Maverick Philosopher

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.)

Related articles

Constituent Ontology Versus Relational Ontology and an Argument Against the Latter

What Exactly is an Ontological Constituent?

Does the Notion of a Bare Particular Make Sense Only in Constituent Ontology?

Constituent Ontology and the Problem of Change

Stanislav Sousedik's "Towards a Thomistic Theory of Predication"

Bare Particulars and Lukáš Novák's Argument Against Them

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.

Related articles

Constituent Ontology Versus Relational Ontology and an Argument Against the Latter

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.  

Bonum Progressionis and the Value of One's Life

The value of a whole is not determined merely by the values of the parts of the whole; the order of the parts also plays a role in determining the value of the whole.  One of several order principles governing the value of a whole is the bonum progressionis.  Glossing Franz Brentano, R. M. Chisholm (Brentano and Intrinsic Value, Cambridge, 1986, p. 71) writes:

The principle of the 'bonum progressionis' or the 'malum regressus' might be put by saying: 'If A is a situation in which a certain amount of value x is increased to a larger amount y, and if B is like A except that in B there is a decrease from the larger amount of value y to the smaller amount x, then A is preferable to B.'  Thus Brentano writes: "Let us think of a process which goes from good to bad or from a great good to a lesser good;then compare it to one which goes in the opposite direction.  The latter shows itself as the one to be preferred.  This holds even if the sum of the goods in the one process is equal to that in the other.  And our preference in this case is one that we experience as being correct." (Foundation, pp. 196-197) (In comparing the two processes, A and B, we must assume that each is the mirror image of the other.  Hence the one should not include any pleasures of anticipation unless the other includes a coresponding pleasure of recollection.)The bonum progressionis, then, would be a good situation corresponding to A, in our formulation above, and the malum regressus would be a bad situation corresponding to B.

Now let's see if we can apply this insight of Brentano to the question of the value of one's life.   A human life can be thought of as a whole the parts of which are its periods or phases.  It seems obvious that the value of the whole will depend on the values of the parts. 

But order comes into it as well.  Suppose lives L1 and L2 are such that the sums of the values of their constituent phases (however you care to individuate them) are  the same quantity of value, however this may be measured.  (There is also the serious question, which I set aside, of whether it even makes sense to speak of an objective measure of the value of a human life.) But whereas L1 begins well in childhood and adolescence but then deteriorates in quality, L2 begins poorly in childhood and adolescence and  gets better. 

If Brentano's bonum progressionis principle applies here, and I would say it does, then L2 is a more valuable life than L1 despite the fact that the sums of the values of their constituent phases are equal in value.  So we can say that the value of a life is more than the sum of the values of its parts when the life is ascending in value, but less than the sum of the values of its parts when the life is descending in value.

This may shed some light on why some people in old age (which I define as beginning at age 60), feel their lives to be not very valuable or satisfying while others in the same age cohort from similar backgrounds find their lives to be valuable and satisfying despite the obvious limitations that old age imposes.

The above analysis of course only scratches the surface.  Another thing to consider is that what is real and important to us is primarily what is real and important now.  The memories of past satisfactions are no match for the perceptions of present miseries.  So if the whole of one's life up to the present has been excellent while the present is miserable, the balance of good over evil cuts little or no ice.  But to explore this further is for another time. 

How Are Form and Matter Related in Compound Material Substances?

Favoring as I do constituent ontology, I am sympathetic to that type of constituent ontology which is hylomorphic ontological analysis, as practiced by Aristotelians, Thomists, et al.  The obscurity of such fundamental  concepts as form, matter, act, potency, substance, and others is, however, troubling. Let's see if we can make sense of the relation between form and matter in an artifact such as a bronze sphere. Now those of you who are ideologically committed to Thomism may bristle at an exposure of difficulties, but you should remember that philosophy is not ideology. The philosopher follows the argument to its conclusion whether it overturns his pet beliefs or supports them, or neither. He knows how to keep his ideological needs in check while pursuing pure inquiry.  If the inquiry terminates in an aporetic impasse, then so be it.

1. Although it perhaps requires arguing, I will here take it for granted that form and matter as these terms are used by Aristotle and his followers are items 'in the real order.' 'Item' is a maximally   noncommittal term in my lexicon: it commits me to very little. Anything in whatever category to which one can refer in any way  whatsoever is an item. 'Real' is that which exists whether or not it is an intentional object of an act of mind. So when I say that form and matter are items in the real order I simply mean that they are not projected by the mind: it is not as if bronze spheres and such have  form and matter only insofar as we interpret them as having form and matter. The bronze sphere is subject to hylomorphic (matter-form) analysis because the thing in reality is made up of form and matter.   'Projectivism' is off the table at least for the space of this post. I am thus assuming a version of realism and am viewing form and matter as distinct ontological constituents or 'principles' of compound   substances.

2. The foregoing implies that the proximate matter of the bronze sphere,  namely, the hunk of bronze itself, is a part of the bronze sphere.  After all, 'ontological constituent' is just a fancy way of saying  'ontological part.'  But an argument I now adapt from E. J. Lowe ("Form Without Matter" in Form and Matter: Themes in Contemporary  Metaphysics, ed. Oderberg, Blackwell 1999, p. 7) seems to show that  the notion that the proximate matter of a compound material substance is a part of it is problematic.  The argument runs as follows.

A. If the hunk of bronze composing the sphere is a part of the sphere, then either it is a proper part or it is an improper part, where an improper part of a whole W is a part of W that overlaps every part of   W.

B. The hunk of bronze is not an improper part since it is not identical to the bronze sphere. (One reason for this is that the persistence conditions are not the same: the piece of bronze will still exist if the sphere is flattened into a disk, but the sphere cannot survive such a deformation. Second, the two are modally discernible: the hunk of bronze is a hunk of bronze in every possible world in which it exists, but the hunk of bronze is not a sphere in every possible world in which it exists.)

C. The hunk of bronze is not a proper part of the bronze sphere since there is no part of the bronze sphere that it fails to overlap.

Therefore

D. The hunk of bronze is not a part of the bronze sphere.

Therefore

E. The composition of form and matter is not mereological. (Lowe, p. 7)

This raises the question of how exactly we are to understand form-matter composition. If the proximate matter of a substance cannot  be a part of it in any sense familiar to mereology, the form-matter composition is 'unmereological,' which is not necessarily an objection except that it raises the question of how exactly we are to understand this unmereological type of composition. This problem obviously extends to essence-existence composition.

3. Now let's look at the problem from the side of form. Could the spherical form of the bronze sphere be a part of it? A form is a principle of organization or arrangement, and it is not quite clear how an arrangement can be a part of the thing whose other parts it arranges. Lowe puts the point like this: ". . . the arrangement of certain parts cannot itself be one of those parts, as this would involve the very conception of an arrangement of parts in a fatal kind of impredicativity." (p. 7)

4. In sum, the difficulty is as follows. Form and matter are real 'principles' in compound substances. They are not projected or supplied by us. We can say that form and matter are ontological constituents of compound substances. This suggests that they are parts of compound substances. But we have just seen that they are not parts in any ordinary mereological sense. So this leaves us in the dark as to just what these 'principles' are and how they combine to constitute compound material substances.

Can the Chariot Take Us to the Land of No Self?

An abbreviated version of the following paper was published under the same title in The Proceedings of the Twenty-First World Congress of Philosophy, vol. 9, ed. Stephen Voss (Ankara, Turkey), 2006, pp. 29-33.

...................

According to Buddhist ontology, every (samsaric) being  is impermanent, unsatisfactory, and devoid of self-nature.  Anicca, dukkha,  anatta: these are the famous three marks (tilakkhana) upon which the whole of Buddhism rests.  I would like to consider a well-known Buddhist argument for the third of these marks, that of anatta, an argument one could call ‘The Chariot.’  The argument aims to show that no (samsaric) being is a self, or has self-nature, or is a substance.  My thesis will be that, successful as this argument may be when applied to things other than ourselves, it fails when applied to ourselves.

Is the Difference Between a Fact and Its Constituents a Brute Difference?

Note to Steven Nemes:  Tell me if you find this totally clear, and if not, point out what is unclear.  Tell me whether you accept my overall argument.

The day before yesterday in conversation Steven Nemes presented a challenge  I am not sure I can meet.  I have maintained (in my book, in published articles, and in these pages) that the difference between a fact and its constituents cannot be a brute difference and must therefore have a ground or explanation.  But what exactly is my reasoning?

Consider a simple atomic fact of the form, a's being F.  This fact has two primary constituents, the individual a, and the monadic property F-ness, which a possesses contingently.  But surely there is more to the fact than these two primary constituents, and for at least two reasons.  I'll  mention just one, which I consider decisive:  the constituents can exist without the fact  existing.  The individual and the property could each exist without the former exemplifying the second.  This is so even if we assume that there are no propertyless individuals and no unexemplified properties.  Consider a world W which includes the facts Ga and Fb.  In W, a is propertied and F-ness is exemplified; hence there is no bar to saying that both exist in W.  But Fa does not exist in W.  So a fact is more than its primary constituents because they can exist without it existing.

A fact is not its constituents, but those constituents unified in a particular way.  Now if you try to secure fact-unity by introducing  one or more secondary constituents such  an exemplification relation, then you will ignite Bradley's regress.  For if the constituents include a, F-ness, and EX, then you still have the problem of their unity since the three can exist without constituting a fact.

So I take it as established that a fact is more than its constituents and therefore different from its constituents.  A fact is different from any one of its constituents, and also from all of them taken collectively, as a mereological sum, say.    The question is:  What is the ontological ground of the difference?  What is it that makes them different?  That they are different is plain.  I want to know what makes them different.  It won't do to say that one is a fact while the other is not since that simply underscores that they are different.  I'm on the hunt for a difference-maker.

To feel the force of the question consider what makes two different sets different.  If S1 and S2 are different sets, then it is reasonable to ask what makes them different, and one would presumably not accept the answer that they are just different, that the difference is a brute difference.  Let S1 be my singleton and S2 the set consisting of me and Nemes.  It would not do to say that they are just different.  We need a difference-maker.  In this case it is easy to specify: Nemes.  He is what makes S1 different from S2.  Both sets contain me, but only one contains him.  Generalizing, we can say that for sets at least,

DM. No difference without a difference-maker.

So I could argue that the difference between a fact and (the sum of) its constituents cannot be a brute difference because (i) there is no difference without a difference-maker and (ii) facts, sets, and sums, being complexes, are relevantly similar.  (I needn't hold that the numerical difference of two simples needs a difference-maker.) But why accept (DM) in full generality as applying to all types of wholes and parts?  Perhaps the principle, while applying to sets, does not apply to facts and their constituents.  How do I answer the person who argues that the difference is brute, a factum brutum, and that therefore (DM), taken in full generality, is false?  As we say in the trade, one man's modus ponens is another's modus tollens.

Can I show that there is a logical contradiction in maintaining that facts and their constituents just differ?  That was my strategy in the book on existence.  The strategy is to argue that without an external ground of unity -- an external unifer -- one lands in a contradiction, or rather cannot avoid a contradiction.  That the unifier, if there is one, must be external as opposed to internal is established by showing that otherwise a vicious infinite regress ensues of the Bradley-type.  I cover this ground in my book and in articles in mind-numbing detail; I cannot go over it again here.  But I will refer the reader to my 2010 Dialectica article  which discusses a fascinating proposal according to which unity is constituted by an internal infinite, but nonvicious, regress.  But for now I assume that the unifier, if there is one, must be external.  If there is one, then the difference between a fact and its constituents cannot be brute.  But why must there be a unifier?

Consider this aporetic triad:

1. Facts exist.
2. A fact is its constituents taken collectively.
3. A fact is not its constituents taken collectively.

What I want to argue is that facts exist, but that they are contradictory structures in the absence of an external unifier that removes the contradiction.  Since Nemes agrees with me about (1), I assume it for present purposes.  (The justification is via the truth-maker argument).

Note that (2) and (3) are logical contradictories, and yet each exerts a strong claim on our acceptance.  I have already argued for (3).  But (2) is also exceedingly plausible.  For if you  analyze a fact, what will you uncover?  Its constituents and nothing besides.  The unity of the constituents whereby it is a fact as opposed to a nonfact like a mereological sum eludes analysis.  The unity cannot be isolated or located within the fact.  For to locate it within the fact you would have to find it as one of the constituents.  And that you cannot do.

Note also that unity is not perceivable or in any way empirically detectable.  Consider a simple Bergmann-style or 'Iowa' example, a red round spot.  The redness and the roundness are perceivable, and the spot is perceivable.  But the spot's being red and round is not perceivable.  The existence of a fact is the unity of its constituents.  So what I am claiming is equivalent to claiming that existence is not perceivable, which seems right: existence is not an empirical feature like redness and roundness.

So when we consider a fact by itself, there seems to be nothing more to it than its constituents.

Each limb of the triad has  a strong claim on our acceptance, but they cannot all be true as formulated.  The contradiction can be removed if we ascend to a higher point of view and posit an external unifier.  What does that mean? 

Well, suppose there is a unifier U external to the fact and thus not identifiable with one or more of its primary or secondary constituents.  Suppose U brings together the constituents in the fact-making way.  U would then be the sought-for ground of the fact's unity.  The difference between a fact and its constituents could then be explained by saying that  the difference is due to U's 'activity':  U operates on the constituents to produce the fact.  Our original triad can then be replaced by the following all of whose limbs can be true:

1. Facts exist
2*. A fact, considered analytically, is its constituents taken collectively.
3.  A fact is not its constituents taken collectively.

This triad is consistent.  The limbs can all be true.  And I think we have excellent reason to say that each IS true.  The truthmaker argument vouches for (1).  (2*) looks to be true by definition.  The argumentation I gave for (3) above strikes me as well-night irresistible.

But if you accept the limbs of the modified triad, then you must accept that there is something external to facts which functions as their unifier.  Difficult questions about what U is and about whether U is unique and the same for all facts remain; but that U exists is 'fallout' from the modified triad.  For if each limb is true, then a fact's being more than its constituents can be accounted for only by appeal to an external unifier.

But how exactly does this show that the difference between a fact and its constituents is not a brute difference?   The move from the original to the modified triad is motivated by the laudable desire to avoid contradiction.  So my argument boils down to this:  If the difference is brute, then we get a logical contradiction. So the difference is not brute. 

But it all depends on whether or not there are facts.  If facts can be reasonably denied, then my reasoning to a unifer can be reasonably rejected.  But that's a whole other can of worms: the truthmaker argument.

Analytically considered, a fact is just its constituents.  But holistically considered it is not.  Unity eludes analysis, and yet without unities there would be nothing to analyze!  Analytic understanding operates under the aegis of two distinctions: whole/part, and complex/simple.  Analysis generates insight by reducing wholes to their parts, and complex parts to simpler and simpler parts, and possibly right down to ultimate simples (assuming that complexity does not extend 'all the way down.')  But analysis is a onesided epistemic procedure.  For again, without unities there would be nothing to analyze. To understand the being-unified of a unity therefore requires that we ascend to a  point of view external to the unity under analysis. 

Review : Modes of Being

Herewith, a little summary of part of what I have been arguing.  Most analytic philosophers would accept (A) but not (B):

A. There are kinds of existent but no kinds of existence.
B. There are kinds of existent and also kinds of existence.

I have been defending the intelligibility of (B) but without committing myself to any particular MOB doctrine.    I use 'modes of being' and 'kinds of existence' interchangeably. Of course I grant to Reinhardt Grossmann and others that the following inference is invalid:

1. K1 and K2 are dramatically different categories of existent
Ergo
2. Instances of K1 differ from instances of K2 in their mode of existence.

But an invalid argument can have a true conclusion.  So one can cheerfully grant the invalidity of the inference from (1) to (2) while insisting that there are categories  the respective members of which differ in their very mode of existence.  For example, although one cannot straightaway infer from the dramatic difference between (primary) substances and accidents that substances and accidents differ in their mode of existence, it is difficult to understand how they could fail to so differ.  After all, accidents depend on substances in that they cannot exist except in substances as modifications of substances, and this dependence is neither causal nor logical.  So I say it is existential dependence. 

Consider a bulge in a carpet.  The bulge cannot exist apart from the carpet whose bulge it is, whereas the carpet can exist without any bulge.  You might be tempted to say that bulge and carpet both simply exist, but that they are counterfactually related: Had the carpet not existed, the bulge would not have existed.  That's true, but what makes it true?  I say it is the fact of the bulge's existential dependence on the carpet.  Accidents exist in a different way than substances.

You could resist this conclusion by simply denying that there are substances and accidents.  Fine, but then I will shift to another example, wholes and parts, say.  Do you have the chutzpah to deny that there are wholes and parts?  Consider again the house made of bricks.  And now try this aporetic pentad on for size:

1. The house exists. 
2. The bricks exist. 
3. The house is not the bricks. 
4. The house is not something wholly diverse from the bricks, something in addition to it, something over and above it. 
5.  'Exist(s)' is univocal. 

The pentad is inconsistent: the limbs cannot all be true.  So what are you going to do?  Deny (1) like van Inwagen?  Maybe that is not crazy, but surely it is extreme.  (2), (3), and (4) are are undeniable.  So I say we ought to deny (5).  The house does not exist in the same way as the bricks.

 

Wholes, Parts, and Modes of Being

Do wholes and their parts exist in different ways?  The analytic establishment is hostile to modes of being, but its case is weak.  Indeed some establishmentarians make no case at all; they simply bluster and asseverate and beg the question.  I wonder how a member of the establishment would counter the following argument.  Consider a house made of bricks and nothing but bricks, and let's list some pertinent truths and see what follows.

1. The house exists.
2. The bricks exist.
3. The house is composed of the bricks, all of them, and of nothing else, and is not something wholly distinct from them or in addition to them.
4. The bricks can exist without the house, but the house cannot exist without the bricks.
5. The relation between the house and the bricks is neither causal nor logical.
Therefore
6. The house has a dependent mode of existence unlike the bricks. 

Peter van Inwagen, one of those establishmentarians who is hostile to the very idea of there being modes of being, will deny (1) as part of his general denial of artifacts.  If artifacts do not exist at all, then questions about how they exist, or in what way or mode, obviously lapse.  But it is evident to me that if we have to choose between denying artifacts and accepting modes of being, then we should accept modes of being!

(2) is undeniable as is (3):  it would obviously be absurd to think of the house as something over and above its constituents, as if it could exist even if they didn't.  The house is just the bricks arranged house-wise.  This is consistent with the truth of (1).  The fact that the house is just the bricks arranged house-wise does not entail that the house does not exist. 

(4) is equally evident and is just a consequence of (3).  I put the point modally but I could also make it temporally: before the Wise Pig assembled the bricks into a house fit to repel the huffing and puffing of the Big Bad Wolf, there was no house, but there were the bricks.

(5)  is also obviously true.  The bricks, taken individually or collectively, do not cause the house.  Now an Aristotelian may want to speak of the bricks as the 'material cause' of the house, but that is not the issue.  The issue is whether the bricks are the efficient cause of the cause.  The answer to that is obviously in the negative.  Nor are the bricks the cause of the house in the Humean sense of 'cause,' or in any modern sense of 'cause.'  For one thing, causation is standardly taken to relate events and neither a house nor a set or sum of its constituents is an event.

Could we say that the relation between bricks and house is logical? No. Logical relations relate propositions and neither the bricks nor the house is a proposition.  It is not a relation of supervenience either since supervenience relates properties and neither bricks nor house is a property.

But I hear an objection. 

I agree with you that the house is not identical to the bricks and that the former depends on the latter but not vice versa.  Why not just say that the two are related counterfactually?  Had the bricks not existed, the house would not have existed either.  Why not  say that and be done with it?  The house depends on the bricks but not conversely.  But the dependence of one existent on another does not seem to require that there are different modes of existence.

True, had the bricks not existed, the house would not have existed.    But what is the truth-maker of this counterfactual?  Your objection is superficial.  Obviously the house is not the bricks.  Obviously the house is dependent on the bricks.  I say that the house, as a whole of parts, exists-dependently.  You said nothing that refutes this.

We should also ask whether it makes sense to speak of a relation between bricks and house. It is certainly not an external relation if an external relation is one whose holding is accidental to the existence of its terms.  If brick A is on top of brick B, then they stand in a dyadic external relation: each can exist without standing in the relation, which is to say that their being related in this way is accidental to both of them.  But a house and its bricks are not externally related: the house cannot exist apart from its 'relation' to the bricks. 

The best thing to say here is that the house has a dependent mode of existence.  The house exists and the bricks exist, but the house exists in a different way than the bricks do.  If you deny this, then you are saying that the house and the bricks exist in the same way.  And what way is that?  Independently.  But it is obvious that the house does not exist independently of the bricks.

I will end by suggesting that van Inwagen's strange denial of artifacts is motivated by his failure to appreciate that there are modes of being.  For if there are no modes of being, and everything that exists exists in the same way, then one is forced to choose between saying either that the house exists independently of its constituent bricks or that the house does not exist at all.  Since van Inwagen perceives that it is absurd to say that the house exists independently of its constituent bricks, he is forced to say that it does not exist at all.

But if there are modes of being we can maintain, rather more sensibly, both that the house exists and that it does not exist independently of its constituent bricks.

 

Two Questions About the Bundle Theory Answered

On the bundle-of-universals theory of ordinary concrete particulars, such a particular is a bundle of its properties and its properties are universals.  This theory will appeal to those who, for various ontological and epistemological reasons, resist substratum theories and think of properties as universals.  Empiricists like Bertrand Russell, for example.  Powerful objections can be brought against the theory, but the following two questions suggested by  some comments of Peter Lupu  in an earlier thread are, I think, easily answered.

Q1.  How may universals does it take to constitute a particular?  Could there be a particular composed of only one or only two universals?

Q2.  We speak of particulars exemplifying properties.  But if a particular is a bundle of its properties, what could it mean to say of a particular that it exemplifies a property?

A1.  The answer is that it takes a complete set.  I take it to be a datum that the ordinary meso-particulars of Sellars' Manifest Image -- let's stick with these -- are completely determinate or complete in the following sense:

D₁. X is complete =_df for any predicate P, either x satisfies P or  x satisfies the complement of  P.

If predicates express properties, and properties are universals, and ordinary particulars are bundles of properties, then for each such particular there must be a complete set of universals.  For example, there cannot be a red rubber ball that has as constituents exactly three universals: being red, being made of rubber, being round.  For it must also have a determinate size, a determinate spatiotemporal location, and so on.  It has to be such that it is either covered with Fido's saliva or not so distinguished.  If it is red, then it must have a color; if it is round, it must have a shape, and so on.  This brings in further universals.  Whatever is, is complete.  That is a law of metaphysics, I should think.  Or perhaps it is only a law of phenomenological ontology, a law of the denizens of the Manifest Image.  (Let's not get into quantum mechanics.) 

A2.  If a particular is a bundle of universals, then it is a whole of parts, the universals being the (proper) parts, though not quite in the sense of classical mereology.  Why do I say that? Well, suppose you have a complete set of universals, and suppose further that they are logically and nomologically compossible.  It doesn't follow that they form a bundle.  But it does follow, by Unrestricted Summation, that there is a classical mereological sum of the universals.  So the bundle is not a sum.  Something more is required, namely, the contingent bundling to make of the universals a bundle, and thus a particular.

Now on a scheme like this there is no exemplification (EX) strictly speaking.  EX is an asymmetrical relation -- or relational tie:  If x exemplifies P-ness, then it is not the case that P-ness exemplifies x.  Bundling is not exemplification because bundling is symmetrical: if U1 is bundled with U2, then U2 is bundled with U1.  So what do we mean when we say of a particular construed as a bundle that is has -- or 'exemplifies' or 'instantiates' using these terms loosely -- a property?  We mean that it has the property as a 'part.'   Not as a spatial or temporal part, but as an ontological part.  Thus:

D₂. Bundle B has the property P-ness =_df P=ness is an ontological 'part' of B.

Does this scheme bring problems in its train?  Of course!  They are for me to know and for you to figure out.

 

Definitions and Axioms of Classical Mereology

Is a wall or a brick house a whole of its parts?  Obviously -- that's a pre-analytic datum.  But is it a sum of its parts?  I have been arguing, with no particular originality, in the negative.  I have been arguing that it is a big mistake to assume  that, just because y is a whole of the xs, that y is a sum of the xs. But it depends on what exactly is meant by 'sum.'  My point is well-taken if 'sum' is elliptical for 'classical mereological sum.'  But what does that mean?  Since 'classical mereological sum' is a technical term, it has all and only the meaning conferred upon it by the definitions and axioms of classical mereology.  I will now present what I take to be the essentials of classical mereology.  I will use 'sum' as short for 'classical mereological sum.'  Later we will look at neoclassical variants that result from tampering with the classical definitions and axioms.

If anything in what follows is original, it is probably a mistake on my part.  Feel free to correct me -- but only if you know the subject matter.

I will take proper parthood and identity as primitives.  To simplify the exposition I will drop universal quantifiers.  They are there in spirit if not in letter.

D1. x is a PART of y =df x is a proper part of y or x = y.

D2. x OVERLAPS y =df there is a z such that z is part of x and z is part of y.

D3. x is DISJOINT from y =df it is not the case that x overlaps y.

D4. y is a SUM of the xs =df z overlaps y iff z overlaps one of the xs.

A1. Asymmetry of Proper Parthood.  If x is a proper part of y, then y is not a proper part of x.

A2. Transitivity of Proper Parthood.  If x is a proper part of y, and y is a proper part of z, then x is a proper part of z.

A3. Supplementation of Proper Parthood.  If x is a proper part of y, then there is a z such that z is a proper part of y and z is disjoint from x.

A4. Uniqueness of Summation.  If u is a sum of the xs and v is a sum of the xs, then u = v.

A5. Unrestricted Summation.  For any xs, there is a y such that y is a sum of the xs.

When I used the word 'sum' in previous posts, I intended that its meaning be not merely the meaning assigned to it by (D4), but the meaning assigned to it by (D4) in conjunction with the rest of the definitions and the axioms (not to mention the theorems that follow as logical consequences of the definitions and axioms). 

Extensionality is a feature of classical mereology.  I leave it as an exercise for the reader to derive Extensionality of Parthood  -- if x and y are sums with the same proper parts, then x = y -- as a theorem from the above.

 

A Closer Look at Material Composition and Modal Discernibility Arguments

(For David Brightly, whom I hope either to convince or argue to a standoff.)

Suppose God creates ex nihilo a bunch of TinkerToy pieces at time t suitable for assembly into various (toy) artifacts such as a house and a fort.  A unique classical mereological sum -- call it 'TTS' -- comes into existence 'automatically' at the instant of the creation ex nihilo of the TT pieces. (God doesn't have to do anything in addition to creating the TT pieces to bring TTS into existence.)   Suppose further that God at t  assembles the TT pieces (adding nothing and subtracting nothing) into a house.  Call this object 'TTH.'  So far we have: the pieces, their sum, and the house.  Now suppose that at t* (later than t) God annihilates all of the TT pieces.  This of course annihilates TTS and TTH.  During the interval from t to t* God maintains TTH in existence.

I set up the problem this way so as to exclude 'historical' and nonmodal considerations and thus to make the challenge tougher for my side.  Note that TTH and TTS are spatially coincident, temporally coincident, and such that every nonmodal property of the one is also a nonmodal property of the other.  Thus they have the same size, the same shape, the same weight, etc.  Surely the pressure is on to say that TTH = TTS?  Surely my opponents will come at me with their battle-cry, 'No difference without a difference-maker!'  There is no constituent of TTH that is not also a constituent of TTS.  So what could distinguish them?

Here is an argument that TTH and TTS are not identical:

1. NecId:  If x = y, then necessarily, x = y. 

2. If it is possible that ~(x = y), then ~(x = y). (From 1 by Contraposition)

3. If it is possible that TTS is not TTH, then TTS is not TTH. (From 2, by Universal Instantiation) 

4. It is possible that TTS is not TTH.  (God might have assembled the parts into a fort instead of a house or might have left them unassembled.)

5. TTS is not TTH. (From 3, 4 by Modus Ponens)

The gist of the argument is that if x = y, then they are identical in every possible world in which both of them exist.  But there are possible worlds in which TTS and TTH both exist but are not identical. (E.g., a world in which the pieces are assembled into a fort instead of a house.)  Therefore, TTS andf TTH are not identical.

If you are inclined to reject the argument, you must tell me which premise you reject.  Will it be (1)? Or will it be (4)? 

Your move, David.

 

Fregean Propositions, Unmereological Compositions, and Bradley's Regress

Steven Nemes writes and I respond in blue:

I know you're in a bit of a mereology phase at the moment, but I figured I'd shoot this by you.

Mereology is the theory of parts and wholes.  Now propositions, whether Fregean or Russellian, are wholes of parts.  So mereology is not irrelevant to questions about the nature and existence of propositions.  The relevance, though, appears to be negative:  propositions are unmereological compositions, unmereological wholes.  That is to say, wholes that cannot be understood in terms of classical mereology.  They cannot be understood in these terms because of the problem of the unity of the proposition.  The problem is to specify what it is about a proposition that distinguishes it from a mere aggregate of its constituents and enables it to be either true or false.  No constituent of an atomic proposition is either true or false, and neither the mathematical set, nor the mereological sum, of the constituents of any such proposition is true or false; so what is it that makes a proposition a truth-bearer?  If you say that a special unifying constituent within propositions does the job,then you ignite Bradley's regress.  Whether or not it is vicious is a further question.  Richard Gaskin maintains the surprising view that Bradley's regress is "the metaphysical ground of the unity of  the proposition."  Far from being vicious, Bradley's regress is precisely that which "guarantees our ability to say anything at all."

For more on this topic, see my "Gaskin on the Unity of the Proposition," Dialectica vol. 64, no. 2 (June 2010), 265-277.  It is part of a five article symposium on the topic.

I am not sure if you believe in Fregean propositions or not. As for myself, I don't look favorably upon the idea of Fregean propositions because of the problem of Bradley's regress. (I am assuming propositions would be composite structured entities, built out of ontologically more basic parts, maybe the senses of the individual terms of the sentences that expresses it, so that the proposition expressed by "Minerva is irate" is a structured entity composed of the senses of "Minvera", "irate", etc.)

I provisionally accept, but ultimately reject, Fregean propositions.  What the devil does that mean?  It means that I think the arguments for them are quite powerful, but that if our system contains an absolute mind, then we can and must reduce Fregean propositions to contents or accuusatives of said mind.  Doing so allows us to solve the problem of the unity of the proposition.

By the way, what you say in parentheses is accurate and lucid. 

In your book, you offer a theistic strategy for solving the problem of Bradley's regress as applied to facts. I don't know that a theistic solution to the problem as applied to propositions works as smoothly because of the queer sort of things senses of individual terms of sentences are supposed to be. The building blocks of facts are universals, which are somewhat familiar entities; but the building blocks of propositions are senses like "Minerva" which are murky and mysterious things indeed. What the hell kind of a thing is a sense anyway?

A sense is a semantic intermediary, an abstract 'third-world' object neither in the mind nor in the realm of concreta, posited to explain certain linguistic phenomena.  One is the phenomenon of informative identity statements.  How are they possible?  'George Orwell is Eric Blair'  is an informative identity statement, unlike 'George Orwell is George Orwell.' How can the first be informative, how can it have what Frege calls cognitive value (Erkenntniswert), when it appears to be of the form a = b, a form all of the substitution-instances of which are false?  Long story short, Frege distinguishes between the sense and the referent of expressions. Accordingly, 'George Orwell' and 'Eric Blair' differ in sense but have the same referent.  The difference in sense explains the informativeness of the identity statement while the sameness of referent explains its truth.

Further, propositions are supposed to be necessarily existent; hence the individual building blocks of the propositions must also exist necessarily. But how could the senses expressed by "Minerva" or "Heidegger's wife", for instance, exist when those individuals do not? (This is the same sort of argument you give against haecceity properties conceived of as non-qualitative thisnesses.)

If proper names such as 'Heidegger' have irreducibly singular Fregean senses, then, as you well appreciate, my arguments against haecceity properties (nonqualitative thisnesses) kick in.  It is particularly difficult to understand how a proper name could express an irreducibly singular Fregean sense when the name in question lacks a referent.  For if irreducibly singular, then the sense is not constructible from general senses by an analog of propositional conjunction.  So one is forced to say that the sense of 'Minerva' is the property of being identical to Minerva.  But since there is no such individual, there is no such property.  Identity-with-Minerva collapses into Identity-with- . . . nothing!  Pace Plantinga, of course.

In the case of identity-with-Heidegger, surely this property, if it exists at all, exists iff Heidegger does.  Given that Heidegger is a contingent being, his haecceity is as well.  And that conflicts with the notion that propositions are necessary beings.  Well, I suppose one could try the idea the some propositions are contingent beings.

Are there any solutions to the former problem (which you've blogged and written about before!) you think are promising? Further, what do you think of the second problem?

Perhaps you think the second problem can be sidestepped by saying that "Heidegger's wife" is just shorthand for some longer description, e.g. "the woman who was married to the man who wrote a book that began with the sentence '...'". I don't know that it is so easy, because that sentence itself makes reference to things that are contingently existent (women, men, books, sentences, marriage...).

Yes,all those things are contingent.  But that by itself does not cause a problem.  The problem is with the notion that proper names are definite descriptions in disguise.  If the very sense of 'Ben Franklin' is supplied by 'the inventor of bifocals' (to use Kripke's example), then the true 'Ben Franklin might not have invented bifocals' boils down to the necessarily false 'The inventor of bifocals might not have invented bifocals.'  (But note the ambiguity of the preceding sentence; I mean the definite description to be taken attributively not referentially.)

Varzi, Sums, and Wholes

Achille C. Varzi, "The Extensionality of Parthood and Composition," The Philosophical Quarterly 58 (2008), p. 109:

Suppose we have a house made of Tinkertoy pieces.  Then the house qualifies as a sum of those pieces: each piece is part of the house and each part of the house overlaps at least one of the pieces . . . . Are there other things that qualify as the sums of those pieces?  UC says there aren't; the house is the only candidate: it is the sum of those pieces.

UC is Uniqueness of Composition: 

UC  If x and y are sums of the same things, then x = y,

where

(1) x is a sum of the zs =_df The zs are all parts of x and every part of x has a part in common with at least one ofthe zs. 

Perhaps commenter John, who knows some mereology and the relevant literature on material composition, can help me understand this.  What I don't understand is what entitles Varzi to assume that the Tinkertoy house -- 'TTH' to give it a name -- is identical to a classical mereological sum.  I do not deny that there is a sum of the parts of TTH.  And I do not doubt that this sum is unique.  Let us name this sum 'TTS.'  (I assume that names are Kripkean rigid designators.)  What I do not understand is the justification of the assumption, made near the beginning of his paper, of the identity of TTH and TTS.  TTH is of course a whole of parts.  But it doesn't straightaway follow that TTH is a sum of parts.

Please note that 'sum' is a technical term, one whose meaning is exactly the meaning it derives from the definitions and axioms of classical mereology.  'Whole' is a term of ordinary language whose meaning depends on context.  It seems to me that one cannot just assume that a given whole of parts is identical to a mereological sum of those same parts.

I am not denying that it might be useful for some purposes  to think of material objects like TTH as sums, but by the same token it might be useful to think of material objects as (mathematical)  sets of their parts.  But surely it would be a mistake to identify TTH with a set of its parts.  For one thing, sets are abstract while material objects are concrete.  For another, proper parthood is transitive while set-theoretic elementhood is not transitive. 

Of course, sums are not sets.  A sum of concreta is itself concrete whereas a set of concreta is itself abstract.  My point is that, just as we cannot assume that that TTH is identical to a set, we cannot assume that TTH is identical to a sum.

What is the 'dialectical situation' when it comes to the dispute between those who maintain that TTH = TTS and those who deny this identity?

It seems to me that the burden of proof rests on those who, like Varzi, identify material objects like TTH with sums especially given the arguments against the identity.  Here is one argument. (a) Taking TTH apart would destroy it, (b) but would not destroy TTS.  Therefore, (c) TTH is not identical to TTS.  This argument relies on the wholly unproblematic Indiscernibility of Identicals as a tacit premise:  If x = y, then whatever is true of x is true of y, and vice versa.  Because something is true of TTH -- namely, that taking it apart would destroy it -- that is not true of TTS, TTH cannot be identical to TTS.

The simplicity and clarity of modal discernibility arguments like this one cast grave doubt on the opening assumption that TTH is a sum.  I am not saying that Varzi and Co. have no response to the argument; they do.  My point is that their response comes too late dialectically speaking.  If you know what a sum is, you know that the identity is dubious from the outset: the discernibility arguments merely make the dubiousness explicit. Responding to these arguments strikes me as too little too late; what the identity theorist needs to do is justify his intitial assumption as soon as he makes it.

My main question, then, is this.  What justifies the initial assumption that material particulars such as Tinkertoy houses are mereological sums?  It cannot be that they are wholes of parts, for a whole needn't be a sum.  TTH is a whole but it is not a sum.  It is not a sum because a sum is a collection that is neutral with respect to the arrangement or interrelation of its parts, whereas it is essential to TTH that its parts be arranged house-wise.

 

Four-Dimensionalism to the Rescue?

Let us return to that impressive product of porcine ingenuity, Brick House.  Brick House, whose completion by the Wise Pig occurred on Friday, is composed entirely of the 10,000 Tuesday Bricks.  I grant that there is a sum, call it 'Brick Sum,' that is the classical mereological sum of the Tuesday Bricks.  Brick Sum is 'generated' -- if you care to put it that way -- by Unrestricted Composition, the classical axiom which states that "Whenever there are some things, then there exists a fusion [sum] of those things." (D. Lewis, Parts of Classes, p. 74)  I also grant that Brick Sum is unique by Uniqueness of Composition according to which "It never happens that the same things have two different fusions [sums]." (Ibid.)  But I deny Lewis' Composition as Identity.  Accordingly, Brick Sum cannot be identical to the Tuesday Bricks.   After all, it is one while they are many.

Now the question I am debating with commenter John is whether Brick House is identical to Brick Sum.  This ought not be confused with the question whether Brick House is identical to the Tuesday Bricks.  This second question has an easy negative answer inasmuch as the former is one while the latter are many.  Clearly, one thing cannot be many things.

The question, then, is whether Brick House is identical to Brick Sum.  Here is a reason to think that they are not identical.  Brick Sum exists regardless of the arrangement of its parts: they can be scattered throughout the land; they can be piled up in one place; they can be moving away from each other; they can be arranged to form a wall, or a corral, or a house, or whatever.  All of this without prejudice to the existence and the identity of Brick Sum.  Now suppose Hezbollah Wolf, a 'porcicide' bomber, enters Brick House and blows it and himself up at time t on Friday evening. At time t* later than t, Brick Sum still exists while Brick House does not.  This shows that they cannot be identical; for if they were identical, then the destruction of Brick House would be the destruction of Brick Sum. 

This argument, however, rests on an assumption, namely, that Brick Sum exists both at t and at t*.   This won't be true if Four Dimensionalism is true.  If bricks and houses are occurrents rather than continuants, if they are composed of temporal parts, then we cannot say, strictly and philosophically, that Brick Sum at t still exists at t*.  And if we cannot say this, then the above argument fails.

But all is not lost since there remains a modal consideration.  Brick House and Brick Sum both exist at time t in the actual world.  But there are plenty of possible worlds in which, at t, the latter exists but not the former.  Thus it might have been the case at t that the bricks were arranged corral-wise rather than house-wise.  So Brick Sum has a property that Brick House lacks, namely, the modal property of being such that its parts could have been arranged in non-house-wise fashion.  Therefore, by the Indiscernibility of Identicals, Brick House is not identical to Brick Sum.

So even if the historical discernibility argument fails on Four Dimensionalism, the modal discernibility argument seems to work even assuming Four Dimensionalism.

Please note that my thesis is not that Brick House is a sum that violates Uniqueness of Composition, but that Brick House is not a classical mereological sum.    If Brick House were a sum, then it would be Brick Sum.  But I have just argued that it cannot be Brick Sum.  So it cannot identified with any classical sum.  It is a whole of parts all right, but an unmereological whole.  What does that mean?  It means that it is a whole that cannot be adequately understood using only the resources of classical mereology.

 

Van Inwagen on Arbitrary Undetached Parts

In order to get clear about Dion-Theon and related identity puzzles we need to get clear about the Doctrine of Arbitrary Undetached Parts (DAUP) and see what bearing it has on the puzzles. Peter van Inwagen provides the following statement of DAUP:

For every material object M, if R is the region of space occupied by M at time t, and if sub-R is any occupiable sub-region of R whatever, there exists a material object that occupies the region sub-R at t. ("The Doctrine of Arbitrary Undetached Parts" in Ontology, Identity, and Modality, CUP, 2001, 75.) 

Suppose I am smoking a cigar. DAUP implies that the middle two-thirds of the cigar is just as much a concrete material object as the whole cigar. This middle two-thirds is an undetached part of the cigar, but also an arbitrary undetached part since I could have arbitrarily selected uncountably many other lengths such as the middle three-fourths. Applied to Tibbles the cat, DAUP implies that Tibbles-minus-one-hair is just as full-fledged a material object as Tibbles. Van Inwagen maintains that DAUP is false.

I will reconstruct van Inwagen's argument for the falsity of DAUP as clearly as I can. Consider Descartes and his left leg L. To keep it simple, we make the unCartesian assumption that Descartes is just a live body. DAUP implies that L is a material object as much as Descartes himself. DAUP also implies that there is a material object we can call D-minus. This is Descartes-minus-L. It is obvious that Descartes and D-minus are not the same. (For one thing, they are differently shaped. For another, they are 'differently abled' in PC jargon.) At time t, D-minus and L are undetached nonoverlapping proper parts of Descartes, and both are just as much full-fledged material objects as Descartes himself is.

Now suppose a little later, at t*, L becomes detached from D-minus. In plain English, Descartes at t* loses his leg. (To avoid certain complications, we also assume that the leg is not only removed but also annihilated.) Does D-minus still exist after t*?  Van Inwagen thinks it is obvious that D-minus does exist after the operation at t*. DAUP implies that the undetached parts of material objects are themselves material objects. So D-minus prior to t* is a material object. Its becoming detached from L does not affect D-minus or its parts, and if the separation of L from D-minus were to cause D-minus to cease to exist, then, van Inwagen claims, D-minus could not properly be called a material object. Descartes himself also exists after the operation at t*. Surely one can survive the loss of a leg. So after t* both D-minus and Descartes exist. But if they both exist, then they are identical. For otherwise there would be two material objects having exactly the same size, shape, position, mass, velocity, etc., and that is impossible.

In sum, at time t, D-minus and Descartes are not identical, while at the later time t* they are identical. The result is the following inconsistent tetrad:

D-minus before t* = D-minus after t*

D-minus after t* = Descartes after t*

Descartes after t* = Descartes before t*

It is not the case that  D-minus before t* = Descartes before t*

The first three propositions entail the negation of the fourth. From this contradiction van Inwagen infers that there never was any such thing as D-minus. If so, then DAUP is false. But as van Inwagen realizes, his refutation of DAUP has a counterintuitive consequence, namely, that L does not exist either: there never was any such thing as Descartes' left leg. For it seems obvious that D-minus and L stand or fall together, to repeat van Inwagen's pun.

That is, D-minus exists if and only if L exists, and D-minus does not exist if and only if L does not exist. D-minus is an arbitrary undetached proper part of Descartes if and only if L is an arbitrary undetached proper part of Descartes. At this point, I think it becomes clear that van Inwagen's solution to the Dion/Theon or Descartes/D-minus puzzle is not compelling. He solves the puzzle by denying that there was ever any such material object as D-minus. But if there was no D-minus, then there was never any such material object as Descartes' left leg. It is obvious, however, that there was such a material object as Descartes' left leg L. So how could it be maintained that there was no such object as Descartes-minus? Van Inwagen makes it clear (p. 82, n. 12) that he does not deny that there are undetached parts. What I take him to be denying is that, for any P and O, where P is an undetached part of material object O, there is a complementary proper part of O, O-minus-P. So perhaps van Inwagen can say that L is a non-arbitrary undetached part of Descartes and that this is consistent with there being no D-minus. If so, he would have to reject the following supplementation principle of mereology which seems intuitively sound:

For any x, y, z, if x is a proper part of y, then there exists a z such that z is a part of y and z does not overlap x , where x overlaps y =df there exists a z such that z is a part of x and z is a part of y.

What the above supplementation principle says is that you cannot have a whole with only one proper part. Every whole having a proper part has a second proper part that supplements or complements the first so as to constitute a whole. Now Descartes' leg is a proper part of Descartes. So the existence of D-minus falls out of the supplementation principle.

It seems, then, that van Inwagen's rejection of DAUP  issues in a dilemma.  If there is no such object as Descartes minus his left leg, then there is no such object as Descartes' left leg, which is highly counterintuitive, to put it mildly.  But if van Inwagen holds onto the left leg, then it seems his must reject the seemingly obvious supplementation principle lately mentioned.

My interim conclusion is that van Inwagen's solution to the Descartes/D-minus puzzle by rejection of DAUP is not compelling.

Can a Mereological Sum Change its Parts?

This post is an attempt to understand and evaluate Peter van Inwagen's "Can Mereological Sums Change Their Parts," J. Phil. (December 2006), 614-630.  A preprint is available online here.

The Wise Pig and the Brick House: My Take

On Tuesday the Wise Pig  takes delivery of 10,000 bricks.  On the following Friday he completes construction of a house made of exactly these bricks and nothing else.  Call the bricks in question the 'Tuesday bricks.'  I would 'assay' the situation as follows.  On Tuesday there are some unassembled bricks laying about the building site.  By Unrestricted Composition, these bricks compose a classical mereological sum.  Call this sum 'Brick Sum.'  (To save keystrokes I will write 'sum' for 'classical mereological sum.' ) By Uniqueness of Composition, there is exactly one sum that the Tuesday bricks compose.  On Friday, both the Tuesday bricks and their (unique) sum exist.  But as I see it, the Brick House is identical neither to the Tuesday bricks nor to their sum.  Thus I deny that the Brick House is identical to the sum of the things that compose it. I give two arguments for this non-identity.

Nonmodal 'Historical' Argument:  Brick Sum has a property that Brick House does not have, namely the property of existing on Tuesday.  Therefore, by the Indiscernibility of Identicals, Brick Sum is not identical to Brick House.

Modal Argument:  Suppose that the actual world is such that Brick Sum and Brick House always existed, exist now, and always will exist:  every time t is such that both exist at t.  This does not alter the plain fact that the house depends for its existence on the bricks, while the bricks do not depend for their existence on the house.  Thus there are possible worlds in which Brick Sum exists but Brick House does not.  (Note that Brick Sum exists 'automatically' given the existence of the bricks.) These worlds are simply the worlds in which the bricks exist but in an unassembled state.  So Brick Sum has a property that Brick House does not have, namely, the modal property of being possibly such as to exist without composing a house.  Therefore, by the Indiscernibility of Identicals, Brick Sum is not identical to Brick House.

In sum (pardon the pun!), The Brick House is not a mereological sum.  (If it were, it would have existed on Tuesday as a load of bricks, which is absurd.)  This is not to say that there is no sum 'corresponding' to the Brick House: there is.  It is just that this sum -- Brick Sum -- is not identical to Brick House.  So what I am saying implies no rejection of Unrestricted Composition.  The point is rather that a material artifact such as a house cannot be identified with the mereological sum of the things it is made of.  This is because sums abstract or prescind from the mutual relations of parts in virtue of which parts form what we might call  'integral wholes' as opposed to a mere mereological sums.  Unassembled bricks do not a brick house make: you have to assemble them properly.  And the assembly, however you want to assay it, is an added ontological ingredient that escapes consideration by a general purely formal part-whole theory such as classical mereology.

I assume with van Inwagen that Brick House can lose a brick (or gain a brick)  without prejudice to its identity.  But, contra van Inwagen, I do not take this to imply that mereological sums can gain or lose parts.  And this for the simple reason that Brick House and things like it are not identical to sums of the things that compose them.  I would say, pace van Inwagen, that mereological sums can no more gain or lose parts than (mathematical) sets can gain or lose elements.

The Wise Pig and the Brick House: Van Inwagen's Take

I agree with van Inwagen that "The Tuesday bricks are all parts of the Brick House and every part of the Brick House overlaps at least one of the Tuesday bricks." (616-617)  But he takes this obvious truth to imply that " . . . 'a merelogical sum' is the obvious thing to call something of which the Tuesday Bricks are all parts and each of whose parts overlaps at least one of the Tuesday Bricks." (617)  Well, he can call it that but only if he uses 'mereological sum' in a way different that the way it is used in classical mereology.

Now if we acquiesce in van Inwagen's usage, and we grant that things like houses can change their parts, then it follows that mereological sums can change their parts.  But why should we acquiesce in van Inwagen's usage of 'mereological sum'?

Is Everything a Mereological Sum?

As I use 'mereological sum,' not everything is such a sum.  The Brick House is not a sum.  It is no more a sum than it is a set.  There are sums and there are sets, but not everything is a sum just as not everything is a set.  There is a set consisting of the Tuesday Bricks, and there is a singleton set of the Brick House.  But neither of these sets is identical to the Brick House.  Neither of them has anything to fear from the pulmonary exertions of the Big Bad Wolf -- not because they are so strong, but because they are abstract objects removed from the flux and shove of the causal order.  Sums of concreta, unlike sets of concreta,  are themselves concrete -- but the Brick House is not a sum.  Van Inwagen disagrees.  For him, "Everything is a mereological sum." (618)

His argument for this surprising claim is roughly as follows. PvI's presentation is tedious and technical but I think I will not be misrepresenting him if I sum up the gist of it as follows:

1. Everything, whether simple or composite, has parts.  (This is a consequence of the following definition: x is a part of y =_df x is a proper part of y or x = y.  Because everything is self-identical, everything has itself as a part, an improper part to be sure, but a part nonetheless. Therefore:

2. Everything is a mereological sum of its parts.  Therefore:

3. Everything is a mereological sum. Therefore:

4. ". . . mereological sums are not a special sort of object." (622)  In this respect they are unlike sets."'Mereological sum' is not a useful stand-alone general term." (622) 'Set' is.

What's At Issue Here?

I confess to not being clear about what exactly is at issue here.  One could of course use 'mereological sum' in the way that van Inwagen proposes, a way that implies that everything is a mereological sum, and that implies that there is no conceptual confusion in the notion of a mereological sum changing its parts.   But why adopt this usage?  How does it help us in the understanding of material composition?

What am I missing?

 

Van Inwagen Contra Lewis on Composition as Identity

Modifying an example employed by Donald Baxter and David Lewis, suppose I own a parcel of land A consisting of exactly two adjoining lots B and C. It would be an insane boast were I to claim to own three parcels of land, B, C, and A. That would be 'double-counting': I count A as if it is a parcel in addition to B and C, when in fact all the land in A is in B and C taken together. Lewis, rejecting 'double-counting,' will say that A = (B + C). Thus A is identical to what composes it. This is an instance of the thesis of composition as identity.

Or suppose there are some cats.  Then, by Unrestricted Composition ("Whenever there are some things, then there exists a fusion [sum] of those things"), there exists a sum that the cats compose.  But by Composition as Identity, this sum is identical to what compose it, taken collectively, not distributively.  Thus the sum is the cats, and they are it.  I agree with van Inwagen that this notion of Composition as Identity is very hard to make sense of, for reasons at the end of the above link.  But Peter van Inwagen's argument against Composition as Identity strikes me as equally puzzling.  Van Inwagen argues against it as follows:

Suppose that there exists nothing but my big parcel of land and such parts as it may have. And suppose it has no proper parts but the six small parcels. . . . Suppose that we have a bunch of sentences containing quantifiers, and that we want to determine their truth-values: 'ExEyEz(y is a part of x & z is a part of x & y is not the same size as z)'; that sort of thing. How many items in our domain of quantification? Seven, right? That is, there are seven objects, and not six objects or one object, that are possible values of our variables, and that we must take account of when we are determining the truth-value of our sentences. ("Composition as Identity," Philosophical Perspectives 8 (1994), p. 213)

In terms of my original example, Lewis is saying that A is identical to what composes it. Van Inwagen is denying this and saying that A is not identical to what composes it. His reason is that there must be at least three entities in the domain of quantification to make the relevant quantified sentences true. A is therefore a third entity in addition to B and C. It is this that I don't understand. Van Inwagen's argument strikes me as a non sequitur. Or perhaps I just don't understand it. Consider this obviously true quantified sentence:

1. For any x, there is a y such that x = y.

(1) features two distinct bound variables, 'x'and 'y.' But it does not follow that there must be two entities in the domain of quantification for (1) to be true. It might be that the domain consists of exactly one individual a. Applying Existential Instantiation to (1), we get

 2. a = a.

Relative to a domain consisting of a alone, (1) and (2) are logically equivalent. From the fact that there are two variables in (1), it does not follow that there are two entities in the domain relative to which (1) is evaluated. Now consider

3. There is an x, y and z such that x is a proper part of z & y is a proper part of z.

(3) contains three distinct variables, but it does not follow that the domain of quantification must contain three distinct entities for (3) to be true. Suppose that Lewis is right, and that A = (B + C). It will then be possible to existentially instantiate (3) using only two entities, thus:

4. B is a proper part of (B + C) & C is a proper part of (B + C).

If van Inwagen thinks that a quantified sentence in n variables can be evaluated only relative to a domain containing n entities (or values), then I refute him using (1) above. If van Inwagen holds that (3) requires three entities for its evaluation, then I say he has simply begged the question against Lewis by assuming that (B + C) is not identical to A. It is important not to confuse the level of representation with the level of reality. That there are two different names for a thing does not imply that there are really two things. ('Hesperus' and 'Phosphorus' both name the same planet, Venus, to coin an example.) Likewise, the fact that there are two distinct bound variables at the level of linguistic representation does not entail that at the level of reality there are two distinct values. There might be or there might not be.

So I cannot see that van Inwagen has given me any reason to think that A is a third entity in addition to B and C. But it doesn't follow that I think that Lewis' thesis is correct. Both are wrong.  Here is the problem. 'A = (B + C)' is the logical contradictory of '~ (A = (B + C)).' Thus one will be tempted to plump for one or the other limb of the contradiction. But there are reasons to reject both limbs.

Surely A is more than the mereological sum of B and C. This is because A involves a further ontological ingredient, namely, the connectedness or adjacency of B and C. To put it another way, A is a unity of its parts, not a pure manifold. The Lewis approach leaves out unity. Suppose B is in Arizona and C is in Ohio. Then the mereological sum (B + C) automatically exists, by Unrestricted Composition.   But this scattered object is not identical to the object which is B-adjoining-C. On the latter I can build a house whose square footage is greater than that of B or C; on the scattered object I cannot. But A is not a third entity. It is obvious that A is not wholly distinct from B and C inasmuch as A is composed of B and C as its sole nonoverlapping proper parts. Analysis of A discloses nothing other than B and C.  But neither is A identical to  B + C.

In short, both limbs of the contradiction are unacceptable. How then are we to avoid the contradiction?

Perhaps we can say that A is identical,  not to the sum B + C, but to B-adjoining-C, an unmereological whole.  But this needs explaining, doesn't  it?

Mereological Nihilism

I put to William the following question: 

Are you prepared to assert the following? It is never the case that whenever there are some things, there is a whole with those things as parts. Equivalently: For any xs, if the xs are two or more, there is no y such that the xs compose y.

To which he replied:  "Agreed, if you are using xs as a plural quantifier, and by implication y as a singular quantifier."

I think William was too hasty in agreeing since his agreement makes him a mereological nihilist, or nihilist for short.  Nihilism  is the logical contrary, not contradictory, of mereological universalism, or universalism for short.  Universalism is what is expressed by Unrestricted Composition:

UC. Whenever there are some things, then there exists a fusion [sum] of those things. (David Lewis, Parts of Classes, Basil Blackwell 1991, p. 74)

Given Extensionality -- no two wholes have the same parts -- (UC) says that whenever there are some individuals, no matter what their character or category, there is a unique individual that they compose.  This is their mereological sum.  Universalism is hard to swallow.  I do not balk at the sum of the books in my house.  But I balk at the sum of : the books in my house, William's last heartbeat, Peter's left foot, and the planet Mercury.  But if, recoiling from Universalism, one embraces Nihilism, then one is committed to the proposition that there are no composite objects, there are only simples.  And surely William does not want to be committed to that.

Mereological Innocence and Composition as Identity

This is the third in a series.  Part I, Part II.  What follows is a 10th example of eliminativist/reductivist ambiguity.

One of the axioms of mereology is Unrestricted Composition.  Here is David Lewis' formulation (Parts of Classes, Basil Blackwell 1991, p. 74):

Unrestricted Composition: Whenever there are some things, then there exists a fusion of those things.

A fusion is a mereological sum, so I'll use 'sum.'  The axiom assures us that, for example, if there are some cats, then there exists a sum of those cats.  The cats are many but the sum is one.  So it is not unreasonable to think that if there are five cats that compose the sum, the sum is a sixth thing.  One could argue as follows:  (a) The sum is distinct from each of the cats.  (b)There are five cats, each of which exists, and by UC the sum also exists.  Therefore, (c) at least six things exist.

But consider this example, adapted from Donald Baxter.  You proceed with six bottles of beer to the supermarket 'six items or fewer' checkout line.  The attendant protests your use of the line on the ground that you have seven items: six bottles of beer plus one mereological sum.  This would be an outrage, of course.  The example suggests that the argument to (c) above has gone wrong.

Lewis avoids the mistake -- assuming it is one -- by pleading that "Mereology is ontologically innocent." (PC 81)  That means that a commitment to a cat-sum is not a further commitment over and above the commitment to the cats that compose the sum.  The cat-sum just is the cats, and they are it.  This is the thesis of Composition as Identity.  The xs compose the y by being identical to the y.  As Lewis says,

Take them together or take them separately, the cats are the same portion of Reality either way.  Commit yourself to their existence all together or one at a time, it's the same commitment either way.  If you draw up an inventory of Reality according to your scheme of things, it would be double counting to list the cats and also list their fusion.  In general, if you are already committed to some things, you incur no further commitment when you affirm the existence of their fusion. (PC 81-82)

I'm sorry, but this doesn't make much sense.  Glance back at Unrestricted Composition.  It is not a tautology.  It does not say that whenever there are some things, then there are some things.  It says that whenever there are some things, then there exists a fusion or sum of those things.  Now if the sum of the xs is just the xs, then UC is a tautology.  But  if UC is not a tautology, then Composition as Identity is false.  How can Unrestricted Composition and Composition as Identity both be true?

The problem is already present at the purely syntactic level.  'Y is identical to the xs' is unproblematic if the xs are identical to one another.  For then the open sentence collapses into 'y is identical to x.'  But if the xs are distinct from each other, then 'y is identical to the xs' is syntactically malformed.  How can one thing be identical to many things?  If one thing is identical to many things, then it is not one thing but many things.  A contradiction ensues: the one thing is one thing and not one thing because it is many things.  The gaps in the predicate '. . . is identical to ____' must either be both filled with singular terms or both filled with plural terms.

And now we come back to our main theme, eliminativist/reductivist ambiguity.  Lewis wants to say that there is the sum of the xs (by Unrestricted Composition) but that the the sum of the xs is identical to the xs.  So he seems to be making a reductionist claim: sums reduce to their members.  But I say the thesis is unstable and topples over into eliminativism:  there are no mereological sums.  For if the sum is just its members, then all that exists is the members so that the sum does not exist!

Fist and Hand, Statue and Lump: The Aporetics of Composition

1. Some maintain that a hand, and that same hand made into a fist, are identical. And there are those who would say the same about a piece of bronze and the statue made out of it, namely, that they are identical at every time at which both exist. This is not an unreasonable thing to say. After all, fist and hand, statue and bronze, are spatially coincident and neither has a physical part the other doesn't have. A fist is just a certain familiar arrangement of hand-parts. There is no part of the fist that is not part of the hand, and vice versa. So at looks as if first and hand are identical.  But we need to be clear as to what identity is.

2. Identity is standardly taken to be an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals (InId) and the Necessity of Identity (NecId). The first principle says that, if two items are numerically identical, then they share all properties. The second says that if two items are numerically identical, then this is necessarily the case.  Both principles strike me as beyond epistemic reproach.  'Identity' is short for 'numerical identity.'

3. Despite the considerations of #1, it looks as if fist and hand, statue and hunk of bronze, cannot be identical since they differ in their persistence conditions. The hunk of bronze can, while the statue cannot, survive being melted down and recast in some other form. The hand can, while the fist cannot, survive adoption of a different 'posture.'  In both cases, something is true of the one that is not true of the other.  So even at the times at which the fist is the hand, and the bronze is the statue, the two are not identical: the 'is' is not the 'is' of identity.  It is the 'is' of composition and what you have are two things, not one.

What I have just given is a modal discernibility argument.  Let me spell it out.  Consider a time t at which the hand is in the shape of a fist.  At t, the hand, but not the fist, has the modal property of being possibly such as to to be unfisted.  So the hand cannot be identical to the fist given that, for any x, y, if x = y, then x, y share all properties.

But there is also this nonmodal discernibility argument.  The hunk of bronze existed long before the statue came into existence, and the hunk of bronze exists while the form of a statue.  So the hunk of bronze exists at more times that the statues does, which implies the the hunk of bronze is not identical to the statue.

There is also this consideration.  Identity is symmetrical.  So we can say either fist = hand or hand = fist.  But is it the fist or the hand that both are?  Intuitively, it is the hand.  The hand is the fundamental reality here, not the fist.  So how can fist and hand be identical?  It seems that fist and hand are numerically distinct, albeit spatially coincident, concrete individuals.

4.  The Law of Excluded Middle seems very secure indeed, especially in application to presently existing things.  So either the fist is identical to the hand, and there is just one thing, a fisted hand, or the fist is not identical to the hand and there are two spatially coincident things, a fist and a hand.  So which is it?

5. If you say that the fist = the hand, then when you make a fist nothing new comes into existence, and when the potter makes a pot out of clay, nothing new comes into existence.  And when a mason makes a wall out of stones, nothing new comes into existence.  He started with some stones and he ended with some stones.  Given that the stones exist, and that the mason's work did not cause anything new to come into existence, must we not say that the single composite entity, the wall, does not exist?  (For if it did exist, then there would be an existent in addition to the stones.)  But it sounds crazy to say that the wall the mason has just finished constructing does not exist.

6. If, on the other hand, you say that the fist is not identical to the hand, then you can say that the making of a fist causes a new thing to come into existence, the fist.  And similarly with the statue and the wall.  After the mason stacks n stones into a wall, he has as a result of his efforts n +1 objects, the original n stones and the wall. 

But this is also counterintuitive.  Consider the potter at his wheel.  As the lump of clay spins, the potter shapes the lump into a series of many (continuum-many?) intermediate shapes before he stops with one that satisfies him.  Thus we have a series of objects (proto-pots) each of which is a concrete individual numericallt distinct from the clay yet (i) spatially conicident with it, and (ii) sharing with it every momentary property.  And that is hard to swallow, is it not?

7.  We appear to be at an impasse.  We cannot comfortably say that the fist = the hand, nor can we comfortably say that the fist is not identical to the hand. Nor can we comfortably give up LEM.  If there are no fists, statues, walls, artifacts generally, then there cannot be any puzzles about their composition.  But we cannot comfortably say that there are no such things either.

Do we have here an example of a problem that is both genuine but insoluble?

Peter van Inwagen, Artifacts, and Moorean Rebuttals

Two commenters in an earlier van Inwagen thread, the illustrious William the Nominalist and the noble Philoponus of Terravita,  have raised Moore-style objections to an implication of PvI's claim that "every physical thing is either a living organism or a simple" (MB 98), namely, the implication that "there are no tables or chairs or any other visible objects except living organisms." (MB 1)  The claim that there are no inanimate objects, no tables, chairs, ships and stars will strike many as so patently absurd as to be not worth discussing.  Arguments to such a conclusion, no matter how clever, will be dismissed as unsound without  evaluation on the simple ground that the conclusion to which they lead is preposterous.  This is the essence of a Moorean objection.  If someone says that time is unreal, you say, 'I ate breakfast an hour ago.'  If someone denies the external world, you hold up your hands.  If someone denies that there are chairs, you point out that he is sitting on one.  And then you clinch your little speech by adding, 'The points I have just made are more worthy of credence than any premises you can marshall in support of their negations.' 

I myself have never been impressed with Moorean rebuttals.  To my mind they signal on the part of those who make them a failure to understand the nature of philosophical (in particular, metaphysical) claims.  See, e.g., Can One See that One is not a Brain in a Vat?

Though I disagree with van Inwagen's denial of artifacts, I think he can be quite easily defended against the charge of maintaining something 'mad' or something refutable by a facile Moorean rejoinder.

Chapter 10 of Material Beings deals with the Moorean objection.  Van Inwagen does not deny that we utter such true sentences as 'There is a wall that separates my property from my neighbor's.'  But whereas most of us would infer from this that walls exist, and thus that composite non-living things exist, van Inwagen refuses to draw this inference maintaining instead that the truth of 'There is a wall that separates my property from my neighbor's' is consistent with there being no walls.

This is not as crazy as it sounds.  For suppose that what the vulgar call a wall is (speaking with the learned) just some stacked stones, some stones arranged wall-wise.  And to simplify the discussion, suppose the stones are simples.  Then the denial that there is a wall is a denial that there is one single thing that the stones compose.  But this is consistent with the existence of the stones.  Accordingly, the sentence 'There is a wall that separates my property from my neighbor's' is true in virtue of the existence of the stones despite the fact that there is no wall as a whole composed of these stony parts.

Or consider the house built by the Wise Pig years ago out of 10, 000 blocks (which for present purposes we may consider to be honorary simples.)  (The tail tale of the Wise Pig is recounted on p. 130 of Material Beings.) At the completion of construction, did something new come into existence?  I would say 'yes.'  Van Inwagen would say 'no.'  All that has happened on PvI's account is that some blocks have been arranged house-wise.  His denial then, is that there is a y such that the xs compose y.  He is not denying the xs (the blocks construed as simples); he is denying that there is a whole that they compose.  And because there is no whole that they compose, the house does not exist.

Furthermore, because the house does not exist, there can be no question whether the house built by the Wise Pig years ago, and kept in good repair by him and his descendants by replacement of defective blocks, is the same as or is not the same as the one that his descendants live in today.  The standard puzzles about diachronic artifact identity lapse if there are no artifacts.   

Does this fly in the face of Moorean common sense?  If  madman Mel were to say that there are no houses he would not mean what the metaphysican means when he says that there are no houses.  If Mel is right, then it cannot be true that I have been living in the same house for the last ten years.  But the truth of 'I have been living in the same house for the last ten years' is consistent with, or at least not obviously inconsistent with,  PvI's denial of houses (which is of course not a special denial, but a consequence of his denial of artifacts in general). This is because PvI is not denying the existence of the simples which we mistakenly construe as parts of a nonexistent whole.

But then how are we to understand a sentence like, 'The very same house that stands here now has stood here for three hundred years'?  Van Inwagen proposes the following paraphrase:

There are bricks (or, more generally, objects) arranged housewise here now, and these bricks are the current objects of a history of maintenance that began three hundred years ago; and at no time in that period were the then-current objects of that history arranged housewise anywhere but here. (133)

I am not endorsing PvI's denial of artifacts, I am merely pointing out that it cannot be dismissed Moore-style. 

 

The Aporetics of Artifacts: Puzzling Over Van Inwagen's Denial of Artifacts

This post is a sequel to Van Inwagen on the Ship of Theseus.  Peter van Inwagen, Material Beings (Cornell UP, 1990), p. 31, writes: 

The question 'In virtue of what do these n blocks compose this house of blocks?' is a question about n + 1 objects, one of them radically different from the others. But the question 'What could we do to get these n blocks to compose something? is a question about n rather similar objects. . . . . questions of the former sort turn our minds to various metaphysical and linguistic questions about the "special" n + 1st [read: n + 1th] object and our words for it: What are the identity conditions for houses of blocks?

Why does van Inwagen think that a house of blocks is an object radically different from the blocks that compose it? And why does he think that if there are, say, 1000 blocks, then in the place where the house is, there are 1001 objects? Not only do I find these notions repugnant to my philosophical sense, I suspect that it is their extremism that motivates van Inwagen to recoil from them and embrace something equally absurd, namely, that there are no such things as houses of blocks or inanimate concrete partite entities generally. 

In other words, if one begins by assuming that if a house of blocks, for example, is a whole of parts, then it is an object radically different from the objects that compose it, an object numerically additional to the objects that compose it; then, recoiling from these extreme positions, one will be tempted to embrace an equal but opposite extremism according to which there are no such inanimate partite entities as houses of blocks. What then should we say about a house of blocks?

First off, it is not identical to any one of its proper parts. Second, it is not identical to the mereological sum of its parts: the parts exist whether or not the house exists. From this it follows that there is a sense in which the house is 'something more' than its parts. But surely it is not an object "radically different" from, or numerically additional to, its proper parts. If there is a house of 1000 blocks in a place, there are not 1001 objects or entities in that place. After all, the house is composed of the blocks, and of nothing else.

So on the one hand the house is 'something more' than its constituent blocks, while on the other hand it is not a "radically different" object above and beyond them. Think of how absurd it would be for me to demand that you show me your house after you have shown me every part of it. "You've shown me every single part of your house, but where is the bloody house?"

The house, thought not identical to the blocks that compose it,  is not wholly diverse from the blocks that compose it .  The house is the blocks arranged housewise. The house is not the blocks, and the house is not some further entity "radically different" from the blocks. The house is just the blocks in a certain familiar arrangement. Should we conclude that the house exists or that it does not exist? I say it exists: the house is the blocks arranged housewise, and the existence of the house is the housewise unity of the blocks. Van Inwagen seems to think that there is no house, there are just the blocks. (Of course, he doesn't believe in the blocks either since they too are inanimate partite entities; but to keep the discussion simple, we may assume that the blocks are simples.)  

Now if it is allowed that the house exists, it seems clear that the house does not exist in the way the blocks do. But this does not strike me as a good reason for saying that the house does not exist at all. What is wrong with saying that the house is a dependent existent? And what is wrong with saying that about partite entities generally? They exist, but they do not exist in addition to their parts, but as the unity or connectedness of their parts. Saying this, we avoid van Inwagen's absurd thesis that inanimate partite entities do not exist. Of course, this commits me to saying that there are at least two modes of existence, a dependent mode and an independent mode. I suspect van Inwagen would find such a distinction incoherent. But that is a topic for a separate post.

The problem can be set forth as an aporetic pentad:

1. The house is not identical to the blocks that compose it.

2. The house is not wholly diverse from the blocks that compose it; it is not an object numerically additional to the blocks that compose it:  given that the house is composed of n blocks, the house itself is not an n + 1th object.

3. The house exists.

4. The constituent blocks exist.

5.  'Exists' is univocal as between wholes and parts: wholes and their parts exist in the same sense.

Each limb has a strong claim on our acceptance.  But they cannot all be true.  Any four of the propositions, taken together, entails the negation of the remaining one.  For example, if the first four are all true, then the fifth must be false.  To solve the problem, one of the limbs must be rejected.  But which one? 

To me it seems obvious that the first four are all true.  So I reject (5).  Rejecting (5), I can say that the house exists as the connectedness of the blocks.  Thus the mode of existence of the whole is different from the mode of existence of its simple parts.  But this solution requires us to believe in modes of existence, which is sure to inspire opposition among analytic philosophers.  Van Inwagen, if I understand him, denies (2) and (3) while accepting the others.

But van I's solution is just crazy, is it not?  Mine is less crazy.  But perhaps you, dear reader, have a better suggestion.