Maverick Philosopher

The Problem of Individuation: Genuine or Pseudo?

1. The ontological problem of individuation is actually two problems.  One is the problem of what makes two or more numerically different individuals numerically different.  What grounds numerical difference?  The other is the problem of what makes an individual an individual as opposed to a member of some other category of entity.  What grounds individuality?  If the first question is about the differentiator (the ground of numerical difference), the second is about the individuator (the ground of  individuality). 

The two questions are often conflated, but as you can see, they are different.  The conflation is aided and abetted by the fact that on some theories the entity posited to do the differentiating job also does the individuating job.  For example, in Gustav Bergmann's ontology, bare particulars are both differentiators and individuators.  But if I both load the truck and drive the truck it doesn't follow that loading and driving are the same job.  So we cannot just assume that what does the differentiating job will also do the individuating job.  I won't say anything at the moment about the details of Hector-Neri Castaneda's ontology, but in it, the individuator is not a differentiator.

Therefore, 'problem of individuation' is a bit of a misnomer.  A better phrase would be 'problem(s) of individuation/differentiation.'  Having said that, I revert to the stock phrase.

Note also that we are talking ontology here, not epistemology.  'Individuate' can be used in an epistemological way to mean: 'single out,' 'pick out,' 'make an identifying reference to,' etc.  Suppose I single out x as the only item that has properties P, Q, R . . . .  It doesn't follow that having exactly those properties is what makes x an individual or makes x numerically different from y.  It could be like this: concrete particulars a and b are told apart by their difference is properties, but that makes them numerically different is that each has a numerically different bare particular, or a different nonqualitative thisness, where this is not understood to be a bare particular.

2. Before going any deeper into this we ought to ask whether our two problems are genuine. 

Taking the first one first, why is there any need for a differentiator?  If S and P are numerically distinct concrete particulars, why not just take that as a brute fact?  Brute facts need no explaining.  That's what their bruteness consists in. 

A constituent ontologist might answer as follows.  Concrete particulars have ontological consituents, among them, their properties.  Properties are universals.  It is possible that two particulars share all their properties.  Since they are not different due to a difference in properties, there must a further ontological factor that accounts for their difference.

This sketch of an answer won't cut any ice with a certain nominalist of our acquaintance.  He will presumably deny both that concrete particulars have ontological constituents, and that there are any universals.  He may even go so far as to claim that the very idea of an ontological constituent is senseless.  He will take our first question as a pseudo-question that rests on false assumptions.

Our nominalist will say something similar about the first question.  'Only if one starts with the assumption that individuals have ontological constituents, that among these are properties,  and that these are universals,  will one have the problem of explaining why the individual is an individual and not a collection or conjunction of universals.  The assumptions are false, so the problem is pseudo.'

Future Individuals and Haecceities

According to a wisecrack of Schopenhauer, the medievals employed only three examples: Socrates, Plato, and an ass.  In keeping with this hoary if not 'asinine' tradition, I too in my capacity as humble footnoter to Plato shall employ Socrates as my example.  To point out the obvious: he stands in for any concrete individual whatsoever, animate or inanimate.

I have been arguing (drawing on the work of the late Barry Miller with whom I was privileged to have enjoyed a lengthy correspondence) that before Socrates came to be there was no such property as identity-with-Socrates.  The astute Franklin Mason objects:

If there is no such thing as Socrates' identity before he came to be, it would seem that there's no such thing as his identity after he ceases to be. If we need the man Socrates if we are to speak about him, then we can't do so either before or after he exists. But clearly we can now speak of Socrates though he is long since dead. Thus we don't need the man to speak of the man, and so whatever reason we had to deny the existence of haecceities that predate the things to which they attach collapses.

Socrates came to exist in 470 B.C.  So we can say:

1. It is now the case that Socrates did exist.

From this it follows that

2. It was the case (e.g. in 470 B.C.) that Socrates does exist.

Mason seems to think that from (2) one can also validly infer

3. It was the case (e.g.. in 472 B.C.) that Socrates will exist.

But if I am right, the second inference fails.  For if I am right, before Socrates came to exist, not only was there no Socrates, there was no singular or  de re possibility of Socrates' existing.  At most there was the general possibility that someone come to have the properties that Socrates subsequently had. 

To appreciate that the inference from (2) is invalid, consider a parallel argument.  Suppose I promise Tom that I will buy him a book for his birthday.  On the morning of his birthday I spy a first-edition copy of On the Road in a book store and I buy it.  Once the purchase has been made we can say:

1*. It is now the case that a copy of OTR was selected for Tom.

From this it follows that

2*. It was the case that a copy of OTR is selected for Tom.

But until I bought the book on the morning of Tom's birthday I had no idea what I would buy.  So before I bought the book no one was entitled to say

3*. It was the case that a copy of OTR will be selected for Tom.

The most one would be entitled to say is

4. It was the case that a book will be selected for Tom.

Just as (3*) does not follow from (2*), (3) does not follow from (2).

Only present and past actual individuals are genuine individuals.  Future 'individuals,' not having yet come into existence, are not genuine individuals.

REFERENCE: Barry Miller, "Future Individuals and Haecceitism," Review of Metaphysics 45 (September 1991), 3-28, esp. 10-11.

Does Classical Theism Require Haecceitism?

Haecceitism is the doctrine that there are haecceities. But what is an haecceity? 

Suppose we take on board for the space of this post the assumptions that (i) properties are abstract objects, that (ii) they can exist unexemplified, and that (iii) they are necessary beings. We may then define the subclass of haecceity properties as follows.

A haecceity is a property H of x such that: (i) H is essential to x; (ii) nothing distinct from x exemplifies H in the actual world; (iii) nothing distinct from x exemplifies H in any metaphysically possible world.

So if there is a property of Socrates that is his haecceity, then there is a property that individuates him, and indeed individuates him across all times and worlds at which he exists: it is a property that he must have, that nothing distinct from him has, and that nothing distinct from him could have. Call this property Socrateity. Being abstract and necessary, Socrateity is obviously distinct from Socrates, who is concrete and contingent. Socrateity exists in every world, but is exemplified (instantiated) in only some worlds. What's more, Socrateity exists at every time in every world that is temporally qualified, whereas Socrates exist in only some worlds and only at some times in the worlds in which he exists.

Now suppose you are a classical theist.  Must you accept haecceitism (as defined above) in virtue of being a classical thesist?  I answer in the negative.  Franklin Mason answers in the affirmative.  In a comment on an earlier post, Mason gives this intriguing argument into which I have interpolated numerals for ease of reference.

[1] When God created the world, he knew precisely which individuals he would get.  Thus [2] he didn't need to have those very individuals in front of him to know which ones they were.  Thus [3] there must be a way to individuate all possible individuals that in no way depends upon their actual existence. [4] Such a thing is by definition a haecceity. Thus [5] there are haecceities.

I don't anticipate any disagreement with Mason as to what an haecceity is.  We are both operating with the Plantingian notion.  We disagree, however, on (i) whether there are any haecceities and (ii) whether classical theism is committed to them. In this post I focus on (ii).  In particular, I will explain why I do not find Mason's argument compelling.

My reservations concern premise [1].  There is a sense in which it is true that when God created Socrates, he knew which individual he would get.  But there is also a sense in which it is not true.  So we need to make a distinction.  We may suppose, given the divine omniscience, that before God created Socrates he had before his mind a completely determinate description, down to the very last detail, of the individual he was about to bring into existence.  In this sense, God knew precisely which individual he would get before bringing said individual into existence.  Now either this description is pure or it is impure.

A pure description is one that includes no proper names, demonstratives or other indexicals, or references to singular properties.  Otherwise the description is impure.  Thus 'snubnosed, rationalist philosopher married to Xanthippe' is an impure description because it includes the proper name 'Xanthippe.'  'Snubnosed, rationalist, married  philosopher,' by contrast, is pure.  (And this despite the fact that 'married' is a relational predicate.)  Pure descriptions are qualitative in that they include no references to specific individuals.  Impure descriptions are nonqualitative in that they do include references to specific individuals.

Now if God has before his mind a complete pure description of the individual he wills to create then it could apply to precisely one individual after creation without being restricted to any precise one.  (Cf. Barry Miller, "Future Individuals and Haecceitism," Review of Metaphysics 45, September 1991, p. 14)  This is a subtle distinction but an important one.  It is possible that Socrates have an indiscernible twin.  So the complete description 'snubnosed, rationalist philosopher, etc.' could apply to precisely one individual without applying to Socrates.  This is because his indiscernible twin would satisfy it just as well as he does.  The description would then apply to precisely one individual without being restricted to any precise one.  So there is a clear sense, pace Mason, in which  God, prior to creation, would not know which individual he would get.  Prior to creation, God knows that there will be an individual satisfying a complete description.  But until the individual comes into existence, he won't know which individual this will be.

Creation is not the bestowal of existence upon a a pre-existent, fully-formed, wholly determinate essence.  It is not the actualization of a wholly determinate mere possible.  There is no individual essence or haecceity prior to creation.  Creation is the creation ex nihilo of a a new individual.  God creates out of nothing, not out of pre-existent individual essences or pre-existent mere possibles.  Thus the very individuality of the individual first comes into being in the creative act.  Socrates' individuality and haecceity do not antedate (whether temporally or logically) his actual existence.

Mason would have to be able rationally to exclude this view of creation, and this view of the relation of existence and individuality, for his argument to be compelling.  As it is, he seems merely to assume that they are false.

Could God, before creation, have before his mind a complete impure description, one that made reference to the specific individual that was to result from the creative act?  No, and this for the simple reason that before the creative act that individual would not exist.  And therein lies the absurdity of Plantingian haecceities.  The property of identity-with-Socrates  is a nonqualitative haecceity that make essential reference to Socrates.  Surely it is absurd to suppose that that this 'property' exists at times and in possible worlds at which Socrates does not exist.  To put it another way, it is absurd to suppose that this 'property' could antedate (whether temporally or logically) the existence of Socrates.

We are now in a position to see why Mason's argument is not compelling.  If [1] is true, then [2] doesn't follow from it.  And if [2] follows from [1], then [1] is false.  Thus [1] conflates two distinct propositions:

1a.  When God created the world, he knew precisely which pure complete descriptions would be satisfied.

1b.  When God created the world, he knew precisely which individuals would exist.

(1a) is true, but it does not entail

2.  God didn't need to have those very individuals in front of him to know which ones they were.

(1b) entails (2), but (1b) is false.

I conclude that classical theism does not entail haecceitism.  One can be such a theist without accepting haecceities.

C. J. F. Williams' Analysis of 'I Might Not Have Existed'

There are clear cases in which 'exist(s)' functions as a second-level predicate, a predicate of properties or concepts or propositional functions or cognate items, and not as a predicate of individuals. The   affirmative general existential 'Horses exist,' for example, is best understood as making an instantiation claim: 'The concept horse is instantiated.' Accordingly, the sentence does not predicate existence of individual horses; it predicates instantiation of the concept horse.

This sort of analysis is well-nigh mandatory in the case of negative general existentials such as 'Flying horses do not exist.' Here we have a true sentence that cannot possibly be about flying horses for the simple reason that there aren't any. (One can make a Meinongian move here, but if possible we should try to get by without doing so.) On a reasonable parsing,  'Flying horses do not exist'  is about the concept flying horse, and says of this concept that it has no instances.

But what about singular existentials? Negative singular existentials like 'Pegasus does not exist' pose no problem. We may analyze it as, 'It is not the case that there exists an x such that x is the winged   horse of Greek mythology.' Or we can take a page from Quine and say that nothing pegasizes. What we have done in effect is to treat the singular term 'Pegasus' as a predicate and read the sentence as a   denial that this predicate applies to anything.

Problems arise, however, with affirmative singular existentials such as 'I exist' and with sentences like 'I might not have existed' which  are naturally read as presupposing the meaningfulness of 'I exist' and thus of uses of 'exists' as a first-level predicate. Thus, 'I might not have existed' is construable in terms of the operator 'It might not have been the case that ____' operating upon 'I exist.'

C.J.F. Williams, following in the footsteps of Frege, maintains the draconian thesis that all meaningful uses of 'exist(s)' are second-level. He must therefore supply an analysis of the true sentence 'I might not have existed' that does not require the meaningfulness of 'I exist.' His suggestion is that

     . . . my assertion that I might not have existed is the assertion
     that there is some property . . . essential to me, which I alone
     possess, and which might never have been uniquely instantiated . .
     (What is Existence?, Oxford 1981, p. 104)

Williams is suggesting that for each individual x there is a property H such that (i) H is essential to x in the sense that x cannot exist  except as instantiating H; and (ii) H, if instantiated, is instantiated by exactly one individual. Accordingly, to say that x  might not have existed is to say that H might not have been instantiated. And to say that x exists is to say that H is instantiated.

This analysis will work only if the right properties are available. What is needed are essentially individuating properties. Suppose Ed is the fastest marathoner. Being the fastest marathoner distinguishes Ed from everything  else, but it does not individuate him since it is not bound up with Ed's identity that he be the fastest marathoner. Ed can be Ed without being the fastest marathoner. So Ed's existence cannot be equivalent to, let alone idenctical with, the instantiation of the property of being the fastest marathoner since this is an accidental property of anything that possesses it, whereas the existence of an individual must be essential to it. After all, without existence a thing is nothing at all! 

On the other hand, Ed's existence is not equivalent to his instantiation of any old essential property such as being human since numerous individuals possess the property whereas the existence of an individual is unique to it.

What is needed is a property that Ed alone has and that Ed alone has in every possible world in which he exists. Such a property will be essentially individuating: it will individuate Ed in every possible world in which Ed exists, one of these being the actual world.

Williams suggests the property of having sprung from sperm cell S and ovum O. Presumably Ed could not have existed without this origin, and anything possessing this origin is Ed. The idea, then, is that the   existence of Ed is the instantiation of this property.

The property in question, however, is one that Michael Loux would call 'impure': it makes essential reference to an individual or individuals, in this case to S and O. Since S and O each exist, the   question arises as to how their existence is to be analyzed.

For an analysis like that of Williams to work, what is needed is a  property that does not refer to or presuppose any existing individual,  a property that somehow captures the haecceity of Ed but without presupposing the existence of an individual. If there were such a haecceity property H, then one could say that Ed's existence just is H's being instantiated.

But as I argue in tedious detail in A Paradigm Theory of Existence and in this post such haecceity properties are creatures of darkness. That is one of  the reasons I reject Frege-style theories of existence.

Existence, real pound-the-table existence, belongs to individuals.  The attempt to 'kick it upstairs' and make it a property of properties or concepts or propositional functions is completely wrongheaded, pace such luminaries as Frege, Russell, and their epigoni.

The Rabbit of Real Existence and the Empty Hat of Mere Logic

Consider again this curious piece of reasoning:

1. For any x, x = x.  Ergo:
2. a = a.  Ergo:
3. (Ex)(x = a). Ergo:
4. a exists.

This reasoning is curious because it seems to show that one can deduce the real existence of an individual a from a purely formal principle of logic, the Law of Identity.  And yet we know that this cannot be done.  We know that the rabbit of real existence cannot be pulled from the empty hat of mere logic. Since the argument cannot be sound, it must be possible to say where it goes wrong.  (It is a strange fact of philosophical experience that arguments that almost all philosophers reject nevertheless inspire the wildest controversy when it comes to the proper diagnosis of the error.  Think of the arguments of Zeno, Anselm, and McTaggart.) 

The move from (1) to (2) appears to be by Universal Instantiation.  One will be forgiven for thinking that if everything is self-identical, then a is self-identical.  But I say that right here is a (or the) mistake.   To move from (1) to (2), the variable 'x' must be replaced by the substituend 'a' which is a constant.   Now there are exactly three possibilities:

Either 'a' refers to something that exists, or 'a' refers to something that does not exist or 'a' does not refer at all.  On the third possibility it would be impossible validly to move from (2) to (3) by Existential Generalization.  The same goes for the second possibility:  if 'a' refers to a Meinongian nonexistent object, then  one could apply existentially-neutral Particular Generalization to (2), but not Existential Generalization.  This leaves the first alternative.  But if 'a' refers to something that exists, then right at this point real existence has been smuggled into the argument. 

I hope the point is painfully obvious.  One cannot move from (1) to (2) by logic alone: one needs an extralogical assumption, namely, that 'a' designates something that exists.  To put it another way, one must assume that the domain of quantification is not only nonempty but inhabited by existing individuals.  After all, (1) is true for every domain, empty or not.  (1) lacks Existential Import.  The truth of (1) is consistent with there being no individuals at all.

Let's now consider Peter's supposed counterexample to the principle that if p entails q and p is necessary, then q is also necessary.  He thinks that the above argument shows that there are cases in which necessary propositions entail contingent ones.  Thus he thinks that the conjunction of (1) and (2) entails (3), but that (3) is contingent.

Well, I agree that if we are quantifying over a domain the members of which are contingent individuals, then (3) is contingent.  But surely the conjunction of (1) and (2) is also contingent.  For the conjunction of a necessary and a contingent proposition is a contingent proposition.  Now of course (1) is necessary.  But (2), despite appearances, is contingent.  For if 'a' designates a contingent individual, then it designates an individual that exists in some but not all worlds, and in those worlds in which a does not not exist it is not true that a = a.

In the worlds in which a exists, a is essentially a.  But a is not necessarily a because there are worlds in which a does not exist.

What accounts for the illusion that if (1) is necessary, then (2) must also be necessary?   Could it be the tendency to forget that while 'x' is a variable,  'a' is an arbitrary constant?

 

Deducing John McCain from the Principle of Identity

What, if anything, is wrong with the following argument:

   1. (x)(x = x) (Principle of Identity)
   Therefore
   2. John McCain = John McCain (From 1 by Universal Instantiation)
   Therefore
   3. (Ex)(x = John McCain) (From 2 by Existential Generalization)
   Therefore
   4. John McCain exists. (From 3 by translation into ordinary idiom)

The initial premise states that everything is identical to itself, that nothing is self-diverse. Surely this is a necessary truth, one true no matter what, or in the jargon of possible worlds: true in every (broadly logically) possible world.

(2) follows from (1) by the intuitively clear inference rule of Universal Istantiation.  Surely, if everything is self-identical, then John McCain is  self-identical. The inferential move from (2) to (3) is also quite obvious: if McCain is self-identical, then something is identical to McCain. But (3) is just a complicated way of saying that John McCain exists. So we get the surprising result that the existence of John McCain is validly deducible from an a priori knowable necessary truth  of logic!

You understand, of course, that the argument is not about John McCain: it is about any nameable entity. Supposedly, Wilhelm Traugott Krug (1770-1842) once demanded of Hegel that he deduce Herr Krug's pen. If we name that pen 'Skip,' we can then put that name in the place of 'John McCain' and run the argument as before.

There is one premise and three inferences. Does anyone have the chutzpah to deny the premise? Will anyone make bold to question inference rules U.I. and E.G.? And yet surely something has gone wrong. Intuitively, the existence of a contingent being such as McCain cannot be deduced from an a priori knowable necessary truth of logic.  For that matter, the existence of a necessary being such as God cannot be deduced from an a priori knowable necessary truth of logic.  Surely nothing concrete, not even God, is such that its existence can be derived from the Law of  Identity.

So what we have above is an ontological argument gone wild whereby the  rabbit of real existence is pulled from the empty hat of mere logic!

St. Bonaventura said that if God is God, then God exists. If such  reasoning does not work in the case of God, then a fortiori it does not work  in the case of McCain or Herr Krug's pen.

Note that (1) is necessarily true. (It doesn't just happen to be the case that each thing is self-identical.) If (2) follows immediately  from (1), (2) is also necessarily true. And if (2) is necessarily true, then (3) is necessarily true. And the same holds for (4). But surely it is not the case that, necessarily, John McCain exists. He cannot be shown to exist by the above reasoning, and he certainly cannot be shown to necessarily exist by it.

So what went wrong? By my count there are three essentially equivalent ways of diagnosing the misstep.

A. One idea is that the argument leaves the rails in the transition from (3) to (4). All that (3) says is that something is identical to John McCain. But from (3) it does not follow that John McCain exists.   For the something in question might be a nonexistent something. After all, if something is identical to Vulcan, you won't conclude that  Vulcan exists. To move validly from (3) to (4), one needs the auxiliary premise:

3.5  The domain of quantification is a domain of existents only.

Without (3.5), John McCain might be a Meinongian nonexistent object. If he were, then everything would be logically in order up to (3). But  to get from (3) to (4) one must assume that one is quantifying over existents only.

But then a point I have been hammering away  at all my philosophical life is once again thrown into relief:  The misnamed 'existential' quantifier, pace Quine, does not express existence, it presupposes existence!

B. Or one might argue that the move from (1) to (2) is invalid. Although (1) is necessarily true, (2) is not necessarily true, but  contingently true: it is not true in possible worlds in which McCain does not exist. There are such worlds since he is a contingent being. To move validly from (1) to (2) a supplementary premise is needed:

1.5 'John McCain' refers to something that exists.

(1.5) is true in some but not all worlds. With this supplementary premise on board, the argument is sound. It also loses the  'rabbit-out-of-the-hat' quality. The original argument appeared to be  deducing McCain from a logical axiom. But now we see that the argument  made explicit does no such thing. It deduces the existence of McCain  from a logical axiom plus a contingent premise which is indeed   equivalent to the conclusion.

C. Finally, one might locate the error in the move from (2) to (3). No doubt McCain = McCain, and no doubt one can infer therefrom that something is identical to McCain. But this inferential move is not existential generalization, if we are to speak accurately and nontendentiously, but particular generalization. On this diagnosis,  the mistake is to think that the particular quantifier has anything to do with existence. It does not. It does not express existence, pace Quine, it expresses the logical quantity someness.

In sum, one cannot deduce the actual existence of a contingent being from a truth of logic alone. One needs existential 'input.' It follows that there has to be more to existence than someness, more than what  the 'existential' quantifier expresses. The thin conception of existence,  therefore, cannot be right.

Now let me apply these results to what Peter Lupu has lately been arguing.   Here he argues:

(i) (x)(x=x);

(ii) a=a, for any arbitrarily chosen object a; (from (i))

(iii) (Ex)(x=a); (from (ii) by existential generalization);

Now, (i) is necessary, but (iii) is contingent. Yet (i) entails (iii) via (ii), which is also necessary. So I simply do not see how the principle (1*) which you and Jan seem to accept applies in modal logics that include quantification plus identity.

Peter thinks he has a counterexample to the principle that if p entails q, and p is necessary, then q is also necessary.  For he thinks that *(x)( x = x)*, which is necessary, entails *(Ex)(x = a)*, which is contingent.

But surely if *a = a* is necessary, i.e. true in all worlds, then *(Ex)(x = a)* is necessary as well.

The mistake in Peter's reasoning comes in with the move from *Necessarily, (x) (x = x)* to *Necessarily, a = a*.   For surely it is false that in every possible world, a = a.  After all, there are worlds in which a does not exist, and an individual cannot have a property in a world in which it doesn't exist.  One must distinguish between essential and necessary self-identity.  Every individual is essentially (as opposed to accidentally) self-identical: no individual can exist without being self-identical.  But only some individuals are necessarily self-identical, i.e, self-identical in every world.  Socrates, for example, is essentially but not necessarily self-identical: he is self-identical in every world in which he exists (but, being contingent, he doesn't exist in every world).  By contrast, God is both essentially and necessarily self-identical: he is self-identical in every world, period (because he is a necessary being).   

An Argument for Direct Reference

Edward Ockham uses  ‘Direct Reference’ to refer to "the theory that part or all of the meaning of a proper name requires the existence of a named object."  This implies that a proper name cannot have a meaning unless there exists an object it names.  He then gives the following argument:

A term signifies either a property or an object.  But properties are repeatable.  A property like being white, or running, or being bald can be instantiated by many individuals.  Even a property that can only be had by one individual at a time (being the tallest living philosopher) can be instantiated by different individuals at successive times, or could be instantiated by a different individual than the one that possesses it now.  If a proper name like 'Socrates' signified a property, even a unique property, it would make sense to say that this individual is Socrates on Tuesday, but that someone else is Socrates on Wednesday.  Or that this individual is Socrates today, but might not have been Socrates.  But that makes no sense.  A proper name does [NOT] signify something that is repeatable, therefore does not signify a property.  Therefore it signifies an object.  Therefore an object is part or all of the meaning of a proper name, and the theory of Direct Reference, as defined above, is true.

As it stands, this argument is not compelling.  To be compelling, it would have to close off the 'haecceity escape route.'  Haecceitas is Latin for 'thisness.'  Let us say that H is an haecceity property, an haecceity for short, if and only if H is a first-level property which, if instantiated, is instantiated by the same individual ('object' in Edward's terminology) at every time and in every possible world in which it is instantiated.  Accordingly, 'the tallest living philosopher' does not express an haecceity property:  it has different instances at different times and at different possible worlds, even though at a given time in a given world it has only one instance.  If there are haecceity properties, then they are not repeatable, i.e., multiply instantiable, whether at different times or in different worlds.

Consider the property of being identical to Socrates. If there is such a property, it can serve as the sense of 'Socrates,' or, to use Edward's word, that which 'Socrates' "signifies."  In the case of a vacuous proper name such as 'Vulcan,' the property of being identical to Vulcan  could serve as its sense.  If this is tenable, then 'Vulcan' is a genuine proper name despite it having no referent, and the Direct Reference theory as defined above is false.

Haecceities can either be nonqualitattive or qualitative.  Identity-with-Socrates is an example of a nonqualitative haecceity.  But one can imagine an haecceity property that is compounded out of qualitative properties where the latter are not tied to specific individuals in the way in which identity-with-Socrates is tied to the individual Socrates.  The logical construction goes like this.  We first form the huge conjunction K1 of all the qualitative properties that Socrates instantiates in the actual world.  K has as conjuncts being snubnosed, being married, being a plebeian, being poor, etc.  We do the same for every possible world in which Socrates exists.  This yields a series of conjunctive properties, K1, K2, K3, etc.  We then make a monstrous disjunctive property each disjunct of which is one of the Ks.  This property is Socrates' qualitative haecceity.  It is a property but it is clearly not repeatable (multiply instantiable).  If there are such properties, they defeat Edward's argument above.

I myself do not believe in haecceity properties, nonqualitative or qualitative.  See A Difficulty With Haecceity Properties.  My point is that Edward's argument above is not compelling unless he can persuasively exclude them.

Now, given that I reject haecceity properties, I ought to find the above argument compelling.  But this lands me in a quandry.  For I hesitate to say that 'Vulcan' or 'Pegasus' are not proper names.  They seem to be perfectly good proper names albeit vacuous.  If so, then no part of their meaning involves the existence of a referent, and the DR theory is false.

Or consider 'Moses.'  Was there some one man who received, or claimed to receive, the Torah from YHWH on Mount Sinai?  Aren't we strongly tempted to say that the meaning of 'Moses' is what it is whether or not Moses existed?  If we say that, then it can be no part of the name's meaning that it have an existing referent.  Nor can it be any part of the name's meaning that there be a causal chain leading back to an initial baptism.  If Moses never existed, then there was nothing to baptize. 

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

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

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

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

Self-Reference and Individual Concepts

The following can happen.  You see yourself but without self-recognition.  You see yourself, but not as  yourself.  Suppose you walk into a room which unbeknownst to you has a mirror covering the far wall.  You are slightly alarmed to see a wild-haired man with his fly open approaching you.  You are looking at yourself but you don't know it.  (The lighting is bad, you've had a few drinks . . . .) You think to yourself

1. That man has his fly open!
but not
2. I have my fly open!

Now these propositions -- assuming they are propositions -- are obviously different.  For one thing, they have different behavioral consequences.  I can believe the first without taking action with respect to my fly, or any fly.  (I'm certainly not going to go near the other guy's fly.)  But if I believe the second I will most assuredly button my fly, or pull up my zipper.

So it seems clear that (1) and (2) are different propositions.  I can believe one without believing the other.  But how can this be given the plain fact that 'that man' and 'I' refer to the same man?  Both propositions predicate the same property of the same subject.  So what makes them distinct propositions?

I know what your knee-jerk response will be.  You will say that, while 'I' and 'that man' have the same referent, they differ in sense just like 'Hesperus' and 'Phosphorus.'  Just as one can believe that Hesperus is F without believing that Phosphorus is F despite the identity of the two, one can believe that (1) without believing that (2) despite the fact that the subject terms are coreferential.

The trouble with this response is that it requires  special 'I'-senses, and indeed a different one for each user of the first-person singular pronoun.  These go together with special 'I'-propositions which are a species of indexical proposition.  When I believe that I am F, I refer to myself via a special Fregean sense which has the following property: it is necessarily a mode of presentation of me alone.  We can also think of this 'I'-sense as an individual concept or haecceity-concept.  It is a concept such that, if it is instantiated, it is instantiated (i) by me, (ii) by nothing distinct from me, (iii) and by the same person in every possible world in which it is instantiated.

But what on earth (or on Twin Earth) could this concept be, and how could I grasp it?  The concept has to 'pin me down' in every possible world in which I exist.  It has to capture my very thisness, or, in Latin, my haecceitas.  But a better Latin word is ipseitas, ipseity, selfhood, my being a self, this one and no other.    In plain old Anglo-Saxon it is the concept of me-ness, the concept of being me.

The theory, then, is that my awareness that

3. I am that man!

consists in my awareness that the concept expressed by 'I' and the concept expressed by 'that man' are instantiated by one and the same individual.  But this theory is no good because, even if my use of 'I' expresses an haecceity-concept, that is not a concept I can grasp or understand.  Maybe God can grasp my haecceity, but I surely can't.  Individuum ineffabile est said the Scholastics, echoing Aristotle. No finite mind can 'eff' the ineffable.  The individual in his individuality, in his very haecceity and ipseity, is ineffable.

Self-reference is not routed though sense, however things may stand with respect to other-reference.  When I refer to myself using the first-person singular pronoun, I do not refer to myself via a Fregean sense.

So here is the problem expressed as an aporetic pentad:

a. (1) and (2) express different Fregean propositions.
b. If two Fregean propositions are different, then they must differ in a constituent.
c. The difference can only reside in a difference in subject constituents.
d. The subject constituent of (2) is ineffable.
e. No sense (mode of presentation) or humanly-graspable concept can be ineffable.

This pentad is inconsistent:  (a)-(d), taken together, entail the negation of (e).  The only limb that has a chance of being false is (a).  One could say that (1) and (2), though clearly different, are not different by expressing different Fregean propositions.  But then what would our positive theory have to be?

 

Intentionality and Haecceity

Steven Nemes inquires:

Do you think that your stand on intentionality not requiring the existence of the intentional object is contradictory with your argument against haecceity properties (as non-qualitative thisnesses)? You say that an individual can have the property of searching after Atlantis, let's say, even if Atlantis doesn't exist. But your argument against haecceities is that identity-with-Socrates would be nonsense if Socrates didn't exist.

How would you solve the apparent contradiction?

Let's first note an ambiguity that infects 'intentional object.' Intentionality is object-directedness.  So there is a clear sense in which every intentional mental state 'takes an accusative,' 'is of or about an object.'  That object could be called the intentional object.  Accordingly, whether I want a three-headed dog or a one-headed dog, my wanting has an intentional object.  The nonexistence of three-headed dogs does not prejudice the object-directedness of my wanting a three-headed dog.  It is equally important to note that the existence of one-headed dogs plays no role in making my wanting a one-headed dog object-directed.  This is because object-directedness is an intrinsic feature of mental acts.  To see this more clearly, suppose I want a one-headed dog that is distinct from every one-headed dog that presently exists.  This mental state is object-directed, but its object-directedness does not derive from the present existence of any one-headed dog, or anything else.

But one could also use 'intentional object' to refer to the mind-independent entity, if there is one, that satisfies the description (definite or indefinite) that expresses the content of the intentional state.  If we use the term in this second way, then my wanting a three-headed dog does not have an intentional object.

It is only in this second sense that intentionality does not require the existence of the intentional object.  It is part of the very essence of wanting as an intentional mental state that it be a wanting of something (that is an objective genitive, by the way, not a subject genitive.)  But it doesn't follow that the something exists.  Similarly for perceiving, imagining, believing, etc.

As for the haecceity-property identity-with-Socrates, it is nothing at all at times and in worlds in which Socrates doesn't exist.  I stick to that self-evident point pace Plantinga. (See A Difficulty With Haecceity Properties)

It seems to me that my line on haecceities is entirely consistent with my line on intentionality.  Socrateity (identity-with-Socrates) essentially involves Socrates himself, that very individual, in a way in which seeking Atlantis (construed as a mental state, not as a physical action or actions) does not essentially involve Atlantis itself.  And this is a good thing since there is no such island.

You seem to think that an intentional mental state acquires its object-directedness from without in virtue of the mind-independent existence of an entity that the state is directed to.  It is this misconception that suggests to you that there is a contradiction in my affirming  both

1. An haecceity H of x is nothing if x does not exist
and
2. It is not the case that a wanting W of x is nothing if x does not exist.

But note that  'H of x' is a subjective genitive whereas 'W of x' is an objective genitive.  The haecceity or nonqualitative thisness of Atlantis is nothing at all because Atlantis does not exist. There is nothing for it to be the haecceity of.   But a wanting of Atlantis is what it is whether or not Atlantis exists. 

And similarly in other cases.  An ancient Greek can be a Zeus-worshipper whether or not Zeus exists.   But the same Greek cannot own a slave unless there exists some slave he owns.  The instance of of ownership requires for its individuation the existence of both relata.  But the instance of worshipping does not require the existence of both relata.

On Our Knowledge of Sameness

How ubiquitous, yet how strange, is sameness!  A structure of reality so pervasive and fundamental that a world that did not exhibit it would be inconceivable. 

How do I know that the tree I now see in my backyard is numerically the same as the one I saw there yesterday? Alvin Plantinga (Warrant and Proper Function, Oxford 1993, p. 124) says in a Reidian vein that one knows this "by induction." I take him to mean that the tree I now see resembles very closely the one I saw yesterday in the same place and that I therefore inductively infer that they are numerically the same. Thus the resemblance in respect of a very large number of properties provides overwhelming evidence of their identity.

But this answer seems open to objection. First of all, there is something instantaneous and immediate about my judgment of identity in a case like this: I don't compare the tree-perceived-yesterday, or my memory of the tree-perceived-yesterday, with the tree-perceived-today, property for property, to see how close they resemble in order to hazard the inference that they are identical. There is no 'hazarding' at all.  Phenomenologically, there is no comparison and no inference. I just see that they are the same. But this 'seeing' is of course not with the eyes. For sameness is not an empirically detectable property or relation. I am just immediately aware -- not mediately via inference -- that they are the same.  Greenness is empirically detectable, but sameness is not.

What is the nature of this awareness given that we do not come to it by inductive inference?   And what exactly is the object of the awareness, identity itself?

A problem with Plantinga's answer is that it allows the possibility that the two objects are not strictly and numerically the same, but are merely exact duplicates or indiscernible twins. But I want to discuss this in terms of the problem of how we perceive or know or become aware of change.  Change  is linked to identity since for a thing to change is for one and the same thing to change. 

Let's consider alterational (as opposed to existential) change. A thing alters iff it has incompatible properties at different times.  Do we perceive alteration with the outer senses? A banana on my counter on Monday is yellow with a little green. On Wednesday the green is gone and the banana is wholly yellow. On Friday, a little brown is included in the color mix. We want to say that the banana, one and the same banana,  has objectively changed in respect of color.

But what justifies our saying this? Do we literally see, see with the eyes, that the the banana has changed in color? That literal seeing would seem to require that I literally see that it is the same thing that has altered property-wise over ther time period. But how do I know that it is numerically the same banana present on Monday, Wednesday, and Friday? How do I know that someone hasn't arranged things so that there are three different bananas, indiscernible except for color, that I perceive on the three different days? On that extraordinary arrangement I could not be said to be perceiving alterational change. To perceive alterational change one must perceive identity over time. For there is change only if one and the same thing has different properties at different times. But I do not perceive the identity over time of the banana.

I perceive a banana on Monday and a banana on Wednesday; but I do not visually perceive that these are numerically the same banana. For it is consistent with what I perceive that there be two very similar bananas, call them the Monday banana and the Wednesday banana.   I cannot tell from sense perception alone whether I am confronting numerically the same banana on two different occasions or two numerically different bananas on the two occasions. If you disagree with this, tell me what sameness looks like. Tell me how to empirically detect the property or relation of numerical sameness. Tell me what I have to look for.

Suppose I get wired up on methamphetamines and stare at the banana the whole week long. That still would not amount to the perception of alterational change. For it is consistent with what I sense-perceive that there be a series of momentary bananas coming in and out of existence so fast that I cannot tell that this is happening. (Think of what goes on when you go to the movies.) To perceive change, I must perceive diachronic identity, identity over time. I do not perceive the latter; so I do not perceive change. I don't know sameness by sense perception, and pace Plantinga I don't know it by induction. For no matter how close the resemblance between two objects, that is consistent with their being numerically distinct. And note that my judgment that the X I now perceive is the same as the X I perceived in the past has nothing tentative or shaky about it. I judge immediately and with assurance that it is the same tree, the same banana, the same car, the same woman. What then is the basis of this judgment? How do I know that this tree is the same as the one I saw in this spot yesterday? Or in the case of a moving object, how do I know that this girl who I now see on the street is the same as the one I saw a moment ago in the coffee house? Surely I don't know this by induction.

How then do I know it?

The Bundle Theory and the Identity of Indiscernibles

I have been defending the bundle-of-universals theory of concrete particulars (BT) against various weak objections over a series of posts, here,  here, here, and here. Now I consider a very powerful objection, one that many will consider decisive.  The objection can be cast in the mold of modus tollendo tollens:  If BT is true, then the Identity of Indiscernibles is a necessary truth.  But the Identity of Indiscernibles is not a necessary truth. Ergo, BT is not true.

1. The Identity of Indiscernibles (IdIn) is the converse of the Indiscernibility of Identicals (InId) and not to be confused with it.  InId is well-nigh self-evident, while IdInis not.  Roughly, the latter is the principle that if x and y share all properties, then x = y.  It is a strictly ontological principle despite the epistemological flavor of 'indiscernible.' As just stated, it is more of a principle-schema than a principle.  We will get different principles depending on what we count as a property.  To arrive at a plausible nontrivial principle we must first rule out haecceity properties.  If, for any x,there is a property of identity-with-x, then no two things could share all properties, and the principle would be trivially true due to the falsehood of the antecedent.  Haecceity properties are creatures of darkness in any case as I argue elsewhere.

A plausible, nontrivial, principle results if we allow as properties all and only relational and  nonrelational pure properties.  A pure property is one that makes no reference to any specific individual.   Being married would then be an example of a pure relational property: to be married is to be married to someone, but not to any specified individual.  Being married to Xanthippe, however, is an impure relational property.  Being obese would be an example of a nonrelational property.  Here then is a plausible version of the Identity of Indiscernibles:

Necessarily, for any x, for any y, and for any relational or nonrelational pure property P, if (x has P iff y has P) then x = y.

2.  It is obvious, I think, that BT entails IdIn in the above form.  Consider a concrete particular, an iron sphere say, at a time.  On BT it is nothing but a bundle of universals. This implies that it is not possible that there be a second iron sphere that shares with the first  all relational and nonrelational pure properties.  This is not possible on BT because on BT a concrete particular is nothing more than a bundle of universals.  Thus there is no ontological ingredient in a concrete particular that could serve to differentiate it from another particular having all the same relational and nonrelational pure properties.  And if it is not possible that there be two things that differ numerically without differing property-wise, then the Identity of Indiscernibles as above formulated is necessarily true.

I am assuming that BT, if true, is necessarily true.  This is a special case of the assumption that the propositions of metaphysics, if true, are necessarily true.  If this assumption is granted, then BT entails IdIn.

3.  But is IdIn true?  Since it is necessarily true if true, all it takes to refute it is a possible counterexample.  Imagine a world consisting of two iron spheres and nothing else.  (The thought experiment was proposed in a 1952 Mind article by Max Black.) They are the same size, shape, volume, chemical composition and so on.  They agree in every nonrelational respect.  But they also agree in every relational respect.  Thus, each has the property of being ten meters from an iron sphere.   What Black's example seems to show is that there can be numerical difference without property-difference.  But then IdIn is false, whence it follows that BT is false.

4.  This is a powerful objection, but is it fatal?  Here are three ways to resist the argument, fit topics for further posts.  He who has the will to blog will never be bereft of topics.

a. Maintain that BT is a contingent truth.  If so, then BT does not entail IdIn as formulated above.

b. Grant that BT entails IdIn, but deny that scenarios such as Black's are really possible.  Admit that they are conceivable, but deny that conceivability entails possibility.

c.  An immanent universal can be wholly present at different places at once.  So why can't a bundle of universals be wholly present in different places at once?  Argue that Black's world can be interpreted, not as two particulars sharing all universals, but as one particular existing in two places at the same time.  From that infer that Black's Gedankenexperiment does show that IdIn is false.

Any other paths of resistance?

A Closer Look at Material Composition and Modal Discernibility Arguments

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

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

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

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

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

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

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

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

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

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

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

Your move, David.

 

Varzi, Sums, and Wholes

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

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

UC is Uniqueness of Composition: 

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

where

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

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

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

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

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

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

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

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

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

 

Four-Dimensionalism to the Rescue?

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

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

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

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

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

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

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

 

Van Inwagen on Arbitrary Undetached Parts

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

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

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

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

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

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

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

D-minus after t* = Descartes after t*

Descartes after t* = Descartes before t*

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

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

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

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

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

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

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

Can a Mereological Sum Change its Parts?

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

The Wise Pig and the Brick House: My Take

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

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

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

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

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

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

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

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

Is Everything a Mereological Sum?

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

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

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

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

3. Everything is a mereological sum. Therefore:

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

What's At Issue Here?

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

What am I missing?

 

Van Inwagen Contra Lewis on Composition as Identity

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

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

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

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

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

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

 2. a = a.

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

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

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

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

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

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

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

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

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

Mereological Innocence and Composition as Identity

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Peter van Inwagen, Artifacts, and Moorean Rebuttals

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

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

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

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

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

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

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

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

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

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

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

 

Van Inwagen on the Ship of Theseus

Peter van Inwagen's Material Beings (Cornell UP, 1990) is a very strange book, but he is a brilliant man, so one can expect to learn something from it. A central claim is that artifacts such as tables and chairs and ships do not exist. One can appreciate  that if there are no ships then the ancient puzzle about identity known as the Ship of Theseus has a very quick (dis)solution. 

The Ship of Theseus is a puzzle about diachronic artifact identity. Here is one version. You have a ship, or a rowboat, or any object, composed entirely of wooden planks. You remove one of the planks and replace it with an aluminum plank of the same size. The wooden plank is placed in a warehouse. After this minor replacement, you have a ship and indeed numerically the same ship as the one you started with. It is not a numerically different ship. Now replace a second wooden plank with an aluminum plank, and place the second wooden plank in the warehouse. Again, the numerical identity of the original ship has been preserved. Continue the replacement process until all of the wooden planks have been replaced with aluminum planks. You now have a wholly aluminum ship that is presumably numerically identical to the original wholly wooden ship despite the fact that none of the original matter is to be found in the aluminum ship. After all, the aluminum ship 'grew out of' the original wooden ship by minor changes each of which is identity-preserving.

Now take the wooden planks from the warehouse and assemble them in the form of a ship and in such a way that the planks bear the same relations to one another as the planks in the original wooden ship bore to one another. You now have two ships, a wooden one and an aluminum one. The question is: which of these ships is identical to the original wooden one?

Suppose the two ships collide on the high seas, and suppose the captain of the original ship had taken a solemn vow to go down with his ship. Where does his duty lie? With the wooden ship or with the aluminum one? Is the original ship identical to the resultant aluminum ship? One will be tempted to say 'yes' since the aluminum ship 'grew out' of the original wooden ship by minor transformations each of which was identity-preserving. Or is the original ship identical to the wooden ship that resulted from the re-assembly of the wooden planks? After all, it consists of the original matter arranged in the original way. Since the resultant wooden and aluminum ships are numerically distinct, they cannot both be identical to the original ship.

Van Inwagen makes short work of the puzzle: "There are no ships, and hence there are no puzzles about the identities of ships." (128) One way van Inwagen supports this bizarre solution is by re-telling the story in language that does not make even apparent reference to ships. Here is his retelling:

Once upon a time, there were certain planks that were arranged shipwise. Call then the First Planks. . . . One of the First Planks was removed from the others and placed in a field. Then it was replaced by a new plank; that is, a carpenter caused the new plank and the remaining First Planks to be arranged shipwise, and in just such a way that the new plank was in contact with the same planks that the removed planks had been in contact with, and at exactly the same points. Call the planks that were then arranged shipwise the Second Planks. A plank that was both one of the First Planks and one of the Second Planks was removed from the others and placed in the field and replaced (according to the procedure laid down above), with the consequence that certain planks, the Third Planks, were arranged shipwise. Then a plank that was one of the First Planks and one of the Second Planks and one of the Third Planks . . . . This process was repeated till all the First Planks were in the field. Then the First Planks were caused to be arranged shipwise, and in just such a way that each of them was in contact with the same planks it had been in contact with when the First Planks had last been arranged shipwise, and was in contact with them at just the same points. (128-129)

If I understand what van Inwagen is claiming here, it is that there is nothing in the standard telling of the story, a version of which I presented above, that is not captured in his re-telling. But since there is no mention of any ships in the re-telling, no puzzle about ship-identity can arise. Perhaps van Inwagen's point could be put by saying that the puzzle about identity is an 'artifact' of a certain way of talking that can be paraphased away. Instead of talking about ships, we can talk about shipwise arrangements of planks. The planks do not then compose a ship, he thinks, and so there is no whole of which they are proper parts, and consequently no question about how this whole maintains its diachronic identity under replacement of its parts.

What are we to say about van Inwagen's dissolution of the puzzle? What I find dubious is van Inwagen's claim that ". . . at no time do two or more of these planks compose anything, and no plank is a proper part of anything." (129) This strikes me as plainly false. If the First Planks are arranged shipwise, then there is a distinction beween the First Planks and their shipwise arrangement. The latter is the whole ship and the former are its proper parts. So how can van Inwagen claim that the planks do not compose a ship? Van Inwagen seems to think that if the planks were parts of a whole, and there were n planks, then the whole would be an n + 1 th entity. Rejecting this extreme, he goes to the other extreme: there is no whole of parts. If there were ships, they would be wholes of parts, but there are no artifactual wholes of parts, so there are no ships. The idea seems to be that when we build an artifact like a ship we are not causing something new to come into existence; we are merely re-arranging what already exists. If so, then although a ship's planks exist, the ship does not exist. Consider what van Inwagen says on p. 35:

If I bring two cubes into contact so that the face of one is conterminous with the face of the other, have I thereby brought into existence a solid that is twice as long as it is wide? Or have I merely rearranged the furniture of the earth without adding to it?

Van Inwagen seems to be saying that when it comes to artifacts, there is only rearrangement, no 'addition to existence.' As a general thesis, this strikes me as false. A ship is more than its planks, and van Inwagen seems to concede as much with his talk of a shipwise arrangement of planks; but this shipwise arrangement brings something new into being, namely, a thing that has causal powers that its constituents do not have. For example, a boat made of metal planks properly arranged will float, while the planks themselves will not float.

A Difficulty With Haecceity Properties

By popular demand, here is revised version of a post that first appeared on the old blog in July of 2005.

Introduction. I find haecceity properties hard to accept, although I grant they they would do various useful jobs if they existed. ('Haecceity' from the Latin haecceitas, thisness.) In this post I explain one or two of my reasons for nonacceptance. If you know your Plantinga, you will know that he is my primary target in these notes.  This post is not about Duns Scotus or any medieval. 

Definition. Suppose we take on board for the space of this post the assumptions that (i) properties are abstract objects, that (ii) they can exist unexemplified, and that (iii) they are necessary beings. We may then define the subclass of haecceity properties as follows.

A haecceity is a property H of x such that: (i) H is essential to x; (ii) nothing distinct from x exemplifies H in the actual world; (iii) nothing distinct from x exemplifies H in any metaphysically possible world.

So if there is a property of Socrates that is his haecceity, then there is a property that individuates him, and indeed individuates him across all times and worlds at which he exists: it is a property that he must have, that nothing distinct from him has, and that nothing distinct from him could have. Call this property Socrateity. Being abstract and necessary, Socrateity is obviously distinct from Socrates, who is concrete and contingent. Socrateity exists in every world, but is exemplified (instantiated) in only some worlds. What's more, Socrateity exists at every time in every world that is temporally qualified, whereas Socrates exist in only some worlds and only at some times in the worlds in which he exists. Haecceity properties have various uses. I'll mention just one.

Use. Suppose I need to analyze 'Socrates might not have existed.' I start with the rewrite, 'Possibly, Socrates does not exist' which features a modal operator operating upon an unmodalized proposition. But 'Socrates does not exist,' being a negative existential proposition, gives rise to an ancient puzzle dating back to Plato. How is reference to the nonexistent possible? The sentence 'Socrates does not exist' is apparently about Socrates, but how so given that he does not exist? If the meaning of 'Socrates' is the name's referent, and nothing can be a referent of a term unless it exists, then Socrates must exist if he is to have nonexistence predicated of him. But the whole point of the sentence is to say that our man does not exist. How can one say of a thing that it does not exist without presupposing that it exists? Haecceities provide a solution. We can understand 'Socrates does not exist' to be about Socrateity rather than about Socrates, and to predicate of Socrateity the property of being exemplified. Recall that Socrateity, unlike Socrates, exists at every time and in every world. So this property, unlike Socrates, is always and necessarily available. Accordingly, we analyze 'Possibly, Socrates does not exist' as 'Possibly, Socrateity is not exemplified.' Socrates' possible nonexistence boils down to Socrateity's possible nonexemplification. It is a nice, elegant solution to the puzzle --assuming that there are haecceity properties.

Problem. One of the stumbling blocks for me, however, is the notion that the thisness of an individual could exist even if the individual whose thisness it is does not exist. Consider the time before Socrates existed. During that time, Socrateity existed. But what content could that property have during that time (or in those possible worlds) in which Socrates does not exist? Socrateity is identity-with-Socrates. Presumably, then, the property has two constituents: identity, a property had by everything, and Socrates. Now if Socrates is a constituent of identity-with-Socrates, then it seems quite obvious that Socrateity can exist only at those times and in those worlds at which Socrates exists. Socrateity would then be like Socrates' singleton, the set consisting of Socrates and Socrates alone: {Socrates}. Clearly, this set cannot exist unless Socrates exists. It is ontologically dependent on him. The same would be true of identity-with-Socrates if Socrates were a constituent of this property.

Problem Exacerbated. If, on the other hand, Socrates is not a constituent of Socrateity, then what gives identity-with-Socrates the individuating content that distinguishes it from identity-with-Plato and identity-with-Pegasus? Consider a possible world W in which Socrates, Plato, and Pegasus do not exist. In W, their haecceities exist since haecceities ex hypothesi exist in every world. What distinguishes these haecceities in W? Nothing that I can see. The only things that could distinguish them would be Socrates, Plato, and Pegasus; but these individuals do not exist in W. It might be said that haecceity properties are simple: identity-with-Socrates is not compounded of identity and Socrates, or of anything else. Different haecceities just differ and they have the content they do in an unanalyzable way. But on this suggestion haecceities seem wholly ungraspable or inconceivable or ineffable, and this militates against thinking of them as properties. I have no problem with the notion of a property that only one thing has, nor do I have a problem with a property that only one thing can have; but a property that I cannot grasp or understand or conceive or bring before my mind -- such an item does not count as a property in my book. It would be more like a bare particular and inherit mutatis mutandis the unintelligibility of bare particulars.

Haecceities must be nonqualitative.  Consider a conjunctive property the conjuncts of which are all the mutiply exemplifiable properties a thing has in the actual world. Such a property would individuate its possessor in the actual world: it would be a property that its possessor and only its possessor would have in the actual world. Such a property is graspable in that I can grasp its components (say, being barefooted, being snubnosed, being married, etc.) and I can grasp its construction inasmuch as I understand property conjunction. But the only way I can grasp Socrateity is by grasping is as a compound of identity and Socrates -- which it cannot be for reasons given above.

Note that Socrateity is not equivalent to the big conjunctive property just mentioned. Take the conjunction of all of Socrates' properties in the actual world and call it K. In the actual world, Socrates has K. But there are possible worlds in which he exists but does not exemplify K. And there are possible worlds in which K is exemplified by someone distinct from him. So Socrateity and K are logically nonequivalent. What we need, then, if we are to construct a qualitative thisness or haecceity of Socrates is a monstrous disjunctive property D[soc] the disjuncts of which are all the K's Socrates has in all the possible worlds in which he exists. This monstrous disjunction of conjunctions is graspable, not in person so to speak, but via our grasp of the operations of conjunction and disjunction and in virtue of the fact that each component property is graspable. But D[soc] is not identical to Socrateity. The former is a qualitative thisness whereas the latter is a nonqualitative thisness. Unless the Identity of Indiscernibles is true, these two thisnesses are nonequivalent. And there are good reasons to think that the Identity of Indiscernibles is not true.  (Max Black's iron spheres, etc.) So D[Soc] is not identical to Socrateity. 

Conclusion. To compress my main point into one sentence: identity-with-Socrates is graspable only as a compound of identity and Socrates; but then this property cannot exist unexemplified. Hence haecceity properties as defined above do not exist.