Accidents of a Substance: Simple or Complex?

Dr. Novak is invited to tell me which of the following propositions he accepts, which he rejects, and why:

0. I have reservations about an ontology in terms of substances and accidents, but anyone who adopts such an ontology needs to provide a detailed theory of accidents.  This post sketches a theory. It has roots in Aristotle, Brentano, Chisholm, Frank A. Lewis, and others who have written about accidental compounds or accidental unities. 

1. Accidents are particulars, not universals, where particulars, unlike universals, are defined in terms of unrepeatability or uninstantiability.

2. The accidents of a substance are properties of that substance.  Tom's redness, for example, is a property of him.  That there are properties is a datanic claim; that some of them are accidents is a theoretical claim. Accidental properties are those a thing need not have to exist.  I am using 'property' in a fairly noncommittal way.  Roughly, a property is a predicable entity.

3. It follows from (1) and (2) that some properties are particulars. 

4. A substance S and its accident A are both particulars.  S is a concrete particular while A is an abstract particular.  For example, Tom is a concrete particular; his redness is an abstract particular.  It is abstract because there is more to Tom than his being red.

5. Accidents are identity- and existence-dependent upon the substances of which they are the accidents.  An accident cannot be the accident it is, nor can it exist, except 'in' the very substance of which it is an accident.  Accidents are not merely dependent on substances; they are dependent on the very substances of which they are the accidents.  'In' is not to be taken spatially but as expressing ontological dependence.  If the being of substances is esse, the being of accidents is inesse.  These are two different modes of being.

6. It follows from (5) that accidents are non-transferrable both over time and across possible worlds.  For example, Peter's fear cannot migrate to Paul: it cannot somehow leave Peter and take up residence in Paul.  Suppose Peter and Paul are both cold to the same degree.  If coldness is an accident, then each has his own coldness.  The coldnesses are numerically distinct.  They cannot be exchanged in the way jackets can be exchanged.  Suppose Peter and Paul both own exactly similar jackets.  The two men can exchange jackets.  What they cannot do is exchange accidents such as the accident, being jacketed.  Each man has his own jacketedness.

Now for a modal point.  There is no possible world in which Peter's coldness exists but Peter does not.  Peter's coldness does not necessarily exist, but it is necessarily such that, if it does exist, then Peter exists.  And of course the accident cannot exist except by existing 'in' Peter.  So we can say that Peter's coldness is tied necessarily to Peter and to Peter alone: in every possible world in which Peter's coldness exists, Peter exists; and in no possible world does Peter's coldness inhere in anything distinct from Peter.  The same goes for Peter's jacketedness.  Peter's jacket, however, is not necessarily tied to Peter: it can exst without him just as he can exist without it.  Both are substances; both are logically capable of independent existence.

The modal point underins the temporal point.  Accidents cannot migrate over time because they are necessarily tied to the substances of which they are the accidents.

7.  It follows that the superficial linguistic similarity of 'Peter's jacket' and 'Peter's weight' masks a deep ontological difference: the first expression makes reference to two substances while the second makes reference to a substance and its accident.

8 If A is an accident of S, then A is not related to S by any external relation on pain of Bradley's regress.

9 If A is an accident of S, then A is not identical to S.  For if A were identical to S, then A would be an accident of itself.  This cannot be since 'x is an accident of y' is irreflexive.

10.  If A is an accident of S, then A cannot be an improper or proper part of S.  Not an improper part for then A would be identical to S.  Not a proper part of S because accidents depend on substances for their identity and existence.  No proper part of a whole, however, depends for its existence and identity on the whole: it is the other way around: wholes depend for their identity and existence on their parts.

11.  How then are we to understand the tie or connection between S and A?  This is the connection expressed when we say, for example, that Socrates is white.  It is an intimate connection but not as intimate as identity.  We need a tie that is is less intimate than identity but more intimate than a relation. 

We saw in #10 that an accident cannot be a part (ontological consituent) of its substance.  But what is to stop us from theorizing that an accident is a whole one of the proper parts of which is the substance?  This is not as crazy as it sounds.

12.  Let our example be the accidental predication, 'Socrates is seated.'  Start by giving this a reistic translation:  'Socrates is a seated thing.'  Take the referent of 'Socrates' to be the  substance, Socrates.  Take the referent of 'a seated thing' to be the accidental compound Socrates + seatedness.  This compound entity has two primary constituents, Socrates, and the property of being seated.  It has as a secondary constituent the tie designated by '+.'  Now read 'Socrates is a seated thing' as expressing, not the strict identity, but the accidental sameness of the two particulars Socrates and Socrates + seatedness.  Thus the 'is' in our original sentence is construed, not as expressing instantiation, or identity, but as expressing accidental sameness.   Accidental sameness ties the concrete particular Socrates to the abstract particular Socrates + seatedness.

13.  The accidental compound is an extralinguistic particular having four constituents:  a concrete particular, a nexus of exemplification, a universal, and a temporal index.  Thus we can think of it as the thin fact of Socrates' being seated.  'Thin' because not all of Socrates' properties are included in this fact.

14. My suggestion, then, is that accidents are thin facts.  To test this theory we need to see if thin facts have all the features of accidents.  Well, we have seen (#1) that accidents are particulars.  Thin facts are as well.  This is a case of what Armstrong calls the Victory of Particularity: a particular's exemplification of a universal is a particular.

Accidents are properties and so are thin facts: both are ways a substance is. Both are predicable entities. 'Socrates is seated' predicates something of something.  On the present theory it predicates an abstract particular of a concrete particular where the predicative tie is not the tie of instantiation (exemplification) but the tie of accidental sameness.

Accidents are abstract particulars, and so are thin facts.  They are abstract because they do not capture the whole reality or quiddity of the substance. 

Accidents depend on substances for their identity and existence.  The same is true of thin facts.  A fact is a whole of parts and depends for its identity and existence on its parts, including the substance. 

Accidents are non-transferrable.  The same holds for thin facts. 

Accidents are necessarily tied to the substances of which they are accidents.  The same goes for thin facts: the identity of a thin fact depends on its substance constituent.

An accident is not identical to its host substance.  The same is true of thin facts. Socrates' being seated is not identical to Socrates. 

An accident is not externally related to its substance.  The same is obviously truth of thin facts. 

Accidents are not parts of substances.  The same holds for thin facts. 

Finally, no accident has two beginnings of existence.  If Elliot is sober, then drunk, then sober again, his first sobriety is numerically distinct from his second: the first sobriety does not come into existence again when our man sobers up.  The same is true of thin facts.  Elliot's beng sober at t is distinct from Elliot's being sober at t*.

15.  On the above theory, an accident is a complex. It follows that an accident is not a trope, pace Dr. Novak.  Tropes are very strange animals.  A whiteness trope is an abstract particular that is also a property and is also ontologically simple.  An example is the particular redness of Tom the tomato.  I can pick out this trope using 'the redness of Tom and Tom alone' where the 'of' is a subjective genitive.  But note that  the 'of Tom and Tom alone' has no ontological correlate.  The trope, in itself, i.e., apart from our way of referring to it, is simple, not complex.  And yet it is necessarily tied to Tom. This, to my mind, makes no sense, as I explained in earlier posts.  So I reject tropes, and with them the identification of accidents with tropes.

My conclusion, then, is that IF -- a big 'if' -- talk of substances and accidents is ultimately tenable and philosophically fruitful, THEN accidents must be ontologically complex entities.  Anyone who endorses accidents is therefore a constituent ontologist. 

Comments

[David Brightly]

Bill,

Two concerns:

1. Accidents appear to be temporal entities in so far as at least some of them have a beginning and an ending in time. I don't understand how a 'temporal index' can figure in their constitution.

This doesn't materially affect the argument, I think. What concerns me more is:

2. The scheme seems open to a runaway regress. Accidents (property exemplifications) are introduced to account for contingent property-possession in substances. They are particulars. It's therefore plausible that they have properties themselves. Indeed, Peter's coldness appears to have a finite lifetime, to have intensity, to have causal powers, and to be divisible into mereological parts. If accidents do have contingent properties of their own we will need property exemplifications to explain this. And hence an infinite regress looms and the 'grounding' of property possession that we seek is forever beyond us. Furthermore, any metaphysical scheme that introduces a category of particulars to ground property-possession seems vulnerable to this general phenomenon.

[Bill Vallicella]

David,

You cause me great pain!

Suppose the accident, Peter's being sad, is identified with this complex entity: [Peter, exemplification nexus, universal sadness, temporal index]. Or: Peter's exemplifying sadness at 10 AM GMT 1 January 2013. Your point, I take it, is that the accident so identified will last as long as Peter does. But that is not what we want. We want that item to being able to cease to exist while Peter continues to exist. That's your point, right?

But suppose I leave out the temporal index. Suppose Peter goes from sad to happy to sad again. What distinguishes the two sadness accidents if there is no temporal index? I am assuming the Lockean principle that nothing has two beginnings of existence.

You may have blown the above theory to pieces -- not that Novak's theory is any better.

I'll consider your second point later.

[David Brightly]

Please don't let it spoil your Sunday, Bill. I understand the motivation for the temporal index now. However, a continuum of instantaneous property-exemplifications seems extravagant (and we'd need to explain how they were connected together). Could we not simply appeal to Locke and say that there's a class of particulars that exist in time and are indviduated by their lifetimes? But then these are abstract particulars and arguably lie outside time?

[Bill Vallicella]

David,

You can't spoil it, the Super Bowl already did.

I should have pointed out that there are two senses of 'abstract' in use among philosophers. The older sense is the one I was invoking. An accident is an abstract particular in that it is but a partial feature of the substance it belongs to. Abstract in this sense does not imply being outside time and space. In the more recent sense, to be abstract is to be causally inert and outside time and space.

[Bill Vallicella]

David,

Your second objection is troubling too. I wonder what Novak would say about it since it would seem to affect his scheme as well.

Peter is cold. So the Aristotelian says that the accident coldness inheres in the substance, Peter. That's his 'ontological assay' of the mundane Moorean datum. So we have an abstract particular inhering in a concrete particular. Your point is that the abstract particular, the accident, itself has properties and powers. For example, Peter's being cold lasts for an hour and causes him to shiver.

For the Brightly regress to start, the properties had by an accident must be contingently had by it. But on my scheme, all the properties of an accident are essential to it since they are parts of it and thus constitutive of its very identity.

So the coldness accident would have duration, intensity, etc. built into it. For example, Peter cannot be cold without being cold to a certain definite degree and for a definite length of time. A tomato can't be red unless it is a definite shade of red over a defnite portion of its surface.

So what do you think? Is it an adequate response to your second objection to say that the properties of accidents are constituents of them and thus essential to them?

This implies that the properties of accidents are not accidents of them. As I recall, Aristotle says that accidents don't have accidents.

[Bill Vallicella]

As for your first objection, did I see a ghost or is there a real problem for me?

Peter goes from sad to happy to sad. I am committed to saying that there are two sadness accidents since nothing has two beginnings of existence. If both sadness 1 and sadness 2 = Peter's exemplifying of the universal sadness, then there is only one sadness accident. But, unless I am becomning confused, the addition of atemporal index
will result in each accident's lasting as long as Peter does. For if Peter is sad at t, that is true at every time at which Peter exists. 'Peter is sad on Jan 1st, 2013' is true at every time or at least at every time at which Peter exists.

[Lukáš Novák]

Dear Bill,

thanks for the clear statement of yourt theory. Here is the first batch of my responses to your points; more will follow later (hopefully).

Ad 1) I agree.

Ad 2)

i) Perhaps this is a an aside but if property is that which is predicable, then accidents are not properties in my view. Properties are concepts, accidents are real things. What is predicable of Peter is not Peter's whiteness, nor the abstract concept "whiteness", but the concrete concept "white". "Whiteness" is predicated not of Peter but of Peter's whiteness. Peter is white, Peter's whiteness is whiteness. Peter is not whiteness.

ii) I deny that a substance has all accidents contingently. There are non-essential de re necessary properties, which are based on necessarily inhering accidents. For example, every human being de re necessarily has its natural human rights. But these rights are not part of human essence, they are not part of what a man is, but flow from it necessarily.

Ad 3) I concede the consequence but deny the consequent.

Ad 4) I take this as a mere stipulation of what "abstract" and "concrete" means, so nothing to agree or disagree with.

Ad 5) I concede that it is naturally the case, but I doubt it with regard to God's absolute power. Let it pass for the sake of the argument.

Ad 6) Let it pass for the sake of the argument.

Ad 7) I concede the ontological difference but deny a semantic difference. IMHO the genitive contruction is not equivocal but rather general in meaning.

Ad 8) At least in a sense I agree. But I reject altogether the notion of a relation as of something "between" the terms that glues them together. For me a relation is something in one term that makes it directed to the other; either identical to that term or not. In the correlative term there may or may not exist an opposing relation. The relations of a substance to an accident and vice versa are identical to the substance and to the accident. It is a kind of the potency-act relation (more later).

Ad 9) Agreed.

Ad 10) I agree that A is in no sense a part of S, but I most emphatically deny the principle that no proper part of a whole depends for existence and identity on that whole. I concede it for "improper" or accidental wholes, i.e. aggregates of beings (forests, peoples, or accidental composites like wise Socrates), but not for essential wholes, i.e. individuals in the metaphysical sense. Here parts depend in their existence and identity on their wholes. This is part of the very notion of what an individual being (as opposed to an aggregate of beings) is.

Ad 11) I take the connexion between S and A to be that of a receptive potency and its corresponding act. S contains an intrinsic relation of "informability" to all its possible accidents, and A contains an intrinsic relation of informing toward S. Together these two constitute an accidental whole of which they are not just parts but complementary intrinsic causes: S is its material cause and A its formal cause. They are unified in jointly intrisically co-causing the one accidental composite.

[Lukáš Novák]

Dear Bill,

my general reply to the rest of your points is that I reject them because I have my own theory. Some of the problems I have with yours are the following:

I. Your theory of predication seems to me unacceptable for several reasons I may expand on later, if you will. In the first place, it seems to me impossible to ground a semantic distinction of various kinds of predication in the distinction between accidental and essential properties. For whereas we always know what we intend when we are predicating, we often do not know whether what we predicate is a necessary or a contingent property. E. g. we do not know whether "human" is not accidental for Socrates unless we know whether essentialism is true. But the question whether "Socrates is seated" has the same semantics as "Socrates is human" must be decidable independently from the question whether the true metaphysical theory is essentialism or antiessentialism, i.e. whether Socrates could or could not fail to be human. Otherwise you could just read metaphysical solutions off your predication patterns.

II. Is your "nexus of exemplification" [NE] an entity or not? If not, it cannot make a difference and/or explain anything. If yes, is it a particular or not? If not, it is a universal, and my argument applies: another entity is needed to explain the difference of [Socrates as connected by the ever-existing NE to ever-existing seatedness] from [Socrates merely coexisting with seatedness and the NE]. So a regress is launched. If the NE is a particular, then -- good news -- you can get rid of your temporal indexes, since your two sadnesses are distinguished by means of their distinct particular NE's. However -- bad news -- such a NE is just a different name for my property-instance, IMHO -- viz. the particular manifestation of a universal's being exemplified by a certain subject.

(More later)

[Lukáš Novák]

Concerning David Brightly's second objection:

I think that accidents can have, in a sense, contingent properties. But no infinite regress is looming, since noone says that all accidents have them.

I say "in a sense" because the accident is not the ultimate subject of "its accidents" and therefore they are not "its" accidents, precisely speaking. For example, active powers (like the will) are, generally speaking, accidents of their bearers (though necessary ones); and they can be further perfected with dispositions (like virtues), and with their proper operations; so that we can say that the will is virtuous or willing, but more properly it is the man who is virtuous and willing by means of his will.

BTW, yesterday I posted two comments to Bill's numbered theses, but they did not appear as yet. Have they been too long again?

[David Brightly]

Bill,

On the first objection, I fear I do not understand what you must mean by 'adding a temporal index' to an ontological complex. My interpretation is that this converts the complex from one that endures in time to one that exists for an instant. But this does not seem to fit with your usage. Could you elaborate?

On the second, the counter is to say that property exemplifications possess their properties necessarily, not contingently, and so further property exemplifications are obviated. My suspicion is that by 'property' we are perhaps equivocating between what we might call 'property-dimension' and 'property-value'. An ordinary material particular necessarily has the property-dimension colour but only contingently has the property-value red on this dimension. Likewise it necessarily has the dimension mass but only contingently a specific mass in kilograms. To say that one of our property exemplification entities necessarily has a beginning time of 10am today seems quite wrong. But it makes perfect sense to say that it is in the nature of such an entity to have a beginning time. I think this second objection stands.

[Bill Vallicella]

David,

I think what you are calling a property-dimension is what philosophers call a determinable and what you call a property-value is what philosophers call a determinate. Agreed, a material particular is necessarily colored but only contingently red.

Suppose some water is boiling hot, and that hotness is an accident of the water. You seem to want to say that the accident exemplifies contingently the property of being boiling hot. But I say that the property of being boiling hot is a constituent of the accident and therefore esential to it. I don't see that I equivocating or making a mistake. Not that I have explained myself very clearly!

I am saying that the substance has the accident contingently, but that the properties of the accident are all included wothin it and are therefore essential to it.

Suppose Tom is clinically depressed. The accident is *clinically depressed* The accident is not *depressed* which has externally and contingently the property of depressed to the clinical degree.

[Bill Vallicella]

Lukas,

Thanks for the excellent commentary. I hope to respond to some of it later. There are many difficult topics here. We might have to back up to a discussion of what we respectively understand by predication before we can talk about accidental predication and accidents.

For example, when I say, of Tom, that he is red, what is being predicated: the word 'red', a mental item such as a concept, or an entity that exists extralinguistically and extramentally?

And whatever that is, what is it being predicated of?

And if the sentence or proposition is true, is there something that makes it true? What?

And what is the nature of the predicative tie? Is it a type of sameness or identity? Instantiation?

[Lukáš Novák]

Dear Bill,

it seems to me, too, that the nature of predication is the crux: not just of this issue but in philosophy in general.

I take predication to be intentional or mental identification of a mental content (expressed by the predicate) with a (usually) particular item or items (referred to by means of the subject). More precisely, by saying that Tom is red you are recognizing Tom as being a particular that is, possibly among other things, representable through the cognitive content expressed by "red", i.e. as a particular in which the cognitive content of "red" is realized as something identical to it. Or yet in other words, you identify Tom as one of the particulars of which a mode of presentation is "something red".

(Note: what is identified with Tom is the conceptual content of "red". Therefore, not "redness", but "that which has redness". Also, not a mental item in the sense of an act of thought or something psychological, but its objective content, what by the Scholastics is called "objective concept" and is nothing else than a piece of reality qua grasped or represented in a certain way.)

A judgement like this is true precisely in case there is adequacy of thought and reality. That is, adequacy of the way the reality referred to by the subject is and the way it is represented by the predicate. So the "truthmaker" is the referent of the subject-term as it really is, and the "truth-bearer" is the entire judgement. Note that this is not the "Cambridge correspondence" between a truth-bearer and a thruth-maker. The correspondence, or adequacy, is between the referent of the subject and the sense of the predicate. It is similar to Austin's theory of truth, with one great difference, viz. that according to Austin one applies types of facts to particular facts, whereas I would say that we apply types of things (universals) to things (particulars).

I would like to argue that this elementary notion of predication, i.e. a mental identification of "thing-as-is-grasped" with "thing-as-really-is" is presupposed by any other notion of predication. Since truth is adequacy of thought and reality, any pretender to a truth-bearer must intrinsically raise a claim to such adequacy, which is nothing else than to claim that certain bit of cognitive content adequately represents certain bit of reality. Unless one raises such a claim to adequate grasp of reality, one can never be true (nor false). The "Cambridge correspondence" theory fails on this point, since it takes truth-bearers as corresponding extrinsically to truth-makers, but there is nothing in the truth-bearer to claim the correspondence. So they don't differ in that from simple concepts which also "correspond" to their objects but are not for that said to be true or false. Austin attempted to mend that, but he should have worked on the level of things, not facts.

[David Brightly]

Thank you, Bill, for introducing me to the determinable/determinate distinction. On reflection, my apologies, you are not equivocating. Let me withdraw my last comment. I was struggling to see the source of the necessary/contingent distinction you were making.

My suggestion is that the intensity of Peter's coldness is a property of the exemplification of coldness in Peter. That still seems reasonable to me. You suggest that the intensity be absorbed into the universal, so we have boiling-hotness and freezing-coldness as exemplifiable universals. This would seem to give rise to a continuum-many distinct temperature universals, but let's accept this for the sake of argument. The exemplification entity still appears to have contingent start-time and end-time properties, and a set of contingent causal effects. Will you say that these too are essential properties of the exemplification entity? If so, wherein lies its contingency?

[Bill Vallicella]

Lukas,

So predicates express objective concepts? Are objective concepts common natures?

David,

No need to apologize. I could easily fall into an equuivocation.

Peter is cold. It is not the case that Peter's being cold is cold.

Suppose Peter walks into a freezer at 12 noon and walks out at 1 PM. Peter starts being cold and then stops being cold. The accident *being cold* begins to exist, persists for an hour, and ceases to exist. But I don't see how that would give rise to a regress. Existence and nonexistence are not built into the nature of an accident.

Peter is contingently cold. Peter is a substance that contingently has the the accident *being cold.*

[David Brightly]

Bill,

Let me press you on this. I think a regress begins if property exemplification (PE) entities have contingent properties. In the case of Peter's coldness I suggested that the intensity freezing, the inception time 12 noon, and the effect Peter's shivering were all candidate contingent properties of this PE entity. At a cost, we have disposed of the intensity property by absorbing it into a universal, so that our PE entity becomes Peter's freezing-coldness. To escape the regress it seems we have to say either that the remaining putative properties are not contingent, or that they aren't in fact properties. I'm not clear which of these options you are taking or whether you have another way of avoiding the conclusion.

[Bill Vallicella]

David,

If Peter is cold, he is cold to some definite degree. So I don't think it is right to say that Peter has the accident *coldness* and that this accident has an intensity property. Peter and Paul can be cold to different degrees. We can abstract from the difference and say that both are cold. But in reality there is no accident *coldness in general.*

Similarly with *shivering.* This is a second accident. Peter is shivering because he is cold. Why do we have to say that the first accident has the property of causing the second?

[David Brightly]

Why do we have to say that the first accident has the property of causing the second?

Do we agree that Peter's coldness causes Peter's shivering? In general, given a dyadic relation R we can form a monadic relation Q by defining Qx <---> xRb for some fixed b. Let R be the cause relation and b be Peter's shivering. Then Q is the monadic relation causes Peter's shivering, and if monadic relations are properties the result follows.

[Lukáš Novák]

Bill,

yes, predicates express objective concepts; and common natures in intentional being are objective concepts. But in a strict sense only essential "in quid" objective concepts, i.e. species, genera, and transcendentals, are said to be common natures in intentional being. Common natures are (parts of) essences, but not all things have (their own) essences and not all concepts express the essence of their object. A concrete accidental concept (or "connotative concept") like "red" expresses nothing of the essence of its object, but relates to it by expressing something of the essence of its accident taken qua inhering in it. But for the general theory of predication these distinctions can be left aside, meseems, since often we do not know whether what is expressed in the concept is something essential or accidental for their objects, and to draw this distinction is a matter of metaphysics not formal semantics.

Also, having thought about it it seems to me that my argument does not hinge on any specific theory of predication; suffice to assume that in predication universals are somehow applied to particulars and that truth/falsity consists in this application being adequate or inadequate, whatever the precise meaning of that be.

[Lukáš Novák]

Bill,

what follows is what I consider the most important objection against your theory.

It seems to me that in order to keep the basic meaning of "universal" and "particular" the following definitions must be assumed:

1. A universal is that which is (truly) predicable of many particular instances.
2. X is an instance of a given universal U iff U is predicated of X.
3. U1 is subordinate to U2 iff all instances of U1 are instances of U2. This is expressed in language in the form "Every U1 is an U2" - for example, "Every man is an animal".
4. Every universal has at least some possible instances, unless it is intrinsically inconsistent.

Now whiteness and color are universals. By common sense, color is superordinate to whiteness. So, every whiteness is a color. Peter's whiteness, on the other hand, is a particular. We must assume that Peter's whiteness is an instance of whiteness, and also of color - since whiteness and color are not intrinsically inconsistent and there are no more plausible candidates to their instances than Peter's whiteness, Bob's blackness etc.

But here comes the problem. If Peter's whiteness contains whiteness, then Peter's color contains color as its constituent. You may perhaps say that Peter's whiteness also contains color because whiteness contains color, but certainly color does not contain whiteness in that case (else they would coincide), and therefore Peter's color does not contain whiteness. Consequently, Peter's color is not an instance of whiteness. But this contradicts the fact that Peter's color just is Peter's whiteness, because Peter's whiteness is a color (by def. 3, assuming that whiteness is subordinate to color), and there is no other color in Peter than his whiteness (let us so stipulate).

Put very simply: if Peter's whiteness is just Peter+whiteness+NE+time, then Peter's color is just Peter+color+NE+time, but then Peter's whiteness is not Peter's color. But this is wrong since whiteness is subordinate to color and so any instance of whiteness must be identical to an instance of color.