Author: Bill Vallicella

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.

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?

 

A Farewell to the Philosophy of Religion? Why not a Farewell to Philosophy?

Steven Nemes  informs me that Keith Parsons is giving up teaching and writing in the philosophy of religion.  His reasons are stated in his post Goodbye to All That.  The following appears to be his chief reason:

I have to confess that I now regard “the case for theism” as a fraud and I can no longer take it seriously enough to present it to a class as a respectable philosophical position—no more than I could present intelligent design as a legitimate biological theory. BTW, in saying that I now consider the case for theism to be a fraud, I do not mean to charge that the people making that case are frauds . . . .  I just cannot take their arguments seriously any more, and if you cannot take something seriously, you should not try to devote serious academic attention to it.

John Beversluis is also quitting:

Keith [Parsons] and I have emailed about getting out of the philosophy of religion. I've made the same decision. I'm through wasting my time trying to convince people who don't want to be convinced of the irrationality of their beliefs. And I have had more than enough verbal abuse from the Richard Purtills, the Peter Kreefts, and the Thomas Talbotts. We are all getting older and I, for my part, would much rather read books I want to read (or reread) and listen to great music that I either don't know or want to know better. Not to mention, spending more time with my wife instead of constantly yielding to the lure of the computer to work on yet another project that will convince few, antagonize some, and be ignored by most. Interestingly, Keith and I came to this conclusion more or less simultaneously but independently.

Steven Nemes comments in his e-mail to me:

I don't imagine you think the case for theism is so bad . . . . Any arguments in particular you think are promising? Any anti-theistic arguments you think are particularly good, too? (It was Parsons who said that the case for atheism/naturalism has been presented about as well as it ever can be by philosophers like Michael Martin, Schellenberg, Oppy, Gale, et al.)

Or perhaps you don't think the issues are so clear and obvious one way or the other in the philosophy of religion? In fact, is such dismissive hand-waving like Parsons' and Beversluis' ever acceptable in philosophy? Are there any issues that are settled?

Steven has once again peppered me with some pertinent and challenging questions.  Here is a quick response.

Of course, I don't consider the case for theism to be a "fraud," to use Parson's word. I also don't understand how the case could be called a fraud if the people who make it are not frauds.  But let's not enter into an analysis of the concept fraud.  We may charitably chalk up Parsons' use of 'fraud' to rhetorical overkill, which is certainly not a censurable offense in the blogosphere.  And when Parsons tells us that he cannot take the theistic arguments seriously any more, he is presumably not making a merely autobiographical remark.  He is not merely informing us about his present disgusted state of mind, although he is doing that.  He is asserting  that the case for theism is not intellectually respectable, while the case for atheism and naturalism (which Parsons in his post brackets together) are intellectually respectable.  (It is worth noting that while nauralism entails atheism, atheism does not entail naturalism: McTaggart was an atheist but not a naturalist.  But this nuance needn't concern us at present.)

Parsons' metaphilosophical assertion does not impress me.  I make a different assertion:  There are intellectually respectable cases to be made both for theism/anti-naturalism and for atheism/naturalism.  I don't think there are any 'knock-down' arguments on either side.  There are arguments for the existence of God, but no proofs of the existence of God.  And there are arguments for  the nonexistence of God, but no proofs of the nonexistence of God.  But of course it depends on what is meant by 'proof.'

I suggest that a proof is a deductive argument, free of informal fallacy, valid in point of logical form, all of the premises of which are objectively self-evident. I will illustrate what I mean by 'objectively self-evident' with an anecdote.   In a discussion with a Thomist a while back  I mentioned that the first premise of his reconstruction of Aquinas' argument from motion (the First of the Five Ways) was not (objectively) self-evident, and that therefore the First Way did not amount to a proof.  The premise in the reconstruction was to the effect that it is evident to the senses that the reduction of potency to act  is a real feature of the world.

I granted to my interlocutor  that what Thomas calls motion, i.e., change, is evident to the senses as a real feature of the world.  But I pointed out that it is not evident to the senses that the actualization of potency is a real feature of the world.  That change is the reduction of potency to act is a theoretical claim that goes beyond what is given to sense perception.  For this reason, the first premise of the reconstruction of the First Way, though plausible and indeed reasonable, is not objectively self-evident.  One can of course give many logically correct arguments for the Aristotelian-Thomistic metaphysics, but we can ask with respect to the premises of these arguments whether they are objectively self-evident.  If they are not, then they do not amount to proofs given my stringent definition of 'proof.'

It is equally true, however, that one cannot prove the nonexistence of God, from evil say. 

But it is no different outside the philosophy of religion.  God and the soul are meta-physical in the sense of supersensible.  But there is nothing supersensible about the bust of Beethoven sitting atop my CD player.  It is a material object, a middle-sized artifact, open to unaided perception.  But such a humble object inspires interminable and seemingly intractable debate among the most brilliant philosophers.  I am currently exploring some of these issues in other threads, and so I won't go into details here.  But consider Peter van Inwagen's denial of the existence of artifacts (which is part of a broader denial of the existence of all nonliving composite objects).  You could say, very loosely, that van Inwagen is an 'atheist' about artifacts. Other philosophers, equally brilliant and well-informed, deny his denial. 

Now it would take an excess of chutzpah to label van Inwagen's carefully argued denial of artifacts as intellectually unrespectable.  I suggest that it takes an equal excess of chutzpah to label the case for theism intellectually unrespectable.

Steven asked me whether the dismissive attitude of Parsons and Beversluis is acceptable.  I would say no.  It is no more acceptable in the philosophy of religion than it is in other branches of philosophy where there are equally genuine but equally difficult and interminably discussable problems.

Let me end with this question:  If one's reason for abandoning the philosophy of religion is that one cannot convince those on the other side — "I'm through wasting my time trying to convince people who don't want to be convinced of the irrationality of their beliefs." (Beversluis) — then is this not also a reason for abandoning philosophy tout court?  After all, the brilliant van Inwagen did not convince the brilliant David Lewis that the latter was wrong about Composition as Identity — and this is a very well-defined and mundane and ideology-free question.

 

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?

Bigot and Anti-Bigot

If the bigot unreasonably and uncritically rejects what is different just because it is different, the anti-bigot unreasonably and uncritically accepts the different just because it is different.  No doubt some conservatives are bigots.  But some liberals are too: they unreasonably and uncritically reject conservatism.  What's more, there are plenty of liberal anti-bigots whose knee-jerk inclusivity makes them useful idiots in the hands of our Islamist enemies. 

It is bad to be a bigot, but it is also bad to be an anti-bigot. Some liberals are bigots and some are anti-bigots.  Some conservatives are bigots but almost none are anti-bigots.  It looks as if conservatives gain the edge in this little comparison.

Sick of the GZ Mosque Yet?

If not, New Yorkers Want Islamic Center Moved.  But Farrakhan wants it built.  Ever watch a speech by Farrakhan?  His oratory is Hitlerian.  It is as if he has studied Hitler's speeches.  He starts out very calmly.  He says things that are reasonable, indeed things that conservatives would applaud.  He preaches self-reliance and self-discipline.  That is certainly a message blacks need to hear from one of their own.  But then gradually, ever so gradually, he works himself into a frenzy, and then comes the reference to the Jews . . . . 

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.

Of ‘Of’

As useful as it is to the poet, the punster, and the demagogue, the ambiguity of ordinary language is intolerable to the philosopher.  Disambiguate we must.  One type of ambiguity is well illustrated by the Old Testament verse, Timor domini initium sapientiae, "The fear of the Lord is the beginning of wisdom."  'Of' functions differently in 'fear of the Lord' and 'beginning of wisdom.'

Clearly, in 'fear of the Lord' the Lord is the object, not the subject of fear: the Lord is the one feared, not the one who fears.  In 'beginning of wisdom,' however, wisdom is the subject of beginning, that which begins; it is not the  object of beginning — whatever that would mean. Thus we could write, "The fear of the Lord is wisdom's beginning," but not, "The Lord's fear is wisdom's beginning."

The foregoing is an example of subject/object ambiguity.  Here is an example of what I will call objective/appositive ambiguity: 'As a young man, I was enamored of the city of Boston.'  The thought here is that the city, Boston, was an object of my love.  Clearly, 'of' is being used in two totally different ways in the sample sentence.

I wonder if all uses of 'of' can be crammed into the following little schema:

A. Subjective Uses of 'Of.'  'The presidency of  Bill Clinton was rocked by scandal.'  'The redness of her face betrayed her embarrasment.'   'She cited the lateness of the hour as her reason for leaving.'  The presidency of Bill Clinton is Bill Clinton's presidency.  And similarly in the other two examples.

Here 'of' expresses possession or belonging.  The sharpness of the knife is the knife's sharpness.  The wife of Tom is Tom's wife.  The uncle of the monkey is the monkey's uncle.  The ace of spades is the ace belonging to the spade suit.  A jack of all trades is all trades' jack.  Of course, if you want to be understood in English you cannot say, 'Marvin is all trades' jack.'  But that's irrelevant.

The set of natural numbers is the natural numbers' set.  The set of all sets is all sets' set. 

'Several are the senses of "of."'   The 'of' which is used — as opposed to mentioned — functions subjectively inasmuch as the thought could be put as follows: '"Of"'s senses are several.'

The square root of -1 is -1's square root.

B. Objective Uses of 'Of.'  'When I first met Mary, thoughts of her occupied my mind from morning until night.' Obviously, her thoughts could not occupy my mind; 'thoughts of her' can only mean my thoughts about her. Note that 'Mary's thoughts' could be construed in three ways: Mary's thoughts; thoughts about Mary; Mary's thoughts about herself.

Pictures of Lily are pictures that depict (are about) Lily.

'What was once called the Department of War is now called the Department of Defense.'  It would not be idiomatic to refer to the Department of Defense as the department about defense, but this is presumably the thought: the DOD is the department concerned with defense.

'The study of logic will profit only those of a certain cast of mind.'    This sentence features first the objective, then the subjective use of  'of.'  The thought is: The study which takes logic as its object will profit only those whose mind's cast is such-and-such.

'The Sage of the Superstitions is a man of leisure.'  This sentence features first the subjective, then the objective use of 'of.'  The thought is: The Superstition Mountains' sage is about (is devoted to) leisure.

'Of all Ponzi schemes, that of Bernie Madoff was the most successful.'  The first 'of' is objective, the second subjective.  The thought is:  Concerning (with respect to) all Ponzi schemes, Bernie Madoff's scheme was the most successful.

C. Dual Uses of 'Of.'  'Thoughts of Mary filled Mary's mind.' In this example, Mary is both the subject and the object of her thoughts, assuming that 'Mary' refers to the same person in all occurrences.  So in 'thoughts of Mary,' 'of' functions both subjectively and objectively.

D. Appositive Uses of 'Of.'  'The train they call The City of New Orleans will go five hundred miles before the day is done.' 'Former NYC mayor Ed Koch referred to the city of Boston as Podunk.' Clearly, 'city of Boston' is not a genitive construction, logically speaking. We could just as well write, 'the city, Boston.' So I call the 'of'  in 'city of Boston' the 'of' of apposition. If the grammarians don't call it that, then they ought to.

The House of the Rising Sun is not the rising sun's house — the sun, rising or setting,  'don't need no stinkin' house' — or the house devoted to the study of the rising sun, but the house, The Rising Sun. 

The kingdom of Heaven is the kingdom, Heaven.

ADDENDUM:  A little more thought reveals that my quick little schema is inadequate.  Where would these examples fit:  'He drank a glass of wine.'  'She purchased ten gallons of gasoline.'  'Boots of Spanish leather are all I'm wishin' to be ownin'." (Bob Dylan)  'He is a man of the cloth.'

'Glass of wine' expresses a relation between a container and what it contains, and that does not seem to fit any of the four heads above.  And note that 'a gallon of gasoline' is unlike 'a glass of wine.'  A gallon is a unit of measure whereas a glass, though it could be a unit of measure, is a receptacle.  A gallon is not a receptacle.  'Hand me that gallon' makes no sense.  'Hand me that gallon can' does.

My Rabbi

I am not now, and never have been, a Jew either religiously or ethnically, and it is certain that I shall never become one ethnically, and exceedingly probable that I shall never become one religiously.  But if I were a Jew, and if Dennis Prager were a rabbi, then I should like to have him as my rabbi.

He often remarks, rightly, that there is no wisdom on the Left.  He's right.  But there is wisdom in him and his broadcasts.  Tune into his 'Happiness Hour' sometime.  And then try to dismiss conservative talk radio as 'hate radio' as so many contemptible liberals do.

I have in my hands Barbara Ehrenreich's Bright-Sided: How the Relentless Promotion of Positive Thinking has Undermined America (Henry Holt 2009, color-coding in original).  On the frontispiece: "To complainers everywhere:  Turn up the volume!"  The book does contain some worthwhile observations, but only a liberal could employ a subtitle and motto like these.  (Even if the publisher chose the title, Ehrenreich had to approve it.) Here we see a fundamental and unbridgeable temperamental difference between conservatives and leftists, between adults and perpetual adolescents.  Yes, I do mean that polemically.  There is a place for polemic.  More polemic later.