Wholes and Parts – Maverick Philosopher

The Hatfields and the McCoys: A Challenge to Reists and Extreme Nominalists

Top of the Substack pile.

Colin McGinn on Paradoxical Paradoxes

The indented material is from Colin McGinn's blog. My responses are flush left and in blue.

Paradoxes exist.

True.

Paradoxes belong either to the world or to our thought about the world.

True, if 'or' expresses exclusive disjunction.

They cannot belong to the world, because reality cannot be intrinsically paradoxical.

True. And so one ought to conclude that paradoxes reside in our thought about the world.

They cannot belong to our thought about the world, because then we would be able to alter our thought to avoid them (they cannot be intrinsic features of thought).

But surely we can alter our thought to avoid the paradoxes that reside in our thought about the world but not in the world.

Therefore, paradoxes don’t exist.

Non sequitur.

Therefore, paradoxes both exist and don’t exist.

Non sequitur. Although paradoxes do not exist in the world, in reality, they do exist in our thinking about the world, thinking that can be altered so as to avoid paradoxicality.

This is the paradox of paradoxes.

There is no such a paradox. It seems to me that McGinn is equivocating on 'paradox.' His first three assertions are all true if 'paradox' means logical contradiction. But for the fourth assertion to be true, McGinn cannot mean by 'paradox' logical contradiction.

The Paradox of the Smashed Vase will help me make my point.

Suppose you inadvertently knock over a priceless vase, smashing it to pieces. You say to the owner, "There's no real harm done; after all it's all still there." And then you support this outrageous claim by arguing:

1) There is nothing to the vase over and above the ceramic material that constitutes it.

2) When the vase is smashed, all the ceramic material that constitutes it remains in existence.

Therefore

3) The vase remains in existence after it is smashed.

"I don't owe you a penny!" (Adapted from Nicholas Rescher, Aporetics, U. of Pittsburgh Press, 2009, p. 91.)

This paradox arises from faulty thinking easily corrected. The mistake is to think that an artifact such as a vase is strictly and numerically identical to the matter that composes it. Not so: the arrangement or form of the matter must also be taken into consideration. This response is structurally the same as the much more detailed response I make to Peter van Inwagen's denial of the existence of artifacts.

Referring to Two Things

Ed writes,

Does ‘these two things’ refer to two things, or not? (Suppose the things are shoes.)

Perhaps not. For there are the two things, but also the plurality of them. The plurality is one thing, identical with neither the first thing, nor the second.

So the phrase ‘these two things’ actually refers to three things? Makes no sense to me.

BV: Perhaps it makes no sense to you because you think that 'thing' can only mean 'material thing.' We agree that 'these two shoes' refers to exactly two shoes, each of which is a material thing, and that there is no third material thing of which they are members. So if that is what our nominalist means when he denies that the two shoes form a plurality, then we agree.

Here is a slightly more complicated example. You have a bolt B and a nut N that fits the bolt, i.e., N can be screwed onto B. Now there is clearly a difference between B, N unconnected and B, N connected. But even here I will grant that there is no third material thing wholly distinct from B and wholly distinct from N when B, N are connected. There is no third material thing 'over and above' the connected bolt and nut. Here is exactly what you have and no material third thing in addition:

Disagreement may begin to set in when I point out that the weight of the object depicted above is strictly greater that the weights of the bolt and the nut taken separately. The total weight is additive such that if the nut weighs 2 ounces and the bolt 16 ounces, then the weight of the object depicted is equal to 2 + 16 = 18 ounces. The predicate '___weighs 18 ounces' is not true of the nut, and it is not true of the bolt, and it is not true of any material third thing 'over and above' the object depicted, and this for the simple reason that there is no such third material thing.

So what is the predicate '___ weighs 18 ounces' true of? I say that it is true of the plurality the sole members of which are N and B. I am not further specifying the nature of this plurality. Thus I am not saying that it is a mathematical set, nor am I saying that it is a mereological sum. I am saying that there is a distinction to be made between a plurality of items and the items.

Note that if our nominalist were to say that a plurality is exhausted by, or reduces to, its members, then will have given up the game by his use of 'its.' So he has to somehow avoid that locution.

Our nominalist will grant that the predicate '___weighs 18 ounces' is not true of the nut, not true of the bolt, and not true of any third material thing wholly distinct from the bolt and the nut. But he might say that it is not true of anything. The predicate is flatus vocis, a mere word, phrase or sound to which nothing extramental and extralinguistic corresponds. I reject this view. It implies that the nut threaded onto the bolt has in objective reality no weight that is the sum of the objective weights of the nut and bolt taken separately.

Our nominalist seems committed to an intolerable linguistic idealism. Suppose all language users were to cease to exist. It would remain that case that the weight of our nut-bolt combo would equal 18 ounces. It would remain the case that Earth is spheroid in shape and has exactly one natural satellite.

But why is he a nominalist in the first place? Is it because he thinks that only material particulars exist? If that is true then of course there cannot be a plurality of two material particulars. Hilary Putnam: "Nominalists must at heart be materialists . . . otherwise their scruples are unintelligible." (Phil Papers, vol. I, 338)

Is he a nominalist because he is an empiricist who thinks that only sensible particulars exist? I see the nut, I see the bolt, I see the nut threaded onto the bolt; but I don't see any plurality of material particulars. Is our man restricting what exists to that which is empirically detectable via our senses and their instrumental extensions (e.g., microscopes, telescopes, etc.)?

Is he both a materialist and an empiricist? How do those two positions cohere?

Pluralities

To what does the plural referring expression, 'the cats in my house,' refer? Not to plurality, but to a plurality. A plurality is one item, not many items. It is one item with many members. 'The guitars in my house' refers to a numerically different plurality. It too refers to one item with many members. It follows that a plurality cannot be identical to its members. For if it were there would be no 'it.'

I am not saying that a plurality is a mathematical set. I am saying that a plurality is not just its members. I am rejecting Composition as Identity. If the Londonistas do not agree with the Phoenician on this one, then I fear that there is little point to further discussion. We are at the non-negotiable. We are at bedrock and "my spade is turned."

On Sets: A Response to Brightly

David Brightly in a comment far below writes:

Bill says, at 03:21 PM.

…a family cannot be reduced to a number of persons; it is not a mere manifold, or a mere many…

The same is true for a pair (of shoes) and other collective terms. They all imply relations of some sort between their members. But this is not so for a mathematical set. No such relations are implied. A set is a pure manifold. Bill also says, at 03:42 PM,

…it also makes no sense to say that an abstract object — which is what math sets are — has Gomer surrounded.

I dispute this: mathematical abstract objects have relations between their parts and sets qua sets do not, so sets cannot be abstract objects. These are the chief reasons for thinking that sets are pure plural referring terms. Artificial, structured, linguistic extensions engineered by us for clarity of mathematical thought and expression.

Respondeo

I am afraid I find most of the above unacceptable. First of all a pair of shoes is not a term, collective or singular. Terms are linguistic items; shoes are not. It is true, though, that mathematical sets abstract from any relation their members bear to one another. But this is not something I denied.

It is also not the case that "a set is a pure manifold." That cannot be right because a set can have sets as elements (members). The Power Set axiom of axiomatic set theory states that for any set S, there exists a set P such that X is an element of P if and only if X is a subset of S. Thus the power set P of a set S is the set of all of S's subsets. So the power set of {1,2} = {{1}, {2}, {1,2}, { }}.

The subsets of S are elements of the power set which fact shows that sets are distinct from their members and are therefore not pure manifolds. Sets are distinct from their members in that they count as objects in their own right. So if there is a set of Ed's dancing shoes, then this set is distinct from the left shoe, the right shoe, and the two taken collectively. This is one of the ways a set differs from a mereological sum/fusion. The sum of Ed's shoes is just those shoes, not an object distinct from them.

Mereology is "ontologically innocent" as David Lewis puts it, whereas set theory is not:

Mereology is innocent . . . we have many things, we do mention one thing that is the many taken together, but this one thing is nothing different from the many. Set theory is not innocent. . . . when we have one thing, then somehow we have another wholly distinct thing, the singleton. And another, and another . . . ad infinitum. (Parts of Classes, Basil Blackwell 1991, p. 87)

Brightly argues: "mathematical abstract objects have relations between their parts and sets qua sets do not, so sets cannot be abstract objects." This makes no sense to me since the mereological notion of parthood does not belong in standard axiomatic set theory. It is at best analogous to the elementhood and subset relations which are essential to set theory. The sum/fusion of Max and Manny has them and their cat-parts as parts. The set {Max, Manny} does not have as elements their whiskers, claws, tails, etc.

If there are sets, they are abstract objects, which is to say that they do not exist in space or time. I can trip over my cat, but I can't trip over my cat's singleton. Where in space is the null set? When did it come to be? How long will it last? Is it earlier or later than the null set's singleton? Is the nondenumerably infinite set of real numbers somewhere in spacetime? These questions involve category mistakes.

I said that if the Hatfields have Gomer surrounded, that cannot be taken to mean that the set having all and only the members of the Hatfield clan as its members has poor Gomer surrounded. What I said is obviously true.

So I conjecture that David is using 'abstract' in some idiosyncratic way. I await his clarification.

The Hatfields and the McCoys

Whether or not it is true, the following has a clear sense:

1. The Hatfields outnumber the McCoys.

(1) says that the number of Hatfields is strictly greater than the number of McCoys. It obviously does not say, of each Hatfield, that he outnumbers some McCoy. If Gomer is a Hatfield and Goober a McCoy, it is nonsense to say of Gomer that he outnumbers Goober. The Hatfields 'collectively' outnumber the McCoys.

It therefore seems that there must be something in addition to the individual Hatfields (Gomer, Jethro, Jed, et al.) and something in addition to the individual McCoys (Goober, Phineas, Prudence, et al.) that serve as logical subjects of number predicates. In

2. The Hatfields are 100 strong

it cannot be any individual Hatfield that is 100 strong. This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate '100 strong.'

So here is a challenge to Ed Buckner the nominalist. Provide truth-preserving analyses of (1) and (2) that make it unnecessary to posit a collective entity (whether set, mereological sum, or whatever) in addition to individual Hatfields and McCoys.

Nominalists and realists alike agree that one must not "multiply entities beyond necessity." Entia non sunt multiplicanda praeter necessitatem! The question, of course, hinges on what's necessary for explanatory purposes. So the challenge for Buckner the nominalist is to provide analyses of (1) and (2) that capture the sense and preserve the truth of the analysanda and yet obviate the felt need to posit entities in addition to concrete particulars.

Now if such analyses could be provided, it would not follow that there are no 'collective entities.' But a reason for positing them would have been removed.

Are You Clumsy? The Paradox of the Smashed Vase

I'm not, but you might be.

Suppose you inadvertently knock over a priceless vase, smashing it to pieces. You say to the owner, "There's no real harm done; after all it's all still there." And then you argue:

1) There is nothing to the vase over and above the ceramic material that constitutes it.

2) When the vase is smashed, all the ceramic material that constitutes it remains in existence.

Therefore

3) The vase remains in existence after it is smashed.

"I don't owe you a penny!"

Adapted from Nicholas Rescher, Aporetics, U. of Pittsburgh Press, 2009, p. 91.

The above may serve as an introduction to the problem of the composition of material artifacts and to Peter van Inwagen's strange thesis that such items do not exist. See Van Inwagen's Denial of Artifacts.

Divine Simplicity and Divine Comprehensibility

From a reader, who is responding to God as Uniquely Unique:

An objection I recently heard to the doctrine of divine simplicity (DDS) that is novel as far as I can tell. Goes like this: if DDS is true, God is unlike anything in our human experience, not having parts. We cannot comprehend God on DDS because he has no parts to comprehend apart from the whole; we can't comprehend the whole of God, and he doesn't have parts to comprehend, so we can't comprehend him at all. This is unacceptable at least on the Abrahamic faiths, which state we can comprehend some things about God, just not fully. Thoughts?

Here is the argument as I understand it:

1) If DDS is true, then God has no parts.

2) If God has no parts, then we cannot understand any part of God.

Therefore

3) If DDS is true, then we cannot understand any part of God.(1, 2)

4) We cannot understand the whole of God.

5) We cannot understand God at all unless we can either understand some part of God, or the whole of God.

Therefore

6) If DDS is true, then we cannot understand God at all. (3, 4, 5)

7) On the Abrahamic faiths, we can understand something about God.

Therefore

8) DDS is inconsistent with the Abrahamic faiths.

I would say that the argument fails at line (5). We can understand something about God without understanding God himself in whole or in part. If we understand God to be the creator of the universe, then we understand something about God without understanding the whole of God or any part of God. We understand God from his effects as that which satisfies the definite description 'the unique x such that x created the world and sustains it in existence.' We can presumably understand this much about God without knowing him in propria persona or any of his parts. The question whether God is simple would seem to be irrelevant to question whether we can know anything about him.

Mundane analogy: I can know something about the burglar from the size and shape of the footprints he left without knowing him or his parts.

Some Questions About Divine Simplicity

This recently over the transom:

Dear Dr. Vallicella, I'm a reader of your blog, and have really enjoyed much of your work. Since you wrote the Stanford Encyclopedia article on the topic of divine simplicity, I thought I might reach out to you to ask your opinions on some things. I am on an e-mail list with a Christian philosopher who is extremely critical toward the idea and I'd like to know what you think of the following:

First, he argues that, while there are some rationally acceptable arguments for divine simplicity, they do not rise to the level of demonstration. Based on some of your recent work, I gather you might agree with this.

BV: I do agree. The doctrine cannot be demonstrated or proven. There are 'good' (rationally acceptable) arguments for the doctrine of divine simplicity (DDS), but they are not rationally compelling. To my mind this is but a special case of a general thesis: few if any substantive theses in philosophy are demonstrable or provable.

It's the second part I'm curious about. Further to his argument is that divine simplicity rests on questionable metaphysical premises, and that many are far too confident in the position given their familiarity with metaphysics. He is exceptionally critical of James Dolezal, saying that consulting him on the topic "is like going to a bike shop to get your car repaired." He believes that, for one to really understand and engage with the ideas, academic training and great philosophical experience is required (which Dolezal may not possess, not having earned his Ph.D. under recognized philosophers). Since you cite Dolezal multiple times in your article, I assume you would disagree with this at least on some level. While I only have undergraduate philosophical training, I am familiar with the debates on the subject, and the metaphysics involved, to have at least some rational justification for my opinions. (The big exception is questions of simplicity and modal logic—I back off when things go into that territory). So, my actual questions: what level of philosophical training (especially official) is necessary to engage in these debates? And is his evaluation of Dolezal in particular correct?

BV: Dolezal is competent, and your friend's 'bike shop' comment does nothing to show otherwise. You don't really need any 'training' other than what you can provide for yourself by careful study of the literature on the topic, assuming you are above average in intelligence and have a strong desire to penetrate the problem. I don't set much store by training and trappings and academic pedigrees. What matters in philosophy is love of truth, intense devotion to her service, intellectual honesty, and the willingness to follow the arguments whither they lead.

Second, he has a criticism of simplicity I haven't seen anywhere else. I'll have to summarize it as the paper has not been published.

It goes like this: a key premise in the argument for simplicity is that whatever has parts depends on those parts, and so must be composed by something else. God is not dependent/composed by anything else, therefore he must be simple. He questions this idea and puts forward an "individuals first" account, suggesting that parts are in some cases only definable by the wholes of which they are parts, thus actually making the parts dependent on the whole. He provides two possible examples: the notions of necessity and possibility, which are dependent on each other for their definitions; and the doctrine of the Trinity, where Father, Son, and Spirit are exclusively defined in terms of relations among them. This suggests, he argues, that we can conceive of wholes that have parts, the parts all being mutually dependent upon one another and thus not composed by anything else. And so, God might have parts while not being composed by anything else.

What are your thoughts on this idea?

BV: One kind of whole can be called compositely complex, while another can be called incompositely complex. A wall of stacked stones is a complex of the first sort: its parts (the stones) can exist without the whole (the wall) existing, and each stone can exist apart from any other. The parts can exist without the whole, but the whole cannot exist without the parts. Such a whole needs an ontological factor, a 'composer' to ground its unity and to distinguish it from a sheer plurality. The wall is not a sheer manifold, a mere mereological sum of stones, but a unitary entity. It is one entity with many parts. God cannot be complex in this way. For then he would depend for his existence and nature on the logically/ontologically prior existence of his parts including his attributes (omniscience, omnipotence, etc.) if these are assayed as 'parts' or ontological constituents of God.

Now your friend's suggestion seems to be that God is an incompositely complex whole of parts. God has parts, but these parts cannot exist apart from the whole of which they are the parts, and no part can exist apart from any other part. The parts are then mutually dependent and inseparable.

I don't think this works. Consider the 'composition' of essence and existence in a contingent being such as Socrates. The 'parts' — in an extended sense of the term — are mutually inseparable. The existence of Socrates cannot itself exist apart from his essence and the essence of Socrates cannot exist apart from his existence. And neither can exist apart from Socrates, the composite of the two. But Socrates is a creature and God transcends all creatures. His absolute transcendence cannot be accommodated by any scheme that allows God to be in any sense partite, not even if the parts are mutually inseparable. God's absolute transcendence requires that he be absolutely simple. God belongs at the fourth level in the following schema:

Level I. Pure manyness or sheer plurality without any real (as opposed to mentally supplied) principle of unity. Mereological sums. The sum just is its members.

Level II. Composite complexity. A whole of parts the unity of which is contingent, as in the case of the stacked stones. There is one wall composed of many parts, but the parts can exist without the whole. The whole, however, cannot exist without the parts.

Level III. Incomposite Complexity. Wholes the parts of which are mutually inseparable, whether weakly inseparable or strongly inseparable. Suppose a particular cannot exist without having some properties or other, but needn't have the very properties it in fact has, and (first-order) properties cannot exist without being had by some particulars or other, but not necessarily the particulars that in fact have them. We then say that particulars and properties are WEAKLY mutually inseparable. If, however, particulars cannot exist without having the very properties they have, and these properties cannot exist without being instantiated by the very particulars that instantiate them, then particulars and properties are STRONGLY mutually inseparable.

Level IV. Absolute Simplicity. The absolutely simple transcends the distinction between whole and parts. Whereas in Socrates there is a real distinction between essence and existence despite their strong mutual inseparability, in God there is not even this distinction.

In sum, God's absolute transcendence requires absolute simplicity. Your friend's suggestion as you have reported it is stuck at Level III and does not reach Level IV.

Were You a Part of Your Mother?

Here

Elselijn Kingma

Mind, Volume 128, Issue 511, July 2019, 609–646.

Abstract

Is the mammalian embryo/fetus a part of the organism that gestates it? According to the containment view, the fetus is not a part of, but merely contained within or surrounded by, the gestating organism. According to the parthood view, the fetus is a part of the gestating organism. This paper proceeds in two stages. First, I argue that the containment view is the received view; that it is generally assumed without good reason; and that it needs substantial support if it is to be taken seriously. Second, I argue that the parthood view derives considerable support from a range of biological and physiological considerations. I tentatively conclude in favour of the parthood view, and end by identifying some of the interesting questions it raises.

I don't have time now to study the above, but I will have to eventually, and then maybe write an evaluation.

Related: The Woman's Body Argument

Did the Universe Have a Beginning in Time?

Some of you may remember the commenter 'spur' from the old Powerblogs incarnation of this weblog. His comments were the best of any I received in over ten years of blogging. I think it is now safe to 'out' him as Stephen Puryear of North Carolina State University. He recently sent me a copy of his Finitism and the Beginning of the Universe (Australasian Journal of Philosophy, 2014, vol. 92, no. 4, 619-629). He asked me to share the link with my readers, and I do so with pleasure. In this entry I will present the gist of Puryear's paper as I understand it. It is a difficult paper due to the extreme difficulty of the subject matter, but also due to the difficulty of commanding a clear view of the contours of Puryear's dialectic. He can tell me whether I have grasped the article's main thrust. Comments enabled.

The argument under his logical microscope is the following:

1. If the universe did not have a beginning, then the past would consist in an inﬁnite temporal sequence of events.
2. An inﬁnite temporal sequence of past events would be actually and not merely potentially inﬁnite.
3. It is impossible for a sequence formed by successive addition to be actually inﬁnite.
4. The temporal sequence of past events was formed by successive addition.
5. Therefore, the universe had a beginning.

Premise (3) is open to a seemingly powerful objection. Puryear seems to hold (p. 621) that (3) is equivalent to the claim that it is impossible to run through an actually infinite sequence in step-wise fashion. That is, (3) is equivalent to the claim that it is impossible to 'traverse' an actual infinite. But this happens all the time when anything moves from one point to another. Or so the objection goes. Between any two points there are continuum-many points. So when my hand reaches for the coffee cup, my hand traverses an actual infinity of points. But if my hand can traverse an actual infinity, then what is to stop a beginningless universe from having run through an actual infinity of events to be in its present state? Of course, an actual infinity of spatial points is not the same as an actual infinity of temporal moments or events at moments; but in both the spatial and the temporal case there is an actual infinity of items. If one can be traversed, so can the other.

The above argument, then, requires for its soundness the truth of (3). But (3) is equivalent to

3*. It is impossible to traverse an actual infinite.

(3*), however, is open to the objection that motion involves such traversal. Pace Zeno, motion is actual and therefore possible. It therefore appears that the argument fails at (3). To uphold (3) and its equivalent (3*) we need to find a way to defang the objection from the actuality of motion (translation). Can we accommodate continuous motion without commitment to actual infinities? Motion is presumably continuous, not discrete. (I am not sure, but I think that the claim that space and time are continuous is equivalent to the claim there are no space atoms and no time atoms.) Can we have continuity without actual infinities of points and moments?

Some say yes. William Lane Craig is one. The trick is to think of a continuous whole, whether of points or of moments, as logically/ontologically prior to its parts, as opposed to composed of its parts and thus logically/ontologically posterior to them. Puryear takes this to entail that a temporal interval or duration is a whole that we divide into parts, a whole whose partition depends on our conceptual activities. (This entailment is plausible, but not perfectly evident to me.) If so, then the infinity of parts in a continuous whole can only be a potential infinity. Thus a line segment is infinitely divisible but not infinitely divided. It is actually divided only when we divide it, and the number of actual divisions will always be finite. But one can always add another 'cut.' In this sense the number of cuts is potentially infinite. Similarly for a temporal duration. In this way we get continuity without actual infinity.

If this is right, then motion needn't involve the traversal of an actual infinity of points, and the above objection brought against (3) fails. The possibility of traversal of an actual infinite cannot be shown by motion since motion, though continuous, does not involve motion through an actual infinity of points for the reason that there is no actual infinity of points: the infinity is potential merely.

We now come to Puryear's thesis. In a nutshell, his thesis is that Craig's defence of premise (3) undermines the overall argument. How? To turn aside the objection to (3), it is necessary to view spatial and temporal wholes, not as composed of their parts, but as (logically, not temporally) prior to their parts, with the parts introduced by our conceptual activities. But then the same should hold for the entire history of the universe up to the present moment. For if the interval during which my hand is in motion from the keyboard to the coffee cup is a whole whose parts are due to our divisive activities, then the same goes for the metrically infinite interval that culminates in the present moment. This entails that the divisions within the history of the universe up to the present are potentially infinite only.

But then how can (1) or (2) or (4) be true? Consider (2). It states that an infinite temporal sequence of past events would be actually and not merely potentially infinite. Think of an event as a total state of the universe at a time. Now if temporal divisions are introduced by us into logically prior temporal wholes such that the number of these actual divisions can only be finite, then the same will be true of events: we carve the history of the universe into events. Since the number of carvings, though potentially infinite is always only actually finite, it follows that (2) is false.

The defense of (3) undercuts (2).

So that's the gist of it, as best as I can make out. I have no objection, but then the subject matter is very difficult and I am not sure I understand all the ins and outs.

Mereology and Trinity: Response to Wong

Kevin Wong offers some astute criticisms:

You wrote: "For one thing, wholes depend on their parts for their existence, and not vice versa. (Unless you thought of parts as abstractions from the whole, which the Persons could not be.) Parts are ontologically prior to the wholes of which they are the parts.This holds even in the cases in which the whole is a necessary being and each part is as well." Chad M. seems to be following William Lane Craig. Craig's partner-in-crime is J. P. Moreland, who argues that with substances, the whole is metaphysically prior to its parts. For example, a heart has its identity only because it is a constituent of the human person. Removed from a human person, it ceases to be a heart.

If a concrete particular such as book counts as an Aristotelian primary substance, and it does, then I should think that the book as a whole is not metaphysically/ontologically prior to its (proper) parts. In cases like this the whole depends for its existence on the prior existence of the parts. First (both temporally and logically) you have the pages, glue, covers, etc., and then (both temporally and logically) you have the book. If, per impossibile, there were a book that always existed, it would still be dependent for its existence on the existence of its proper parts logically, though not temporally. So it is not true in general that "with substances, the whole is metaphysically prior to the parts."

But a book is an artifact whereas Kevin brings up the case of living primary substances such as living animals. The heart of a living animal is a proper part of it. Now does it depend for its existence on the whole animal of which it is a proper part? Is it true, as Kevin says, that the heart is identity-dependent on the animal whose heart it is?

I don't think so. Otherwise, there couldn't be heart transplants. Suppose Tom, whose heart is healthy, dies in a car crash. Tom's heart is transplanted into Jerry whose diseased heart has been removed. Clearly, one and the same heart passes from Tom to Jerry. Therefore, the heart in question is not identity-dependent on being Tom's heart. In principle if not in practice, every part of an animal can be transplanted. So it seems as if the whole is not metaphysically prior to its parts in the case of animals.

Accidents and Parts

Tom's smile cannot 'migrate' from Tom to Jerry, but his heart can (with a little help from the cardiologists). This is the difference between an accident of a substance and a proper part of a substance. If A is an accident of substance S, then not only is A dependent for its existence on a substance, it is dependent for its existence on the very substance S of which it is an accident. This is why an accident cannot pass from one substance to another. The accidents of S cannot exist apart from S, but S can exist without those very accidents (though presumably it must have some accidents or other). So we can say that a substance is metaphysically prior to its accidents. But I don't think it is true that a substance is metaphysically/ontologically prior to its parts. The part-whole relation is different from the accident-substance relation.

So as far as I can see what I originally said is correct.

Further, you wrote, "The divine aseity, however, rules out God's being dependent on anything." Would it not be more accurate to say that divine aseity is the thesis that God's being is not dependent upon anything external and distinct from himself? If that is the case, the dependence of God (proper) upon his members (the Father, Son, and Holy Spirit) would be a dependence upon nothing external to himself (unlike a Platonic rendition of God which postulates that God is dependent upon the properties he instantiates, these properties being external to himself). There is a strong strand in Christian tradition that states that the Son is God of God, that he is begotten of the Father and yet retains full divinity. If his divinity is not in jeopardy because of dependence upon the Father, why should the one God's divinity be in jeopardy because he depends upon the members of the
Trinity?

The reason I said what I said is because it makes no sense to say that God is dependent on God. God can no more be dependent on himself than he can cause himself to exist. I read causa sui privatively, not positively. To say that God is causa sui is to say that he is not caused by another; it is not to say that he causes himself. 'Self-caused' is like 'self-employed': one who is self-employed does not employ himself; he is not employed by another.

For you, however, God can be said to depend on God in the sense that God as a whole depends on his proper parts, the Persons of the Trinity. The problem, however, is that you are assuming the mereological model that I am questioning. You are assuming that the one God is a whole of parts and the each of the Persons (F, S, HS) is a proper part of the whole.

And isn't your second criticism inconsistent with your first? Your first point was that a whole is prior to its parts. But now you are saying that God can depend on God by depending in his proper parts.

Properties as Parts: More on Constituent Ontology

Skin and seeds are proper parts of a tomato, and the tomato is an improper part of itself. But what about such properties as being red, being ripe, being a tomato? Are they parts of the tomato? The very idea will strike many as born of an elementary confusion, as a sort of Rylean category mistake. "Your tomato is concrete and so are its parts; properties are abstract; nothing concrete can have abstract parts." Or: "Look, properties are predicable entities; parts are not. Having seeds is predicable of the tomato but not seeds! You're talking nonsense!"

I concede that the notion that the properties of an ordinary particular are parts thereof, albeit in some extended unmereological sense of 'part,' is murky. Murky as it is, the motivation for the view is fairly clear, and the alternative proposed by relational ontologists is open to serious objection. First I will say something in motivation of the constituent-ontological (C-ontological view). Then I will raise objections to the relational-ontological (R-ontological) approach.

For C-Ontology

Plainly, the blueness of my coffee cup belongs to the cup; it is not off in a realm apart. The blueness (the blue, if you will) is at the cup, right here, right now. I see that the cup before me now is blue. This seeing is not a quasi-Platonic visio intellectualis but a literal seeing with the eyes. How else would I know that the cup is blue, and in need of a re-fill, if not by looking at the cup? Seeing that the cup is blue, I see blueness (blue). I see blueness here and now in the mundus sensibilis. How could I see (with the eyes) that the cup is blue without seeing (with the same eyes) blueness? If blueness is a universal, then I see a universal, an instantiated universal. If blueness is a trope, then I see a trope, a trope compresent with others. Either way I see a property. So some properties are visible. This would be impossible if properties are abstract objects as van Inwagen and the boys maintain. Whether uninstantiated or instantiated abstract properties are invisible.

Properties such as blueness and hardness, etc. are empirically detectable. Blueness is visible while hardness is tangible. That looks to be a plain datum. Their being empirically detectable rules out their being causally inert abstracta off in a quasi-Platonic realm apart. For I cannot see something without causally interacting with it. So not only is the cup concrete, its blueness is as well.

This amounts to an argument that properties are analogous to parts. They are not parts in the strict mereological sense. They are not physical parts. So let's call them metaphysical or ontological constituents. The claim, then, is that ordinary particulars such as tomatoes and cups have their properties, or at least some of them, by having them as ontological constituents. To summarize the argument:

1. Some of the properties of ordinary concrete material particulars are empirically detectable at the places the particulars occupy and at the times they occupy them.

2. No abstract object is empirically detectable. Therefore:

3. Some properties of ordinary concrete material particulars are not abtract objects. Therefore:

4. It is reasonable to conjecture that some of the properties of ordinary concrete material particulars are analogous to (proper) parts of them.

Against R-Ontology

I grant that the above is not entirely clear, and that it raises questions that are not easy to answer. But does R-ontology fare any better? I don't think so.

Suppose an R-ontologist is staring at my blue cup. Does he see something colorless? Seems he would have to if the blueness of the cup is an abstract object merely related by exemplification to the concrete cup. Abstracta are invisible. Suppose we introduce 'stripped particular' to designate the R-ontological counterpart of what C-ontologists intend with 'bare particular' and 'thin particular.' A stripped particular is an ordinary particular devoid of empirically detectable properties. If the R-ontologist thinks that my cup is a stripped particular, then he is surely wrong. Call this the Stripped Particular Objection.

But if the R-ontologist agrees with me that the blueness is empirically detectable, then he seems to be involved in an unparsimonious duplication of properties. There is the invisible abstract property in Plato's heaven or Frege's Third Reich that is expressed by the open sentence or predicate '___ is blue.' And there is the property (or property-instance) that even the R-ontologist sees when he stares at a blue coffee cup.

Isn't that one property too many? What work does the abstract property do? More precisely, what ontological work does it do? I needn't deny that it does some semantic work: it serves as the sense (Fregean Sinn) of the corresponding predicate. But we are doing ontology here, not semantics. We want to understand what the world — extramental, extralinguistic reality — must be like if a sentence like 'This cup is blue' is true. We want to understand the property-possession in reality that underlies true predications at the level of language. We are not concerned here with the apparatus by which we represent the world; we are concerned with the world represented.

In my existence book I called the foregoing the Duplication Objection, though perhaps I could have hit upon a better moniker. The abstract property is but an otiose duplicate of the property that does the work, the empirically detectable propery that induces causal powers in the thing that has it.

So I present the R-ontologist with a dilemma: either you are embracing stripped particulars or you are involved in a useless multiplication of entities.

Coda

It's Christmas Eve and there is more to life than ontology. So I'll punch the clock for today. But there are two important questions we need to pursue. (1) Couldn't we reject the whole dispute and be neither a C- nor an R-ontologist? (2) Should ontologists be in the business of explanation at all? (My point that abstract properties are useless for purposes of accounting for predication and property-possession presupposes that there is such a legitimate enterprise as philosophical explanation.)

Constituent Ontology and the Problem of Change

In an earlier entry I sketched the difference between constituent ontology (C-ontology) and relational ontology (R-ontology) and outlined an argument against R-ontology. I concluded that post with the claim that C-ontology also faces serious objections. One of them could be called the 'argument from change.'

The Argument from Change

Suppose avocado A, which was unripe a week ago is ripe today. This is an example of alterational (as opposed to existential) change. The avocado has become different. But it has also remained the same. It is different in respect of ripeness but it is one and the same avocado that was unripe and is now ripe.

Alterational change is neither destruction nor duplication. The ripening of an avocado does not cause it to cease to exist. The ripening of an avocado is not the ceasing to exist of one particular (the unripe avocado) followed by the coming into existence of a numerically distinct avocado (the ripe one).

It is also clear that one cannot speak of change if there are two avocados, A and B, indiscernible except in respect of ripeness/unripeness, such that A is unripe at time t while B is ripe at time t* (t*> t). If my avocado is unripe at t while yours is ripe at t*, that circumstance does not constitute a change. Alteration requires that one and the same thing have incompatible properties at different times. This is necessary for alteration; whether it is sufficient is a further question.

That there is alterational change is a datum. That it requires that one and the same thing persist over an interval of time during which it has incompatible properties follows from elementary 'exegesis' or 'unpacking' of the datum.

The question before us is whether any C-ontology can do justice to the datum and its exegesis.

All C-ontologists are committed to what Michael J. Loux calls "Constituent Essentialism." ("What is Constituent Ontology?" Novak et al. eds., p. 52) It is the C-ontological analog of mereological essentialism. We can put it like this:

Constituent Essentialism: A thing has each of its ontological parts necessarily. This implies that a thing cannot gain or lose an ontological part without ceasing to be same thing.

Mereological Essentialism: A thing has each of its commonsense parts necessarily. This implies that a thing cannot gain or lose a commonsense part without ceasing to be the same thing.

To illustrate, suppose an ordinary particular (OP) is a bundle of compresent universals. The universals are the ontological parts of the OP as a whole. The first of the two principles entails that ordinary particulars cannot change. For (alterational) change is change in respect of properties under preservation of numerical diachronic identity. But preservation of identity is not possible on Constituent Essentialism. The simple bundle-of-universals theory appears incompatible with the fact of change.

I agree with Loux that Constituent Essentialism is a "framework principle" (p. 52) of C-ontology. It cannot be abandoned without abandoning C-ontology. And of course the fact of change and what it entails (persistence of the same thing over time) cannot be denied. So the 'argument from change' does seem to score against primitive versions of the bundle-of-universals theory.

Can the Objection Be Met?

The foregoing objection can perhaps be met met by sophisticating the bundle theory and adopting a bundle-bundle theory. Call this BBT. Accordingly, a thing that persists over time such as an avocado is a diachronic bundle of synchronic or momentary bundles. The theory has two stages.

First, there is the construction of momentary bundles from universals. Thus my avocado at a time is a bundle of universals. Then there is the construction of a diachronic bundle from these synchronic bundles. The momentary bundles have universals as constituents while the diachronic bundles do not have universals as constituents, but individuals. This is because a bundle of universals at a time is an individual. At both stages the bundling is contingent: the properties are contingently bundled to form momentary bundles and these resulting bundles are contingently bundled to form the persisting thing.

Accordingly, the unripe avocado is numerically the same as the ripe avocado in virtue of the fact that the earlier momentary bundles which have unripeness as a constituent are ontological parts
of the same diachronic whole as the later momentary bundles which have ripeness as a constituent.

A sophisticated bundle theory does not, therefore, claim that a persisting thing is a bundle of properties; the claim is that a persisting thing is a bundle of individuals which are themselves bundles of properties. This disposes of the objection from change at least as formulated above.

There are of course a number of other objections that need to be considered — in separate posts. But on the problem of change C-ontology looks to be in better shape than Loux makes it out to be.

I should add that I am not defending the bundle-bundle theory. In my Existence book I take a different C-ontological tack.

Reduction, Elimination, and Material Composition

Yesterday I wrote, "And yet if particular a reduces to particular b, then a is nothing other than b, and is therefore identical to b." This was part of an argument that reduction collapses into elimination. A reader objects: "I am not sure that this is an accurate definition of reduction."

He gives an argument having to do with material composition. I'll put the argument in my own way, so as to strengthen it and make it even more of a challenge for me.

1. Whether or not minds are physically reducible, physical reductionism is surely true of some things, statues for example. A statue is reducible to the matter that composes it, a hunk of bronze, say. No one is a statue-hunk dualist. It is not as if there are two things in the same place, the statue and the hunk of bronze. Nor is anyone an eliminativist when it comes to statues.There are such things, but what they are is just hunks of matter. We avoid both dualism and eliminativism by adopting reductionism.

2. But surely the matter of the statue might have been configured or worked in some other way to make a different statue or a non-statue. Before the sculptor went to work on it, the hunk of bronze was just a hunk, and after it became a statue it could have reverted back to being a mere hunk if it were melted down.

Therefore

3. The statue and the hunk differ property-wise: the hunk, but not the statue, has the property of existing at times at which the statue does not exist. And at every time at which both hunk and statue exist, the hunk, but not the statue, has the modal property of being possibly such as to be a non-statue.

Therefore

4. By the indiscernibility of Identicals, statue and hunk are not identical.

Therefore

5. The statue is reducible to its constituent matter but not identical to it. (By 1, 4)

Therefore

6. It is not the case that if particular a reduces to particular b, then a is identical to b.

This is an impressive argument, but I don't see that it shows that one can have reduction without identity of the reduced to the reducer. I take the argument as further evidence of the incoherence of the notion of the reduction of one particular to another. The first premise, though plausible, is not obviously true. What's more, it seems inconsistent with the second premise. I have argued many times before that in cases like these, statue and lump, fist and hand, brick house and bricks, the thing and its matter differ property-wise and so cannot be identical. They are both temporally and modally discernible. If fist and hand cannot be numerically identical, then they must be numerically distinct. When I take my hand and make a fist of it, the hand does not cease to exist, but something new comes into existence, a fist. Hand and fist, as long as both exist, are two numerically different things occupying exactly the same spatiotemporal position. Admittedly, that sounds strange. Nevertheless, I claim here is just as much reason to be a hand-fist dualist as there is to be a fist-to-hand reductionist.

One could also be an eliminativist. Amazingly, Peter van Inwagen — no slouch of a philosopher; you don't get a chair if you slouch — is an eliminativist about artifacts such as the house built by the Wise Pig. See here.

Perhaps I can drive the reductionist onto the horns of a dilemma. Either fist and hand are identical or they are not. They cannot be identical because they differ property-wise. If two things are not numerically identical, however, then they are numerically different. But if fist and hand are numerically different, then the fist does not reduce to the hand.

So I persist in my view that reduction is an incoherent notion. There is no viable via media between dualism and eliminativism.