Author: Bill Vallicella

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.)

Hitchens on Mother Teresa’s Dark Night of the Soul

In some measure one must admire that professional contrarian, Christopher Hitchens, whose mind is incandescent in its brilliance, and whose speech is preternatural in its articulateness, and who has the audacity to go after anyone, including Mother Teresa. In a  piece in Newsweek he comments on her Dark Night of the Soul.

But what are his qualifications for such commentary?

Hitchens, like the other members of the 'Dawkins Gang' as I like to call them, does not have a religious bone in his body. He simply does not understand religion, and has no sympathy for it, so much so that he must dismiss it as nonsense.

Lack of religious sensibility is like lack of aesthetic sensibility.  There are people who lack entirely any feel for poetry and music. They lack the 'spiritual organ' to appreciate them, and so their comments on them are of little interest except as indicative of the critics' own limitations. Others are bereft of philosophical sensibility.  I have met mathematicians and scientists who have zero philosophical aptitude and sense and for whom philosophy cannot be anything other than empty verbiage. These people do not lack intelligence, they lack a certain 'spiritual organ,' a certain depth of personality. And of course there are those with no inkling of the austere beauty of mathematics and logic and (let's not leave out) chess. To speak of their beauty to such people would be a waste of time. They lack the requisite appreciative organs.

Hitchens, who remains a man of the Left in his total lack of understanding of religion, doesn't seem to appreciate that Teresa was a mystic and that her dark night of the soul was not a crisis of faith, where faith is construed as intellectual assent to certain dogmas, but an experiencing of the divine withdrawal, an experiencing of God as deus absconditus. A believing non-mystic might lose his faith after applying his reason to his religion's dogmatic content and then finding it impossible rationally to accept. Although I haven't read Teresa's letters, I suspect that this is not what happened in her case. After the fullness of her mystical experience, she experienced desolation when the mystical experiences subsided. So, contra   Hitchens, it was not a realization of the "crushing unreasonableness"  of Roman Catholic dogma that triggered Teresa's dark night, but her experience of the divine absence, an absence that is an expression of the divine transcendence.

I suggest that an atheist like Hitchens, for whom theism is simply not a live existential option, cannot understand the spititual life of a person like Mother Teresa. He can understand it only by caricaturing
it.

And the same goes for the whole gang (Dawkins,Dennett, Hitchens, Harris.)

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.

 

Cartoonist Molly Norris Driven into Hiding by Muslim Extremism

Story here. 

Among the great religions of the world, where 'great' is to be taken descriptively not normatively, Islam appears uniquely intolerant and violent.  Or are there contemporary examples of Confucians, Taoists, Buddhists, Hindus, Jews, or Christians who, basing themselves on their doctrines, publically  issue and carry out credible death threats against those who mock the exemplars of their faiths?  For example, has any Christian, speaking as a Christian, publically  put out a credible murder contract on Andres Serrano for his "Piss-Christ"?  By 'credible,' I mean one that would force its target, if he were rational, to go into  hiding and erase his identity?

UPDATE 9/19.   Commentary by James Taranto here.  Why doesn't Obama speak up for First Amendment rights in this case?

On Budgets

I have never made a budget in my life. Never having made one, I have never had to adhere to one. The budgeter is involved in a negative enterprise: he essays to control and curtail spending. He allocates so much money for this, and so much for that, and strives to stick to his limits. But positive methods are often superior to negative ones. If you want to lose weight, for example, it is better to exercise and burn more calories, while holding your caloric intake constant, than to eat less while holding steady on caloric expenditure. (Aside from the optimal course which is to do both at the same time.) Part of the reason for this is that it is harder to break an old habit than to begin a new one.

Similarly with budgeting. To budget is to approach your personal finances negatively when a positive approach is superior. Instead of setting limits to spending in various categories, specify target savings and investing amounts, and aim high. The Wealthy Barber has a chapter entitled "The Ten Percent Solution." As I recall, the author recommends investing 10% of gross income for long-term growth. That's chickenfeed to my conservative mind. We save and invest far more than this.  The best way to do this, of course, is by automatic payroll deduction. You arrange for your employer to direct deposit some percentage of your income into the account of your choice. You then live on what is left over. 

Why do you need a budget? If you are self-disciplined you will naturally watch your spending, and of course you will never ever use a credit card for its credit feature. You will use it only for its float, record-keeping, rebate, and convenience features. Allow me to brag so as to make a point that is very important for everyone. I have never paid a cent of credit card interest in my life, and in the last several years, each year I have received $300- $400  cash in rebates for the use of a couple of cards which charge me no fee for their use. The credit lines are huge but I go nowhere near them, and the interest rates I could not care less about. Not only that, but the 'float' makes me even more money. Let's say I have the use of $2,000 for six weeks. During that period the goods are in my possession but the money is at my disposal in a cash reserve account earning interest.

Suppose you are a leftie who hates 'corporate America.' What better way to stick it to the credit card companies than by becoming a free-rider?

So I ask again, why do you need a budget? If you are self-disciplined you will naturally watch your spending, and if you are not self-disciplined then you will lack the discipline to adhere to your budget.  Or is this a false alternative?

When I was a graduate student, 'back in the day,' I lived on 2-3 K per annum. And then I got a job which paid for starters the princely sum of 12 K per annum. I said to myself: "Surely, I can save and invest half of that!" But attitude is everthing. Attitude and will and good judgment. For example, if you are inclined to become financially independent, then you would be a fool to marry someone whose idea of Nirvana is a wallet full of charge cards with unlimited credit lines.

The moral side of the economic problem is paramount to a conservative like me. Those who can deny themselves and defer gratification can become financially well-off in a stable political and economic
environment such as we enjoy in these United States. But of course people will not deny themselves and defer gratification. So they must suffer the consequences. The problem is akrasia, weakness of the will. The fundamental problem is not predatory credit card companies, subprime mortgage scammers, and the payday loan sharks. For if you are self-disciplined, cautious, and diligent, they will not be able to get a handle on you.

Apologies to E-Mailers

If you have e-mailed me and haven't received a response, I apologize.  During the last three days I have been revamping my 'work station,' including configuring and getting used to a new computer.  It may be a day or two before I figure out how to access my e-mail account.  There are some old e-mails that it looks as if I will not be able to answer.  I don't have the time or energy to answer everything, and I do have a life away from the computer.

Time was when I couldn't understand how people could fail to respond to e-mail.  "It's so easy; just click on reply and type something.  The least the guy could do is acknowledge receipt." Now I understand, having become what I criticized – there is just too much of it and too many other self- and other-imposed tasks to contend with. 

If the Universe Can Arise out of Nothing, then so can Mind

Over breakfast yesterday morning, Peter Lupu uncorked a penetrating observation.  The gist of it I took to be as follows.  If a naturalist maintains that the physical universe can arise out of nothing without divine or other supernatural agency, then the naturalist cannot rule out the possibility that other things so arise, minds for example — a result that appears curiously inconsistent with both the spirit and the letter of naturalism.  Here is how I would spell out the Lupine thought.

The central thrust of naturalism as an ontological thesis is that the whole of reality is exhausted by the space-time system and what it contains.  (To catalog what exactly it contains is a job for the physicist.)  But this bald thesis can be weakened in ways consistent with the spirit of naturalism.  The weakening makes naturalism more defensible.  And so I will irenically assume that it is consistent with the spirit of a latitudinarian naturalism to admit abstracta of various sorts such as Fregean propositions and mathmatical sets.  We may also irenically allow the naturalist various emergent/supervenient properties so long as it is understood that emergence/supervenience presupposes an emergence/supervenience base, and that this base is material in nature.  I will even go so far as to allow the naturalist emergent/supervenient substances such as individual minds.  But again, if this is to count as naturalism, then (i) their arisal must be from matter, and (ii) they cannot, after arising, exist in complete independence of matter.

What every naturalism rules out, including the latitudinarian version just sketched, is the existence of God, classically conceived, or any sort of Absolute Mind, as well as the existence of unembodied and disembodied finite minds. 

The naturalist, then, takes as ontologically basic the physical universe, the system of space-time-matter, and denies the existence of non-emergent/supervenient concreta distinct from this system.  Well now, what explains the existence of the physical universe, especially if it is only finitely old?  One answer, and perhaps the only answer available to the naturalist, is that it came into existence ex nihilo without cause, and thus without divine cause.  Hence

1. The physical universe came into existence from nothing without cause.

Applying Existential Generalization and the modal rule ab esse ad posse we get

2. It is possible that something come into existence  from nothing without cause.

If so, how can the naturalist exclude the possibility of minds coming into existence but not emerging from a material base?  If he thinks it possible that the universe came into existence ex nihilo, then he must allow that it is possible that divine and finite minds also have come into existence ex nihilo.  But this is a possibility he cannot countenance given his commitment to saying that everything that exists is either physical or determined by the physical.

This seems to put the naturalist in an embarrassing position.  If the universe is finitely old, then it came into existence.  You could say it 'emerged.'  But on naturalism, there cannot be emergence except from a material base.  So either the universe did not emerge or it did, in which case (2) is true and the principle that everything either is or is determined by the physical is violated.

“We’re Just a Bit of Pollution,” Cosmologist Says

(People have been asking me to comment on Stephen Hawking's new book.  As a sort of warm-up, I have decided to repost the following entry from the old site.)

I am all for natural science and I have studied my fair share of it. I attended a demanding technical high school where I studied electronics and I was an electrical engineering major in college with all the mathematics and science that that entails. But I strongly oppose scientism and the pseudo-scientific blather that too many contemporary physicists engage in. Case in point: Lawrence M Krauss's recent comment quoted in the pages of the New York Times that “We’re just a bit of pollution,” . . . “If you got rid of us, and all the stars and all the galaxies and all the planets and all the aliens and everybody, then the universe would be largely the same. We’re completely irrelevant.”

Saturday Night at the Oldies: Beethoven, Billy Bob and Peggy Lee

The Man Who Wasn't There is one of my favorite movies, and the best of Ludwig van Beethoven is as good as classical music gets.  So enjoy the First Movement of the Moonlight Sonata to the masterful cinematography of the Coen Brothers.

Here is the final scene of the movie.  Ed Crane's last words:

I don't know where I'm being taken.  I don't know what I'll find beyond the earth and sky.  But I am not afraid to go.  Maybe the things I don't understand will be clearer there, like when a fog blows away.  Maybe Doris will be there. And maybe there I can tell her all those things they don't have words for here.

That is the way I see death, as an adventure into a dimension in which we might come to understand what we cannot understand here, a movement from night and fog into the clear light of day.  It is a strange idea, I admit, the idea that only by dying can one come into possession of essential knowledge.  But no more strange  than the idea that  death leaves the apparent absurdity of our existence unredeemed, a sentiment expressed in Peggy Lee's 1970 Is That All There is?

Where Were You on 9/11/01?

I remember exactly where I was and what I was doing when I first of heard about the acts of 9/11 Islamoterrorism.  It was a cool and bright Arizona morning, dry and delightful as only the desert can be.  I had just returned from a long hard bike ride.  Preliminary to some after-ride calisthenics I switched on the TV only to see  one of the planes enter one of the Trade Towers.

I suspected correctly what was up and I remarked to my wife, "Well, two good things will come of this: Gary Condit will be out of the news forever, and finally something will be done about the porosity of the southern border."  I turned out to be right on one count.  Gary Condit, who had come to national prominence because of his adulterous affair with Chandra Levy, and who had dominated the news that summer of aught-one, dropped out of sight.  And good riddance.

But I was sadly mistaken on the second count.  So here we are, nine years later, with such abominations Obaminations as Department of Justice lawsuits against the State of Arizona for attempting to do what the Feds ought to do yet refuse to do while Mexican drug cartels control some portions of the state.

For detailed analysis, see my Arizona category.

Legality and Propriety: What One Has a Right to Do is Not Always Right to Do

What do the following have in common:  Flag burning, Koran burning, suspending a crucifix in urine and calling it art, building a mosque near Ground Zero, calling a black person 'nigger,' affixing a 'Fuck Your Honor Student' bumpersticker on your car?

They are all offensive, but they are all legal.

Flag burning.  If you steal my flag and burn it, then you violate my property rights and do something illegal.  If you burn a public flag, then that is illegal on grounds of vandalism.  If you burn a flag you own but in a way that causes a public disturbance or endangers members of the public, then  those acts fall under other existing statutes.  But if you buy an American flag and burn it on your property, then you are within your legal rights.  You are in the vast majority of cases a contemptible punk if you do so, and I have a right to my opinion on this score.  But you are within the law.  That is why calls for a flag-burning (or rather anti-flag-burning) amendment to the U. S. Constitution are pointless and just so much political grandstanding. Such appeals are just another way politicians evade the job of making tough decisions about matters of moment.

Ought flag burning come under the rubric of protected speech?  Logically prior question: Is it speech at all?  What if I make some such rude gesture in your face as 'giving you the finger.'  Is that speech?  If it is, I would like to know what proposition it expresses.  'Fuck you!' does not express a proposition.  Likewise for the corresponding gesture with the middle finger.  And if some punk burns a flag, I would like to know what proposition the punk is expressing.  The Founders were interested in protecting reasoned dissent, but the typical act of flag burning by the typical leftist punk does not rise to that level.  Without going any further into this issue, let me just express my skepticism at arguments that try to subsume gestures and physical actions under speech.  But the main point is that we don't need a flag-burning amendment and we ought not have a general legal prohibition on the burning or other desecration of privately owned national symbols if the burning or other desecration is done in a way that does not violate existing laws.

Koran burning.  If it is legal to burn the flag in certain circumstances, then it it legal to burn the Koran or any book in similar circumstances.  If you own a copy of the book, you can do anything you want with it.  You can use it for toilet paper.  So if the Gainesville yahoo wants to organize a Koran burning on private property with privately-owned copies of the Muslim holy book, that must be tolerated no matter how stupid and offensive it is.

But there must be no double standards.  If you condemn Koran burning, then you ought to condemn crucifix desecration and flag burning.  And if you tolerate the latter, then you ought to tolerate the former.

The media both Left and Right are piling on Terry Jones, the Gainesville pastor, while failing to see that his brand of red-necked push-back is exactly what one should expect in the face of Islamist provocation.

And there must be no kow-towing to Muslim hypersensitivity. 

Continue reading “Legality and Propriety: What One Has a Right to Do is Not Always Right to Do”

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.