Maverick Philosopher

Constituent Ontology and the Problem of Change

In an earlier entry I sketched the difference between constituent ontology (C-ontology) and relational ontology (R-ontology) and outlined an argument against R-ontology.  I concluded that post with the claim that C-ontology also faces serious objections.  One of them could be called the 'argument from change.'

The Argument from Change

Suppose avocado A, which was unripe a week ago is ripe today. This is an example of alterational (as opposed to existential) change.  The avocado has become different. But it has also remained the same. It is different in respect of ripeness but it is one and the same avocado that was unripe and is now ripe.

Alterational change  is neither destruction nor duplication. The ripening of an avocado does not cause it to cease to exist. The ripening of an avocado is not the ceasing to exist of one particular (the unripe avocado) followed by the coming into existence of a numerically distinct avocado (the ripe one).

It is also clear that one cannot speak of change if there are two avocados, A and B, indiscernible except in respect of ripeness/unripeness, such that A is unripe at time t while B is ripe at time t* (t*> t). If my avocado is unripe at t while yours is ripe at t*, that circumstance does not constitute a change.  Alteration requires that one and the same thing have incompatible properties at different times. This is necessary for alteration; whether it is sufficient is a further question.

That there is alterational change is a datum.  That it requires  that one and the same thing persist over an interval of time during which it has incompatible properties follows from elementary  'exegesis' or 'unpacking' of the datum.

The question before us is whether any C-ontology can do justice to the datum and its exegesis.

All C-ontologists are committed to what Michael J. Loux calls "Constituent Essentialism."  ("What is Constituent Ontology?" Novak et al. eds., p. 52) It is the C-ontological analog of mereological essentialism.  We can put it like this:

Constituent Essentialism: A thing has each of its ontological parts necessarily.  This implies that a thing cannot gain or lose an ontological part without ceasing  to be same thing.

Mereological Essentialism: A thing has each of its commonsense parts necessarily.  This implies that a thing cannot gain or lose a commonsense part without ceasing to be the same thing.

To illustrate, suppose an ordinary particular (OP) is a bundle of compresent universals.  The universals are the ontological parts of the OP as a whole.  The first of the two principles entails that ordinary particulars cannot change.  For (alterational) change is change in respect of properties under preservation of numerical diachronic identity.  But preservation of identity is not possible on Constituent Essentialism.  The simple  bundle-of-universals theory appears incompatible with the fact of change.

I agree with Loux that Constituent Essentialism is a "framework principle" (p. 52) of C-ontology.  It cannot be abandoned without abandoning C-ontology.  And of course the fact of change and what it entails (persistence of the same thing over time)  cannot be denied.  So the 'argument from change' does seem to score against primitive versions of the bundle-of-universals theory.

Can the Objection Be Met?

The foregoing objection can perhaps be met met by sophisticating the bundle theory and adopting a bundle-bundle theory.  Call this BBT.  Accordingly, a thing that persists over time such as an avocado is a diachronic bundle of synchronic or momentary bundles.  The theory  has two stages. 

First, there is the construction of momentary bundles from universals.  Thus my avocado at a time  is a bundle of universals. Then there is the construction of a diachronic bundle from these synchronic bundles. The momentary bundles have universals as constituents while the diachronic bundles do not have universals as constituents, but individuals.  This is because a bundle of universals at a time is an individual.  At both stages the bundling is contingent: the properties are contingently bundled to form momentary bundles and these resulting bundles are contingently bundled to form the persisting thing.

Accordingly, the unripe avocado is numerically the same as the ripe avocado in virtue of the fact that the earlier momentary bundles which have unripeness as a constituent  are ontological parts
of the same diachronic whole as the later momentary bundles which have ripeness as a constituent.  

A sophisticated bundle theory does not, therefore, claim that a persisting thing is a bundle of properties; the claim is that a persisting thing is a bundle of individuals which are themselves bundles of properties.  This disposes of the objection from change at least as formulated above. 

There are of course a number of other objections that need to be considered -- in separate posts.  But on the problem of change C-ontology looks to be in better shape than Loux makes it out to be.

I should add that I am not defending the bundle-bundle theory.  In my Existence book I take a different C-ontological tack.

Related articles

Constituent Ontology Versus Relational Ontology and an Argument Against the Latter

Constituent Ontology Versus Relational Ontology and an Argument Against the Latter

Two Different Aproaches to Ontology

Uncontroversially, ordinary material particulars such as cats and cups have parts, material parts.  Equally uncontroversial is that they  have properties and stand in relations.  That things have properties and stand in relations is a plain Moorean fact.  After all, my cat is black and he is sleeping next to my blue coffee cup.  So far we are at the 'datanic,' pre-philosophical level.  We start philosophizing when we ask what properties are and what it is for a thing to have a property.   So the philosophical question is not whether there are properties -- of course there are! -- but what they are.  Neither is it a philosophical question whether things have properties -- of course they do!   The question concerns how this having is to be understood.

For example, is the blueness of my cup a universal or a particular (e.g.,a trope)?  That is  one of several questions one can ask about properties.  A second is whether the cup has the property by standing in a relation to it -- the relation of exemplification -- or by  containing it as an ontological or metaphysical part  or constituent.  Can property-possession be understood quasi-mereologically?

It is this second question that will exercise me in this post. 

At a first approximation, the issue that divides constituent ontologists (C-ontologists) and those that N. Wolterstorff rather infelicitously calls 'relational ontologists' (R-ontologists) is whether or not ordinary particulars  have ontological or metaphysical parts.  C-ontologists maintain that ordinary particulars have such parts, and that among these parts are (some of) the properties of the ordinary particular.  R-ontologists deny that ordinary particulars have ontological parts, and consequently deny that ordinary particulars have any of their properties by having them as parts.

Bundle theories are clear examples of C-ontology.  If my cup is nothing more than a bundle of compresent properties,  then (i) it has parts that are not ordinary physical parts, and (ii) its properties are these parts.  The properties could be either universals or particulars (tropes, say).  Either way you have a constituent ontology.

Suppose you think that there has to be more to an ordinary particular than its properties suitably bundled.  You might reason as follows. If properties are universals, and it is possible that there be two numerically distinct particulars that share all property consituents, then there must be an additional constituent that accounts for their numerical difference.  Enter bare or thin particulars. Such substratum theories also count as C-ontologies. 

Hylomorphic theories are also examples of C-ontology.   The form of a thing is not a property external to it to which the  thing is related by exemplification or instantiation, and this is a fortiori true of its matter, whether proximate or prime.  It follows that form and matter are ontological constituents of ordinary particulars.

The notion that ordinary particulars have ontological parts in addition to their commonsense parts is admittedly not the clearest.  'Part' in exactly what sense?  So it is no surprise that many of the best analytic metaphysicians are R-ontologists.  These philosophers think of properties as abstract objects residing in a realm apart.  Having decided on that view of properties, they naturally conclude that it makes no sense to maintain that a coffee cup, say, could have causally inert, nonspatiotemporal abstract objects as constituents.  So they maintain that for a concrete thing to have a property is for it to stand in a exemplification relation  or tie or nexus to an abstract property.  According to Michael J. Loux, relational ontologists

. . . restrict the parts of ordinary objects to their commonsense parts.  Nonetheless, they insist that ordinary objects stand in a variety of significant nonmereological connexions or ties to things that have character kath auto or nonderivatively; and they tell us that in virtue of doing so those objects have whatever character they do. ("What is Constituent Ontology?" in Novak et al. eds. Metaphysics: Aristotelian, Scholastic, Analytic, Ontos Verlag 2012, p. 44, emphasis added)

Why I am Inclined to Reject Relational Ontology

What follows is a sketch of argumentation more rigorously presented, with the standard scholarly apparatus, in my A Paradigm Theory of Existence, Kluwer 2002, pp. 170 -176, "Rejection of Nonconstituent Realism."

1. The 'Nude Particular' Objection

Relational ontologists don't deny that things have properties; what they deny is that those properties are at or in the things that have them in a way that would justify talk of properties being special metaphysical parts of ordinary concrete things.  They maintain that properties are abstracta in a realm apart, and that things are related to them.  Hence the phrase 'relational ontology.'  It seems to me, however, that on this view of properties and property-possession, ordinary particulars turn out to be what I will call  'nude particulars.'

Nude particulars are similar to, but not to be confused with, Gustav Bergmann's bare particulars or David Armstrong's thin particulars. Bare and thin particulars are constituents of ordinary or thick particulars.  Nude particulars are not ontological constituents of anything. A nude particular is an ordinary particular all of whose properties are abstracta.  Like bare particulars, nude particulars lack natures.  Lacking natures, there is nothing about them that dictates which properties they have.  This won't stop an R-ontologist from speaking of essential properties. He will say that an essential property of x is a property x has in every possible world in which it exists.  He cannot say, however, that what grounds this circumstance is that ordinary particulars as he conceives them have natures in them or at them.

I maintain that (i) R-ontologists are committed to nude particulars, but that (ii) there are no such critters.  Certainly, the meso-particulars that surround me now are not nude.  My trusty coffee cup, for example, is blue at this time and in this place. 

The cup is blue, and I see (with my eyes) that it is blue.  This seeing  is not a visio intellectualis, after all, a 'seeing' wth the 'eye of the mind,' as would befit the inspection of some colorless, atemporal, nonspatial, abstract Platonic object in a realm insulated from the flux and shove of the real order.    It is a seeing with the eyes of the head.  When I see the cup's being blue, I am not seeing a state of affairs that spans the abyss separating concreta from abstracta; I am seeing a state of affairs that is itself concrete. 

Moreover, I see blue (or blueness), again with my eyes.  (How could I see that the cup is blue without seeing blue?) It is therefore phenomenologically evident that at least some of the properties of my trusty cup are empirically detectable via ordinary outer perception.  But they wouldn't be empirically detectable if they were abstract objects in a realm apart, a Platonic or quasi-Platonic topos ouranos. Empirical detection involves causation; abstracta, however, are causally inert. Therefore, at least some of a thing's properties are at it or in it, and in this sense ontological constituents of it.  If so, R-ontology is mistaken.

The empirically detectable properties of an ordinary particular cannot be stripped from it and installed in a realm of abstracta. For then what you would have here below would be a nude particular.

You might object that I have made a travesty of the R-ontologist's position.  After all, doesn't Loux in the bolded passage above imply that ordinary particulars have "character" where they are, namely, in the sensible world and that they are therefore not nude?  If this is the response that is made to my first objection, then it triggers my

2. Duplication Objection

Suppose the R-ontologist grants that my cup has the character blue (or blueness) and other empirical features  at the cup, and that this character can be seen with the eyes of the head, and is therefore not a denizen of a realm of abstracta separated by an ontological chasm from the realm of concreta.  I will then ask what work  abstract properties do.  Why do we need them if the blueness and hardness and so on of the cup are already right here at or in the cup?  What is the point of positing 'duplicates' of these empirical characters in a realm of abstracta?  They are explanatorily otiose.

The R-ontologist appears to face a dilemma.   Either he must say that my coffee cup is a nude particular in denial of the plain fact that the blueness of the cup is an empirically detectable feature at the cup and not a colorless abstract object in a realm apart; or, denying that the cup is nude, he must admit that his abstract properties are explanatorily idle and fit candidates for Occam's Razor.

3.  Conclusion

Can we infer that C-ontology is in the clear?  Not so fast!  Loux brings powerful arguments against it, arguments to be considered in a separate post.  My suspicion is that that both styles of ontology lead to insurmountable aporiai. 

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. 

Holes and Their Mode of Being

Consider a particular hole H in a piece of swiss cheese.  H is not nothing.  It has properties.  It has, for example, a shape: it is circular.  The circular hole has a definite radius, diameter, and circumference.  It has a definite area equal to pi times the radius squared.  If the piece of cheese is 1/16th of an inch thick, then the hole is a disk having a definite volume.  H has a definite location relative to the edges of the piece of cheese and relative to the other holes.  H has causal properties: it affects the texture and flexibility of the cheese and its resistance to the tooth.  H is perceivable by the senses: you can see it and touch it.  You touch a hole by putting a finger or other appendage into it and experiencing no resistance.

Now if anything has properties, then it exists.  H has properties; so H exists. 

H exists and the piece of cheese exists.  Do they exist in the same way?  Not by my lights.  The hole depends for its existence on the piece of cheese; the latter does not depend for its existence on the former.  H is a particular, well-defined, indeed wholly determninate, absence of cheese.  It is a particular, existing absence.  As an absence of cheese it depends for its existence on the cheese of which it is the hole.

So I say the hole exists in a different way than the piece of cheese.  It has a dependent mode of existence whereas the piece of cheese has a relatively independent mode of existence.

On the basis of this and other examples I maintain that there are modes of being.  To be precise, I maintain that it is intelligible that there be modes of being.  This puts me at odds with those, like van Inwagen, who consider the idea unintelligible and rooted in an elementary mistake:

. . . the thick conception of being is founded on the mistake of transferring what properly belongs to the nature of a chair -- or of a human being or of a universal or of God -- to the being of the chair. (Ontology, Identity, and Modality, Cambridge 2001, p. 4)

Did I make a mistake above, the mistake van Inwagen imputes to thick theorists?  Did I mistakenly transfer what properly belongs to the nature of the hole -- its dependence on the piece of cheese -- to the being (existence) of the hole?

I plead innocent.  Perhaps it is true that it is the nature of holes in general that they depend for their existence on the things in which they are holes.  But H is a particular, spatiotemporally localizable, hole in a particular piece of cheese.  Since H is a particular existing hole, it cannot be part of H's multiply exemplifiable nature that it depend for its existence on the particular piece of cheese it is a hole in.  The dependence of H on its host is due to H's mode of existence, not to its nature.

Suppose there are ten quidditatively indiscernible holes in the piece of cheese: H1, H2, . . . H10.  Each exists.  Each has its own existence.  But each has the very same nature.  How then can this common nature be the factor responsible for making H1 or H2 or H3, etc.,  dependent on the particular piece of cheese?  The dependence of each hole on its host is assignable not to the nature common to all ten holes but to each hole's existence as a mode of its existence.

Now of course this will not convince any thin theorist.  But then that is not my goal.  My goal is to show that the thick theory is rationally defensible and not sired by any obvious 'mistake.'  If any 'mistakes' are assignable then I 'd say they are assignable with greater justice to the partisans of the thin theory.

Talk of 'mistakes,' though, is out of place in serious philosophy.  For apart from clear-cut logical blunders such as affirming the consequent, quantifier shift fallacies, etc. any alleged 'mistakes' will rest on debatable substantive commitments.

Metaphysical Grounding I: True Of

(Note to Peter L:  This begins our discussion of metaphysical grounding and metaphysical explanation, topics of common interest.  We need, over a series of posts, to uncover and discuss as many examples as we can find.  My aim, and perhaps yours as well, is to demonstrate that metaphysical grounding and metaphysical explanation are legitimate topics, and that metaphysics is not a going enterprise unless they are legitimate topics.  This is connected with our presumably common opposition to scientism and our presumably common defense of the autonomy of philosophy.)

Let 'Tom' name a particular tomato.  Let us agree that if a predicate applies to a particular, then the predicate is true of the particular.  Predicates are linguistic items.  If Tom is red, then 'red' is true of Tom, and if 'red' is true of Tom, then Tom is red. This yields the material biconditional

1. Tom is red iff 'red' is true of Tom.

Now it seems to me that the following question is intelligible:  Is Tom red because 'red' is true of Tom, or is 'red' true of Tom because Tom is red?  'Because' here does not have a causal sense.  So the question is not whether Tom's being red causes 'red' to be true of Tom, or vice versa.  So I won't speak of causation in this context.  I will speak of metaphysical/ontological grounding.  The question then is what grounds what, not what causes what.   Does Tom's being red ground the application (the being-applied)  of 'red' to Tom, or does the appplication (the being-applied) of 'red' to Tom ground Tom's being red?

I am not primarily concerned with the correct answer to this question, but with meaningfulness of the question.

Grounding is asymmetrical: if x grounds y, then y does not ground x.  (It is also irreflexive and transitive.)  Now if there is such a relation as grounding, then there will be a distinctive form of explanation we can call metaphysical/ontological explanation.  (Grounding, though not causation, is analogous to c ausation, and metaphysical explanation, though distinct from causal explanation, is analogous to causal explanation.)

Explaining is something we do: in worlds without minds there is no explaining and there are no explanations, including metaphysical explanations.  But I assume that, if there are any metaphysical grounding relations, then  in every world metaphysical grounding relations obtain.  (Of course, there is no grounding of the application of predicates in a world without languages and predicates, but there are other grounding relations.)

Grounding is not causation. It is not a relation between event tokens such as Jack's touching a live wire and Jack's death by electrocution.  Grounding is also not a relation between propositions.  It is not the relation of material implication, nor is it entailment (the necessitation of material implication), nor any other semantic relation wholly situated at the level of propositions.  Propositions, let us assume, are the primary truth-bearers. 

In our example, grounding is not a relation between propositions -- it is not a logical relation -- since neither Tom nor 'red' are propositions. 

I want to say the following.  Tom's being red grounds the correctness of the application of 'red' to Tom.  'Red' is true of Tom because (metaphysically, not causally or logically) Tom is red, and not vice versa.  'Red' is true of Tom in virtue of  Tom's being red.  Tom's being red is metaphysically prior to the truth of 'Tom is red' where this metaphysical priority cannot be reduced to some ordinary type of priority, whether logical, causal, temporal, or what have you.  Tom's being red metaphysically accounts for the truth of 'Tom is red.'

I conclude that there is at least one type of metaphysical grounding relation, and at least one form of irreducibly metaphysical explanation. 

The Problems of Order and Unity and Their Difference

Last Thursday, Steven N. and I had a very enjoyable three-hour conversation with ASU philosophy emeritus Ted Guleserian on Tempe's Mill Avenue.  We covered a lot of ground, but the most focused part of the discussion concerned the subject matter of this post.  If I understood Guleserian correctly, he was questioning whether there is any such problem as the problem of the unity of a fact.  I maintained that there is such a problem and that it is distinct from the problem of order.

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

The problem of order arises for relational facts and relational propositions in which there is a relation R that is either asymmetrical or nonsymmetrical. If dyadic R is asymmetrical, and x stands in R to y, then it follows that y does not stand in R to x. For example, greater than and taller than are asymmetrical relations. If I am taller than you, then you are not taller than me. If dyadic R is nonsymmetrical, and x stands in R to y, then it does not follow, though it may be the case, that y stands in R to x. For example, loves and hates are nonsymmetrical relations. If I love you, it does not follow that you love me, nor does it follow that you do not love me. But if I weigh the same as you, then you weigh the same as me: 'weigh the same as' picks out a symmetrical relation.

Well, suppose R is either asymmetrical or nonsymmetrical. Then the relational facts Rab and Rba will be distinct. For example, Al's loving Bill, and Bill's loving Al are distinct facts. A fact is a complex. Now the following principle seems well-nigh self-evident:

   P. If two complexes, K1 and K2, differ numerically, then there exists
   a constituent C such that C is an element of K1 but not of K2, or vice
   versa.

In other words, if two complexes differ, then they differ in a constituent. 'Complex' is intended quite broadly. Mathematical sets are complexes and it is clear that they satisfy the principle. There cannot be two sets that have all the same members.  Ditto for mereological sums.

Now if Rab and Rba are distinct, then, by principle (P), they must differ in a constituent. But they seem to have all the same constituents. Both consist of a, b, and R, and if you think there must also be a triadic nexus of exemplification present in the fact, then that item too is common to both. And if you think there is a benign infinite regress of exemplification nexuses in the fact, then those items too are common to both. Since both facts have all the same constituents, what is the ontological ground of the numerical difference of the two facts?  What makes them different?  The question is not whether they differ; it is obvious that they do.  The question concerns the ground of their difference.  What explains their difference?  Of course, I am not asking for an explanation in terms of empirical causes.  Consider {1, 2} and {1, 2, 3}.  What is the ontological ground of the difference of these two sets?  It would be a poor answer to say that they just differ, that their difference is a factum brutum.  The thing to say is that they differ in virtue of one set's having a member the other doesn't have.  When I say that 3 makes the difference between the two sets I am obviously not giving a causal explanation.  I am specifying a factor in reality that 'makes' the two entities numerically different.

So what, if anything, is the ontological ground of the difference between aRb and bRa when R is either asymmetrical or nonsymmetrical?  This, I take it,  the problem of order, or, in the jargon of Gustav Bergmann, the problem of providing an 'assay' of order.  It may be that no assay is possible.  It may be that the difference is a brute difference.  But that cannot be assumed at the outset.

It seems to me that the problem of unity is different although related.  What is the difference between the fact aRb and the set or sum of its constituents?  If a contingently stands in R to b, then it is possible that a, R, and b all exist without forming a relational fact.  So what is the difference between aRb and {a, R, b}?  Here we have two complexes that share all their constituents,  but they are clearly different complexes: one is a fact while the other is not.  What is the ground of fact-unity, that peculiar form of unity found in facts but not it other types of complex?

Suppose you deny that they share all constituents.  Suppose you maintain that the fact includes a triadic exemplification nexus that is not present in the set.  I will then re-formulate the problem as follows.  What is the difference between aRb and {a, R, NEX, }?

The problem of order is different from the problem of unity. The latter is the problem of accounting for the peculiar unity of those complexes that attract such properties as truth, falsity, and obtaining. For some of these complexes, no problem of order arises. For example, a monadic fact of the form, a's being F, precisely because it is nonrelational does not give rise to any problem of order. Since the problem of unity can arise in cases where the problem of order does not arise, the two problems are distinct.

The unity problem is the more fundamental of the two. The question as to the ground of the difference of a fact and the mere collection of its consituents is more fundamental than the question as to the ground of the difference between two already constituted facts which appear to share all their constituents.

Related:  Is the Difference Between a Fact and its Constituents a Brute Difference?

Kenny, Geach, and the Perils of Reading Frege Back Into Aquinas

I have been studying Anthony Kenny, Aquinas on Being (Oxford 2002).  I cannot report that I find it particularly illuminating.  I am troubled by the reading back of Fregean doctrines into Aquinas, in particular in the appendix, "Frege and Aquinas on Existence and Number." (pp. 195-204)  Since Kenny borrows heavily from Peter Geach, I will explain one of my misgivings in connection with a passage from Geach's important article, "Form and Existence" in God and the Soul.  Geach writes,

Frege, like Aquinas, held that there was a fundamental distinction in rebus answering to the logical distinction between subject and predicate -- the distinction between Gegenstand (object) and Begriff (concept). [. . .] And for Frege the Begriff, and it alone, admits of repetition and manyness; an object cannot be repeated -- kommt nie wiederholdt vor. (45-46)

So far, so good.  Geach continues:

Understood in this way, the distinction between individual and form is absolutely sharp and rigid; what can be sensibly said of one becomes nonsense if we try to say it of the other. [. . .] Just because of this sharp distinction, we must reject the Platonic doctrine that what a predicate stands for is is some single entity over against its many instances, hen epi pollon. On the contrary:  the common nature that the predicate 'man' (say) stands for can be indifferently one or many, and neither oneness nor manyness is a mark or note of human nature itself.  This point is made very clearly by Aquinas in De Ente et Essentia.  Again we find Frege echoing Aquinas; Frege counts oneness or manyness (as the case may be) among the properties (Eigenschaften) of a concept, which means that it cannot at the same time be one of the marks or notes (Merkmalen) of that concept. (46)

I smell deep confusion here.  But precisely because the confusion runs deep I will have a hard time explaining clearly wherein the confusion consists.  I will begin by making a list of what Geach gets right.

1. Objects and individuals are unrepeatable. 
2. Concepts and forms are repeatable.
3. Setting aside the special question of subsistent forms, no individual is a form, and no object is a concept.
4. Frege distinguishes between the marks of a concept and the properties of a concept. The concept man, for example, has the concept animal as one of its marks.  But animal is not a property of man, and this for the simple reason that no concept is an animal.  Man has the property of being instantiated.  This property, however, is not a mark of man since it is not included within the latter's conceptual content:  one cannot by sheer analysis of the concept man determine whether or not there are any men.  So there is a sense in which "neither oneness nor manyness is a mark or note of human nature itself."  This is true if taken in the following sense: neither being instantiated singly nor being instantiated multiply is a mark of the concept man.

But how do these points, taken singly or together, support Geach's rejection of "the Platonic doctrine that what the predicate stands for is some single entity over against its many instances"?  They don't!

It seems obvious to me that Geach is confusing oneness/manyness as the relational property of single/multiple instantiation with oneness/manyness as the monadic property of being one or many.  It is one thing to ask whether a concept is singly or multiply instantiated.  It is quite another to ask whether the concept itself  is one or many.  It is also important to realize that a Fregean first-level concept, when instantiated, does not enter into the structure of the individuals that instantiate it.  Aquinas is a constituent ontologist, but Frege is not.  This difference is deep and causes a world of trouble for those who attempt to understand Aquinas in Fregean terms.  For Frege, concepts are functions, and no function enters into the structure of its argument.  The propositional function x is a man is not a constituent of Socrates.  What's more, the value of the function for Socrates as argument is not a state of affairs with Socrates and the function as constituents. The value of the function for Socrates as argument is True; for Stromboli as argument, False.  And now you know why philosophers speak of truth-values.  It's mathematical jargon via Frege the mathematician.

The Fregean concept man is one, not many.  It is one concept, not many concepts.  Nor is it neither one nor many.  It can have one instance, or many instances, or no instance.   The Thomistic form man, however, is, considered in itself, neither one nor many.  It is one in the intellect but (possibly) many in things.  In itself, however, it is neither.  And so it is true to say that the form is not "some single entity over against its many instances."  It is not a single entity because, considered in itself, it is neither single nor multiple.

But this doesn't follow from point (3) above.  And therein consists Geach's mistake.  One cannot validly move from the "sharp distinction" between individuals/objects and forms/concepts  to the conclusion that what a predicate stands for is not a single entity.  Geach makes this mistake because of the confusion  exposed two paragraphs supra.  The mutual exclusion of objects and concepts does not entail that concepts cannot be single entities.

There is another huge problem with reading Frege back into Aquinas, and that concerns modes of existence (esse).  A form in the intellect exists in a different way than it does in things.  But if Frege is right about existence, there cannot be modes of existence.  For if existence is instantiation, then there cannot be modes of existence for the simple reason that there cannot be any modes of instantiation.

I'll say more about this blunder in another post.  It rests in turn on a failure to appreciate  the radically different styles of ontology practiced by Aquinas and Frege.  In my jargon, Aquinas is a constituent ontologist while Frege is a nonconstituent ontologist.  In the jargon of Gustav Bergmann, Aquinas is a compex ontologist while Frege is a function ontologist.

Are Facts Perceivable? An Aporetic Pentad

'The table is against the wall.'  This is a true contingent sentence.  How do I know that it is true except by seeing (or otherwise sense perceiving) that the table is against the wall?  And what is this seeing if not the seeing of a fact, where a fact is not a true proposition but the truth-maker of a true proposition?  This seeing of a fact  is not the seeing of a table (by itself), nor of a wall (by itself), nor of the pair of these two physical objects, nor of a relation (by itself).  It is the seeing of a table's standing in the relation of being against a wall.  It is the seeing of a truth-making fact.  (So it seems we must add facts to the categorial inventory.)  The relation, however, is not visible, as are the table and the wall.  So how can the fact be visible, as it apparently must be if I am to be able to see (literally, with my  eyes) that the table is against the wall? That is our problem. 

Let 'Rab' symbolize a contingent relational truth about observables such as 'The table is against the wall.'  We can then set up the problem as an aporetic pentad:

1. If one knows that Rab, then one knows this by seeing that Rab (or by otherwise sense-perceiving it).
2. To see that Rab is to see a fact.
3. To see a fact is to see all its constituents.
4. The relation R is a constituent of the fact that Rab
5. The relation R is not visible (or otherwise sense-perceivable).

The pentad is inconsistent: the conjunction of any four limbs entails the negation of the remaining one.  To solve the problem, then, we must reject one of the propositions.  But which one?

(1) is well-nigh undeniable: I sometimes know that the cat is on the mat, and I know that the cat is on the mat by seeing that she is. How else would I know that the cat is on the mat?  I could know it on the basis of the testimony of a reliable witness, but then how would the witness know it?  Sooner or later there must be an appeal to direct seeing.  (5) is also undeniable: I see the cat; I see the mat; but I don't see the relation picked out by 'x is on y.'  And it doesn't matter whether whether you assay relations as relation-instances or as universals.  Either way, no relation appears to the senses.

Butchvarov denies (2), thereby converting our pentad into an argument against facts, or rather an argument against facts about observable things.  (See his "Facts" in Javier Cumpa ed., Studies in the Ontology of Reinhardt Grossmann, Ontos Verlag 2010, pp. 71-93, esp. pp. 84-85.)  But if there are no facts about observable things, then it is reasonable to hold that there are no facts at all.

So one solution to our problem is the 'No Fact Theory.'  One problem I have with Butchvarov's denial of facts is that (1) seems to entail (2).  Now Butch grants (1).  (That is a loose way of saying that Butch says things in his "Facts' article that can be reasonably interpreted to mean that if (1) were presented to him, then would grant it.)  So why doesn't he grant (2)?  In other words, if I can see (with my eyes) that the cat is on the mat, is not that excellent evidence that I am seeing a fact and not just a cat and a mat?  If you grant me that I sometimes see that such-and-such, must you not also grant me that I sometimes see facts? 

And if there are no facts,then how do we explain the truth of contingently true sentences such as 'The cat is on the mat'? There is more to the truth of this sentence than the sentence that is true.  The sentence is not just true; it is true because of something external to it.  And what could that be?  It can't be the cat by itself, or the mat by itself, or the pair of the two.  For the pair would exist if the sentence were false.  'The cat is not on the mat' is about the cat and the mat and requires their existence just as much as 'The cat is on the mat.'  The truth-maker, then, must have a proposition-like structure, and the natural candidate is the fact of the cat''s being on the mat.  This is a powerful argument for the admission of facts into the categorial inventory.

Another theory arises by denying (3).  But this denial is not plausible.  If I see the cat and the mat, why can't I see the relation -- assuming that I am seeing a fact and that a fact is composed of its constituents, one of them being a relation?  As Butch asks, rhetorically, "If you supposed that the relational fact is visible, but the relation is not, is the relation hidden?  Or too small to see?"  (85)

A third theory comes of denying (4).  One might think to deny that R is a constituent of the fact of a's standing in R to b.  But surely this theory is a nonstarter. If there are relational facts, then relations must be constituents of some facts. 

Our problem seems to be insoluble.  Each limb makes a very strong claim on our acceptance.  But they cannot all be true.  

Butchvarov Against Facts

In his essay, "Facts," (Studies in the Ontology of Reinhardt Grossmann, Javier Cumpa, ed., Ontos Verlag, 2010, p. 83) Panayot Butchvarov generously cites me as a defender of realism and a proponent of facts.  He credits me with doing something William P. Alston does not do in his theory of facts, namely, specifying their mode of reality:

However, William Vallicella, also a defender of realism, does.  He argues that true propositions require "truth-making facts." And he astutely points out that facts could be truth-making only if they are "proposition-like," "structured in a proposition-like way" -- only f a fact has a structure that can mirror the the structure of a proposition." (A Paradigm Theory of Existence, 13, 166-7,192-3)  Vallicella's view is firmly in the spirit of Wittgenstein's account in the Tractatus of the notions of fact and correspondence to fact, but his formulation of it may invite deflationist attacks like Strawson's.

Butchvarov, however, is firmly against adding the category of facts to our ontological inventory. This post will consider one of his arguments.  Butchvarov tells us (p. 86) that

The metaphysical notion of fact is grounded in our use of declarative sentences, and the supposition that there are facts in the world depends at least in part on the assumption that sentences must correspond to something in the world, that somehow they must be names.  But this assumption seems absurd.  Sentences are not even nouns, much less names.  They cannot serve as grammatical subjects or objects of verbs, which is the mark of nouns. [. . .] Notoriously, "p is true," if taken literally, is gibberish.  "Snow is white is true" is just ill-formed. "'Snow is white' is true" is not, but its subject-term is not a sentence -- it is the name of a sentence. 

Here is what I take to be Butchvarov's argument in the above passage and surrounding text:

1. If there are facts, then some declarative sentences are names.
2. Every name can serve as the grammatical subject of a verb.
3. No declarative sentence can serve as the grammatical subject of a verb.
Therefore
4. No declarative sentence is a name. (2, 3)
Therefore
5. There are no facts. (1, 4)

The friend of facts ought to concede (1).  If there are truth-making facts, then some declarative sentences refer to them, or have them as worldly correspondents.  The realist holds that if a contingent sentence such as  'Al is fat' is true, then that is not just a matter of language, but a matter of how the extralinguistic world is arranged.  The sentence is true because of Al's being fat.  Note that Al by himself cannot be the truth-maker of the sentence, nor can fatness by itself, nor can the set, sum, or ordered pair of the two do the job.  If {Al, fatness} is the truth-maker of 'Al is fat,' then it is also the truth-maker of 'Al is not fat' -- which is absurd. 

As for (2), it is unproblematic.  So if the argument is to be neutralized -- I prefer to speak of 'neutralizing' rather than 'refuting' arguments -- we must give reasons for not accepting (3).  So consider this argument for the negation of (3).

6. 'Snow is white' is true.
7. No name is true or false.
Therefore
8. 'Snow is white' is not a name.
9. Anything either true or false is a declarative sentence.
Therefore
10. 'Snow is white' is a declarative sentence.
Therefore
11. 'Snow is white'  serves as the grammatical subject of the verb 'is a declarative sentence.'
Therefore
12. Some declarative sentences can serve as the grammatical subjects of a verb.
Therefore
~3. It is not the case that no declarative sentence can serve as the grammatical subject of a verb.

The argument just given seems to neutralize Butchvarov's argument.

The Paradox of the Horse and 'the Paradox of Snow'

Butchvarov's view is deeply paradoxical.  He holds that 'Snow is white ' in (6) is not a sentence but the name of a sentence.  The paradox is similar to the paradox of the horse in Frege.  Frege notoriously held that the concept horse is not a concept.  Butchvarov is maintaining  that the sentence 'Snow is white' is not a sentence. 

What is Frege's reasoning?  He operates with an absolute distinction between names and predicates (concept words).  Corresponding to this linguistic distinction there is the equally absolute ontological distinction between  objects and concepts.  Objects are nameable while concepts are not.  So if you try to name a concept you willy-nilly transform it into an object.  Since 'the concept horse' is a name, its referent is an object.  Hence the concept horse is not a concept but an object.

Similarly with Butchvarov.  To refer to a sentence, I must use a name for it.  To form the name of a sentence, I enclose it in quotation marks.  Thus the sentence 'snow is white' is not a sentence, but a name for a sentence.  

Butchvarov finds it "absurd" that a sentence should name a fact.  His reason is that a sentence is not a name.  But it strikes me as even more absurd to say that the sentence 'Snow is white' is not a sentence, but  a name.   

My tentative conclusion is that while realism about facts is dubious, so is anti-realism about them.  But there is also what Butchvarov calls "semi-realism" which I ought to discuss in a separate post.

Indeterminate Yet Existent? The Aporetics of Prime Matter and Pure Consciousness

Scott Roberts e-mails in reference to my post Hylomorphic Ontological Analysis and the Puzzle of Prime Matter: 

I have also been perplexed at hylomorphism's dependence on something called [prime]  'matter', for the same reason as you give. But I think there is a way out, though perhaps not one a hylomorphist will like. You say "Something bare of determinateness is unthinkable and hence nonexistent." But I can think of three words that refer to something one might consider real yet bare of determinateness, namely mass (or energy), consciousness (considered apart from all intentional objects of consciousness), and God (of classical theism). In each case you have something that can be thought of as giving form actuality. But that leads to an inversion of hylomorphism, namely, that now it is form that is potential, and what was formally [formerly?] thought of as matter is now Pure Act.  For example, a mathematical object which is not being thought of is a potential form that consciousness gives actuality as a thought. [. . .]

The reader is right to point out that there is something dubious about my claim that "Something bare of determinateness is unthinkable and hence nonexistent." Of the three counterexamples he gives, the clearest and best is "consciousness considered apart from all intentional objects of consciousness."  Consciousness so considered is not nothing, and yet it is indeterminate since all determinations fall on the side of the objects.  Consciousness is no-thing, a Sartrean theme which is also developed by Butchvarov. 

The reader has made me see that there is a certain structural analogy between prime matter and consciousness conceived of as pure of-ness bare of all determinacy.  For one thing, both, considered in themselves, are indeterminate or formless, and necessarily so.  If consciousness were determinate, it would be an object of consciousness and not the consciousness without which there are no (intentional) objects.  And if prime matter were determinate, it would be formed matter and thus not prime matter.  Second, neither can exist apart from its other.  There is no consciousness without objects, and there is no prime matter that exists on its own in the manner of a substance.  So, while consciousness is other than every object, it cannot exist except as the consciousness of objects (objective genitive).  And while prime matter is other than every form, and in itself formless, it requires formation to be something definite and substantial.

A third point of analogy is that both consciousness and prime matter give rise to a structurally similar puzzle.   Consider a mind-independent hylomorph A whose matter (H) is prime matter and whose form (F) is composed of lowest forms.  Which is ontologically prior, A, or its ontological parts H and F?  If the parts are prior in the manner of pre-existing ontological building blocks -- think (by analogy) of the way the stones in a stone wall are prior to the wall -- then H could not be a 'principle' in the scholastic sense but would have to something capable of independent existence.  And that is unacceptable: surely prime matter cannot exist on its own.  If, on the other hand, A is prior to its parts, then the parts would exist only for us, or in our consideration, as aspects which we bring to A.  But that won't do either because A ex hypothesi exists extramentally and so cannot in its ontological constitution require any contribution from us.

The consciousness puzzle is similar. Is consciousness (conceived as pure diaphanous of-ness of objects in the manner of Sartre, Butchvarov, and perhaps Moore) something really existent in itself or is it rather an abstract concept that we excogitate?  In other words, when we think of consciousness transcendentally as the sheer revelation of objects, are we thinking of a really existent condition of their revelation, or is consciousness so conceived merely a concept that we bring to the data?  If consciousness really exists, then we substantialize it (reify it, hypostatize it) in a manner analogous to the way we substantialize prime matter when we think of its as something capable of independent existence.  And that is puzzling.  How can something exist that is not an object of actual or possible awareness?  If, on the other hand, consciousness is not something that exists on its own but is a concept that we excogitate, then how do we account for the real fact that things are apparent to us, that things are intentional objects for us?  Besides, if consciousness were a mere concept, then consciousness as a reality would be presupposed: concepts are logically subsequent to consciousness.

So the two puzzles are structurally similar. 

Let us see if we can abstract the common pattern.  You have a term X and a distinct term Y.  The terms are introduced to make sense of a phenomenon Z.  Z is the analysandum whose analysis into X and Y is supposed to generate understanding.   X cannot exist without Y, hence it cannot exist on its own.  The same goes for Y.  The terms cannot exist without each other on pain of (i) hypostatization of each, and (ii) consequent sundering of the unity of Z.  (The diremption of Z into X and Y gives rise to the ancient problem of the unity of a complex which no one has ever solved.)  That the terms cannot exist without each other suggests that the unitary phenomenon Z is split into X and Y only by our thoughts such that the factoring into X and Y is our contribution.  On the other hand, however, the terms or factors must be capable of some sort of existence independent of our conceptual activities if the explanation that invokes them is an explanation of a real mind-independent phenomenon.

Here is a sharper form of the common aporia.  Both prime matter and pure consciousness are real.  But they are also both unreal.  Nothing, however,  can be both real and unreal on pain of violating Non-Contradiction.  How remove the contradiction without giving rise to a problem that is just as bad?

I don't say that the aporiai are insoluble, but I suspect that any solution proffered with give rise to problems of its own . . . .

Hylomorphic Ontological Analysis and the Puzzle of Prime Matter

Recent posts have discussed  hylomorphic dualism in the philosophy of mind. It is a serious contender in the arena of competing positions -- unlike say, eliminative materialism, which is not. (If you think I'm just gassing off about EM, read the entries in the eponymous category.) But now I want to take a step back from the special topic of the mind-body problem to the more general theme of hylomorphic ontological analysis as such.  In this post I examine some ideas in John Haldane's "A Return to Form in the Philosophy of Mind" in Form and Matter: Themes in Contemporary Metaphysics, ed. David S. Oderberg, Blackwell, 1999, pp. 40-64. But first some background.

In the 20th century Anglosphere, most philosophical analysis has been conceptual and linguistic. Moore and Russell were major practitioners. Decidedly less popular has been phenomenological analysis. Think Husserl. And least popular has been ontological analysis. The Iowa School (Gustav Bergmann and Co.) and Thomism are  the two major representatives of it. Ontological analysis takes as its object the (mind-independently) existent. It operates on the assumption that ordinary particulars have ontological constituents, and it tries to specify what these constituents are. These constituents are of course not spatial parts and they 'lie deeper' (whatever exactly this means) than the targets of chemical and physical analysis. They are items like these: universals, tropes, non-relational ties, Castaneda's ontological operators, Armstrong's thin particulars, Bergmann's bare particulars, and others besides.

2. Hylomorphic analysis is one type of ontological analysis. One analyzes meso-particulars such as a statue or a horse into form (morphe) and matter (hyle) among other constituents. These constituents are sometimes called principles, using the word in an old-fashioned way. Thus one speaks of the principium individuationis, the principle of individuation, or of the soul as life principle. The principle of individuation is not a statement or proposition but a real factor 'in' things that accounts for their numerical difference.

3. What motivates the hylomorphic approach? John Haldane has something interesting to say on this point:

. . . a condition of there being something for thought to take hold of is that the something has structure. Equivalently, a condition of there being thought is that there be relevant structuring principles (sortal and characterizing concepts plus logical constants.)

So we arrive at hylomorphic analysis. Every particular may be understood in terms of the instantiation of a formal principle. Its form makes it to be the kind of thing it is, providing its definitive structure, its characteristic powers and liabilities, and so on. However, since, ex hypothesi, things of the same specific sort have formally identical principles there arises the question of numerical difference. The analysis is completed by introducing the idea of matter as that which is structured and is the basis of numerical individuation within species. (49-50)

The motivation for hylomorphism is something like this. Thinking, in virtue of its intentionality, refers beyond itself to what it is not, namely, to 'objective' things and states of affairs. Whether thinking succeeds in referring beyond itself to things that exist independently of thought is of course a further question; but it is clear that thinking and indeed all forms of intentionality purport so to refer. For example, my perceiving of a distant mountain purports to reveal a physical object that exists whether I or anyone perceives it. This purport is part of the very sense of outer perception. Borrowing a line from the neglected German philosopher Wolfgang Cramer, outer perceiving is of objects as non-objects. The meaning, I hope, is clear: in outer perceiving the object is intended as more than a mere intentional object or accusative of awareness; it is intended as precisely something that exists as a non-object, as something that exists in itself, apart from the consciousness that posits it as existing in itself.

Now if one, setting aside skeptical worries, simply assumes that thought sometimes makes contact with reality, then one can ask: what must real things be like if thought is to be able to make contact with them? What must these things be like if it is to be possible for thought to "take hold of" them as Haldane puts it? The answer is that these mind-independent things must be conformable to our thought, and our thought to them. There must be some sort of isomorphism between thought and thing. Since we cannot grasp anything unstructured, reality must have structure. So there have to be principles of form and organization in things. But these formative principles must form something or determine something which, in itself, is at least relatively formless or indeterminate. There must be something which, in itself is (relatively) formless, is susceptible of being informed, or receptive of formation. In this way matter comes into the picture.

4. But now let's consider some puzzles. The proximate matter of a chair consists of its legs, seat, back. But this proximate matter itself has form. A leg, for example, has a shape and thus a form. (Form is not identical to shape, since there are forms that are not shapes; but shapes are forms.) Suppose the leg has the geometrical form of a cylinder. (Of course it will have other forms as well, the forms of smoothness and brownness, say.) The cylindrical form is the form of some matter. The matter of this cylindrical form is wood, say. But a piece of wood is a composite entity the parts of which have form and matter. For example, the complex carbohydrate cellulose is found in wood. It has a form and a proximate matter. But cellulose is made of beta-glucose molecules. Molecules are made of atoms, atoms of subatomic particles like electrons, and these of quarks, and so it goes.

The idea is that hylomorphic analysis is iterable. The iteration has a lower limit in prime or primordial or ultimate matter (materia prima.). Ultimate matter, precisley because it is ultimate, has no form of its own. As Haldane describes it, it is "stuff of no kind." (50)

Now one puzzle is this. Prime matter is not nothing. If it were nothing, then there would be no proximate matter either. Consider the lowest level of proximate matter. Consider a particle whose matter is prime matter. If prime matter is nothing at all, then this smallest particle could not exist, (since it is built up out of its components and one of them does not exist), and nothing having it as a component could exist. So prime matter is not nothing. But it is not something either. For if it were something it would have form or structure or organization. Obviously nothing can exist that is not definite and determinate. If you say the indeterminate, the apeiron, exists, WHAT are you saying exists? WHAT are you talking about? There has to be a whatness, a form, for it to be intelligible to say that something exists. 'X exists' says nothing. Recall the isomorphism between thought and reality that is part of the motivation for hylomorphic analysis. Something bare of determinateness is unthinkable and hence nonexistent.

We are driven to the conclusion that prime matter is not nothing and also not something. This certainly looks like a contradiction. But it is a contradiction apparently forced upon us if we embrace hylomorphic ontological analysis. For this analysis is iterable. One cannot stop shy of primate matter, for if there is no ultimate matter then there is no proximate matter either.

To avoid the contradiction one might say that prime matter, though not something actual is not nothing in that it is pure potency: the pure potentiality to receive forms is essentially the way Haldane puts it. (50) Does this help? Not much. What exactly is the difference between a pure potentiality to receive any form and nothing at all? Something that is not F or G or H, etc. but is receptive to these forms has no determinate nature. Without a determinate nature, how can it be anything at all?

5. Furthermore, a pure potency cannot be an ontological building block out of which to construct something actual. So should we say that prime matter is a mere abstraction? But then forms free of matter would also be mere abstractions. How can a substance be built up out of abstractions?

This second  problem concerns the status of the so-called 'principles' form and matter.  They don't have an independent existence, else they would be substances in their own right.  Is their status then merely mental?  That can't be right either since a hylomorph (a hylomorphic compound) cannot  be compounded of  components whose status is merely mental.  Why not?  Well, the typical hylomorph enjoys extramental existence, and it is difficult to see how such a thing could be built up out of constituents whose status was wholly intramental.

Feser Defends Hylomorphic Dualism Against My Criticism

I want to thank Edward Feser for responding to my recent post, A Problem for the Hylomorphic Dualist.  And while you are at Ed's site, please read his outstanding entry, So you think you understand the cosmological argument?, an entry with which I agree entirely.

Ed writes,

Naturally, since I am a hylemorphic dualist, I completely disagree with Bill here. Let’s start with the last charge -- that hylemorphic dualism “make[s] an exception in the case of the human soul [that] is wholly unmotivated and ad hoc and inconsistent with hylomorphic ontology.” That the view is not “unmotivated and ad hoc” is easily shown. Bill himself would surely acknowledge that there are serious philosophical arguments for hylemorphism, even if he doesn’t accept that view himself. He would also acknowledge that there are serious philosophical arguments for dualism, a view he is sympathetic with. But then he should also acknowledge that someone could find both sorts of arguments convincing. And in that case he should acknowledge that someone could have good philosophical reasons for thinking that there must be some way to combine hylemorphism and dualism.

I agree that there are serious arguments for hylomorphism, and I especially agree that there are strong arguments for dualism.  And I agree that someone who finds both hylomorphism and dualism persuasive will have a motivation to try to combine them by showing how the special-metaphysical thesis of dualism can be accommodated within the general-metaphysical scheme of hylomorphism. 

But if one has good arguments for position A and good arguments for position B, it doesn't follow that one has good arguments for the combined position A + B.  For there may be a good reason why the two positions cannot be combined.  And so it is in the present case.  The case for hylomorphism and the case for dualism do not add up to a case for  hylomorphic dualism.  So while I agree with Ed that one who has good reason to be a hylomorphist and good reason to be a dualist will be powerfully motivated to combine the two positions, I do not agree that the reasons for hylomorphism and dualism, respectively, add up to reasons for the hylomorphic dualism.  A psychological motivation is not the same as a justificatory reason. 

Ed continues:

Nor, contrary to what Bill implies, is Aquinas somehow departing radically from Aristotle. For Aristotle too was committed both to hylemorphism and to the view that the intellect is immaterial -- indeed, to the view that the active intellect is immortal. To be sure, that does not by itself show that Aristotle’s views are identical to or entail Aquinas’s; the Averroists took Aristotle’s position in a very different direction, and contemporary commentators often find it simply puzzling. But the reason they do -- namely, that it seems odd to say both that the soul is the form of the body and that one of its capacities is somehow separable from the body -- is similar to the reason Bill finds Aquinas’s position puzzling. Needless to say, Aristotle had no Christian theological ax to grind; he was simply following the philosophical arguments where they led. There is no reason to accuse Aquinas of doing anything different, and it is hardly unreasonable to suggest that the way to harmonize the various aspects of Aristotle’s position is the way Aquinas does. That does not mean that one might not still question whether Aquinas’s position is ultimately coherent (as Bill does), or criticize it on other grounds. But the charge that it is “wholly unmotivated and ad hoc” -- a piece of Christian apologetics with no independent philosophical rationale -- is, I think, completely unwarranted. 

Clearly, Aristotle had no Christian axe to grind.  And so if the active intellect (nous poietikos) mentioned in De Anima III, v (430a) is a subsistent element of the human soul, capable of existence independent of matter, then Aquinas' position on the human soul would have been anticipated by Aristotle, and what I said, or rather suspected, about Aquinas implanting Christian  notions in the foreign soil of Aristotelianism would be insupportable.  But the interpretation of De Anima III, v is a vexed and vexing matter as the material in the hyperlink Ed provided makes clear.  If, as some commentators maintain, Aristotle is discussing the divine mind and not the human mind, then it cannot be maintained that Aristotle was anticipating Aquinas.

The important question, of course, is whether the human soul, or any part theoreof, can be coherently conceived as a subsistent form, whether this is maintained by Aristotle or Aquinas or both.  Ed now addresses my puzzle head on:

The soul is, for Aquinas, the form of the body. So how could it possibly exist apart from the body? Bill asks why things should be any different with human beings than they are with Fido. But Aquinas is quite clear about the answer to that question: The difference is that the human soul carries out immaterial operations (i.e. intellectual ones) while a dog’s soul does not. And if it operates apart from matter and agere sequitur esse, then it must subsist apart from matter.

I grant that the human soul, unlike the canine, carries out immaterial operations.  The argument is this:

a.  The human soul engages in immaterial operations
b.  Agere sequitur esse: whatever operates I-ly must be (exist) I-ly.
Therefore
c.  The human soul, qua executing immaterial operations, exists immaterially.

But how is this relevant to the issue I am raising?  Let's assume that the above argument is sound.  What it shows is that the human soul enjoys an immaterial mode of being.  But it does not show that a form of an animal body enjoys an immaterial mode of being.  It is one thing to establish that the human soul, or an element thereof, exists immaterially; quite another to show that this immaterial element is a form.  I hesitate to say that Ed is conflating these two questions.  What he might be doing is begging the question against me: he may be just assuming what I am questioning, namely, that the human soul is a form, and then taking an argument for the immateriality of the soul to be an argument for the immaterial existence of a form of the human body.  Quoting further from Feser:

Necessarily, a form is a form of that of which it is the form. But a subsistent form is possibly such as to exist apart from that of which it is the form. These propositions cannot both be true.

That they can both be true can be seen when we keep in mind how Aristotelians understand concepts like necessity, possibility, essence, and the like. Suppose we say that it follows from the nature or essence of a dog that it has four legs. Does that mean every single dog necessarily has four legs? No, because a given dog might have lost a leg in an accident, or failed to develop all four legs due to some genetic defect, or (if only recently conceived and still in the womb) may simply not yet have developed all four legs. What it does mean is rather that a mature dog in its normal state will necessarily have four legs. As Michael Thompson and Philippa Foot have emphasized, “Aristotelian categoricals” of the form S’s are F convey a norm and are not accurately represented as either existential or universal statements of the sort familiar to modern logicians. “Dogs have four legs” is not saying “There is at least one dog, and it has four legs” and neither is it saying “For everything that is a dog, it is four legged.” It is saying that the typical dog, the normal (mature) dog, has four legs.

I of course agree with the bit about the dog and his nature.  But I question its relevance to my point.  I grant that from the fact that it is the nature of a dog to have four legs it does not follow that every dog has four legs.  In parallel with this, Ed seems to be suggesting that while it is the nature of a form to be a form of something, it does not follow that every form is a form of something. I deny the parallel.  The claims are on different levels.  The 'canine' claim is about a particular nature (essence), dog-nature.  My claim is about the principles (in the scholastic sense) deployed by hylomorphic ontologists  in their ontological assays.  A form is a 'principle' not capable of independent existence in the manner of a primary substance.

How form and matter operate in the analysis of material substances becomes clearer if we examine a criticism the distinguished Aristotelian Henry Veatch lodges against Gustav Bergmann. (See here for the rest of the post from which the following blue section is excerpted and for bibliographical data.)

Veatch Contra Bergmann

Veatch now lodges a reasonable complaint against Bergmann. How could "matter or bare particulars [be] among the ultimates that one arrives at in a process of analysis. . ."? "For how could anything which in itself is wholly indeterminate and characterless ever qualify as a 'thing' or 'existent' at all?" (81) On Bergmann's assay, an ordinary particular has more basic entities as its ontological constituents. But if one of these constituents is an intrinsically indeterminate and intrinsically characterless entity, how could said entity exist at all, let alone be a building block out of which an ordinary particular is constructed?

For Veatch, form and matter are not ontological atoms in the way bare particulars and simple universals are ontological atoms for Bergmann. "Matter and form are not beings so much as they are principles of being." (80) 'Principle' is one of those words Scholastics like to use. Principles in this usage are not propositions. They are ontological factors invoked in the analysis of primary substances, but they are not themselves primary substances. They cannot exist on their own. Let me try to make Veatch's criticism as clear as I can.

An ordinary particular is a this-such. The thisness in a this-such is the determinable element while the suchness is the determination or set of determinations. Veatch's point against Bergmann is not that ordinary particulars are not composites, this-suches, or that the thisness in a this- such is not indeterminate yet determinable; his point is that the determinable element cannot be an ontological atom, an entity more basic than the composite into which it enters as ontological building block. The determinable element cannot be a basic existent; it must be a principle of a basic existent, where the basic existent is the this-such. This implies, contra Bergmann, that what is ontologically primary is the individual substance, the this-such, which entails that matter and form in an individual substance cannot exist apart from each other. They are in some sense 'abstractions' from the individual substance. The form in a material this-such is not merely tied to matter in general, in the way that Bergmannian first-order universals are tied to bare particulars in general; the form is tied to the very matter of the this-such in question. And the same goes for the matter: the designated matter (materia signata) of Socrates cannot exist apart from Socrates' substantial form.

Veatch says that Bergmann cannot have it both ways: "His bare particulars cannot at one and the same time be utterly bare and characterless in the manner of Aristotelian prime matter and yet also be 'things' and 'existents' in the manner of Aristotelian substances." (82-83)

 The point I want to underscore is that, as Veatch puts it,  "Matter and form are not beings so much as they are principles of being."  Ed continues,

Similarly, to say “Human souls are associated with bodies” is to say that the human soul in its normal state is associated with its body, just like the human hand in its normal state is associated with its body. But it doesn’t follow that it cannot exist apart from the body, any more than it follows that the hand (at least while its tissues are still alive) can exist apart from the body. And again, the reason this is possible with the human soul and not with Fido’s soul is that the human soul, unlike Fido’s soul, carries out immaterial operations even when it is associated with the body.

Here again I think Ed is failing to engage the problem I raised.  I do not question that the human soul in its normal state is associated with its body.  And I do not question that it can exist apart from its body.  What I am questioning is the conceptualization of the human soul as a form.  And so, while Ed has said many things with which I agree, he has not given me a reason to retract my criticism.  To put it another way, he has not given me a reason why I should accept argument A below over argument B:

Argument A:  The human soul can exist apart from its body; the human soul is the form of the human body; therefore, there are forms that can exist apart from the matter they inform.

Argument B:  The human soul can exist apart from its body; no form can exist apart from the matter it informs; therefore, the human soul is not the form of the human body.

I have another argument that Ed may recall from our discussions at my old Powerblogs site, namely, an argument based on the premise that a form cannot be a subject of experience, which is what a soul must be.  But that's a separate post.

How Are Form and Matter Related in Compound Material Substances?

Favoring as I do constituent ontology, I am sympathetic to that type of constituent ontology which is hylomorphic ontological analysis, as practiced by Aristotelians, Thomists, et al.  The obscurity of such fundamental  concepts as form, matter, act, potency, substance, and others is, however, troubling. Let's see if we can make sense of the relation between form and matter in an artifact such as a bronze sphere. Now those of you who are ideologically committed to Thomism may bristle at an exposure of difficulties, but you should remember that philosophy is not ideology. The philosopher follows the argument to its conclusion whether it overturns his pet beliefs or supports them, or neither. He knows how to keep his ideological needs in check while pursuing pure inquiry.  If the inquiry terminates in an aporetic impasse, then so be it.

1. Although it perhaps requires arguing, I will here take it for granted that form and matter as these terms are used by Aristotle and his followers are items 'in the real order.' 'Item' is a maximally   noncommittal term in my lexicon: it commits me to very little. Anything in whatever category to which one can refer in any way  whatsoever is an item. 'Real' is that which exists whether or not it is an intentional object of an act of mind. So when I say that form and matter are items in the real order I simply mean that they are not projected by the mind: it is not as if bronze spheres and such have  form and matter only insofar as we interpret them as having form and matter. The bronze sphere is subject to hylomorphic (matter-form) analysis because the thing in reality is made up of form and matter.   'Projectivism' is off the table at least for the space of this post. I am thus assuming a version of realism and am viewing form and matter as distinct ontological constituents or 'principles' of compound   substances.

2. The foregoing implies that the proximate matter of the bronze sphere,  namely, the hunk of bronze itself, is a part of the bronze sphere.  After all, 'ontological constituent' is just a fancy way of saying  'ontological part.'  But an argument I now adapt from E. J. Lowe ("Form Without Matter" in Form and Matter: Themes in Contemporary  Metaphysics, ed. Oderberg, Blackwell 1999, p. 7) seems to show that  the notion that the proximate matter of a compound material substance is a part of it is problematic.  The argument runs as follows.

A. If the hunk of bronze composing the sphere is a part of the sphere, then either it is a proper part or it is an improper part, where an improper part of a whole W is a part of W that overlaps every part of   W.

B. The hunk of bronze is not an improper part since it is not identical to the bronze sphere. (One reason for this is that the persistence conditions are not the same: the piece of bronze will still exist if the sphere is flattened into a disk, but the sphere cannot survive such a deformation. Second, the two are modally discernible: the hunk of bronze is a hunk of bronze in every possible world in which it exists, but the hunk of bronze is not a sphere in every possible world in which it exists.)

C. The hunk of bronze is not a proper part of the bronze sphere since there is no part of the bronze sphere that it fails to overlap.

Therefore

D. The hunk of bronze is not a part of the bronze sphere.

Therefore

E. The composition of form and matter is not mereological. (Lowe, p. 7)

This raises the question of how exactly we are to understand form-matter composition. If the proximate matter of a substance cannot  be a part of it in any sense familiar to mereology, the form-matter composition is 'unmereological,' which is not necessarily an objection except that it raises the question of how exactly we are to understand this unmereological type of composition. This problem obviously extends to essence-existence composition.

3. Now let's look at the problem from the side of form. Could the spherical form of the bronze sphere be a part of it? A form is a principle of organization or arrangement, and it is not quite clear how an arrangement can be a part of the thing whose other parts it arranges. Lowe puts the point like this: ". . . the arrangement of certain parts cannot itself be one of those parts, as this would involve the very conception of an arrangement of parts in a fatal kind of impredicativity." (p. 7)

4. In sum, the difficulty is as follows. Form and matter are real 'principles' in compound substances. They are not projected or supplied by us. We can say that form and matter are ontological constituents of compound substances. This suggests that they are parts of compound substances. But we have just seen that they are not parts in any ordinary mereological sense. So this leaves us in the dark as to just what these 'principles' are and how they combine to constitute compound material substances.

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.'

Is the Difference Between a Fact and Its Constituents a Brute Difference?

Note to Steven Nemes:  Tell me if you find this totally clear, and if not, point out what is unclear.  Tell me whether you accept my overall argument.

The day before yesterday in conversation Steven Nemes presented a challenge  I am not sure I can meet.  I have maintained (in my book, in published articles, and in these pages) that the difference between a fact and its constituents cannot be a brute difference and must therefore have a ground or explanation.  But what exactly is my reasoning?

Consider a simple atomic fact of the form, a's being F.  This fact has two primary constituents, the individual a, and the monadic property F-ness, which a possesses contingently.  But surely there is more to the fact than these two primary constituents, and for at least two reasons.  I'll  mention just one, which I consider decisive:  the constituents can exist without the fact  existing.  The individual and the property could each exist without the former exemplifying the second.  This is so even if we assume that there are no propertyless individuals and no unexemplified properties.  Consider a world W which includes the facts Ga and Fb.  In W, a is propertied and F-ness is exemplified; hence there is no bar to saying that both exist in W.  But Fa does not exist in W.  So a fact is more than its primary constituents because they can exist without it existing.

A fact is not its constituents, but those constituents unified in a particular way.  Now if you try to secure fact-unity by introducing  one or more secondary constituents such  an exemplification relation, then you will ignite Bradley's regress.  For if the constituents include a, F-ness, and EX, then you still have the problem of their unity since the three can exist without constituting a fact.

So I take it as established that a fact is more than its constituents and therefore different from its constituents.  A fact is different from any one of its constituents, and also from all of them taken collectively, as a mereological sum, say.    The question is:  What is the ontological ground of the difference?  What is it that makes them different?  That they are different is plain.  I want to know what makes them different.  It won't do to say that one is a fact while the other is not since that simply underscores that they are different.  I'm on the hunt for a difference-maker.

To feel the force of the question consider what makes two different sets different.  If S1 and S2 are different sets, then it is reasonable to ask what makes them different, and one would presumably not accept the answer that they are just different, that the difference is a brute difference.  Let S1 be my singleton and S2 the set consisting of me and Nemes.  It would not do to say that they are just different.  We need a difference-maker.  In this case it is easy to specify: Nemes.  He is what makes S1 different from S2.  Both sets contain me, but only one contains him.  Generalizing, we can say that for sets at least,

DM. No difference without a difference-maker.

So I could argue that the difference between a fact and (the sum of) its constituents cannot be a brute difference because (i) there is no difference without a difference-maker and (ii) facts, sets, and sums, being complexes, are relevantly similar.  (I needn't hold that the numerical difference of two simples needs a difference-maker.) But why accept (DM) in full generality as applying to all types of wholes and parts?  Perhaps the principle, while applying to sets, does not apply to facts and their constituents.  How do I answer the person who argues that the difference is brute, a factum brutum, and that therefore (DM), taken in full generality, is false?  As we say in the trade, one man's modus ponens is another's modus tollens.

Can I show that there is a logical contradiction in maintaining that facts and their constituents just differ?  That was my strategy in the book on existence.  The strategy is to argue that without an external ground of unity -- an external unifer -- one lands in a contradiction, or rather cannot avoid a contradiction.  That the unifier, if there is one, must be external as opposed to internal is established by showing that otherwise a vicious infinite regress ensues of the Bradley-type.  I cover this ground in my book and in articles in mind-numbing detail; I cannot go over it again here.  But I will refer the reader to my 2010 Dialectica article  which discusses a fascinating proposal according to which unity is constituted by an internal infinite, but nonvicious, regress.  But for now I assume that the unifier, if there is one, must be external.  If there is one, then the difference between a fact and its constituents cannot be brute.  But why must there be a unifier?

Consider this aporetic triad:

1. Facts exist.
2. A fact is its constituents taken collectively.
3. A fact is not its constituents taken collectively.

What I want to argue is that facts exist, but that they are contradictory structures in the absence of an external unifier that removes the contradiction.  Since Nemes agrees with me about (1), I assume it for present purposes.  (The justification is via the truth-maker argument).

Note that (2) and (3) are logical contradictories, and yet each exerts a strong claim on our acceptance.  I have already argued for (3).  But (2) is also exceedingly plausible.  For if you  analyze a fact, what will you uncover?  Its constituents and nothing besides.  The unity of the constituents whereby it is a fact as opposed to a nonfact like a mereological sum eludes analysis.  The unity cannot be isolated or located within the fact.  For to locate it within the fact you would have to find it as one of the constituents.  And that you cannot do.

Note also that unity is not perceivable or in any way empirically detectable.  Consider a simple Bergmann-style or 'Iowa' example, a red round spot.  The redness and the roundness are perceivable, and the spot is perceivable.  But the spot's being red and round is not perceivable.  The existence of a fact is the unity of its constituents.  So what I am claiming is equivalent to claiming that existence is not perceivable, which seems right: existence is not an empirical feature like redness and roundness.

So when we consider a fact by itself, there seems to be nothing more to it than its constituents.

Each limb of the triad has  a strong claim on our acceptance, but they cannot all be true as formulated.  The contradiction can be removed if we ascend to a higher point of view and posit an external unifier.  What does that mean? 

Well, suppose there is a unifier U external to the fact and thus not identifiable with one or more of its primary or secondary constituents.  Suppose U brings together the constituents in the fact-making way.  U would then be the sought-for ground of the fact's unity.  The difference between a fact and its constituents could then be explained by saying that  the difference is due to U's 'activity':  U operates on the constituents to produce the fact.  Our original triad can then be replaced by the following all of whose limbs can be true:

1. Facts exist
2*. A fact, considered analytically, is its constituents taken collectively.
3.  A fact is not its constituents taken collectively.

This triad is consistent.  The limbs can all be true.  And I think we have excellent reason to say that each IS true.  The truthmaker argument vouches for (1).  (2*) looks to be true by definition.  The argumentation I gave for (3) above strikes me as well-night irresistible.

But if you accept the limbs of the modified triad, then you must accept that there is something external to facts which functions as their unifier.  Difficult questions about what U is and about whether U is unique and the same for all facts remain; but that U exists is 'fallout' from the modified triad.  For if each limb is true, then a fact's being more than its constituents can be accounted for only by appeal to an external unifier.

But how exactly does this show that the difference between a fact and its constituents is not a brute difference?   The move from the original to the modified triad is motivated by the laudable desire to avoid contradiction.  So my argument boils down to this:  If the difference is brute, then we get a logical contradiction. So the difference is not brute. 

But it all depends on whether or not there are facts.  If facts can be reasonably denied, then my reasoning to a unifer can be reasonably rejected.  But that's a whole other can of worms: the truthmaker argument.

Analytically considered, a fact is just its constituents.  But holistically considered it is not.  Unity eludes analysis, and yet without unities there would be nothing to analyze!  Analytic understanding operates under the aegis of two distinctions: whole/part, and complex/simple.  Analysis generates insight by reducing wholes to their parts, and complex parts to simpler and simpler parts, and possibly right down to ultimate simples (assuming that complexity does not extend 'all the way down.')  But analysis is a onesided epistemic procedure.  For again, without unities there would be nothing to analyze. To understand the being-unified of a unity therefore requires that we ascend to a  point of view external to the unity under analysis. 

How Prevent a Proliferation of Modes of Being?

An astute reader comments:

Allowing for multiple modes of being may lead to too many or infinitely many modes. Using your own example and oversimplifying on purpose: if the mode of being of the house made of bricks is different from that of the bricks, what prevents us from claiming that there are different modes of being for all other structures that could be made from these bricks? I think there should be explicit arguments against this motivation.

A side note/question:  "no individual can be instantiated." You state this as a self evident truth. It would help if you elaborate on this point.

I have read your blog for over a year, mostly due to my interest in identity, existence and other basic notions that I consider fundamental. I respect your intellectual honesty and find your general reflections stimulating and deep but not dry.

1. My claim is not that a house, a corral, a wall, etc. made of the same bricks each has a different mode of being.  These wholes have the same mode of being as each other.  The claim is rather that certain types of whole -- not necessarily every type of whole --  possess a different mode of being than their parts. 

In the argument I gave, I made the simplifying assumption that the bricks are simples.  But of course they are not and so the argument can be iterated in their case assuming that each brick is a whole of parts of the same type as the whole of bricks.  Iterating the argument 'all the way down' we come finally to simples which exist-independently while all the wholes 'on the way up' exist-dependently.

My concern is to legitimate the very idea of there being modes of being as against the analytical orthodoxy according to which there cannot be any such modes.  I grant, however,  that if the MOB doctrine led to an endless proliferation of modes then that upshot would strongly count against it. 

2.  "No individual can be instantiated."  This follows if you accept the following definitions.

D1. X is an individual =_df X has properties but is not itself a property.
D2. X is a property =_df X is possibly such that it is instantiated. 

Since no individual is a property and only properties can be instantiated, no individual can be instantiated.  To be instantiated is to have an instance. 

3. "I respect your intellectual honesty and find your general reflections stimulating and deep but not dry."  I shall try to live up to that comment.  Thank you!

 

In Defense of Modes of Being: Substance and Accident

The 'thin' conception of being or existence, lately explained, entails that there are no modes of being. Most analytic philosophers accept the thin conception and reject modes of being. Flying in the face of analytic orthodoxy, I maintain that the modes-of-being doctrine is defensible. Indeed, I should like to say something stronger, namely, that it is indispensable for metaphysics.

My task in this series of posts is not to specify what the modes of being are, but the preliminary one of defending the very idea of there being different modes of being. So I plan to look at a range of   examples without necessarily endorsing the modes of being they  involve.  Against van Inwagen (see post linked above), I maintain that no mistake is made by partisans of the thick conception.  They do not, pace van Inwagen, illicitly transfer what properly belongs to the nature of a thing to its existence.

This post focuses on substances and accidents and argues that an accident and a substance of which it is the accident differ in their very mode of being, and not merely in their respective natures.

1. Intuitively, some items exist on their own while others are dependent in their existence on items that exist on their own. Smiles, grimaces, frowns, white caps, carpet bulges are items that exist, but
not on their own. They need -- as a matter of metaphysical necessity -- faces, waves, and carpets to exist in. This suggests some definitions:

D1. S is a (primary) substance =_df S is metaphysically capable of independent existence.

D2. A is an accident =_df A is not metaphysically capable of independent existence, but exists, if it exists, in a substance.

By 'metaphysically' I mean broadly logically in Plantinga's sense. So if a particular statue is a substance, then it is broadly logically possible that it exist even if nothing else exists. And if the smoothness or color of the statue are accidents, then it is broadly logically impossible that they exist (i) apart from some substance or other and indeed (ii) apart from the very substance of which they are the accidents.

The second point implies that accidents are particulars, not universals. Accidents cannot be shared. They are not 'repeatable' in the manner of universals. Nor can they 'migrate' from one substance to   another. You can't catch my cold if my cold is an accident of me as substance. Your cold is your numerically distinct cold. Socrates' whiteness is his whiteness and is as such numerically distinct from   Plato's whiteness. The connection between a substance and its accidents is an intimate one.

2. Now suppose there is a substance S and an accident A of S. I do not deny that there is a sense of 'exist' according to which both S and A  exist.  Suppose that S and A are the only two items that exist. Then of course there is a sense in which both items exist: each is something and not nothing. Both are there to be quantified over. We can say '(Ex)(x = S)' and '(Ex)(x = A)':  'Something is (identically) S' and 'Something is (identically) A.'

3. Now the issue is this: Does what I said in #2 exhaust what there is to be said about the being or existence of S and A? On the thin conception, that is all there is to it. To be is to be something or   other. If there are substances and accidents then both are in the same sense and in the same mode. ('Sense' a semantic term; 'mode' an ontological term.) Since S and A both exist in the same way on the thin conception, they are not distinguished by their mode of being.  They are distinguished by their respective natures alone.

4. In order to see what is wrong with the thin conception, let us ask how the two entities S and A are related. Indeed, can one speak of a relation at all? Traditionally, one speaks of inherence: A inheres in   S. Inherence cannot be an external relation since if a and b are externally related, then a and b can each exist apart from the relation. But A cannot exist apart from the inherence 'relation' to S. On the other hand, if S and A were internally related, then neither  could exist without the other. But S can exist without A. Since S can exist without A, but A cannot exist without S, A is existentially  dependent on S, dependent on S for its very existence, while S is capable of independent existence. But this is just to say that A  exists in a different way than S exists. Thus S and A differ in their  modes of being. One cannot make sense of inherence without  distinguishing substantial and accidental modes of being.

5. In sum: Talk of substances and their accidents is intelligible. But it is intelligible only if there are two modes of being, substantial and accidental. Therefore, talk of modes of being is intelligible. Since the thin conception of being entails that there cannot be modes of being, that the very idea is unintelligible, the thin conception ought to be rejected.

An Argument for Mental Acts

An earlier post explains the distinction between mental acts and mental actions.  But a logically prior question is whether there are any mental acts in the first place.  Suppose I hear the characteristic rumble of a Harley-Davidson engine and then suddenly think of Peter.  One cannot move straightaway from such a commonplace observation recorded in ordinary English to talk of mental acts of perceiving and of remembering.  This is because 'mental act' is a terminus technicus embedded within a theory.  It is a term that drags behind it a load of theoretical baggage that one may not want to take on board.  Every mental act is a mental state, a state of a mind.  (A state is necessarily a state of something; a mental state is necessarily a state of a mental something.)  So talk of mental acts seems to commit one to talk of minds or mental subjects.  But their existence is denied by those (Sartre, Butchvarov, et al.) who maintain that consciousness is subjectless.  That theoretical denial, however, is consistent with the commonplace that we sometimes hear and remember.  On the other hand, talk of mental acts commits one to an act-object distinction, a distinction that adverbialists deny.  So although it is obvious that we sometimes hear and remember, it is not obvious that there are mental acts.  So we need an argument.  Here is one.  It is my reconstruction of what I think Laird Addis is saying on p. 71 et passim of Natural Signs: A Theory of Intentionality (Temple University Press, 1989).

1. Consider two states of affairs, S1 and S2.  In S1 I am imagining a unicorn (and nothing else) at time t, while in S2 I am imagining  a mermaid (and nothing else) at t.  S1 and S2 are individually possible, though not jointly compossible.

2. S1 and S2 are numerically different, and this difference requires a ground, a 'difference-maker.'

3. One cannot locate the difference-maker on the side of the object, because there are no unicorns and there are no mermaids.  (For an analogy, compare two mathematical sets, one whose sole member is a unicorn, the other whose sole member is a mermaid. These sets are the same  set, the null set, inasmuch as there is nothing that could ground their difference.)

4. Since both S1 and S2 involve the same type of mental directedness, namely, imagination, the difference between S1 and S2 cannot be ascribed to a difference in type of mental directedness.

5. Since one and the same subject is the imaginer in both cases, the difference between S1 and S2 is not on the side of the subject.  Therefore:

6. There must be something that grounds the difference between S1 and S2, and this all men call 'mental act.' 

Cuteness and quinque viae parody aside, there must be something that grounds the difference between S1 and S2 assuming the Difference-Maker Principle: No difference without a difference-maker.  This principle strikes me as well-nigh self-evident: how on Earth (or on Twin Earth for that matter) could two different complexes just differ?  S1 and S2 are complexes not simples: their numerical difference requires an ontological ground.  Suppose someone insisted that the unordered set {Bill, Peter} is just different -- barely different -- from the unordered set {Peter, Bill}.  You would show him the door, right?  I can swallow a bare difference of simples but not of complexes. 

The difference between S1 and S2, then, traces back to a difference between two mental acts.  If you ask me what makes these two mental acts different, my answer will be that they differ in their object-directedness: one has unicorn-directedness, the other mermaid-directedness.  Perhaps this could be explained further by saying that a mental act is a mental state, where a mental state is a mind's exemplification of an intentional property.  So in S1 my mind exemplifies the intentional property unicorn-directedness while in S2 my mind exemplifies the intentional property mermaid-directedness.  These property-exemplifications just are the mental acts.

This is pretty close to a Bergmann-Addis assay of the act.  If it could be made to work in all details, then we could avoid Meinongianism, Adverbialism, and Sartreanism (Sartvarovianism?).  But being an aporetician, I am not sanguine.

 

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?

Bundling is Symmetrical But not Transitive

Over the phone the other day, Peter L. suggested the following objection to the bundle-of-universals theory of ordinary particulars, 'BT' hereafter.  (I leave out of consideration for the nonce bundle-of-tropes bundle theories.)  I am not sure I understood what Peter was driving at.  But here is the gist of what I thought he was saying. 

1. Suppose x is a proper (spatial) part of y, y being a physical thing.  On BT, both y and x are bundles of universals.  Now it often happens that a whole has a property that is not had by all its parts.  Think of a rubber ball.  The ball is spherical (or spheroid, if you  insist).  But it has proper parts that are not spherical.  For example, its hemispheres are not spherical.  Nor are the cubes of rubber internal to it spherical.  (They too are proper parts of it on classical mereology. These cubes could be 'liberated' by appropriate cutting of the ball.) The ball is red, let us say, but beneath the surface it is black.  And so on.  in sum, wholes often have properties that their parts do not have.

2.  On BT, property-possession is understood, not in terms of the asymmetrical relation of exemplification, but in terms of the symmetrical relation of bundling.  Accordingly, for a property to be possessed by something is not for it to be exemplified by this thing, but for it to be bundled with other logically and nomologically compossible properties.  Exemplification, the asymmetrical relation that connects a substratum to a first-level property is replaced by bundling  which is a symmetrical relation that connects sufficiently many properties (which we are assuming to be universals) so as to form a particular.  When the universals are bundled, the result is a whole of which the universals are ontological constituents, with the bundling relation taking over the unifying job of the substratum.  While bundling is symmetrical -- if U1 is bundled with U2, then U2 is bundled with U1-- ontological constituency is asymmetrical:  if U is an ontological constituent of B, then B is not an ontological constituent of U.

3.  Given that the  ball is a bundle of universals, and that the ball is spherical, it follows that the ball has as one of its ontological 'parts' the universal, sphericality.  Now sphericality and cubicality are not broadly-logically compossible.  Hence they cannot be bundled together to form an individual.  But our ball has a proper part internal to it which is a cube.  That proper part has cubicality as a constituent universal.  So it seems a broadly-logical contradiction ensues:  the ball has as constituents both sphericality and cubicality, universals that are not compossible.

4. An interesting objection!  But note that it assumes Transitivity of Bundling:  it assumes that if sphericality is bundled  with sufficiently many other Us to form a complete individual, and cubicality is bundled with one of these Us -- say being made of rubber -- then sphericality is bundled with cubicality. But it is well-known that bundling is not transitive.  Suppose roundness and redness are bundled in our ball, and redness and stickiness are bundled in a numerically distinct disk, but there is nothing that is both round and sticky. That's a possible scenario which shows that Transitivity of Bundling fails. From the fact that U1 is bundled with U2, and U2 with U3, one cannot infer that U1 is bundled with U3.  So from the fact that sphericality is bundled with rubberness, and rubberness with cubicality, it does not follow that sphericality is bundled with cubicality.

The  bundle theory can accommodate the fact that a property of a whole needn't be a property of all its proper parts.  Or am I missing something?

 

Can a Bundle Theory Accommodate Change?

0.  Peter L. has been peppering me with objections to bundle theories.  This post considers the objection from change.

1. Distinguish existential change (coming into being and passing out of being) from alterational change, or alteration.  Let us think about ordinary meso-particulars such as avocados and coffee cups.  If an avocado is unripe on Monday but ripe on Friday, it has undergone alterational change: it has changed in respect of the property of being ripe.  One and the same thing has become different in respect of one or more properties. (An avocado cannot ripen without becoming softer, tastier, etc.)  Can a bundle theory make sense of an obvious instance of change such as this?  It depends on what the bundle theory (BT) amounts to.

2. At a first approximation, a bundle theorist maintains that a thing is nothing more than a complex of properties contingently related by  a bundling relation, Russellian compresence say.    'Nothing more' signals that on BT there is nothing in the thing that exemplifies the properties: there is no substratum (bare particular, thin particular) that supports and unifies them. This is not to say that on BT a thing is just its properties: it is obviously more, namely, these properties contingently bundled.  A bundle is not a mathematical set, a mereological sum, or a conjunction of its properties.  These entities exist 'automatically' given the existence of the properties.  A bundle does not. 

3.  Properties are either universals or property-instance (tropes).  For present purposes, BT is a bundle-of-universals theory.  Accordingly, my avocado is a bundle of universals.  Although a bundle is not a whole in the strict sense of classical mereology, it is a whole in an analogous sense, a sense sufficiently robust to be governed by a principle of extensionality: two bundles are the same iff they have all the same property-constituents.  It follows that the unripe avocado on Monday cannot be numerically the same as the ripe avocado on Friday.  And therein lies the rub.  For they must be the same if it is the case that an alteration in the avocado has occurred. 

So far, then, it appears that the bundle theory cannot accommodate alterational change.  Such change, however, is a plain fact of experience.  Ergo, the bundle theory in its first approximation is untenable.

4.  This, objection, however, can be easily met by sophisticating the bundle theory and adopting a bundle-bundle theory.  Call this BBT.  Accordingly, a thing that persists over time such as an avocado is a diachronic bundle of synchronic or momentary bundles.  The theory then has two stages.  First, there is the construction of momentary bundles from universals.  Then there is the construction of a diachronic bundle from these bundles. The momentary bundles have properties as constituents while the diachronic bundles do not have properties as constituents, but individuals.  At both stages the bundling is contingent: the properties are contingently bundled to form momentary bundles and these resulting bundles are contingently bundled to form the persisting thing.

Accordingly, the unripe avocado is numerically the same as the ripe avocado in virtue of the fact that the earlier momentary bundles which have unripeness as a constituent  are ontological parts of the same diachronic whole as the later momentary bundles which have ripeness as a constituent.

5. A sophisticated bundle theory does not, therefore, claim that a persisting thing is a bundle of properties; the claim is that a persisting thing is a bundle of individuals which are themselves bundles of properties.  This disposes of the objection from change at least as formulated in #3 above.

6. BBT also allows us to accommodate the intuition  that things have accidental properties.  On the proto-theory BT according to which a persisting thing is a bundle of properties, it would seem that all properties must be essential, where an essential property is one a thing has in every possible world in which it exists.    For if wholes have their parts essentially, and if bundles are wholes in this sense, and things are bundles of properties, then things have their properties essentially.  But surely our avocado is not essentially ripe or unripe but accidentally one or the other.  On BBT, however, it is a contingent fact that a momentary bundle MB1 having ripeness as a constituent is bundled with other momentary bundles.  This implies that the diachronic bundle of bundles could have existed without MB1 and without other momentary bundles having ripeness as a constituent.  It therefore seems to follow that BBT can accommodate accidental properties.

7. That is, BBT can accommodate the modal intuition that our avocado might never have been ripe.  But what about the modal intuition that, given that the avocado is ripe at t, it might not have been ripe at t?  This is a thornier question and the basis of a different objection that is is not defused by what I have said above.  And so we reserve this objection for a separate post.

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.

 

Metaphysics at Cindy's: The Ontological Stucture of Contingent Conreta

Over Sunday breakfast at Cindy's, a hardscrabble Mesa, Arizona eatery not unwelcoming to metaphysicians and motorcyclists alike, Peter  Lupu fired a double-barreled objection at my solution to Deck's Paradox.  The target, however, was not hit.  My solution requires that (a) concrete particulars can be coherently 'assayed' (to use a favorite word of Gustav Bergmann), or given an ontological analysis in terms of constituents some or all of which are universals, and (b) modally contingent concrete particulars can be coherently assayed as composed of necessary beings.

Peter denies both of (a) and (b), without good reason as it seems to me.  Let's begin with some definitions pithily presented.

Definitions

Abstract =df causally inert.

Concrete =df not abstract.

Universal =df repeatable (multiply exemplifiable).

Particular =df unrepeatable.

Modally contingent=df existent in some but not all broadly-logically possible worlds.

Modally necessary =df not modally contingent and not modally impossible.

Ad (a).  One form of the question is:  Could a concrete particular be coherently construed as a bundle universals?  Peter thinks not: "But the unification of two universals U and V is another universal W, not a particular." (From a two page handout he brought to breakfast.  How many people that you know bring handouts to breakfast?!)  Now bundle-of-universals theories of particulars face various standard objections, but as far as I know no one in the literature has made Peter's objection.  Presumably for good reason: it is a bad objection that confuses conjunction with the bundling relation.

We understand conjunction as a propositional connective.  Given the propositions a is red and b is round we understand that the conjunction a is red & b is round is true iff both conjuncts are true.  It is clear that a conjunction of propositions is itself a proposition.  By a slight extension we can speak meaningfully of a conjunction of propositional functions, and from there we can move to talk of conjunctions of properties.  Assuming that properties are universals, we can speak of conjunctions of universals.  It is clear that a conjunction of universals is itself a universal.  Thus the conjunction of Redness and Roundness is itself a universal, a multiply exemplifiable entity.  I will use 'Konjunction'  to single out conjunction of universals.

Now it should be obvious that a bundle of universals is not a conjunction of universals.  Let K be the Konjunction operator: it operates upon  universals to form universals.  Let B be the bundling operator: it operates upon universals to form particulars.  Bundling is not Konjunction.  So far, then, Peter seems to have failed to make an elementary distinction.

Now suppose Peter objects that nothing could operate upon universals to form a particular.  Universals in, universals out.  Then I say that he is just wrong: the set-theoretical braces -- { } -- denote an operator that operates upon items of any category to form sets of those items.  Now it should be obvious that a set of universals is not itself a universal, but a particular.  A Konjunction of universals is a universal, but a set of universals is not a universal, but a particular.  The Konjunction of Redness and Roundness is exemplifiable; but no set is exemplifiable.

Am I saying that a bundle of universals is a set of universals?  No.  I am saying that it is false to assume that any operation upon universals will result in a universal.  What I have said so far suffices to refute Peter's first objection, which was that the unification of two universals yields a third universal. You can see that to be false by noting that the unification into a set of two or more universals does not yield a universal but a particular.

Ad (b).  Our second question is whether a contingent particular could have as ontological constituents necessary beings.  Peter thinks not.  He thinks that anything composed of necessary beings will itself be a necessary being.  And so, given that universals are necessary beings, and that concrete particulars are composed of universals, no concrete particular can be modally contingent.

This objection fares no better than the first.  Suppose Redness and Roundness are compresent.  (You will recall that Russell took the bundling relation to be the compresence relation.  See An Inquiry into Meaning and Truth, 1940, Chapter 6.)  Each of these universals, we are assuming, is a necessary being.  But it doesn't follow that their compresence is necessary; it could easily be contingent.  Here and now I see a complete complex of compresence two of whose constituent universals are Redness and Roundness.  But surely there is no necessity that these two universals co-occur or be com-present.  After all, Redness is often encountered compresent with shapes that are logically incompatible with Roundness.  Compresence, then, is a contingent relation.  It follows that complexes of compresence are contingent.  Necessarily, Rednessexists.  Necessarily, Roundness exists.  But it does not follow that, necessarily, Redness and Roundness are compresent: surely there are possible worlds in which they are not.

Peter's argument for his conclusion commits the fallacy of composition:

1. Every universal necessarily exists.

2. Every concrete particular is composed of universals. Therefore,

3. Every concrete particular is composed of things that necessarily exist. Therefore,

4. Every concrete particular necessarily exists.

The move from (3) to(4) is the fallacy of composition.  One cannot assume that if the parts of a whole have a certain property, then the whole has those properties.

 

Ontological Analysis in Aristotle and Bergmann: Prime Matter Versus Bare Particulars

Hardly anyone reads Gustav Bergmann any more, but since I read everything, I read Bergmann. It is interesting to compare his style of ontological analysis with that of the great hylomorphic ontologists, Aristotle and Aquinas. The distinguished Aristotelian Henry B. Veatch does some of my work for me in a fine paper, "To Gustav Bergmann: A Humble Petition and Advice" in M.S.Gram and E.D.Klemke, eds. The Ontological Turn: Studies in the Philosophy of Gustav Bergmann (University of Iowa Press, 1974, pp. 65-85)

I want to focus on Veatch's comparison of Aristotle and Bergmann on the issue of prime matter/bare particulars. As Veatch correctly observes, "all of the specific functions which bare particulars perform in Bergmannian ontology are the very same functions as are performed by matter in Aristotle . . . ." (81) What are these functions?

Christology, Reduplicatives, and Their Truth-Makers

Consider this triad, and whether it is logically consistent:

1. The man Jesus = the 2nd Person of the Trinity.
2. The 2nd Person of the Trinity exists necessarily.
3. The man Jesus does not exist necessarily.

Each of these propositions is one that a Christian who understands his doctrine ought to accept.   But how can they all be true? In the presence of the Indiscernibility of Identicals, the above triad appears inconsistent: The conjunction of (1) and (2) entails the negation of (3). Can this apparent inconsistency be shown to be merely apparent?

Supposita

We have been discussing the question of the logical consistency of the orthodox doctrine of the Trinity.  Dr. Lukas Novak (Charles University, Prague) has offered a solution to the consistency problem that relies crucially on the notion of a suppositum or supposit.  If I have understood him, his suggestion is that there is nothing logically problematic in the suggestion that the individual divine nature has three supposits, The Father, the Son, and the Holy Spirit.

It is worth reminding ourselves that any solution to the consistency problem will depend on one's background logic and general ontology.  And the same holds if one decides that the problem is insoluble.

But being none too clear about what a supposit is supposed to be, I asked Novak  if he could define the term and how it stands vis-a-vis such terms as 'bare particular' (Gustav Bergmann) and 'thin particular' (David Armstrong).  He responded as follows:

Ad 4) X is a suppositum iff X is something endowed with individual nature and suppositality, that is, X is both uninstantiable and incommunicable to a subject (and not a part nor an aggregate).

Ad 5) It is better said that Socrates' humanity inheres in Socrates, who is a suppositum. Suppositum is not a bare or thin particular. If there were bare particulars, they would probably be classified as supposita, but classically supposita are not considered to be "thin" or "bare" - they have their rather "thick" essences or natures de re necessarily. Socrates is identical to Socrates' suppositum. Socrates' humanity inheres in Socrates and is a metaphysical constituent of Socrates. Socrates' humanity plus his suppositality makes up Socrates. Neither Socrates' humanity nor his suppositality are entities in their own right, they are just aspects or metaphysical constituents of Socrates. So I use "inhere" here as _not_ implying any particular kind of distinction between the nature and the suppositum.