Month: September 2010

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.

Purveyor/Proprietor

Bill O'Reilly of the Fox News O'Reilly Factor has been introducing Dick Morris as the "purveyor" of dickmorris.com.  That should offend your linguistic sensibilities — assuming you have some.  The word he wants is 'proprietor.'  In plain Anglo-Saxon, a proprietor is an owner.  A purveyor is someone who supplies provisions such as food. 

Suppose you own the Glass Crutch bar and grill.  Is it that eating and drinking establishment that you provide to the public for consumption?  No, you provide food and drink at that place.  So you are the proprietor of the Glass Crutch, not its purveyor.  It is the same with Dick Morris.  He doesn't purvey his site; his site is the place where he purveys his political commentary.

Whether you have the audience of Bill O. or of Bill V. you have the responsibility to honor and protect the English language, our alma mater (nourishing mother), the enabler, if not the source,  of our thoughts.

Companion post:  What is Language? Tool, Enabler, Dominatrix?

Existence, Elimination,and Changing the Subject

This is the fourth in a series on the metaphilosophical problem of sorting out the differences and similarities of analysis, identification, reduction, elimination, and cognate notions.  Parts I, II, III.  This post features existence, a topic I find endlessly fascinating and inexhaustibly rich.

Consider the position of a philosopher I will call Gottbert Fressell.  (A little known fact about him is that in his spare time he writes pro-capitalist novels under the pseudonym 'Randlob Ruge.') Fressell intends a reductionist line about existence.   He maintains that

1. There is (the property of) existence, but what this property is is the property of being instantiated.

This is a reductionist line because our philosopher admits that while there is existence, it can be reductively identified with something better understood, namely, the second-level property of being instantiated.  But I say that despite Fressell's intentions, his position is in truth an eliminativist one.  Thus I maintain that (1) collapses willy-nilly into

2.  There is no (property of) existence.

So if Fressell understood the implications of what he is saying, he would come out of the closet and forthrightly declare himself an existence denier, a denier that there is any such 'property' as existence.  And if he understood his position he would plead 'guilty' to the charge of having changed the subject.

The subject is existence, that in virtue of which me, you, and the moon exist, are, have Being, are not nothing — however you want to put it.  Existence is what Russell has (speaking tenselessly) but his celestial teapot lacks.  The subject is singular existence, the existence of non-instantiable items, the existence of that which I prove when I enact the Cogito.   But what Fressell does is change the subject to what could be called general existence, which is just the being-instantiated of first-level properties.

Note the difference between 'Mungojerrie exists' and 'Cats exist.'  The latter, but not the former, can be reasonably understood as predicating a second-level property (the property of beng instantiated) of a first-level property, the property of being a cat.  Thus 'Cats exist' is analyzable as 'The property of being a cat has instances.'  But 'Mungojerrie exists' cannot be analyzed as 'The property of being identical to Mungojerrie is instantiated' because there is no such haecceity property.  But even if there were, the analysis would fail due to circularity.  If you want to explain what it is for individual a to exist, you move in an explanatory circle of embarrassingly short diameter if you say that the existence of a is a's instantiation of a-ness: a's existence is logically prior to its instantiation of any property. 

If you say that general existence is instantiation, then I have no quarrel with you.  But 'general existence' is a misleading expression with which we can easily dispense by using in its stead 'the property of being instantiated.'  General existence, if you  insist on the phrase, presupposes singular existence.  And because 'general existence' is dispensable, we don't need the qualifier 'singular': existence just is singular existence. If, having understood all of this, you insist that existence is instantiation, then I say you are an eliminativist about existence who has changed the subject from existence to instantiation.

Exercise for the reader:  find more examples of changing the subject in philosophy.  Replacing truth with warranted assertibility would be an example, as would replacing knowledge by what passes for knowledge in a given society (a move some sociologists of knowledge make).

 

The Most Boring Philosophers

Nowadays philosophy so absorbs me in all its branches and movements that I find no philosopher boring. Indeed,  no subject is boring except to the bored who make it  so. Dry texts, like dry wines, are often delightfully subtle and simply require an educable and educated palate. Although no philosophers now bore me, here is a list of philosophers who bored me, or would have bored me, when I was one and twenty:

   1. G. E. Moore
   2. Elizabeth Anscombe
   3. Paul Ziff
   4. Norman Malcolm
   5. John Wisdom
   6. Roderick Chisholm

Philosophers who excited my 21 year old self:

   1. Nicholas Berdyaev
   2. Miguel de Unamuno
   3. Karl Jaspers
   4. Friedrich Nietzsche
   5. Martin Heidegger
   6. Jean-Paul Sartre

Now imagine a philosophy department composed of the twelve aforementioned. Do you think it would split into two factions? What, if anything, do they have in common that justifies subsuming them under the rubric, philosophers?

I have become in many ways more analytic and less Continental over the years. I tend to think that this a lot like becoming less liberal and more conservative, as these terms are popularly understood. One becomes more cautious, careful, precise, piece-meal, rigorous, attentive to details and differences and empirical data, less romantic, more patient, more logical, less impressionistic, less sanguine about big sweeping once-and-for-all solutions. . . .

In sum, and in a manner to elicit howls of protest:  In philosophy, the trajectory of maturation is from Continental to analytic.  In politics, from liberal to conservative.

Howl on, muchachos.

Are Opponents of the Ground Zero Mosque Bigots?

The mavens of what Bernard Goldberg calls the 'lame-stream' media have been trumpeting the canard that opponents of the Ground Zero mosque are 'bigots.'  No doubt some are.  But not in virtue of their opposition to the GZM.  There is nothing inherently bigoted about opposition to the GZM.  Or so I shall argue.  But first we need a definition of 'bigot.'

A bigot is one who is blindly and obstinately intolerant of opinions other than his own, and blindly and obstinately attached to his own point of view.  A bigot, then, is one who without good reason opposes the beliefs and  practices of others and without good reason adheres to his own.    Whether opposition to the building of a mosque near Ground Zero is inherently bigoted, then, hinges on whether there are any good reasons for such opposition.  I say there are.

Continue reading “Are Opponents of the Ground Zero Mosque Bigots?”

Mereological Innocence and Composition as Identity

DavidLewis 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!