and a number—that is, for any categories x and y, such that x and y are on opposite sides of the table of categories, necessarily, nothing instantiates both x and y.

3 Ontological Neutrality

I turn now to the task of clarifying what I mean by the ontological neutrality and the ontological commitments of a metaphysical analysis. This I do in terms of what I call a Principle of Ontological Neutrality (PON):

(PON) Metaphysical analysis A is ontologically neutral with respect to ontological kind K (or to entity E) = df. the adequacy of A does not entail either that Ks exist or that Ks do not exist (or that E exists or that E does not exist).

By the adequacy of an ontological analysis, I mean that the analysis does not conflict with the data for that analysis. For example, if one were to try to analyze what being concrete is, then one’s analysis should imply that what intuitively are concrete entities satisfy the analysans, and that what are intuitively not concrete entities do not satisfy that analysans.8 In other words, the analysis is adequate only if there are no counterexamples to it.

It follows from (PON) that if A1, an analysis of being F, entails that universals do not exist, or that Cartesian souls do not exist, or that God does not exist, then A1 is not ontologically neutral with respect to universals, or to Cartesian souls, or to God. In other words, such an analysis has an ontological commitment to the nonexistence of universals, or of Cartesian souls, or of God, since if any of them exists, then A1 is not an adequate analysis of being F. Likewise, if an analysis, A2, of the same property, being F, entails that universals do exist, or that Cartesian souls exist, or that God exists, then that analysis is also not ontologically neutral with respect to universals, Cartesian souls, or God. Furthermore, if a third analysis of being F, A3, does not have any of the entailments just cited of A1 and of A2, then A3 is ontologically neutral with respect to universals, or to Cartesian souls, or to God. If so, then to that extent, A3 is more ontologically neutral than are A1 and A2. Of course, it is often the case that comparisons between competing analyses are not so straightforward (just as it is often the case in science that two competing theories cannot be compared regarding their simplicity in any straightforward fashion). It may happen, for example, that analysis A1 of property P is ontologically neutral with respect to Fs and Gs, and not with respect to Ms and Ns, while analysis A2 of property P is ontologically neutral with respect to Ms and Ns, but not with respect to Fs and Gs. Many other permutations are possible, but, at least sometimes, we will be able to say that one analysis is more ontologically neutral than another, and we should seek to be aware of the sorts of ontological commitments assumed by any metaphysical analysis.

It is plausible to say, I think, that the more ontologically neutral a philosophical analysis is, the better. Why should this be so? Because which kinds of entities, and which entities, actually or possibly exist, is often a matter of philosophical controversy. It is controversial whether or not substances exist, whether or not universals exist, whether or not tropes exist, and so forth. Witness the eternal debate over universals between realists and nominalists. Hence, if one can analyze what it is to be a substance without thereby being committed either to the existence or non-existence of universals, then that is preferable, other things being equal, to analyzing substance in such a way as to be committed to the existence or non-existence of universals. Perhaps this principle about ontological neutrality is a special case of Ockham’s Razor. It also seems likely that there are further principles for evaluating the ontological neutrality of philosophical analyses, but I shall not attempt to state them here.

4 Aristotle’s Change Analysis of Substance

In examining analyses of substance by means of (PON), I will confine myself to non-reductionist analyses. Recall that such analyses assume that being a substance is a Level C category.

My first test case for determining the ontological neutrality or lack of it in an analysis of substance is Aristotle’s analysis of substance in terms of change. Aristotle offers a second analysis of substance in terms of “being said of a subject” and “being in a subject,” but this second analysis faces difficulties that are different (and perhaps more serious) than his analysis of substance in terms of change.9 We find Aristotle’s change analysis of substance in his Categories, where he says:

It seems most distinctive of substance that what is numerically one and the same is able to receive contraries. In no other case could one bring forward anything, numerically one, which is able to receive contraries.10

What does Aristotle mean by something’s being able to receive contraries? It’s clear that by ‘receive’ he means have. However, there is a sense in which a proposition is able to have (or bear) contraries, since the very same proposition (i.e., which is “numerically one”) may be able to be true at one time and false at another, for example, the proposition that today is Wednesday. A given quality, being round, can at one time be instantiated by six objects and at another time instantiated by 7 objects. Aristotle, however, did not overlook these possible counterexamples. His analysis of substance in terms of change should be understood to imply not that only a substance can have or bear contrary properties or relations (an implausible claim), but rather that only a substance can have contrary (intrinsic) properties. On this more plausible interpretation of Aristotle, a proposition’s being able to be true at one time and false at another is not an example of its being able to have contrary properties at different times, but only an example of its being able to bear contrary relations at different times.11 The same is true of the example of roundness being exemplified by different things at different times. Thus, it certainly seems that Aristotle’s analysis of substance in terms of change should be understood to be the following:
  • (Di) x is a substance = df. x can undergo intrinsic change.

Let us consider various possible counterexamples to (Di). Consider, first, a snowstorm that is more intense at one time than at another. Since a snowstorm’s intensity is an intrinsic feature of it, is this a counterexample to (Di)? That is, if a snowstorm, which is an event (and a particular), can undergo intrinsic change, then (Di) does not provide a logically sufficient condition of something’s being a substance. However, it is not plausible that the variation in a snowstorm’s intensity is actually an intrinsic change in it, for it is not plausible that any event can undergo intrinsic change.12 Rather, it is more plausible to describe our snowstorm example as one in which certain parts or stages of an event differ in their intrinsic properties from other parts or stages of that event. The snowstorm, unlike a substance, does not exist wholly at every time that it exists. Instead, it is temporally extended throughout its existence: it has temporal parts. Therefore, the fact that the snowstorm has different intensities at different times does not imply that it (the whole snowstorm) undergoes intrinsic change.

Related to the first sort of purported counterexample to (Di) is the view that substances are four-dimensional, and that they have temporal parts as well as spatial parts.13 On this view of substances, it is arguable that it cannot truly be said that substances can literally undergo intrinsic change. All that can truly be said of such objects is that their temporal stages can differ in their intrinsic properties (while these stages also cannot undergo intrinsic change). Thus, if four-dimensionalism were correct, then (Di) would not, it seems, provide a logically necessary condition of something’s being a substance. Of course, the four-dimensionalist conception of substance is so far removed from the commonsense conception that it is hardly surprising that an analysis of the latter should prove to be incompatible with the former. Nevertheless, we have here an example of Aristotle’s analysis lacking a certain kind of ontological neutrality: (Di) is not ontologically neutral with respect to the existence of four-dimensional substances. If four-dimensional substances are possible, then (Di) is not an adequate analysis of substance.

A third kind of possible counterexample may prove to be more troubling for three-dimensionalists. Consider an inflated rubber tube, like the inner tube of a bicycle tire. This tube may be stretched into different shapes. In doing so, the surface of the tube changes its shape. The shape of a surface seems to be an intrinsic property of that surface. Surfaces are a species of limit, and being a limit is one of the candidate categories at Level C. Thus, if a surface can undergo intrinsic change, and if limits are possible, then (Di) does not provide a logically sufficient condition for something’s being a substance.

Aristotle would probably reply that limits are impossible—he does not include them in his list of categories of being. I can see no plausible alternative way for Aristotle to defend (Di). It is not obvious, however, that limits, such as surfaces, lines, and points are impossible or even not actual.14 Thus, we have here a second example of how Aristotle’s analysis lacks a certain kind of ontological neutrality: (Di) is not ontologically neutral with respect to the existence of limits. If limits are possible, then (Di) is not an adequate analysis of substance.

The example of the inflated inner tube points to another possible counterexample to (Di). There appears to be a hole that the inner tube surrounds. A hole is a kind of absence or privation, another candidate Level C category. Other kinds of absences are shadows and silences. (Shadows, also seem to be able to undergo intrinsic change, e.g., in their shape.) If the inner tube is pressed inward a bit or stretched outward a bit, then the hole it surrounds changes its shape, i.e., it undergoes an intrinsic change. Thus, if absences are possible, then since an absence can satisfy the analysans of (Di), it does not provide a sufficient condition for being a substance. Again, Aristotle would no doubt reject the possibility of absences. Nevertheless, it is also controversial in the case of absences whether or not they are possible or even actually exist; for instance, two recent books offer impressive defenses of the reality of holes and shadows.15 Hence, (Di) is not ontologically neutral with respect to the existence of absences. If absences are possible, then (Di) is not an adequate analysis of substance.

Finally, and perhaps most seriously, the adequacy of (Di) is not compatible with the existence or possible existence of atoms or basic, unsplittable particles. Such particles cannot undergo intrinsic change—indeed, that was one of the motivations for their initial postulation.16 Unlike the two preceding cases, where the possible existence of limits and absences posed a threat to the logical sufficiency of the analysans of (Di), but like our first example of four-dimensional substances, the possibility of atoms threatens the logical necessity of the analysans of (Di). If atoms are possible, then (Di) does not provide a logically necessary condition for being a substance, since atoms cannot undergo intrinsic change, yet they are substances.

Aristotle rejected the existence of atoms, even though he was well aware of the theory of Democritus and Leucippus. Perhaps he realized that his change analysis of substance is incompatible with their existence. Note that his view would have to be that atoms are impossible, not just that they actually don’t exist, if his analysis is to be adequate.17 From a contemporary perspective, of course, these rejections of the actuality and even of the possibility of atomic particles are unreasonable and the arguments for them unsound. Thus, (Di) is not ontologically neutral with respect to the existence of atomic substances. If atomic substances are possible, then (Di) is not an adequate analysis of substance.

To sum up the evaluation of Aristotle’s analysis of substance in terms of intrinsic change, I have found that this analysis is not ontologically neutral with respect to four-dimensional substances, absences or privations, limits, and atomic particles. If any of those kinds of entities are possible, then the analysis in question is inadequate.18

5 Independence Analyses of Substance

I turn next to a contemporary attempt to analyze substance, that of Jonathan Lowe, in his The Possibility of Metaphysics.19 Lowe’s analysis is framed in terms of ontological independence, an idea about substance that has a distinguished history. For example, Aristotle himself said:

“Some things can exist apart and some cannot, and it is the former that are substances.”20

Descartes offered the following independence analysis of substance:

(Dii) “The answer is that the notion of substance is just this—that it can exist all by itself, that is, without the aid of any other substance.”21

More carefully, he stated this analysis:

(Diii) “By substance, we can understand nothing other than a thing which exists in such a way as to depend on no other thing for its existence.”22

Descartes also believed that created bodies and souls depend upon God for their existence, so he thought that only God could satisfy (Diii). It seems that Descartes thought that we must distinguish between created substances and God, and that created substances would satisfy not (Diii) but (Div):

(Div) x is a created substance = df. It is possible that x exists without any other entity existing, except for God.

Spinoza also defended an independence analysis of substance, and an extreme, conceptual version of that idea:

(Dv) “By substance, I understand that which is in itself and is conceived through itself, in other words, that, the conception of which does not need the conception of another thing from which it must be formed.”23

Finally, there is David Armstrong:

(Dvi) “A particular is a substance, logically capable of independent existence. It could exist although nothing else existed.”24

Elsewhere I have argued that none of these independence analyses of substance are adequate to the data.25 With this historical background, I turn to Lowe’s analysis.

6 Lowe’s Independence Analysis of Substance

In order to understand Lowe’s independence analysis of substance, it is necessary first to state several definitions and theorems that it presupposes and which he provides. These are as follows:

(D1**) x depends for its existence upon y = df. Necessarily, the identity of x depends on the identity of y.26

(D3) The identity of x depends on the identity of y = df. Necessarily, there is a function F such that it is part of the essence of x that x is the F of y.27

(T5) If the identity of x depends on the identity of y, then, necessarily, x exists only if y exists.28

(T6) If x is not identical with y and the identity of x depends on the identity of y, then the identity of y does not depend on the identity of x.29

(D2*) x is a substance = df. x is a particular and there is no particular y such that y is not identical with x and x depends for its existence on y.30

(T7) x is a substance = df. x is a particular and there is no particular y such that y is not identical with x and the identity of x depends on the identity of y.

The main idea behind these principles of Lowe is that substances possess some sort of ontological independence, while recognizing (as Descartes, Spinoza, and others before him did not) that it does not work to attribute individually to each substance a straightforward metaphysical independence from all other entities. What is needed, Lowe thinks, is a type of metaphysical independence that is both asymmetric and stronger than the relation of not being metaphysically entailed by the existence of (some other entity). (D1**), (D3), (T5), and (T6) purport to explain what that relation is, while the ingenious (D2*) and, ultimately, (T7), incorporate it in an analysis of substance.31

(D2*) and (T7) employ the notion of a particular, by which Lowe understands (correctly, I think) an entity that is not multiply exemplifiable or instantiable. Thus, (D2*) states that something is an individual substance just when it is a particular that does not depend upon another particular for its existence. A particular x depends for its existence upon a particular y only if: (1) the existence of x entails the existence of y, and (2) the identity of x depends on the identity of y. This latter notion, that of the identity of x depending on the identity of y, is defined by (D3) as occurring just when “necessarily, there is a function F such that it is part of the essence of x that x is the F of y.” If it is part of the essence of x that x is the F of y, then being the F of y is an individual essence of x.

An example or two may help to clarify what Lowe has in mind with (D2*) and (T7). First, Lowe argues that the unit set, x, that contains the substance y as its only member, fails—as it should, if (D2*) and (T7) are to be adequate analyses—to satisfy the definiens of (D2*) and of (T7). This is because there is a particular, namely y, whose existence is entailed by that unit set, and because it is part of the essence of that set that it is identical with the function, F of y, where F is the being something that has as its only element function.32 Second, Lowe argues that the marriage of y and z, presumably an event, fails—again, as it should—to satisfy the definiens of (D2*) and of (T7). Let x be the marriage of y and z. Then, he says, there is a particular, y (say, the bride), such that the existence of y is entailed by that particular marriage, x. Moreover, there is a function, F, such that it is part of the essence of x that x is identical with that function of y, namely, being something married to z (or, as Lowe puts it, marriage to z).33

Lowe stipulates that the relation of the identity of x depending on the identity of y (i.e., “identity dependence”) is an “antisymmetric” relation. Such a relation does allow for the identity of x to depend on its own identity, but does not allow for the possibility of the identity of x to depend on the identity of y and for the identity of y to depend on the identity of x.34 More about this stipulation below. I turn now to the examination of the ontological neutrality of Lowe’s analysis of substance, (T7).

A first issue concerns particularized attributes or tropes—a category of entity that Lowe includes in his ontology.35 Lowe himself is concerned about the compatibility of his analysis of substance with a trope that is essential to the substance to which it belongs. Lowe cites the example of the particular humanity of Socrates, but one could also cite the particular animality and the particular mammality of Socrates, and so forth. He also makes the following concession: “…if there is such a thing as the particular humanity of Socrates, he cannot lose it without ceasing to exist.”36 Are there such tropes? Lowe does not give a completely straightforward answer to this question, for he seems both to concede that there are, and also wants to identify them with Socrates himself. I find this puzzling, for it seems evident that a trope cannot be identical to a substance—to assert this is to commit a category mistake. So it seems to me that Lowe must either deny that there are such tropes (those essential to a substance) or else concede that they are not identical to substances. I see no good reason to adopt the former alternative; there is nothing about tropes that seems to imply that there are no tropes that are essential to a substance. What happens if Lowe concedes that there are such tropes? In that case, he has a fallback argument, that they pose no threat to (T7), or, by implication, to (D2*), because of (T6), which, recall, implies that the identity-dependence relation is antisymmetrical. Based on (T6), Lowe can argue that while the identity of a trope essential to a substance depends for its identity on that substance, the converse is not true. It is at this point, however, that there are questions that arise about the plausibility of (T6). It is not at all clear why it cannot be that the identity of x as a substance depends on the identity of y as an essence of x, while the identity of y as a particularized property also depends on the identity of x, the only substance to which it possibly belongs. After all, what Socrates is (a human being) seems to depend on the identity of Socrates’s humanity, and Socrates’s humanity also seems to depend for what it is (the humanity of that particular person) on the identity of Socrates.37 Each plausibly depends on the other for its identity (at least in part), but each in a different way.If all of the preceding is right, then Lowe has not provided a plausible motivation for (T6), and neither a good reason to deny the existence of essential tropes, nor a good reason to identify them with the substances to which they belong. Thus, the possibility of essential tropes that are not identical with the substances to which they belong is incompatible with (T7), and since (T6) is not plausible, then the adequacy of (T7)—more specifically, the failure of its analysans to provide a necessary condition for being a substance—is incompatible with the possibility of essential tropes. (T7) is not neutral with respect to the possibility of a substance’s having essential tropes.

A second problem for (T7) concerns the possibility of abstract individual essences, also known as thisnesses or haecceities. For example, the haecceity of Socrates would be being-identical-with-Socrates.38 Such an entity would be a particular, since it is not possible for it to be multiply exemplified. Since it is highly plausible that Socrates would depend for his identity on the identity of his haecceity (were it to exist), the possibility of haecceities is incompatible with the adequacy of (T7)—more specifically, with the analysans of (T7) providing a necessary condition for something’s being a substance.39Hence, (T7) is not ontologically neutral with respect to haecceities.

A third difficulty arises for (T7) with respect to sets. Sets are (abstract) particulars. Consider the null set. As far as I can see, the identity of the null set does not depend on the identity of any other particular (unlike the unit set whose only element is Socrates, which depends for its identity on the identity of Socrates). Thus, it seems that the null set satisfies the analysans of (T7), and (T7) implies that the null set is a substance. If the null set is possible—and the axioms of set theory imply that it is—then (T7) does not provide a logically sufficient condition for something to be a substance. Hence, (T7) is not ontologically neutral with respect to the null set (and, it seems, to the existence of sets in general, which presuppose the existence of the null set).

Fourth, consider the proposition, that red is a color. Propositions are (abstract) particulars.40 Once more, it does not seem the identity of this proposition depends on the identity of any other particular.41 Thus, (T7) implies that some propositions are substances, and the adequacy of (T7) is not compatible with their possibility. Hence, (T7) is not ontologically neutral with respect to (certain purely general) propositions.42

A fifth and final problem for (T7) concerns compound bodies that, unlike either organisms or artifacts, have their parts essentially. I shall call such bodies “mereological compounds.”43 Such objects are best understood as either solid pieces of matter, for example, a piece of gold or a piece of plastic, or else a particular atom (e.g., of hydrogen), or a particular molecule. Suppose body x is such a compound, and that y and z are the essential proper parts of x. Consider the function, being the one and only whole that consists of z being joined together in way w with. It certainly seems that x is identical with this function of y, so that the identity of x depends in the required way on the identity of y. Hence, it follows that no mereological compound can satisfy the analysans of (T7), and no mereological compound is compatible with the adequacy of (T7). Lowe considers this difficulty at one point. He disputes the claim that compounds with essential proper parts would fail to satisfy (T7): “The point is that if y is an essential proper part of a composite substance x, then while it is true that if y ceases to be a proper part of x, then x must cease to exist, it is still possible for y to become an essential proper part of another composite substance z, whence the presence of y as an essential proper part of a substance has no bearing on the identity of that substance.”44 I am puzzled by this argument, since the possibility that y is now an essential proper part of compound body x is also (either now or at some other time) an essential proper part of compound body z does not seem to me to be relevant to the fact that the identity of x depends on the identity of y. There is nothing in (T7) or any of the other of Lowe’s theorems and definitions that rule out a given particular’s being depended on by two or more other particulars for their identities, whether at different times, or even at the same time. Suppose that x is a proper part of y and that y is a proper part of z. Then, it certainly seems, the identities of both y and z depend on the identity of x. Clearly, when mereological compound x is partly composed of y, then the identity of x, what compound x is, depends on the identity of y, and when mereological compound z is partly composed of y, then the identity of z, what compound z is, depends on the identity of y.45 I conclude that (T7)’s adequacy is not compatible with the existence of mereological compounds, and that (T7) is not ontologically neutral with the existence of mereological compounds.

7 Conclusion

Scrutinizing metaphysical analyses, such as Aristotle’s change analysis of substance, and Lowe’s independence analysis of substance, with respect to their ontological neutrality is an important methodology for metaphysicians. It is rare that any such analysis would be neutral in all of the ways that we would ideally want it to be, so that comparisons of competing analyses will often have to be weighed with respect to the degree to which they are not ontologically neutral and with respect to the ways in which they are not ontologically neutral.46

Footnotes
1

So claims Soames (2003, pp. xi–xii).

 
2

Van Inwagen (1990). It isn’t clear, I think, whether or not van Inwagen would say that artifacts and other inanimate compounds are impossible, and he offers no analysis of substance in any case.

 
3

That such arguments are thought by many to be needed seems to confirm the view that many metaphysical propositions are necessary, but synthetic a posteriori. For a survey and critique of several arguments that purport to show that souls are impossible, see Hoffman and Rosenkrantz (1994, chap. 5).

 
4

For a highly ambitious attempt to analyze the property of being an ontological category and to solve this problem, see Rosenkrantz (2006).

 
5

For an analysis of the distinction between abstract and concrete, see Hoffman and Rosenkrantz (1994, pp. 182–187).

 
6

There are those, of course, who would replace the categories of time and place with a single category of space–time.

 
7

However, see Rosenkrantz (2006) for one answer to this question.

 
8

I shall ignore here the more complicated situation that arises when no analysis can be formulated that is in this sense adequate to the data, so that we have either to choose among proposed analyses none of which is entirely adequate, or conclude that there is no analysis of the property in question. If we opt for the former, then we must reject some of the data as mistaken.

 
9

Categories, in Aristotle (1984, 2:4). For a thorough critique of this analysis of substance, see Hoffman and Rosenkrantz (1994, pp. 33-46).

 
10

Aristotle (1984, 1:7).

 
11

Aristotle himself cites the example of a belief that is at one time true and at another false as a possible objection to his analysis. Aristotle (1984, 1:7). He replies that “in the case of substances it is by themselves changing that they are able to receive contraries…statements and beliefs, on the other hand, themselves remain completely unchangeable in every way.” Ibid. Aristotle’s reply clearly presupposes the distinction between intrinsic and relational change, and implies that his analysis of substance is to be understood in terms of intrinsic change.

 
12

Two authors who come to this conclusion are Geach (1972, pp. 302–318), and Mellor (1981, chaps. 7 and 8). One argument for this conclusion is that if changes can undergo change, then it appears that a vicious regress threatens, with changes “all the way down.” Ockham’s Razor seems to militate against such a regress.

 
13

See, for example, Sider (2003).

 
14

Two recent authors who argue for their reality are Chisholm (1989, pp. 83–89), and Stroll (1988).

 
15

For a defense of shadows, see Sorensen (2007); for holes, see Varzi and Casati (1994).

 
16

A number of scholars of ancient philosophy have argued that the ancient atomism of Democritus and Leucippus was formulated partly in response to the arguments of Parmenides against the possibility of change. Ancient atomism concedes the point with respect to the possibility of intrinsic change of atoms, though relational change is permitted in the form of motion.

 
17

In the early modern period, Descartes, Leibniz, and Berkeley all rejected the possibility of atoms as well. Leibniz and Berkeley explicitly argued for their impossibility—further evidence of the unreliability of at least some of our intuitions in metaphysics.

 
18

Aristotle’s analysis could be improved in the following way: x is a substance = df. x belongs to a Level C category which possibly has an instance that can undergo intrinsic change. This reformulation is compatible with the possibility of atomic particles, since while atoms cannot themselves undergo intrinsic change, they belong to a Level C category (namely, that of being a substance), which possibly has an instance that can undergo intrinsic change, for example, an organism. While this avoids what is perhaps the most serious problem for a change analysis of substance, this reformulation remains incompatible both with the possibility of absences or privations and with the possibility of limits.

 
19

Lowe (1998, chap. 6).

 
20

Aristotle (1984, 2:1691).

 
21

Descartes (1984, 2:159). This particular formulation is obviously circular.

 
22

Descartes (1984, 2:210).

 
23

Spinoza (1982, p. 31).

 
24

Armstrong (1978, 1:115).

 
25

Hoffman and Rosenkrantz (1994, pp. 53–57).

 
26

Lowe (1998, p. 147). The labels for this and the following definitions and theorems are Lowe’s.

 
27

Op. cit., p. 149.

 
28

Op. cit., p. 150.

 
29

Ibid.

 
30

Op. cit., p. 151.

 
31

Lowe regards (D2*) and (T7) as equivalent, via (D1**).

 
32

Op. cit., p. 148.

 
33

Ibid.

 
34

Op. cit., p. 146.

 
35

Lowe (2009).

 
36

Lowe (1998, p. 142).

 
37

As Lowe puts it in explaining what it is for something to depend for its identity on another thing, “To say that the identity of x depends on the identity of y—or more briefly, that x depends for its identity upon y—is to say that which thing of its kind y is fixes (or at least helps to fix) which thing of its kind x is.” Op. cit., p. 147.

 
38

For an extended defense of haecceities, see Rosenkrantz (1993).

 
39

Indeed, the main motivation for postulating haecceities has been to provide identity conditions for concrete things, particularly substances.

 
40

It might be thought by some that all propositions are universals, and that they are instantiable by concrete events. For example, it might be thought that the proposition, that red is a color, is instantiable by the red fire engine being colored. If this were correct, then no proposition would satisfy the definiens of (T7). It is implausible, however, that all propositions can be so understood. For instance, the proposition, that the null set exists, is not plausibly instantiable by any such concrete event or state of affairs, and is not, therefore, plausibly understood as a universal.

 
41

I am assuming that there are abstract universals, so that redness is a universal, and not as some nominalists would have it, a set. Lowe accepts the existence of (Aristotelian) universals.

 
42

It might be thought that Lowe can avoid the difficulties posed by my third and fourth examples by arguing as follows (call this Strategy S). There is a particular upon whose identity the null set depends, and there is a particular upon whose identity the proposition that red is a color depends. In the former case it is the proposition that the null set exists, and in the second case it is the proposition, that the proposition that red is a color exists. The function in question in each case is being the truthmaker for. The null set is the truthmaker for the proposition that the null set exists, and the proposition that red is a color is the truthmaker for the proposition that the proposition that red is a color exists. Thus, neither the null set nor the proposition that red is a color satisfies the analysans of (T7). I have two replies to this strategy. First, it is not plausible that the proposition that the null set exists partly or wholly determines what sort of thing the null set is. Second, even if this were plausible, Strategy S would come at too heavy a cost. For then nosubstance would satisfy (T7), since it would be the case that for any substance, there is a particular upon which the identity of that substance depends, namely, the proposition that that substance exists, for which that substance is the truthmaker. Thus, either the null set and the proposition that red is a color satisfy (T7), or no substance satisfies (T7).

 
43

There are widely divergent views about the possibility of such compounds. Van Inwagen (1990) rejects their actual existence, but the reasons he gives for this conclusion, based on the purported implications of the actual laws of nature, do not seem to imply that such compounds are impossible unless the laws of nature are necessary. For a defense of the actual existence of such mereological compounds, see Hoffman and Rosenkrantz (1997, chap. 3). Chisholm (1973) also defends their actuality. Both science and common sense seem to acknowledge the existence of such compounds. Moreover, it is difficult to see why someone who, like Lowe, seems to acknowledge the reality of artifacts, would question the reality of mereological compounds. It is the latter that figure in the laws of nature that we rely upon when we explain the dispositions of the former. For example, the chemical and physical properties of a chair made of steel are determined by the corresponding properties of the piece(s) of steel that constitutes the chair.

 
44

Lowe (1998, p. 151, n. 12).

 
45

Of course, since in this example y is a proper part of compounds x and z, then the identities of both of the latter compounds also depend on the identities of their other proper parts as well.

 
46

Portions of this paper are based on one delivered to the SUNY Buffalo symposium on The Metaphysics of E. J. Lowe in 2006. I would like to thank Gary Rosenkrantz and E. J. Lowe for their helpful comments.

 

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