Predication – Page 2 – Maverick Philosopher

The Ramsey Problem and the Problem of the Intrinsically Unpropertied Particular

What exactly is the distinction between a universal and a particular? Universals are often said to be repeatable entities, ones-over-many or ones-in-many. Particulars, then, are unrepeatable entities. Now suppose the following: there are universals; there are particulars; particulars instantiate universals; first-order facts are instantiations of universals by particulars.

One and the same universal, F-ness, is repeated in the following facts: Fa, Fb, Fc. But isn't one and the same particular repeated in Fa, Ga, Ha? If so, particulars are as repeatable as universals, in which case repeatability cannot be the mark of the universal. How can it be that all and only universals are repeatable? I stumbled upon this problem the other day. But Frank Ramsey saw it first. See his "Universals," Mind 34, 1925, 401-17.

Instantiation as holding between particulars and universals is asymmetric: if a instantiates F-ness, then F-ness does not instantiate a. (Instantiation is not in general asymmetric, but nonsymmetric: if one universal instatiates a second, it may or may not be the case that the second instantiates the first.) The asymmetry of first-level instantiation may provide a solution to the Ramsey problem. The asymmetry implies that particulars are non-instantiable: they have properties but cannot themselves be properties. By contrast, universals are properties and have properties.

So we can say the following. The repeatability of a universal is its instantiability while the unrepeatability of a particular is its non-instantiability. So, despite appearances, a is not repeated in Fa, Ga, and Ha. For a is a particular and no particular is instantiable (repeatable).

Solve a problem, create one or more others. I solved the Ramsey problem by invoking the asymmetry of instantiation. But instantiation is a mighty perplexing 'relation' (he said with a nervous glance in the direction of Mr. Bradley). It is dyadic and asymmetric. But it is also external to its terms. If a particular has its properties by instantiating them, then its properties are 'outside' it, external to it. Note first that to say that a is F is not to say that a is identical to F-ness. The 'is' of predication is not the 'is' of identity. (For one thing, identity is symmetric, predication is not.) It would seem to follow that a is wholly distinct from F-ness. But then a is connected to F-ness by an external relation and Bradley's regress is up and running. But let's set aside Bradley's regress and the various responses to it to focus on a different problem.

If a and F-ness are external to each other, then it is difficult to see how a could have any intrinsic (nonrelational) properties. Suppose a is an apple and that the apple is red. Being red is an intrinsic property of the apple; it is not a relational property like being in my hand. But if a is F in virtue of standing in an external instantiation relation to the universal F-ness, then it would seem that F-ness cannot be an intrinsic property of a. So an antinomy rears its ugly head: a is (intrinsically) F and a is not (intrinsically) F.

Call this the Problem of the Intrinsically Unpropertied Particular. If there are particulars and universals and these are mutually irreducible categories of entity, then we have the problem of bringing their members together. Suppose it is contingently true that a is F. We cannot say that a is identical to F-ness, nor, it seems, can we say that a and F-ness are wholly distinct and connected by the asymmetric, external tie of instantiation. Is there a way between the horns of this dilemma?

David Armstrong at the end of his career suggested that instantiation is partial identity. The idea is that a and F-ness overlap, are partially identical. This bring a and F-ness together all right, but it implies that the connection is necessary. But then the contingency of the connection is lost. It also implies that instantiation is symmetrical! But then Ramsey is back in the saddle.

More later.

Being is Said in Many Ways: On the Uses of ‘Is’

Chad reports:

In the opening pages of More Kinds of Being: A Further Study of Individuation, Identity, and the Logic of Sortal Terms (Blackwell, 2009), E. J. Lowe distinguishes five uses of ‘is’ as a copula: 1. The ‘is’ of attribution, as in ‘Socrates is wise’ and ‘Grass is green’.2. The ‘is’ of identity, as in ‘Napoleon is Bonaparte’ and ‘Water is H2O’.3. The ‘is’ of instantiation, as in ‘Mars is a planet’ and ‘A horse is a mammal’.4. The ‘is’ of constitution, as in ‘This ring is gold’ and ‘A human body is a collection of cells’.5. The ‘is’ of existence, as in ‘The Dodo is no more’.He says some may be reducible to others, and that one or two must be primitive. I thought this was a helpful spread.

That is indeed helpful, but here are some comments and questions.

1. First of all, I would be surprised if Lowe referred to the five uses as five uses of 'is' as a copula. The 'is' of existence is not a copula because it doesn't couple. There is no copulation, grammatical or logical, in 'God is.' The 'is' of existence does not pick out any sort of two-termed relation such as identity, instantiation, or constitution. Calling the 'is' of identity a copula is a bit of a stretch, and I don't think most philosophers would.

2. Is there a veritative use of 'is'? 'It is so.' 'It is the case that Frege died in 1925.' One could say, though it is not idiomatic: 'Obama's being president is.' One would be expressing that the state of affairs obtains or that the corresponding proposition is true. So it looks as if there is a veritative use of 'is.'

3. Reducibility of one use to another does not show that they are not distinct uses. Perhaps the veritative use can be reduced to what Lowe calls the attributive use. Attributions of truth, however, imply that truth is a property. Frege famously argued that truth cannot be a property. That is a messy separate can of worms.

4. There are also tensed and tenseless uses of 'is.' 'Obama is president' versus '7 + 5 is 12.' With respect to the latter, it would be a bad joke, one reminiscent of Yogi Berra, were I to ask,"You mean now?" Yogi Berra was once asked the time. He said,"You mean now?"

'Hume is an empiricist' can be used both in a tensed way and an untensed way. If I say that Hume is an empiricist what I say is true despite the present nonexistence of Hume. 'Grass is green,' however, is never used in a tensed way, though one can imagine circumstances in which it could.

5. One and the same tokening of 'is' can do more than one job. Is the 'is' in 'Max is black' as used by me in the presence of my cat Max the 'is' of predication merely? I don't think so. It also expresses existence. But this requires argument:

1. 'Max is black' and 'Black Max exists' are intertranslatable.
2. Intertranslatable sentences have the same sense.
Therefore
3. 'Max is black' and 'Black Max exists' express the very same (Fregean) sense.
Therefore
4. Both sentences express both predication and existence: a property is predicated of something that cannot have properties unless it exists.
Therefore
5. The 'is' in 'Max is black' has a double function: it expresses both predication and existence.

Note that both sentences include a sign for the predicative tie. The sign is 'is' in the first sentence and in the second sentence the sign is the immediate concatenation of 'black' and 'Max' in that order. This shows that to refer to logical (as opposed to grammatical) copulation does not require a separate stand-alone sign. 'Black Max exists' expresses both existence via the sign 'exsts' and predication via the immeditae concatenation of 'black' and 'Max' in that order in the context of the sentence in question.

Against Ostrich Nominalism

As magnificent a subject as philosophy is, grappling as it does with the ultimate concerns of human existence, and thus surpassing in nobility any other human pursuit, it is also miserable in that nothing goes uncontested, and nothing ever gets established to the satisfaction of all competent practitioners. (This is true of other disciplines as well, but in philosophy it is true in excelsis.) Suppose I say, as I have in various places:

That things have properties and stand in relations I take to be a plain Moorean fact beyond the reach of reasonable controversy. After all, my cat is black and he is sleeping next to my blue coffee cup. ‘Black’ picks out a property, an extralinguistic feature of my cat.

Is that obvious? Not to some. Not to the ornery and recalcitrant critter known as the ostrich nominalist. My cat, Max Black, is black. That, surely, is a Moorean fact. Now consider the following biconditional and consider whether it too is a Moorean fact:

1. Max is black iff Max has the property of being black.

As I see it, there are three main ways of construing a biconditional such as (1):

A. Ostrich Nominalism. The right-hand side (RHS) says exactly what the left-hand side (LHS) says, but in a verbose and high-falutin' and dispensable way. Thus the use of 'property' on the RHS does not commit one ontologically to properties beyond predicates. (By definition, predicates are linguistic items while properties are extralinguistic and extramental.) Predication is primitive and in need of no philosophical explanation. On this approach, (1) is trivially true. One needn't posit properties, and in consequence one needn't worry about the nature of property-possession. (Is Max related to his blackness, or does Max have his blackness quasi-mereologically by having it as an ontological constituent of him?)

B. Ostrich Realism. The RHS commits one ontologically to properties, but in no sense does the RHS serve to ground or explain the LHS. On this approach, (1) is false if there are no properties. For the ostrich realist, (1) is true, indeed necessarily true, but it is not the case that the LHS is true because the RHS is true. Such notions as metahysical grounding and philosophical explanation are foreign to the ostrich realist, but not in virtue of his being a realist, but in virtue of his being an ostrich.

C. Non-Ostrich Realism. On this approach, the RHS both commits one to properties, but also proffers a metaphysical ground of the truth of the LHS: the LHS is true because (ontologically or metaphysically speaking) the concrete particular Max has the property of being black, and not vice versa.

Note 1: Explanation is asymmetrical; biconditionality is symmetrical.

Note 2: Properties needn't be universals. They might be (abstract) particulars (unrepeatables) such as the tropes of D. C. Williams and Keith Campbell. Properties must, however, be extralinguistic and extramental, by definition.

Note 3: Property-possession needn't be understood in terms of instantiation or exemplification or Fregean 'falling-under'; it might be construed quasi-mereologically as constituency: a thing has a property by having it as a proper ontological part.

Against Ostrich Nominalism

On (A) there are neither properties, nor do properties enter into any explanation of predication. Predication is primitive and in need of no explanation. In virtue of what does 'black' correctly apply to Max? In virtue of nothing. It just applies to him and does so correctly. Max is black, but there is no feature of reality that explains why 'black' is true of Max, or why 'Max is black' is true. It is just true! There is nothing in reality that serves as the ontological ground of this contingent truth. Nothing 'makes' it true. There are no truth-makers and no need for any.

I find ostrich nominalism preposterous. 'Black' is true of Max, 'white' is not, but there is no feature of reality, nothing in or at or about Max that explains why the one predicate is true of him and the other is not!? This is not really an argument but more an expression of incomprehension or incredulity, an autobiographical comment, if you will. I may just be petering out, pace Professor van Inwagen.

Can I do better than peter? 'Black' is a predicate of English. Schwarz is a predicate of German. If there are no properties, then Max is black relative to English, schwarz relative to German, noir relative to French, and no one color. But this is absurd. Max is not three different colors, but one color, the color we use 'black' to pick out, and the Krauts use schwarz to pick out. When Karl, Pierre, and I look at Max we see the same color. So there is one color we both see — which would not be the case if there were no properties beyond predicates. It is not as if I see the color black while Karl sees the color schwarz. We see the same color. And we see it at the cat. This is not a visio intellectualis whereby we peer into some Platonic topos ouranos. Therefore, there is something in, at, or about the cat, something extralinguistic, that grounds the correctness of the application of the predicate to the cat.

A related argument. I say, 'Max is black.' Karl says, Max ist schwarz. 'Is' and ist are token-distinct and type-distinct words of different languages. If there is nothing in reality (no relation whether of instantiation or of constituency, non-relational tie, Bergmannian nexus, etc.) that the copula picks out, then it is only relative to German that Max ist schwarz, and only relative to English that Max is black. But this is absurd. There are not two different facts here but one. Max is the same color for Karl and me, and his being black is the same fact for Karl and me.

Finally, 'Max is black' is true. Is it true ex vi terminorum? Of course not. It is contingently true. Is it just contingently true? Of course not. It is true because of the way extralinguistic reality is arranged. It is modally contingent, but also contingent upon the way the world is. There's this cat that exists whether or not any language exists, and it is black whether or not any language exists.

Therefore, I say that for a predicate to be contingently true of an individual, (i) there must be individuals independently of language; (ii) there must be properties independently of language; and there must be facts or truth-making states of affairs independently of language. Otherwise, you end up with (i) total linguistic idealism, which is absurd; or (ii) linguistic idealism about properties which is absurd; or (iii) a chaos, a world of disconnected particulars and properties.

The above is a shoot-from-the hip, bloggity-blog exposition of ideas that can be put more rigorously, but it seems to to me to show that ostrich nominalism and ostrich realism for that matter are untenable — and this despite the fact that a positive theory invoking facts has its own very serious problems.

Metaphilosophical Coda: If a theory has insurmountable problems, these problems are not removed by the fact that every other theory has problems. For it might be that no theory is tenable,while the poroblem itself is genuine.

A Question About Predication and Identity

Chad M. sent me a paper of his in which he illustrates the distinction between the 'is' of predication and the 'is' of identity using the following examples:

1. Joseph Ratzinger is [the] Pope

and

2. Water is H₂O

where the first sentence is proposed as an example of a predication and the second as an identity sentence. If I were to explain the distinction, I would use these examples:

3. Joseph Ratzinger is German

and (for consistency of subject matter)

4. Joseph Ratzinger is Pope Benedict XVI.

(2) and (4) are clearly sentences expressing strict, numerical, identity. Identity is an equivalence relation: reflexive, symmetrical, transitive. It is also governed by the Indiscernibility of Identicals: if x = y, then whatever is true of x is true of y, and vice versa. By these four tests, the 'is' in (4) is the 'is' of identity. The 'is' in (3) expresses a different relation. Frege would say that it is the relation of falling under: the object JR falls under the concept German. That relation fails each of the four tests. It is not reflexive, not symmetrical, etc.

Now my problem is that I don't find (1) to be a clear example of a predication in the way that (3) is a clear example.

Although 'The Pope' is a definite description, not a name (Kripkean rigid designator), (1) could be construed as asserting an identity, albeit a contingent identity, between the object picked out by 'JR' and the object picked out by 'the Pope.' After all, the sentence passes the four tests, at least if we confine ourselves to the present time and the actual world. The relation is reflexive, symmetrical, and transitive. For example, if JR is the Pope, and the Pope is the vicar of Christ, then JR is the vicar of Christ. Furthermore, whatever is true of JR now is also true of the Pope now, and vice versa. So the indiscernibility test is satisfied as well.

Why not then say that (1) expresses contingent identity and that the 'is' is an 'is' of identity, not of predication? The fact that one could maintain this, with some show of plausibility, indicates that Chad's example is not a clear one. That is my only point, actually.

I grant that the notion of contingent identity can be questioned. How could x and y just happen to be identical? For Kripke, identity is governed by the Necessity of Identity: if x = y, then necessarily x = y. This has the interesting implication that if it is so much as possible that x and y are distinct, then x and y are distinct. (Shades of the ontological argument!)

But there are philosophers who propose to speak of contingent sameness relations. Hector Castaneda is one. So I am merely asking Chad why he uses the puzzling and provocative (1) as illustrative of the 'is' of predication.

There is a labyrinth of deep questions lurking below the surface, questions relevant to Chad's real concern, namely the coherence of the Trinity doctrine and its (in)coherence with the doctrine of divine simplicity.

Properties as Parts: More on Constituent Ontology

Skin and seeds are proper parts of a tomato, and the tomato is an improper part of itself. But what about such properties as being red, being ripe, being a tomato? Are they parts of the tomato? The very idea will strike many as born of an elementary confusion, as a sort of Rylean category mistake. "Your tomato is concrete and so are its parts; properties are abstract; nothing concrete can have abstract parts." Or: "Look, properties are predicable entities; parts are not. Having seeds is predicable of the tomato but not seeds! You're talking nonsense!"

I concede that the notion that the properties of an ordinary particular are parts thereof, albeit in some extended unmereological sense of 'part,' is murky. Murky as it is, the motivation for the view is fairly clear, and the alternative proposed by relational ontologists is open to serious objection. First I will say something in motivation of the constituent-ontological (C-ontological view). Then I will raise objections to the relational-ontological (R-ontological) approach.

For C-Ontology

Plainly, the blueness of my coffee cup belongs to the cup; it is not off in a realm apart. The blueness (the blue, if you will) is at the cup, right here, right now. I see that the cup before me now is blue. This seeing is not a quasi-Platonic visio intellectualis but a literal seeing with the eyes. How else would I know that the cup is blue, and in need of a re-fill, if not by looking at the cup? Seeing that the cup is blue, I see blueness (blue). I see blueness here and now in the mundus sensibilis. How could I see (with the eyes) that the cup is blue without seeing (with the same eyes) blueness? If blueness is a universal, then I see a universal, an instantiated universal. If blueness is a trope, then I see a trope, a trope compresent with others. Either way I see a property. So some properties are visible. This would be impossible if properties are abstract objects as van Inwagen and the boys maintain. Whether uninstantiated or instantiated abstract properties are invisible.

Properties such as blueness and hardness, etc. are empirically detectable. Blueness is visible while hardness is tangible. That looks to be a plain datum. Their being empirically detectable rules out their being causally inert abstracta off in a quasi-Platonic realm apart. For I cannot see something without causally interacting with it. So not only is the cup concrete, its blueness is as well.

This amounts to an argument that properties are analogous to parts. They are not parts in the strict mereological sense. They are not physical parts. So let's call them metaphysical or ontological constituents. The claim, then, is that ordinary particulars such as tomatoes and cups have their properties, or at least some of them, by having them as ontological constituents. To summarize the argument:

1. Some of the properties of ordinary concrete material particulars are empirically detectable at the places the particulars occupy and at the times they occupy them.

2. No abstract object is empirically detectable. Therefore:

3. Some properties of ordinary concrete material particulars are not abtract objects. Therefore:

4. It is reasonable to conjecture that some of the properties of ordinary concrete material particulars are analogous to (proper) parts of them.

Against R-Ontology

I grant that the above is not entirely clear, and that it raises questions that are not easy to answer. But does R-ontology fare any better? I don't think so.

Suppose an R-ontologist is staring at my blue cup. Does he see something colorless? Seems he would have to if the blueness of the cup is an abstract object merely related by exemplification to the concrete cup. Abstracta are invisible. Suppose we introduce 'stripped particular' to designate the R-ontological counterpart of what C-ontologists intend with 'bare particular' and 'thin particular.' A stripped particular is an ordinary particular devoid of empirically detectable properties. If the R-ontologist thinks that my cup is a stripped particular, then he is surely wrong. Call this the Stripped Particular Objection.

But if the R-ontologist agrees with me that the blueness is empirically detectable, then he seems to be involved in an unparsimonious duplication of properties. There is the invisible abstract property in Plato's heaven or Frege's Third Reich that is expressed by the open sentence or predicate '___ is blue.' And there is the property (or property-instance) that even the R-ontologist sees when he stares at a blue coffee cup.

Isn't that one property too many? What work does the abstract property do? More precisely, what ontological work does it do? I needn't deny that it does some semantic work: it serves as the sense (Fregean Sinn) of the corresponding predicate. But we are doing ontology here, not semantics. We want to understand what the world — extramental, extralinguistic reality — must be like if a sentence like 'This cup is blue' is true. We want to understand the property-possession in reality that underlies true predications at the level of language. We are not concerned here with the apparatus by which we represent the world; we are concerned with the world represented.

In my existence book I called the foregoing the Duplication Objection, though perhaps I could have hit upon a better moniker. The abstract property is but an otiose duplicate of the property that does the work, the empirically detectable propery that induces causal powers in the thing that has it.

So I present the R-ontologist with a dilemma: either you are embracing stripped particulars or you are involved in a useless multiplication of entities.

Coda

It's Christmas Eve and there is more to life than ontology. So I'll punch the clock for today. But there are two important questions we need to pursue. (1) Couldn't we reject the whole dispute and be neither a C- nor an R-ontologist? (2) Should ontologists be in the business of explanation at all? (My point that abstract properties are useless for purposes of accounting for predication and property-possession presupposes that there is such a legitimate enterprise as philosophical explanation.)

Stanislav Sousedik’s “Towards a Thomistic Theory of Predication”

Enough of politics, back to some hard-core technical philosophy. If nothing else, the latter offers exquisite escapist pleasures not unlike those of chess. Of course I don't believe that technical philosophy is escapist; my point is a conditional one: if it is, its pleasures suffice to justify it as a form of recuperation from this all-too-oppressive world of 'reality.' It's what I call a 'fall-back position.'

I have been commissioned to review the collection of which the above-captioned article is a part. The collection is entitled Metaphysics: Aristotelian, Scholastic, Analytic (Ontos Verlag 2012) and includes contributions by Peter van Inwagen, Michael Loux, E. J. Lowe, and several others. My review article will address such topics as predication, truth-makers, bare particulars, and the advantages and liabilities of constituent ontology. I plan a series of posts in which I dig deep into some of the articles in this impressive collection.

Stanislav Sousedik argues for an "identity theory of predication" according to which a predicative sentence such as 'Peter is a man' expresses an identity of some sort between the referent of the subject 'Peter' and the referent of the predicate 'man.' Now to someone schooled in modern predicate logic (MPL) such an identity theory will appear wrongheaded from the outset. For we learned at Uncle Gottlob's knee to distinguish between the 'is' of identity ('Peter is Peter') and the 'is' of predication ('Peter is a man').

But let's give the Thomist theory a chance. Sousedik, who is well aware of Frege's distinction, presents an argument for the identity in some sense of subject and predicate. He begins by making the point that in the declarative 'Peter is a man' and the vocative 'Peter, come here!' the individual spoken about is (or can be) the same as the individual addressed. But common terms such as 'man' can also be used to address a person. Instead of saying, 'Peter, come here!' one can say 'Man, come here!' And so we get an argument that I will put as follows:

1. Both 'Peter' and 'man' can be used to refer to the same individual. Therefore

2. A common term can be used to refer to an individual. But

3. Common terms also refer to traits of individuals. Therefore

4. The traits must be identical in some sense to the individuals. E.g., the referent of 'Peter' must be in some sense identical to the referent of 'man.'

But in what sense are they identical? Where Frege distinguishes between predication and identity, Sousedik distinguishes between weak and strong identity. 'Peter is Peter' expresses strong identity while 'Peter is a man' expresses weak identity. "Strong identity is reflexive, symmetric, and transitive, weak identity has none of these formal properties." (254) It thus appears that strong identity is the same as what modern analytic philosophers call (numerical) identity. It is clear that 'Peter is a man' cannot be taken to express strong identity. But what is weak identity?

S. is a constituent ontologist. He holds that ordinary substances such as Peter have what he calls "metaphysical parts." Whereas Peter's left leg is a physical part of him, his traits are metaphysical parts of him. Thus the referents of the common terms 'man,' 'animal,' living thing,' etc. are all metaphysical parts of Peter. Clearly, these are different traits of Peter. But are they really distinct in Peter? S. says that they are not: they are really identical in Peter and only "virtually distinct" in him. The phrase is defined as follows.

(Def. 1) Between x, y there is a virtual distinction iff (i) x, y are really identical; (ii) x can become an object of some cognitive act Φ without y being the object of the same act Φ . . . . (251)

For example, humanity and animality in Peter are really identical but virtually distinct in that humanity can be the intentional object of a cognitive act without animality being the object of the same act. I can focus my mental glance so to speak on Peter's humanity while leaving out of consideration his animality even though he is essentially both a man and an animal and even though animality is included within humanity.

The idea, then, is that Peter has metaphysical parts (MPs) and that these items are really identical in Peter but virtually distinct, where the virtual distinctness of any two MPs is tied to the possibility of one of them being the object of a cognitive act without the other being the object of the same act.

Is S. suggesting that virtual distinctness is wholly mind generated? I don't think so. For he speaks of a potential distinction of MPs in concrete reality, a distinction that becomes actual when the understanding grasps them as distinct. (253) And so I take the possibility mentioned in clause (ii) of the above definition to be grounded not only in the mind's power to objectify and abstract but also in a real potentiality in the MPs in substances like Peter.

One might be tempted to think of weak identity as a part-whole relation. Thus one might be tempted to say that 'Peter' refers to Peter and 'man' to a property taken in the abstract that is predicable not only of Peter but of other human beings as well. 'Peter is a man' would then say that this abstract property is a metaphysical part of Peter. But this is not Sousedik's or any Thomist's view. For S. is committed to the idea that "Every empirical individual and every part or trait of it is particular." (251) It follows that no metaphysical part of any concrete individual is a universal. Hence no MP is an abstract property. So weak identity is not a part-whole relation.

What is it then?

First of all, weak identity is a relation that connects a concrete individual such as Peter to a property taken abstractly. But in what sense is Peter identical to humanity taken abstractly? In this sense: the humanity-in-Peter and the humanity-in-the-mind have a common constituent, namely, humanity taken absolutely as common nature or natura absoluta or natura secundum se. (254) What makes weak identity identity is the common constituent shared by the really existing humanity in Peter and the intentionally existing humanity in the mind of a person who judges that Peter is human.

So if we ask in what sense the referent of 'Peter' is identical to the referent of 'man,' the answer is that they are identical in virtue of the fact that Peter has a proper metaphysical part that shares a constituent with the objective concept referred to by 'man.' Sousedik calls this common constituent the "absolute subject." In our example, it is human nature taken absolutely in abstraction from its real existence in Peter and from its merely intentional existence in the mind.

Critical Observations

I am deeply sympathetic to Sousedik's constituent-ontological approach, his view that existence is a first-level 'property,' and the related view that there are modes of existence. (253) But one of the difficulties I have with S.'s identity theory of predication is that it relies on common natures, and I find it difficult to make sense of them as I already spelled out in a previous post. Common natures are neither one nor many, neither universal nor particular. Humanity is many in things but one in the mind. Hence taken absolutely it is neither one nor many. It is this absolute feature that allows it be the common constituent in humanity-in-Peter and humanity-in-the-mind. And as we just saw, without this common constituent there can be no talk of an identity between Peter and humanity. The (weak) identity 'rides on' the common constituent, the natura absoluta. Likewise, humanity is particular in particular human beings but universal in the mind (and only in the mind). Hence taken absolutely it is neither particular nor universal.

But it also follows that the common nature is, in itself and taken absolutely, neither really existent nor intentionally existent. It enjoys neither esse naturale (esse reale) nor esse intentionale. Consequently it has no being (existence) at all. This is not to say that it is nonexistent. It is to say that it is jenseits von Sein und Nichtsein to borrow a phrase from Alexius von Meinong, "beyond being and nonbeing."

The difficulty is to understand how there could be a plurality of distinct items that are neither universal nor particular, neither one nor many, neither existent nor nonexistent. Note that there has to be a plurality of them: humanity taken absolutely is distinct from animality taken absolutely, etc. And what is the nature of this distinctness? It cannot be mind-generated. This is because common natures are logically and ontologically prior to mind and matter as that which mediates between them. They are not virtually distinct. Are they then really distinct? That can't be right either since they lack esse reale.

And how can these common or absolute natures fail to be, each of them, one, as opposed to neither one nor many? The theory posits a plurality of items distinct among themselves. But if each is an item, then each is one. An item that is neither one nor many is no item at all.

There is also this consideration. Why are common natures more acceptable than really existent universals as constituents of ordinary particulars such as Peter? The Thomists allow universals only if they have merely intentional existence, existence 'in' or rather for a mind. "Intentional existence belongs to entities which exist only in dependence upon the fact that they are objects of our understanding." (253) They insist that, as S. puts it, "Every empirical individual and every part or trait of it is particular." (251) S. calls the latter an observation, but it is not really a datum, but a bit of theory. It is a datum that 'man' is predicable of many different individuals. And it is a datum that Peter is the subject of plenty of essential predicates other than 'man.' But it is not a clear datum that Peter is particular 'all the way through.' That smacks of a theory or a proto-theory, not that it is not eminently reasonable.

One might 'assay' (to use G. Bergmann's term) an ordinary particular as a complex consisting of a thin or 'bare' particular instantiating universals. This has its own difficulties, of course, but why should a theory that posits common natures be preferrable to one that doesn't but posits really existent universals instead? Either way problems will arise.

The main problem in a nutshell is that it is incoherent to maintain that some items are such that they have no being whatsoever. 'Some items are such that they have no being whatsoever' is not a formal-logical contradiction, pace van Inwagen, but it is incoherent nonetheless. Or so it seems to me.

Still Trying to Understand Van Inwagen’s Half-Way Fregeanism about Existence

In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that

. . . existence is analogous to number. Affirmation of existence is in fact nothing but denial of the number nought. Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)

Frege is here advancing a double-barreled thesis that splits into two subtheses.

ST1. Existence is analogous to number.

ST2. Existence is a property (Eigenschaft) of concepts and not of objects.

In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal). Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it. The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts. And so one cannot validly argue from the concept of God to the existence of God.

Existence as a property of concepts is the property of being-instantiated. We can therefore call the Fregean account of existence an instantiation account.

My concern in this entry is the logical relation between the subtheses. Does the first entail the second or are they logically independent? There is a clear sense in which (ST1) is true. Necessarily, if horses exist, then the number of horses is not zero, and vice versa. 'So 'Horses exist' is logically equivalent to 'The number of horses is not zero.' This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects. But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications. So it remains an open question whether one can take the further step of reducing existence to instantiation, or identifying existence with instantiation, or even eliminating existence in favor of instantiation.

(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.' My question is whether (ST1) entails (ST2). Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:

I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero. Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero. 'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate. But so are many predicates that can hardly be regarded as predicates of concepts. The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates. When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse. ("Being, Existence, and Ontological Commitment," pp. 483-484)

It is this passage that I am having a hard time understanding. It is of course clear what van Inwagen is trying to show, namely, that the Fregean subtheses are logically independent and that one can affirm the first without being committed to the second. One can hold that existence is denial of the number zero without holding that existence is a property of concepts.

But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is 'variably polyadic' and the examples van Inwagen employs. 'Robbed a bank together' is an example of a variably polyadic predicate. It is polyadic because it expresses a relation and it is variably polyadic because it expresses a family of relations having different numbers of arguments. For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on. (Example from Chris Swoyer and Francesco Orilia.)

Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse. What I don't understand is why van Inwagen says that 'the number of . . . is not zero' is a variably polyadic predicate. As far as I can see, it is not even polyadic, let alone variably polyadic. What is the relation that the predicate expresses, and why is that relation multigrade? I grant that there are indefinitely many ways the number of horses could be not zero: there could be one horse, two, three, and so on. But what is the relation between or among horses that this supposedly polyadic predicate expresses?

'. . .exist(s)' is monadic. It expresses no relation. Why not say the same about 'such that their number is not zero'?

Now consider 'are ungulates.' If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic. 'Are hooved mammals' is monadic.

The other example is 'Horses have an interesting evolutionary history.' This sentence is clearly not about the concept horse. But it is not about any individual horse either. Consider Harry the horse. Harry has a history. He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age. He went through all sorts of changes. But Harry didn't evolve, and so he had no evolutionary history. No individual evolves; populations evolve:

Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental (e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes.
While it would be handy if there were a way for environmental changes to cause
adaptive changes in our genes — who wouldn't want a gene for malaria resistance
to come along with a vacation to Mozambique? — evolution just doesn't work that
way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.

'Horses have an interesting evolutionary history,' then, is not about the concept horse or about any individual horse. The predicate in this sentence appears to be non-distributive or collective. It is like the predicate in 'Horses have been domesticated for millenia.' That is certainly not about the concept horse. No concept can be ridden or made to carry a load. But it is also not about any individual horse. Not even the Methuselah of horses, whoever he might be, has been around for millenia.

A predicate F is distributive just in case it is analytic that whenever some things are F, then each is F. Thus a distributive predicate is one the very meaning of which dictates that if it applies to some things, then it applies to each of them. 'Blue' is an example. If some things are blue, then each of them is blue.

If a predicate is not distributive, then it is non-distributive (collective). If some Occupy-X nimrods have the building surrounded, it does not follow that each such nimrod has the building surrounded. If some students moved a grand piano into my living room, it does not follow that each student did. If bald eagles are becoming extinct, it does not follow that each bald eagle is becoming extinct. Individual animals die, but no individual animal ever becomes extinct. If the students come from many different countries, it does not follow that each comes from many different countries. If horses have an interesting evolutionary history, it does not follow that each horse has an interesting evolutionary history.

My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evlutionary history' example when he is committed to saying that each horse exists. His view , I take it, is that 'exist(s)' is a first-level non-distributive predicate. 'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate. Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?

Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent. I incline toward the latter. He is trying to show that (ST1) doe not entail (ST2). He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic. But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evilutionary history.' 'Horses exist,' however, cannot be non-distributive. If some horses exist, then each of them exists. And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.

The ComBox is open if there is anyone who knows this subject and has read PvI's paper and can set me straight.

My Argument That ‘Exist(s)’ is not Univocal Revisited: No ‘Is’ of Predication?

On August 11th I wrote:

Suppose we acquiesce for the space of this post in QuineSpeak.

Then 'Horses exist' says no more and no less than that 'Something is a horse.' And 'Harry exists' says no more and no less than that 'Something is Harry.' But the 'is' does not have the same sense in both translations. The first is the 'is' of predication while the second is the 'is' of identity. The difference is reflected in the standard notation. The propositional function in the first case is Hx. The propositional function in the second case is x = h. Immediate juxtaposition of predicate constant and free variable [with the predicate constant coming first] is the sign for predication. '=' is the sign for identity. Different signs for different concepts. Identity is irreducible to predication which is presumably why first-order predicate logic with identity is so-called.

Those heir to the 'Fressellian' position, such as Quine and his epigoni, dare not fudge the distinction between the two senses of 'is' lately noted. That, surely, is a cardinal tenet of their brand of analysis.

So even along Quinean lines, the strict univocity of 'exist(s)' across all its uses cannot [pace van Inwagen] be upheld. It cannot be upheld across the divide that separates general from singular existentials.

But the next morning I had a doubt about what I had written. Is there an 'is' of predication in MPL (modern predicate logic)? I argued (above) that 'exist(s)' is not univocal: it does not in MPL have the same sense in 'Fs exist' and 'a exists.' The former translates as 'Something is (predicatively) an F' while the latter translates as 'Something is (identically) a.' Kicked out the front door, the equivocity returns through the back door disguised as an equivocation on 'is' as between predication and identity.

But if the 'is' in 'Grass is green' or 'Something is green' is bundled into the predicate in the Fregean manner, then it could be argued that there is no 'is' of predication in MPL distinct from the 'is' of identity and the 'is' of existence. If so, my equivocity argument above collapses, resting as it does on the unexpungeable distinction between the 'is' or identity and the 'is' of predication.

Yesterday a note from Spencer Case shows that he is on to the same (putative) difficulty with my argument:

Hey Bill, I have a professor whose pet peeve is the claim that there is an 'is' of identity and an 'is' of predication. I don't know his arguments for thinking so, but his view is that 'is' is univocal and what differs is the content of the copula. If he's right, that would be a problem for you here. Do you know more about this position than I do?

To sort this out we need to distinguish several different questions:

Q1. Is there a predicative use of 'is' in English? Yes, e.g., 'Al is fat.' This use is distinct from the existential use and the identitative use (and others that I needn't mention). So I hope Spencer's professor is not denying the plain linguistic fact that in English there is an 'is' of predication and an 'is' of identity and that they are distinct.

Q2. Must there be a separate sign for the predicative tie in a logically perspicuous artificial language such as MPL (modern predicate logic, i.e., first-order predicate logic with identity)? No. When we symbolize 'Al is fat' by Fa, there is no separate sign for the predicative tie. But there is a sign for it, namely, the immediate juxtaposition of the predicate constant and the individual constant with the predicate constant to the left of the individual constant. So we shouldn't confuse a separate or stand-alone sign with a sign. Other non-separate signs are conceivable exploiting different fonts and different colors, etc.

Q3. Must there be some sign or other for predication in a logically adequate language such as MPL? How could there fail to be? If our logical language is adequate, then it has to be able to symbolize predications such as 'Al is fat.' And note that existentials such as 'Fat cats exist' cannot be put into MPL without a sign for predication. '(∃x)(Fx & Cx)' employs non-separate signs for predication.

Q4. Is the predicative tie reducible or eliminable? No. For Frege, there is no need for a logical copula or connector to tie object a to concept F when a falls under F. The concept is "unsaturated" (ungesaettigt). Predicates and their referents (Bedeutungen) are inherently gappy or incomplete. So the predicate 'wise' would be depicted as follows: '___ wise.' What is thereby depicted is a sentential function or open sentence. A (closed) sentence results when a name is placed in the gap. The concept to which this predicate or sentential function refers is gappy in an analogous sense. Hence there is no need for for an 'is' of predication in the logical language or for an instantiation relation. Object falls under concept without the need of a tertium quid to connect them.

I would imagine that Spencer Case's professor has some such scheme in mind. One problem is that it is none too clear what could be meant by a gappy or incomplete or unsaturated entity. That a predicate should be gappy is tolerably clear, but how could the referent of a predicate be gappy given that the referent of a predicate is a single item and not the manifold of things to which the predicate applies? The idea is not that concepts exist only when instantiated, but that their instantiation does not require the services of a nexus of predication: the concept has as it were a slot in it that accepts the object without the need of a connector to hold them together. (Think of a plug and a socket: there is no need for a third thing to connect the plug to the socket: the 'female' receptacle just accepts the 'male' plug.)

There are other problems as well.

But here is the main point. Frege cannot avoid speaking of objects falling under concepts, of a's falling under F but not under G. If the notion of the unsaturatedness of concepts is defensible, then Frege can avoid speaking of a separate predicative tie that connects objects and concepts. But he cannot get on without predication and without a sign for predication.

I conclude that my original argument is sound. There is is and must be a sign for predication in any adequate logic, but it needn't be a stand-alone sign. (Nor need its referent be a stand-alone entity.) Compare '(∃x)Hx' to '(∃x)(x = h)' as translations of 'Horses exist' and 'Harry exists,' respectively. The identity sign occurs in only one of the translations, the second. And the sign for predication occurs only in the first. There is no univocity of 'exist(s)' because there is no univocity of 'is' in the translations.

David Brightly’s Weblog and a Punctilio Anent Predication and Inclusion

The unduly modest David Brightly has begun a weblog entitled tillyandlola, "scribblings of no consequence." In a recent post he criticizes my analysis of the invalidity of the argument: Man is a species; Socrates is a man; ergo, Socrates is a species. I claimed that the argument equivocates on 'is.' In the major premise, 'is' expresses a relation of conceptual inclusion: the concept man includes the subconcept species. In the minor premise, however, the 'is' is the 'is' of predication: Socrates falls under man, he doesn't fall within it.

I am afraid that my analysis is faulty, however, and for the reasons that David gives. There is of course a difference between the 'is' of inclusion and the 'is' of predication. 'Man is an animal' expresses the inclusion of the concept animal within the concept man. 'Socrates is a man,' however, does something different: it expresses the fact that Socrates falls under the concept man.

But as David notes, it is not clear that species is included within the concept man. If we climb the tree of Porphyry we will ascend from man to mammal to animal; but nowhere in our ascent will we hit upon species.

Transitivity of Predication?

I dedicate this post to London Ed, who likes sophisms and scholastic arcana.

Consider these two syllogistic arguments:

A1. Man is an animal; Socrates is a man; ergo, Socrates is an animal.
A2. Man is a species; Socrates is a man; ergo, Socrates is a species.

The first argument is valid. On one way of accounting for its validity, we make two assumptions. First, we assume that each of the argument's constituent sentences is a predication. Second, we assume the principle of the Transitivity of Predication: if x is predicable of y, and y is predicable of z, then x is predicable of z. This principle has an Aristotelian pedigree. At Categories 3b5, we read, "For all that is predicated of the predicate will be predicated also of the subject." So if animal is predicable of man, and man of Socrates, then animal of Socrates.

Something goes wrong, however, in the second argument. The question is: what exactly? Let's first of all see if we can diagnose the fallacy while adhering to our two assumptions. Thus we assume that each occurrence of 'is' in (A2) is an 'is' of predication, and that predication is transitive. One suggestion — and I take this to be the line of some Thomists — is that (A2) equivocates on 'man.' In the major, 'man' means 'man-in-the-mind,' 'man as existing with esse intentionale.' In the minor, 'man' means 'man-in-reality,' 'man as existing with esse naturale.' We thus diagnose the invalidity of (A2) by saying that it falls afoul of quaternio terminorum, the four-term fallacy. On this diagnosis, Transitivity of Predication is upheld: it is just that in this case the principle does not apply since there are four terms.

But of course there is also the modern Fregean way on which we abandon both of our assumptions and locate the equivocation in (A2) elsewhere. On a Fregean diagnosis, there is an equivocation on 'is' in (A2) as between the 'is' of inclusion and the 'is' of predication. In the major premise, 'is' expresses, not predication, but inclusion: the thought is that the concept man includes within its conceptual content the subconcept species. In the minor and in the conclusion, however, the 'is' expresses predication: the thought is that Socrates falls under the concepts man and species. Accordingly, (A2) is invalid because of an equivocation on 'is,' not because of an equivocation on 'man.'

The Fregean point is that the concept man falls WITHIN but not UNDER the concept animal, while the object Socrates falls UNDER but not WITHIN the concepts man and animal. Man does not fall under animal because no concept is an animal. Animal is a mark (Merkmal) not a property (Eigenschaft) of man. In general, the marks of a concept are not its properties. But concepts do have properties. The property of being instantiated, for example, is a property of the concept man. But it is not a mark of it. If it were a mark, then man by its very nature would be instantiated and it would be a conceptual truth that there are human beings, which is false.

Since on the Fregean scheme the properties of concepts needn't be properties of the items that fall under the concepts, Transitivity of Predication fails. Thus, the property of being instantiated is predicable of the concept philosopher, and the concept philosopher is predicable of Socrates; but the property of being instantiated is not predicable of Socrates.

Another Round with Hennessey on Accidental Predication

Having had my say about what is known in the trade as Occam's Razor, and having secured some welcome agreement with the proprietor of Beyond Necessity in the combox of the aforelinked post, I am now ready to address the meat of Richard Hennessey's response to my three-post critique of what I took to be his theory of accidental predication.

There is no need to stray from our hoary example of accidental predication: 'Socrates is seated.' I took Hennessey to be saying that in a true accidental predication of this simple form subject and predicate refer to exactly the same thing. If they didn't, the sentence could not be true. Here is how Hennessey puts it:

Let us take the proposition “Socrates is sitting” or the strictly equivalent “Socrates is a sitting being.” The referent of the subject term here is the sitting Socrates and that of the predicate term is one and the same sitting Socrates. . . . only if the referent of the “Socrates” and that of the “sitting” of “Socrates is sitting” are identical can it be true that Socrates is actually the one sitting.

Since Hennessey uses the word 'identity' we can call this an identity theory of accidental predication: in true predications of this sort, the referent of the subject term and the referent of the predicate term are identical, and this identty is what insures that the predication is true. If so, then the same goes for all other true predications which are about Socrates. So consider 'Socrates is standing' which is the logical contrary (not contradictory) of 'Socrates is sitting.' These sentences cannot both be true at the same time, but they can be true at different times. Suppose we ask what the truth-maker is in each case. Given that subject and predicate terms refer to exactly the same thing, namely, Socrates, it follows that in each case it is Socrates and Socrates alone that is the truth-maker of both sentences. When he is sitting, Socrates makes-true 'Socrates is sitting' and when he is standing Socrates makes-true 'Socrates is standing.'

What I do not understand, however, is how these obviously different sentences, which differ in their truth-conditions, can have one and the same entity as truth-maker. The same problem does not seem to arise for such essential predications as 'Socrates is human.' For there is no time when he is not human, and (this is a distinct modal point), at every time at which he is human he is not possibly such as to be nonhuman. In the case of essential predications an identity theory may be workable. Perhaps we can say that Socrates himself is the truth-maker of 'Socrates is human,' 'Socrates is rational,' and Socrates is animal.'

In the case of accidental predications, however, it seems definitely unworkable. This is because different accidental predications about Socrates need different truth-makers. It is not Socrates, but Socrates' being seated that is the truth-maker of 'Socrates is seated' and it is not Socrates, but Socrates' standing that is the truth-maker of 'Socrates is standing.'

Without worrying about what exactly the italicized phrases pick out (facts? states of affairs? tropes?), one thing seems crystal clear: there cannot be a strict identity of, e.g., the referent of 'Socrates' and the referent of 'seated.' And since there cannot be a strict identity, there must be some difference between the referents of the subject and predicate terms. Hennessey seems to show an appreciation of this in his response (second hyperlink above):

If we tweak the [B.V.] passage a bit, we can, it strikes me, improve the thesis about the referencing at work in the sentence “Socrates is sitting” so that it offers a more satisfactory support of the neo-Aristotelian thesis of anti-realism in the theory of universals, one indeed getting along “without invoking universals.” First, let us speak of “particular property” instead of “particularized property,” for the latter expression suggests, at least to me, that the property would be, prior to some act of particularization, a universal and not a particular. Let us then accept, but with a precision, Bill’s statement that “‘sitting’ refers to a particularized property (a trope),” saying instead that while the “Socrates” in our statement refers to Socrates, the person at present sitting, the “sitting” primarily refers to Socrates, the person at present sitting, and also co-refers to the particular property of sitting that inheres in Socrates. (An alternative terminology might have it that the “Socrates” in our statement denotes Socrates and the “sitting” primarily denotes Socrates, still the person sitting, and also connotesthe property of sitting that inheres in Socrates; come to think of it, I believe I recall having read, long ago, a similar distinction in the Petite logique of Jacques Maritain, a book which I no longer have, thanks to a flooded basement.)

This is definitely an improvement. It is an improvement because it tries to accommodate the perfectly obvious point that there must be some difference or other between the worldly referents of the subject and predicate terms in accidental predications. Hennessey is now telling us that 'Socrates' in our example refers to exactly one item, Socrates, while 'sitting' refers to two items, Socrates and the particular property (trope, accident) seatedness which inheres in Socrates.

But Hennessey is not yet in the clear. For I will now ask him what the copula 'is' expresses. It seems he must say that it expresses inherence. He must say that it is because seatedness inheres in Socrates that 'Socrates is seated' is true. Now inherence is an asymmetrical relation: if x inheres in y, then it is not the case that y inheres in x. But there is no sameness relation (whether strict identity, contingent identity, accidental sameness, Castaneda's consubstantiaton, etc) that is not symmetrical. Thus if x is in any sense the same as y, then y is (in the same sense) the same as x. Therefore, Hennessey's bringing of inherence into the picture is at odds with his claims of identity. Inherence, being asymmetrical, is not a type of identity or sameness. So why the talk of identity in the first passage quoted above?

Why does Hennessey say that 'seated' refers primarily to Socrates but also to the particular property seatedness? Why not just say this: 'Socrates' refers to the primary substance (prote ousia) Socrates and nothing else; 'is' refers to the inherence relation or nexus and nothing else; 'seated/sitting' refers to the particular property (trope, accident) seatedness and nothing else. This would give him what he wants, a theory of predication free of universals.

But this is not what Hennessey says. He is putting forth some sort of identity theory of predication. He thinks that in some sense the subject and predicate terms refer to the very same thing. He tells us that 'seated' refers both to a substance and to an accident. The upshot is that Hennessey has given birth to a hybrid theory which I for one do not find intelligible.

Here is the question he needs to confront directly: what, in the world, makes it true that 'Socrates is seated' (assuming of course that the sentence is true)? Here is a clear answer: the sentence is true because seatedness inheres in Socrates. But then of course there can be no talk of the identity of Socrates and seatedness. They are obviously not identical: one is a substance and the other an accident. The relation between them, being asymmetrical, cannot be any sort of sameness relation.

The other clear answer which, though clear, is absurd is this: the sentence is true because 'Socrates' and 'seated' refer to the very same thing with the result that the copula expresses identity. Now this is absurd for the reasons given over several posts. This was his original theory which he has wisely moved away from.

Instead of plumping for one of these clear theories, Hennessey gives us an unintelligible hybrid, a monster if you will, as we approach Halloween.

Accidental Sameness and its Logical Properties

I should thank Richard Hennessey for motivating me to address a topic I haven't until these last few days discussed in these pages, namely, that of accidental sameness. Let us adopt for the time being a broadly Aristotelian ontology with its standard nomenclature of substance and accident, act and potency, form and matter, etc. Within such a framework, how can we account for an accidental predication such as 'Socrates is seated'?

In particular, what is expressed by 'is' in a sentence like this? Hennessey seems to maintain that it expresses an identity which holds, if the sentence is true, between the referent of the subject term 'Socrates' and the referent of the predicate term 'seated.' Here is what Hennessey says:

Let us take the proposition “Socrates is sitting” or the strictly equivalent “Socrates is a sitting being.” The referent of the subject term here is the sitting Socrates and that of the predicate term is one and the same sitting Socrates. Similarly, the referent of the subject term of “Plato is sitting” is the sitting Plato and that of its predicate term is one and the same sitting Plato. Here, once again, only if the referent of the “Socrates” and that of the “sitting” of “Socrates is sitting” are identical can it be true that Socrates is actually the one sitting. And, only if the referent of the “Plato” and that of the “sitting” of “Plato is sitting” are identical can it be true that Plato is actually the one sitting.

Hennessey is making two moves in this passage. The first is the replacement of 'Socrates is seated' with 'Socrates is a seated being.' (I am using 'seated' instead of 'sitting' for idiosyncratic stylistic reasons; the logic and ontology of the situation should not be affected.) I grant that the original sentence and its replacement are logically equivalent. Hence I have no objection to the first move.

The second move is to construe the 'is' of the replacement sentence as expressing identity. Together with this move goes Hennessey's claim that ONLY in this way can the truth of the sentence be insured. This claim is false for reasons given earlier, but this is not my present concern. My concern at present is the second move by itself. Can the 'is' of the replacement sentence be construed as expressing identity?

The answer to this is in the negative if by 'identity' is meant strict identity. Strict identity, symbolized by '=,' is an equivalence relation: it is reflexive, symmetrical, and transitive. It is furthermore governed by the Indiscernibility of Identicals (If a = b, then everything true of a is true of b and vice versa) and the Necessity of Identity (If a = b, then necessarily a = b). Now if the referent of 'Socrates' and the referent of 'seated' are strictly identical, then this is necessarily so, true in every possible world in which Socrates exists, in which case our sentence cannot be contingently true as it obviously is. Socrates is seated only at some of the times at which he exists, not at all such times. And at any time at which he is seated he is possibly such as not to be seated at that time. (The modality in question is broadly logical.)

So if Hennessey wants to construe the 'is' as expressing a type of sameness, it cannot be that sameness which is strict identity. An option which is clearly open to him as an Aristotelian is to construe the 'is' as expressing accidental sameness. But what is that?

It is a dyadic relation that connects one substance and one accidental compound. (Thus by definition it never connects two substances or two compounds.) An accidental compound is a particular, not a universal. It is a hylomorphic compound the matter of which is a substance and the form of which an accident inhering in that substance. It is admittedly a somewhat 'kooky' object, to borrow an epithet from Gareth Mathews. An example is seated-Socrates. Socrates is a substance. His seatedness is an accident inhering in him. The two together form an accidental compound which can be denoted by 'seated-Socrates' or by 'Socrates + seatedness.' Seated-Socrates is neither a substance nor an accident, but a transcategorial hybrid composed of one substance and one accident, but only if the accident inheres in the substance. (An accidental compund is therefore not a mereological sum of a substance and any old accident.)

The compound is not a substance because it cannot exist on its own, but it is parasitic upon its parent substance, in our example, Socrates. It is also not a substance because it is not subject to alterational change. Change for an accidental compound is existential change, either coming into being or passing out of being. When Socrates sits down, seated-Socrates comes into being, and when he stands up it passes out of being. An accidental compound is not an accident because it is not related to its parent substance by inherence, but by accidental sameness. A key difference is that inherence is an asymmetrical relation, while accidental sameness is symmetrical.

Hennessey can say the following: 'Socrates is seated' expresses the accidental sameness of Socrates with the accidental compound, seated-Socrates. He needs to posit two objects, not one: a substance and an accidental compound. If he holds that the referent of 'Socrates' and the referent of 'seated' are strictly identical, then the accidentality of the predication cannot be accommodated, and all predications become essential. That was my initial objection to Hennessey's view before I figured out a way to salvage it.

What are the logical properties of the accidental sameness relation? Like strict identity, it is symmetrical. This should be obvious. If Socrates is accidentally the same as seated-Socrates, then the latter is accidentally the same as the former. The inherence relation, by contrast, is asymmetrical: if A inheres in S, then S does not inhere in A. This is one of the differences between the accidental sameness relation and the inherence relation.

Accidental sameness is irreflexive. This can be proven as follows:

1. No substance is an accidental compound.
2. If a is accidentally the same as b, then either a is a subtance and b a compound, or vice versa.
Therefore
3. No object, whether substance or compound, is accidentally the same as itself.

It can also be proven that accidental sameness is intransitive. Thus, if a is accidentally the same as b, and b accidentally the same as c, it follows that a is not accidentally the same as c. Suppose a is a substance. Then b is a compound. But if b is a compound, then c is a substance, with the result that a substance is accidentally the same as a substance, which violates the definition of accidental sameness. On the other hand, if a is a compound, then b is a substance, which makes c a compound, with the result that a compound is accidentally the same as a compound, which also violates the definition. So accidental sameness is intransitive.

Clearly, there is accidental sameness only if there are accidental compounds. But are there any of the latter? Consider a fist. A fist is not strictly identical to the hand whose fist it is. (They have different persistence conditions.) But a fist is not strictly different from the hand whose fist it is. But surely there are fists, and surely what we have in a situation like this is not two individuals in the same place. So it is reasonable to maintain that a fist is an accidental compound which is accidentally the same as the hand whose fist it is.

Still, there is something 'kooky' about accidental compounds. So I'll end with a challenge to Hennessey, enemy of universals. Why are accidental compounds less 'kooky' than universals, whether immanent or transcendent?

Accidental Sameness: Defending Hennessey Against My Objection

Yesterday I made an objection to Richard Hennessey's neo-Aristotelian theory of accidental predication. But this morning I realized that he has one or more plausible responses. By the way, this post has, besides its philosophical purpose, a metaphilosophical one. I will be adding support to my claim lately bruited that philosophy — the genuine article — is not a matter of debate, as I define both 'philosophy' and 'debate.' For have you ever been to a debate in which debater A, having made an objection to something debater B has said, says, "Wait a minute! I just realized that you have one or more plausible ways of turning aside my objection. The first is . . . ."?

1. 'Socrates is seated' is an example of an accidental predication. For surely it is no part of Socrates' essence or nature that he be seated. There is no broadly logical necessity that he be seated at any time at which he is seated, and there are plenty of times at which he is not seated. 'Socrates is seated' contrasts with the essential predication 'Socrates is human.' Socrates is human at every time at which he exists and at every world at which he exists.

2. Hennessey's theory is that ". . . only if the referent of the 'Socrates' and that of the 'sitting' of 'Socrates is sitting' are identical can it be true that Socrates is actually the one sitting." The idea seems to be that accidental predications can be understood as identity statements. Thus 'Socrates is seated' goes over into (what is claimed to be) the logically equivalent 'Socrates is (identical to) seated-Socrates.' Accordingly, our sample sentence is construed, not as predicating a property of Socrates, a property he instantiates, but as affiming the identity of Socrates with the referent of 'seated-Socrates.'

3. But what is the referent of 'seated-Socrates'? If the referent is identical to the referent of 'Socrates,' namely Socrates, then my objection kicks in: how can the predication be contingently true, as it obviously is, given that it affirms the identity of Socrates with himself? Socrates is essentially Socrates but only accidentally seated.

4. Perhaps Hennessey could respond to this objection by saying that 'Socrates' and 'Socrates-seated' do not refer to the same item: they refer to different items which are, nonetheless, contingently identical. This would involve distinguishing between necessary identity and contingent identity where both are equivalence relations (reflexive, symmetrical, transitive) but only the former satisfies in addition the Indiscernibility of Identicals (InId) and the Necessity of Identity (NI). It is obvious that if a and b are contingently identical, but distinct, then these items must be discernible in which case InId fails. It is also obvious that NI must fail for contingent identity.

5. Closer to Aristotle is a view described by Michael C. Rea in "Sameness Without Identity: An Aristotelian Solution to the Problem of Material Constitution" in Form and Matter, ed. Oderberg, Blackwell 1999, pp. 103-115. I will now paraphrase and interpret from Rea's text, pp. 105-107. And I won't worry about how the view I am about to sketch differs — if it does differ — from the view sketched in #4.

When Socrates sits down, seated-Socrates comes into existence. When he stands up or adopts some other nonseated posture, seated-Socrates passes out of existence. This 'kooky' or 'queer' object is presumably a particular, not a universal, though it is not a substance. It is an accidental unity whose existence is parasitic upon the existence of its parent substance, Socrates. It cannot exist without the parent substance, but the latter can exist without it. The relation is like that of a fist to a hand made into a fist. The fist cannot exist without the hand, but the hand can exist without being made into a fist.Though seated-Socrates is not a substance it is like a substance in that it is a hylomorphic compound: it has Socrates as its matter and seatedness as its form. As long as Socrates and seated-Socrates exist, the relation between them is accidental sameness, a relation weaker than strict identity.

Accidental sameness is not strict identity presumably because the former is not governed by the Indiscernibility of Identicals. Clearly, Socrates and seated-Socrates do not share all properties despite their sameness. They differ temporally and modally. Socrates exists at times at which seated-Socrates does not exist (though not conversely). And it is possible that Socrates exist without seated-Socrates existing (though not conversely).

Are Socrates and seated-Socrates numerically the same? They count as one and so they are one in number though not one in being. So says Aristotle according to Rea. After all, if Socrates and Alcibiades are seated at table we count two philosophers not four. We don't count: Socrates, seated-Socrates, Alcibiades, seated-Alcibiades.

But I will leave it to Hennessey to develop this further. It looks as if this is the direction in which he must move if his theory is to meet my objection.

What about essential predication? Is there a distinction between Socrates and human-Socrates? These two cannot be accidentally the same. They must be strictly identical. If 'Socrates is human' is parsed as 'Socrates is identical to human-Socrates' then how does the latter differ from 'Socrates is Socrates'? The sense of 'Socrates is human' differs from the sense of 'Socrates is Socrates.' How account for that? 'Socrates is Socrates' is a formal-logical truth, trivial and uninformative. 'Socrates is human' is not a formal-logical truth; it is informative.

Comments on Richard Hennessey’s Neo-Aristotelian Theory of Predication

Richard Hennessey of Gnosis and Noesis sketches a neo-Aristotelian theory of predication in Another Aristotelian Basis for a Neo-Aristotelian Anti-Realism in the Theory of Universals. Drawing as he does upon my discussion in Scholastic Realism and Predication, he has asked me to comment on his post. I will do so with pleasure.

I first want to agree partially with something he says at the close of his post:

. . . we have in the so-called problem of universals not a genuine problem, but merely a pseudo-problem. That is, we have a problem of universals only if we posit their existence. If we do not posit them, there is no genuine problem.

I would put the point somewhat differently. The phrase 'problem of universals' is a misnomer. For what is in dispute in the so-called problem of universals is the nature of properties. Not their existence, but their nature. That there are properties is a given, a datum. What alone can be reasonably questioned is their nature. If you deny that sugar is sweet, then I show you the door. But if you deny that sweetness is a universal, then I listen to your arguments. For it is not at all obvious that the sweetness of a sugar cube is a universal. (Nor is it obvious that it isn't) That it is a universal is a theoretical claim that goes beyond the data. It is consistent with the data that the sweetness be a particular, an unrepeatable item, such as a trope (as in the theories of D. C. Williams and Keith Campbell, et al.) or some other sort of particular.

The correct phrase, then, is 'problem of properties,' not 'problem of universals.' But that is not to say that there is no legitimate use for 'problem of universals.' If one posits universals, then one will face various problems such as the problem of how they connect to particulars. Those problems are genuine, not pseudo, given that there are universals.

In any case, Richard sees no need to posit universals, whether Platonic or Aristotelian, to explain either essential or accidental predication. Here is the gist of Richard's theory:

Let us take the proposition “Socrates is sitting” or the strictly equivalent “Socrates is a sitting being.” The referent of the subject term here is the sitting Socrates and that of the predicate term is one and the same sitting Socrates. Similarly, the referent of the subject term of “Plato is sitting” is the sitting Plato and that of its predicate term is one and the same sitting Plato. Here, once again, only if the referent of the “Socrates” and that of the “sitting” of “Socrates is sitting” are identical can it be true that Socrates is actually the one sitting. And, only if the referent of the “Plato” and that of the “sitting” of “Plato is sitting” are identical can it be true that Plato is actually the one sitting.

What we have here could be called an identity theory of predication: if 'Socrates is a sitting being' is true, then the referent of the subject term 'Socrates' and the referent of the predicate term 'sitting being' are numerically identical. Accordingly, the 'is' is the 'is' of identity. ONLY on this analysis, says Richard, can the sentence be true. I rather doubt that, but first we need to consider whether Richard's theory is not open to serious objection.

If x and y are identical, then this is necessarily so. Call this the Necessity of Identity. More precisely: for any x, y, if x = y, then necessarily, x = y. Equivalent contrapositive: if possibly ~(x = y), then ~(x = y). It follows that if Socrates is identical to some sitting being, then necessarily he is identical to that sitting being. But in that case it would not be possible for Socrates not to be a sitting being. This, however, is possible. Sometimes he is on his feet walking around, other times he is flat on his back, and he has even been observed standing on his head. And please note that even if, contrary to fact, Socrates was always seated, it would still be possible for him not to be seated. The mere possibility of his not being seated shows that he cannot be identical to some sitting being.

This is an objection that Richard needs to address if his theory is to be tenable. Note that my objection can be met without invoking universals. One could say that 'Socrates' in our sample sentence refers to Socrates, that 'sitting' refers to a particularized property (a trope), and that the 'is' is the 'is' of predication, not identity. Accordingly, there is not an identity between Socrates and a sitting being; the particularized property being-seated inheres in Socrates, where inherence, unlike identity, is asymmetrical.

The other claim that Richard makes is that ONLY on his theory can the truth of 'Socrates is sitting' be accommodated. That strikes me as false. I just gave an analysis on which the truth of the predication is preserved. And of course there are others.

Two Questions About the Bundle Theory Answered

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

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

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

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

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

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

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

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

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

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