Maverick Philosopher

Trope Troubles: An Exercise in Aporetics

Elliot C. asked me about tropes. What follows is a re-post from 30 March 2016, slightly emended, which stands up well under current scrutiny.  Perhaps Elliot will find the time to tell me whether he finds it clear and convincing and whether it answers his questions.

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

A reader  has been much exercised of late by trope theory and other questions in ontology.  He has been sharing his enthusiasm with me.   He espies 

. . . an apparent antinomy at the heart of trope theory. On the one hand, tropes are logically prior to objects. But on the other hand, objects (or, more precisely, the trope-bundles constituting objects) are logically prior to tropes, because without objects tropes have nowhere to be – without objects (or the trope-bundles constituting objects) tropes cannot be. Moreover, as has I hope been shown, a trope cannot be in (or constitute) any object or trope-bundle other than that in which it already is.

How might a trope theorist plausibly respond to this?  Can she? [My use of the feminine third-person singular pronoun does not signal my nonexistent political correctness, but is an anticipatory reference to Anna-Sofia Maurin whom I will discuss below.  'Anna-Sofia'! What a beautiful name, so aptronymic. Nomen est omen.)

What are tropes?

It is a 'Moorean fact,' a pre-analytic datum, that things have properties.  This is a pre-philosophical observation.  In making it we are not yet doing philosophy.  If things have properties, then there are properties.  This is a related pre-philosophical observation.  We begin  to do philosophy when we ask: given that there are properties, what exactly are they?  What is their nature?  How are we to understand them?  This is not the question, what properties are there, but the question, what are properties?  The philosophical question, then, is not whether there are properties, nor is it the question what properties there are, but the question what properties are.

On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on the standard  bundle version of trope theory) or by being a substratum in which a redness trope inheres (on a nonstandard theory championed by C. B. Martin which I will not further discuss). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ 'Has' and cognates are words of ordinary English: they do not commit us to ontological theories of what the having consists in.  So don't confuse 'a has F-ness' with 'a instantiates F-ness.'  Instantiation is a term of art, a terminus technicus in ontology.  Or at least that is what it is in my book.  More on instantiation in a moment.

Thus a redness trope is red, but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness.

It is therefore inaccurate to speak of tropes as property instances.  A trope is not a property instance on one clear understanding of the latter.  First-order instantiation is a dyadic asymmetrical relation: if a instantiates F-ness, then it is not the case that F-ness instantiates a.  (Higher order instantiation is not asymmetrical but  nonsymmetrical.  Exercise for the reader: prove it!)  Suppose the instantiation relation connects the individual Socrates here below to the universal wisdom in the realm of platonica.  Then a further item comes into consideration, namely, the wisdom of Socrates. This is a property instance.  It is a particular, an unrepeatable, since it is the wisdom of Socrates and of no one else. This distinguishes it from the universal, wisdom, which is repeated in each wise individual.  On the other side, the wisdom of Socrates is distinct from Socrates since there is more to Socrates that his being wise.  There is his being snub-nosed, etc.  Now why do I maintain that a trope is not a property instance? Two arguments. 

Tropes are simple, not complex.  (See Maurin, here.)  They are not further analyzable.  Property instances, however, are complex, not simple.   'The F-ness of a'  --  'the wisdom of Socrates,' e.g. -- picks out a complex item that is analyzable into F-ness, a, and the referent of 'of.'  Therefore, tropes are not property instances.

A second, related,  argument.  Tropes are in no way proposition-like.  Property instances are proposition-like as can be gathered from the phrases we use to refer to them.  Ergo, tropes are not property instances. 

One can see from this that tropes on standard trope theory, as ably presented by Maurin in her Stanford Encyclopedia of Philosophy entry, are very strange items, so strange indeed that one can wonder whether they are coherently conceivable at all by minds of our discursive constitution.  Here is one problem.

How could anything be both predicable and impredicable?

Properties are predicable items.  So if tropes are properties, then tropes are predicable items.  If the redness of my tomato, call it 'Tom,'  is a trope, then this trope is predicable of Tom. Suppose I assertively utter a token of 'Tom is red.'  On one way of parsing this we have a subject term 'Tom' and a predicate term '___ is red.'  Thus the parsing: Tom/is red.  But then the trope would appear to have a proposition-like structure, the structure of what Russell calls a propositional function.  Clearly, '___ is red' does not pick out a proposition, but it does pick out something proposition-like and thus something complex.  But now we have trouble since tropes are supposed to be simple.  Expressed as an aporetic triad or antilogism:

a. Tropes are simple.
b. Tropes are predicable.
c.  Predicable items are complex.

The limbs of the antilogism are each of them rationally supportable, but they cannot all be true. Individually plausible, collectively inconsistent. The conjunction of any two limbs entails the negation of the remaining one.  Thus the conjunction of (b) and (c) entails ~(a).

We might try to get around this difficulty by parsing 'Tom is red' differently, as: Tom/is/red.  On this scheme, 'Tom' and 'red' are both names.  'Tom' names a concrete particular whereas 'red' names an abstract particular.  ('Abstract' is here being used in the classical, not the Quinean, sense.)   As Maurin relates, D. C. Williams, who introduced the term 'trope' in its present usage back in the '50s, thinks of the designators of tropes as akin to names and demonstratives, not as definite descriptions. But then it becomes difficult to see how tropes could be predicable entities. 

A tomato is not a predicable entity.  One cannot predicate a tomato of anything.  The same goes for the parts of a tomato; the seeds, e.g., are not predicable of anything.  Now if a tomato is a bundle of tropes, then it is a whole of ontological parts, these latter being tropes.  If we think of the tomato as a (full-fledged) substance, then the tropes constituting it are "junior substances." (See D. M. Armstrong, 1989, 115) But now the problem is: how can one and the same item -- a trope --  be both a substance and a property, both an object and a concept (in Fregean jargon), both impredicable and predicable?  Expressed as an aporetic dyad or antinomy:

d. Tropes are predicable items.
e. Tropes are not predicable items.

Maurin seems to think that the limbs of the dyad can both be true:  ". . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance."  If the limbs can both be true, then they are not contradictory despite appearances.

How can we defuse the apparent contradiction in the d-e dyad?  Consider again Tom and the redness trope R.  To say that R is predicable of Tom  is to say that Tom is a trope bundle having R as an ontological (proper) part.  To say that R is impredicable or  a substance is to say that R is capable of independent existence.  Recall that Armstrong plausibly defines a substance as anything logically capable of independent existence.

It looks as if we have just rid ourselves of the contradiction.  The sense in which tropes are predicable is not the sense in which they are impredicable.  They are predicable as constituents of trope bundles; they are impredicable in themselves. Equivalently, tropes are properties when they are compresent with sufficiently many other tropes to form trope bundles (concrete particulars); but they are substances in themselves apart from trope bundles as the 'building blocks' out of which such bundles are (logically or rather ontologically) constructed.

Which came first: the whole or the parts?

But wait!  This solution appears to have all the advantages of jumping from the frying pan into the fire.   For now we bang up against the above Antinomy, or something like it, to wit:

f. Tropes as substances, as ontological building blocks, are logically prior to concrete particulars.
g. Tropes as properties, as predicable items, are not logically prior to concrete particulars.

This looks like an aporia in the strict and narrow sense: an insoluble problem.  The limbs cannot both be true.  And yet each is an entailment of standard (bundle) trope theory.  If tropes are the "alphabet of being" in a phrase from Williams, then they are logically prior to what they spell out.  But if tropes are unrepeatable properties, properties as particulars, then a trope cannot exist except as a proper ontological part of a trope bundle, the very one of which it is a part.  For if a trope were not tied to the very bundle of which it is a part, it would be a universal, perhaps only an immanent universal, but a universal all the same. 

Furthermore, what makes a trope abstract in the classical (as opposed to Quinean) sense of the term is that it is abstracted from a concretum.  But then the concretum comes first, ontologically speaking, and (g) is true.

Interim conclusion: Trope theory, pace Anna-Sofia Maurin, is incoherent. But of course we have only scratched the surface. 

Pictured below, left-to-right:  Anna-Sofia Maurin, your humble correspondent, Arianna Betti, Jan Willem Wieland. Geneva, Switzerland, December 2008.  It was a cold night.

Related articles

Armstrong, Quine, Universals, Abstract Objects, and Naturalism

Peter van Inwagen, "A Theory of Properties," Exposition and Critique

Atheism and Ontological Simplicity: A Retraction and a Repair

God and Mann: Divine Simplicity and Property-Instances

God, Simplicity, and Tropes

Tropes as Truth-Makers? Or Do We Need Facts?

In a Philosophical Conversation, Three's a Crowd

 

Elliot C. asked me about tropes. What follows is a re-post from 30 March 2016, slightly emended, which stands up well under current scrutiny.  Perhaps Elliot will find the time to tell me whether he finds it clear and convincing and whether it answers his questions.

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

A reader  has been much exercised of late by trope theory and other questions in ontology.  He has been sharing his enthusiasm with me.   He espies 

. . . an apparent antinomy at the heart of trope theory. On the one hand, tropes are logically prior to objects. But on the other hand, objects (or, more precisely, the trope-bundles constituting objects) are logically prior to tropes, because without objects tropes have nowhere to be – without objects (or the trope-bundles constituting objects) tropes cannot be. Moreover, as has I hope been shown, a trope cannot be in (or constitute) any object or trope-bundle other than that in which it already is.

How might a trope theorist plausibly respond to this?  Can she? [My use of the feminine third-person singular pronoun does not signal my nonexistent political correctness, but is an anticipatory reference to Anna-Sofia Maurin whom I will discuss below.  'Anna-Sofia'! What a beautiful name, so aptronymic. Nomen est omen.)

What are tropes?

It is a 'Moorean fact,' a pre-analytic datum, that things have properties.  This is a pre-philosophical observation.  In making it we are not yet doing philosophy.  If things have properties, then there are properties.  This is a related pre-philosophical observation.  We begin  to do philosophy when we ask: given that there are properties, what exactly are they?  What is their nature?  How are we to understand them?  This is not the question, what properties are there, but the question, what are properties?  The philosophical question, then, is not whether there are properties, nor is it the question what properties there are, but the question what properties are.

On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on the standard  bundle version of trope theory) or by being a substratum in which a redness trope inheres (on a nonstandard theory championed by C. B. Martin which I will not further discuss). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ 'Has' and cognates are words of ordinary English: they do not commit us to ontological theories of what the having consists in.  So don't confuse 'a has F-ness' with 'a instantiates F-ness.'  Instantiation is a term of art, a terminus technicus in ontology.  Or at least that is what it is in my book.  More on instantiation in a moment.

Thus a redness trope is red, but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness.

It is therefore inaccurate to speak of tropes as property instances.  A trope is not a property instance on one clear understanding of the latter.  First-order instantiation is a dyadic asymmetrical relation: if a instantiates F-ness, then it is not the case that F-ness instantiates a.  (Higher order instantiation is not asymmetrical but  nonsymmetrical.  Exercise for the reader: prove it!)  Suppose the instantiation relation connects the individual Socrates here below to the universal wisdom in the realm of platonica.  Then a further item comes into consideration, namely, the wisdom of Socrates. This is a property instance.  It is a particular, an unrepeatable, since it is the wisdom of Socrates and of no one else. This distinguishes it from the universal, wisdom, which is repeated in each wise individual.  On the other side, the wisdom of Socrates is distinct from Socrates since there is more to Socrates that his being wise.  There is his being snub-nosed, etc.  Now why do I maintain that a trope is not a property instance? Two arguments. 

Tropes are simple, not complex.  (See Maurin, here.)  They are not further analyzable.  Property instances, however, are complex, not simple.   'The F-ness of a'  --  'the wisdom of Socrates,' e.g. -- picks out a complex item that is analyzable into F-ness, a, and the referent of 'of.'  Therefore, tropes are not property instances.

A second, related,  argument.  Tropes are in no way proposition-like.  Property instances are proposition-like as can be gathered from the phrases we use to refer to them.  Ergo, tropes are not property instances. 

One can see from this that tropes on standard trope theory, as ably presented by Maurin in her Stanford Encyclopedia of Philosophy entry, are very strange items, so strange indeed that one can wonder whether they are coherently conceivable at all by minds of our discursive constitution.  Here is one problem.

How could anything be both predicable and impredicable?

Properties are predicable items.  So if tropes are properties, then tropes are predicable items.  If the redness of my tomato, call it 'Tom,'  is a trope, then this trope is predicable of Tom. Suppose I assertively utter a token of 'Tom is red.'  On one way of parsing this we have a subject term 'Tom' and a predicate term '___ is red.'  Thus the parsing: Tom/is red.  But then the trope would appear to have a proposition-like structure, the structure of what Russell calls a propositional function.  Clearly, '___ is red' does not pick out a proposition, but it does pick out something proposition-like and thus something complex.  But now we have trouble since tropes are supposed to be simple.  Expressed as an aporetic triad or antilogism:

a. Tropes are simple.
b. Tropes are predicable.
c.  Predicable items are complex.

The limbs of the antilogism are each of them rationally supportable, but they cannot all be true. Individually plausible, collectively inconsistent. The conjunction of any two limbs entails the negation of the remaining one.  Thus the conjunction of (b) and (c) entails ~(a).

We might try to get around this difficulty by parsing 'Tom is red' differently, as: Tom/is/red.  On this scheme, 'Tom' and 'red' are both names.  'Tom' names a concrete particular whereas 'red' names an abstract particular.  ('Abstract' is here being used in the classical, not the Quinean, sense.)   As Maurin relates, D. C. Williams, who introduced the term 'trope' in its present usage back in the '50s, thinks of the designators of tropes as akin to names and demonstratives, not as definite descriptions. But then it becomes difficult to see how tropes could be predicable entities. 

A tomato is not a predicable entity.  One cannot predicate a tomato of anything.  The same goes for the parts of a tomato; the seeds, e.g., are not predicable of anything.  Now if a tomato is a bundle of tropes, then it is a whole of ontological parts, these latter being tropes.  If we think of the tomato as a (full-fledged) substance, then the tropes constituting it are "junior substances." (See D. M. Armstrong, 1989, 115) But now the problem is: how can one and the same item -- a trope --  be both a substance and a property, both an object and a concept (in Fregean jargon), both impredicable and predicable?  Expressed as an aporetic dyad or antinomy:

d. Tropes are predicable items.
e. Tropes are not predicable items.

Maurin seems to think that the limbs of the dyad can both be true:  ". . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance."  If the limbs can both be true, then they are not contradictory despite appearances.

How can we defuse the apparent contradiction in the d-e dyad?  Consider again Tom and the redness trope R.  To say that R is predicable of Tom  is to say that Tom is a trope bundle having R as an ontological (proper) part.  To say that R is impredicable or  a substance is to say that R is capable of independent existence.  Recall that Armstrong plausibly defines a substance as anything logically capable of independent existence.

It looks as if we have just rid ourselves of the contradiction.  The sense in which tropes are predicable is not the sense in which they are impredicable.  They are predicable as constituents of trope bundles; they are impredicable in themselves. Equivalently, tropes are properties when they are compresent with sufficiently many other tropes to form trope bundles (concrete particulars); but they are substances in themselves apart from trope bundles as the 'building blocks' out of which such bundles are (logically or rather ontologically) constructed.

Which came first: the whole or the parts?

But wait!  This solution appears to have all the advantages of jumping from the frying pan into the fire.   For now we bang up against the above Antinomy, or something like it, to wit:

f. Tropes as substances, as ontological building blocks, are logically prior to concrete particulars.
g. Tropes as properties, as predicable items, are not logically prior to concrete particulars.

This looks like an aporia in the strict and narrow sense: an insoluble problem.  The limbs cannot both be true.  And yet each is an entailment of standard (bundle) trope theory.  If tropes are the "alphabet of being" in a phrase from Williams, then they are logically prior to what they spell out.  But if tropes are unrepeatable properties, properties as particulars, then a trope cannot exist except as a proper ontological part of a trope bundle, the very one of which it is a part.  For if a trope were not tied to the very bundle of which it is a part, it would be a universal, perhaps only an immanent universal, but a universal all the same. 

Furthermore, what makes a trope abstract in the classical (as opposed to Quinean) sense of the term is that it is abstracted from a concretum.  But then the concretum comes first, ontologically speaking, and (g) is true.

Interim conclusion: Trope theory, pace Anna-Sofia Maurin, is incoherent. But of course we have only scratched the surface. 

Pictured below, left-to-right:  Anna-Sofia Maurin, your humble correspondent, Arianna Betti, Jan Willem Wieland. Geneva, Switzerland, December 2008.  It was a cold night.

Related articles

Armstrong, Quine, Universals, Abstract Objects, and Naturalism

Peter van Inwagen, "A Theory of Properties," Exposition and Critique

Atheism and Ontological Simplicity: A Retraction and a Repair

God and Mann: Divine Simplicity and Property-Instances

God, Simplicity, and Tropes

Tropes as Truth-Makers? Or Do We Need Facts?

In a Philosophical Conversation, Three's a Crowd

Non-Substantial Change, Trope Bundle Theory, and States of Affairs

I am presently writing a review article for Metaphysica about Bo R. Meinertsen's Metaphysics of States of Affairs: Truthmaking, Universals, and a Farewell to Bradley's Regress (Springer 2018). Since I will probably incorporate the following critical remarks into my review, I want to give Bo a chance to respond. 

Substantial and Non-Substantial Change

One way a thing can change is by coming into being or passing away. This is called substantial change.  We could also call it existential change. The other way could be called alterational change. This occurs when a thing, persisting for a time, alters in respect of its intrinsic properties during that time.  Consider the ripening of a tomato. This typically involves the tomato's going from green to red.  This change in respect of color is an alterational, or accidental, or non-substantial change. One and the same entity (substance) persists through a non-zero interval of time and instantiates different properties (accidents) at different times.  As I would put it, there is no alterational change without existential unchange: numerically the same tomato is green, hard, inedible, etc. at time t and red, soft, and edible at later time t*. Bo and I are both assuming that things in time persist by enduring, not by perduring. 

The Problem of Non-Substantial Change of Continuants

This is 

. . . the problem of how to ground the fact that continuants 'persist through change'. For instance, a tomato's changing from red to green [sic] is a case of non-substantial change, and how do we ground the fact that the tomato that has changed exists both before and after the change? The bundles of basic trope theory essentially have the members they actually have and are therefore incompatible with such change. (Meinertsen 2018, 49)

The problem is that we want to say that one and the same tomato goes from being green to being red. We want to be able to uphold the diachronic identity of the tomato as it alters property-wise.  But this is impossible on basic bundle-theoretic trope theory because trope bundles have their members essentially.  This means that if bundle B has trope t as a member, then it is impossible that B exist without having t as a member. The counterintuitive upshot is that a green tomato assayed as a bundle of tropes ceases to exist when it ceases to be green.  This implies that our tomato when so assayed cannot undergo alterational, or accidental, or non-substantial change when it goes from green to red, hard to soft, etc.  It implies that every change is a substantial change. I agree with Meinertsen that this is a powerful objection to the basic bundle-of-tropes assay of ordinary particulars.

Does a State of Affairs Ontology Face the Same Problem?

Meinertsen says that it does not:

State of affairs ontology has no problem in dealing with the problem of non-substantial change. None of the properties of a particular in a state of affairs -- which as we shall see in Chap. 5 is a bare particular -- is included in it, as opposed to instantiated by it. Hence, it changes non-substantially if and only it ceases to instantiate at least one of these properties or whenever it instantiates a new property. (49)

It seems to me, though, that states of affairs (STOA) ontology faces, if not the very same problem, then a closely related one.

Critique

It is true that a bare particular does not include its properties: the bare or thin particular stands to its properties in the asymmetrical external relation of instantiation.  So what Meinertsen is telling us is that it is the bare particular that remains numerically the same over time while some of its properties are replaced by others. This is what grounds the diachronic numerical identity of the continuant.  The substratum of change is the bare particular 'in' the tomato, not the tomato as a whole.

But this answer is less than satisfactory. What changes over time is not a thin particular, but a thick particular. It is the green tomato with all its properties that loses one or more of them and becomes a red tomato.  This is supported by the fact that we do not see or otherwise perceive the thin particular; we do, however, see and otherwise perceive thick particulars.  What we have before us is a tomato that we see to be green and feel to be  hard, etc.,  and that we then later see to be red and feel  to be soft, etc.  

Arguably, then, it is the thick particular that is the substratum of non-substantial change, not the thin particular. If so, then a problem arises similar to the problem that arose for the bundle-of-tropes theory. How?

Well, the green tomato is a STOA whose nature is N1, where N1 is a conjunctive property the conjuncts of which are all the intrinsic properties of the green tomato. The red tomato is a STOA whose nature is N2, where N2 is a conjunctive property the conjuncts of which are all the intrinsic properties of the red tomato.  These STOAs differ numerically for they differ in one or more constituents.  The first has greenness as a constituent, the second does not. A STOA is a complex, and two complexes are the same iff they have all the same constituents. 

So what's the problem? The problem is that any non-substantial change in the green tomato assayed as a STOA destroys its identity just as surely as any non-substantial change in the green tomato assayed as a bundle of tropes destroys its identity. On either account, there is no adequate explanation of non-substantial change. This is because there is no numerically self-same substratum of change that endures through the change in properties. The thin particular is not plausibly regarded as the substratum. I note en passant that Gustav Bergmann regarded bare particulars as momentary entities, not as persisting entities.

The problem set forth as an aporetic sextad:

1. There is no change in intrinsic properties of an ordinary particular over time without a numerically self-same substratum of change. (endurantist assumption)
2. The green tomato changes to red. (pre-theoretical datum)
3. The green tomato that changes to red is a thick particular. (pre-theoretical datum)
4. Thick particulars are STOAs. (theoretical claim)
5. STOAs are complexes. (true by definition)
6. Two complexes are the same iff they share all constituents. (theoretical claim)

These six propositions are collectively inconsistent. My question to Meinertsen: which of these propositions will you reject? Presumably, he will have to reject (3) and say that 'the green tomato' refers to an invisible thin particular, and it is this item that changes from green to red and that serves as the substratum of change.

What do I say?  For now I say merely that, pace Bo, on the issue before us, STOA ontology is no better than the bundle-of-tropes theory.

Van Inwagen: No Truck with Tropes or Constituent Ontology Generally

Thanks again to Professor Levy to getting me 'fired up' over this topic.

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

Is the notion of a trope intelligible?

If not, then we can pack it in right here and dispense with discussion of the subsidiary difficulties.  Peter van Inwagen confesses, "I do not understand  much of what B-ontologists write."  (Ontology, Identity, and Modality, Cambridge UP, 2001, p. 2)  'B' is short for 'Bergmann' where the reference is to Gustav Bergmann, the founder of the Iowa School.  B-ontology is what I call constituent ontology.  I will refer to it, and not just out of perversity, as C-ontology and I will contrast it with NC-ontology.  Van Inwagen is a premier example of an NC-ontologist, a non-constituent ontologist. 

The fundamental idea of C-ontology is that concreta have ontological parts in addition to their spatial parts if the concreta in question are material things.  To invoke a nice simple 'Iowa' example, consider a couple of round red spots on a white piece of paper.  Each spot has spatial parts.  On C-ontology, however, each spot also has ontological parts, among them the properties of the spots. For a C-ontologist, then, the properties of a thing are parts of it.  But of course they are not spatial or mereological parts of it.  A spot can be cut in two, and an avocado can be disembarrassed of its seed and exocarp, but one cannot physically separate the roundness and the redness of the spot or the dark green of the exocarp from the exocarp.  So if the properties of a thing are parts thereof, then these parts are 'ontological' parts, parts that figure in the ontological structure of the thing in question.

Examples of C-ontologies: a) trope bundle theory, b) universals bundle theory, c) tropes + substratum theory, d) Castaneda's Guise Theory, e) Butchvarov's object-entity theory, f) the ontological theories of Bergmann, Armstrong, and Vallicella according to which ordinary particulars are concrete facts, g) Aristotelian and Scholastic hylomorphic doctrines according to which form and matter are 'principles' (in the Scholastic not the sentential sense) ingredient in primary substances. 

If van Inwagen is right, then all of the above are unintelligible. Van Inwagen claims not to understand such terms as 'trope,' 'bare particular,' 'immanent universal' and 'bundle' as these terms are used in C-ontologies. He professes not to understand how a thing could have what I am calling an ontological structure.  "What I cannot see is how a chair could have any sort of structure but a spatial or mereological structure." (Ibid.) He cannot see how something like a chair could have parts other than smaller and smaller spatial parts such as legs made of wood which are composed of cellulose molecules along with other organic compounds, and so on down. If this is right, then there is no room for what I call ontological analysis as opposed to chemical analysis and physical analysis.  There can be no such intelligible project as an ontological factor analysis that breaks an ordinary particular down into thin particular, immanent universals, nexus of exemplification, and the like, or into tropes and a compresence relation, etc.

In sum: trope theory stands and falls with C-ontology; the project of C-ontology is unintelligible; ergo, trope theory is unintelligible resting as it does on such unintelligible notions as trope, and bundle of tropes.  Van Inwagen delivers his unkindest cut with the quip that he has never been able to understand tropes as "anything but idealized coats of paint."  (Ibid.)  Ouch!

Let's assume that van Inwagen is right and that the properties of concrete particulars cannot be construed as parts of them in any intelligible sense of 'part.'  If so, this puts paid to every C-ontology I am familiar with.  But can van Inwagen do better?  Is his NC-ontology free of difficulties?  I don't think so.  It bristles with them no less than C-ontology does.  I refer the interested reader to my "Van Inwagen on Fiction, Existence, Properties, Particulars, and Method" in Studia Neoaristotelica, vol, 12, no. 2 (2015), pp. 99-125.  Here is a pre-print version.  I will now reproduce some of it so that you can see how a C-ontologist can go on the attack:

Van Inwagen's Ostrich Realism and Commitment to Bare Particulars

Van Inwagen rejects both extreme and moderate nominalism. So he can't possibly be an ostrich nominalist. He is, however, as he himself appreciates, an ostrich realist or ostrich platonist. (214-15)

Suppose Max is black. What explains the predicate's being true of Max? According to the ostrich nominalist, nothing does. It is just true of him. There is nothing in or about Max that serves as the ontological ground of the correctness of his satisfying the predicate. Now 'F' is true of a if and only if 'a is F' is true. So we may also ask: what is the ontological ground of the truth of 'Max is black'? The ostrich reply will be: nothing. The sentence is just true. There is no need for a truth-maker.

The ostrich realist/platonist says something very similar except that in place of predicates he puts abstract properties, and in place of sentences he puts abstract propositions. In virtue of what does Max instantiate blackness? In virtue of nothing. He just instantiates it. Nothing explains why the unsaturated assertible expressed by 'x is black' is instantiated by Max. Nothing explains it because there is nothing to explain. And nothing explains why the saturated assertible expressed by 'Max is black' is true. Thus there is nothing concrete here below that could be called a state of affairs in anything like Armstrong's sense. There is in the realm of concreta no such item as Max-instantiating-blackness, or the concrete fact of Max's being black. Here below there is just Max, and up yonder in a topos ouranos are 'his' properties (the abstract unsaturated assertibles that he, but not he alone, instantiates). But then Max is a bare particular in one sense of this phrase. In what sense, then?

Four Senses of 'Bare Particular'

1. A bare particular is an ordinary concrete particular that lacks properties. I mention this foolish view only to set it aside. No proponent of bare particulars that I am aware of ever intended the phrase in this way. And of course, van Inwagen is not committed to bare particulars in this sense. Indeed, he rejects an equivalent view. “A bare particular would be a thing of which nothing could be said truly, an obviously incoherent notion.” (179)

2. A bare particular is an ontological constituent of an ordinary concrete particular, a constituent that has no properties. To my knowledge, no proponent of bare particulars ever intended the phrase in this way. In any case, the view is untenable and may be dismissed. Van Inwagen is of course not committed to this view. He is a 'relation' ontologist, not a 'constituent' ontologist.

3. A bare particular is an ontological constituent of an ordinary concrete particular, a constituent that does have properties, namely, the properties associated with the ordinary particular in question, and has them by instantiating (exemplifying) them. This view is held by Gustav Bergmann and by David Armstrong in his middle period. Armstrong, however, speaks of thin particulars rather than bare particulars, contrasting them with thick particulars (what I am calling ordinary concrete particulars). When he does uses 'bare particular,' he uses the phrase incorrectly and idiosyncratically to refer to something like (1) or (2). For example, in Universals and Scientific Realism, Cambridge UP, 1978, vol. I, p. 213, he affirms something he calls the "Strong Principle of the Rejection of Bare Particulars":

For each particular, x, there exists at least one non-relational property, P, such that x is P.

This principle of Armstrong is plausibly read as a rejection of (1) and (2). It is plainly consistent with (3). But of course I do not claim that van Inwagen is committed to bare or thin particulars in the sense of (3). For again, van Inwagen is not a constituent ontologist.

4. A bare particular is an ordinary concrete particular that has properties by instantiating them, where instantiation is a full-fledged external asymmetrical relation (not a non-relational tie whatever that might come to) that connects concrete objects to abstract objects, where abstract objects are objects that are not in space, not in time, and are neither causally active nor causally passive. What is common to (3) and (4) is the idea that bare particulars have properties all right, but they have them in a certain way, by being externally related to them. A bare particular, then, is nothing like an Aristotelian primary substance which has, or rather is, its essence or nature. The bareness of a bare particular, then, consists in its lacking an Aristotle-type nature, not it its lacking properties. My claim is that van Inwagen is committed to bare particulars in sense (4). Let me explain.

Van Inwagen's Bare Particulars

Consider my cat Max. Van Inwagen is committed to saying that Max is a bare particular in sense (4). For while Max has properties, these properties are in no sense constituents of him, but lie (stand?) outside him in a realm apart. These properties are in no sense at him or in him or on him, not even such properties as being black or being furry, properties that are plausibly held to be sense-perceivable. After all, one can see black where he is and feel furriness where he is. None of Max's properties, on van Inwagen's construal of properties, are where he is or when he is. None of them has anything to do with the concrete being of Max himself. As I made clear earlier, the realms of the concrete and the abstract are radically disjoint for van Inwagen. They are jointly exhaustive and mutually exclusive realms: for all x, x is either concrete or abstract, but not both and not neither. So Max is here below in the realm of space, time, change, and causality while his properties exist in splendid isolation up yonder in the realm of abstracta. They are far, far away, not spatially and not temporally, but ontologically.

Max and his properties are of course connected by instantiation which is a relation that is both external and abstract. In what sense is the relation external? X and y are externally related just in case there is nothing intrinsic about the relata that entails their being related. Max is two feet from me at the moment. This relation of being two feet from is external in that there are no intrinsic properties of me or Max or both that entail our being two feet from each other. Our intrinsic properties would be just the same if we were three feet from each other. But Max and his brother Manny are both black. In virtue of their both being intrinsically black, they stand in the same color as relation. Hence the latter relation is not external but internal. Internal relatedness is supervenient upon the intrinsic features of the relata; external relatedness is not.

Suppose I want to bring it about that two balls have the same color. I need do only two things: paint the one ball red, say, and then paint the other ball red. But if I want to bring it about that there are two balls having the same color ten feet from each other, I have to do three things: paint the one ball red, say; paint the other ball red; place them ten feet from each other. The external relatedness does not supervene upon the intrinsic properties of the relata. Given that concrete particulars are externally related to their properties, these particulars are bare particulars in the sense defined in #4 above.

And What is Wrong with That?

Suppose you agree with me that van Inwagen's concrete particulars are bare, not in any old sense, but in the precise sense I defined, a sense that comports well with what the actual proponents of bare/thin particulars had in mind. So what? What's wrong with being committed to bare particulars? Well, the consequences seem unpalatable if not absurd.

A. One consequence is that all properties are accidental and none are essential. For if Max is bare, then there is nothing in him or at him or about him that dictates the properties he must instantiate or limits the properties he can instantiate. He can have any old set of properties so long as he has some set or other. Bare particulars are 'promiscuous' in their connection with properties. The connection between particular and property is then contingent and all properties are accidental. It is metaphysically (broadly logically) possible that Max combine with any property. He happens to be a cat, but he could have been a poached egg or a valve lifter. He could have had the shape of a cube. Or he might have been a dimensionless point. He might have been an act of thinking (temporal and causally efficacious, but not spatial).

B. A second consequence is that all properties are relational and none are intrinsic. For if Max is black in virtue of standing in an external instantiation relation to the abstract object, blackness, then his being black is a relational property and not an intrinsic one.

C. A third consequence is that none of Max's properties are sense-perceivable. Van Inwagen-properties are abstract objects and none of them are perceivable. But if I cup my hands around a ball, don't I literally feel its sphericalness or spheroidness? Or am I merely being appeared to spheroidally?

D. Finally, given what van Inwagen himself says about the radical difference between the abstract and the concrete, a difference so abysmal (my word) that it would be better if we could avoid commitment to abstracta, it is highly counter-intuitive that there should be this abymal difference between a cucumber, say, and its greenness. It is strange that the difference between God and a cucumber should “pale into insignificance” (156) compared to the difference between a cucumber and the property of being green. After all, the properties of a thing articulate its very being. How can they be so ontologically distant from the thing?

If you deny that concrete things as van Inwagen understands them are bare in the sense I have explained, then you seem to be committed to saying that there are two sorts of properties, van Inwagen properties in Plato's heaven and 'sublunary' properties at the particulars here below. But then I will ask two questions. First, what is the point of introducing such properties if they merely duplicate at the abstract intensional level the 'real' properties in the sublunary sphere? Second, what justifies calling such properties properties given that you still are going to need sublunary properties to avoid saying that van Inwagen's concreta are bare particulars?

Perceivability of Properties

Let us pursue point C above a bit further. "We never see properties, although we see that certain things have certain properties." (179) I honestly don't know what to make of the second clause of the quoted sentence. I am now, with a brain properly caffeinated, staring at my blue coffee cup in good light. Van Inwagen's claim is that I do not see the blueness of the cup, though I do see that the cup is blue. Here I balk. If I don't see blueness, or blue, when I look at the cup, how can I literally see that the cup is blue? 'That it is blue' is a thing that can be said of the cup, and said with truth. This thing that can be said is an unsaturated assertible, a property in van Inwagen's sense. Van Inwagen is telling us that it cannot be seen. 'That the cup is blue' is a thing that can be said, full stop. It is a saturated assertible, a proposition, and a true one at that. Both assertibles are abstract objects. Both are invisible, and not because of any limitation in my visual power or in human visual power in general, but because abstract objects cannot be terms of causal relations, and perception involves causation. Both types of assertible are categorially disbarred from visibility. But if both the property and the proposition are invisible, then how can van Inwagen say that "we see that certain things have certain properties"? If van Inwagen says that we don't see the proposition, then what do we see when we see that the cup is blue? A colorless cup? A cup that is blue but is blue in a way different from the way the cup is blue by instantiatiating the abstract unsaturated assertible expressed by 'that it is blue'? But then one has duplicated at the level of abstracta the property that one sees at the concrete cup. If there is blueness at the cup and abstract blueness in Plato's heaven, why do we need the latter? Just what is going on here?

To van Inwagen's view one could reasonably oppose the following view. I see the cup. I see blueness or blue at the cup. I don't see a colorless cup. To deny the three foregoing sentences would be to deny what is phenomenologically given. What I don't literally see, however, is that the cup is blue. (Thus I don't literally see what van Inwagen says we literally see.) For to see that the cup is blue is to see the instantiation of blueness by the cup. And I don't see that. The correlate of the 'is' in 'The cup is blue' is not an object of sensation. If you think it is, tell me how I can single it out, how I can isolate it. Where in the visual field is it? The blueness is spread out over the visible surfaces of the cup. The cup is singled out as a particular thing on the desk, next to the cat, beneath the lamp, etc. Now where is the instantiation relation? Point it out to me! You won't be able to do it. I see the cup, and I see blue/blueness where the cup is. I don't see the cup's BEING blue.

It is also hard to understand how van Inwagen, on his own assumptions, can maintain that we see that certain things have certain properties. Suppose I see that Max, a cat of my acquaintance, is black. Do I see a proposition? Not on van Inwagen's understanding of 'proposition.' His propositions are Fregean, not Russellian: they are not resident in the physical world. Do I see a proposition-like entity such as an Armstrongian state of affairs? Again, no. What do I see? Van Inwagen claims that properties are not objects of sensation; no properties are, not even perceptual properties. I should think that some properties are objects of sensation, or better, of perception: I perceive blueness at the cup by sight; I perceive smoothness and hardness and heat at the cup by touch. If so, then (some) properties are not abstract objects residing in a domain unto themselves.

Van Inwagen's view appears to have the absurd consequence that things like coffee cups are colorless. For if colors are properties (179) and properties are abstract objects, and abstract objects are colorless (as they obviously are), then colors are colorless, and whiteness is not white and blueness is not blue. Van Inwagen bites the bullet and accepts the consequence. But we can easily run the argument in reverse: Blueness is blue; colors are properties; abstract objects are colorless; ergo, perceptual properties are not abstract objects. They are either tropes or else universals wholly present in the things that have them. Van Inwagen, a 'relation ontologist' cannot of course allow this move into 'constituent ontology.'

There is a long footnote on p. 242 that may amount to a response to something like my objection. In the main text, van Inwagen speaks of "such properties as are presented to our senses as belonging to the objects we sense . . . ." How does this square with the claim on p. 179 that properties are not objects of sensation? Can a property such as blueness be presented to our senses without being an object of sensation? Apparently yes, "In a noncausal sense of 'presented.'" (243, fn 3) How does this solve the problem? It is phenomenologically evident that (a definite shade of) blue appears to my senses when I stare at my blue coffee cup. Now if this blueness is an abstract object as van Inwagen claims then it cannot be presented to my senses any more than it can be something with which I causally interact.

Related articles

Peter van Inwagen, "A Theory of Properties," Exposition and Critique

Van Inwagen, Properties, and Bare Particulars

Two Recent Publications of Mine

Trope Troubles: An Exercise in Aporetics with the Help of Professor Levy

Peter van Inwagen on Burden of Proof in Philosophy

A List of Bars Philosophers Opened On Being Denied Tenure

What the Meinongian Means by 'Has Being' and 'Lacks Being'

Senses of 'Abstract' with a Little Help from Hegel

A Question for Trope Theorists

Trope bundle theory is regularly advertised as a one-category ontology.  What this means is that everything is either a trope or a logical construction from tropes.  Standard trope theory is a metaphysic that implies that everything can be accounted for in terms of ontologically basic simples, namely, tropes.  So what about the cat in my lap, or any individual substance? On trope theory, individual substances  (concrete particulars) are assayed as bundles of compresent tropes.  To put it crudely, sufficiently many of the right tropes tied together by relations of compresence yield an individual substance.  Concrete particulars are reductively analyzable into systems of compresent tropes.  So far, so good.

But my cat Max Black is black and furry and so is his brother Manny K. Black.  How do we account for furriness and blackness as properties had by both of these critters and innumerable actual and possible others?  How do we account for universals in our one-category ontology if all we have to work with are tropes?  How can we construct universals out of abstract particulars?

The standard answer is in terms of classes or sets of exactly resembling tropes.  Black₁ and black₂ are numerically distinct, as numerically distinct as Max and Manny.  But they resemble each other exactly.  The same goes for all black tropes.  Take the set of them all.  That is the universal blackness.  Thus universals are reductively analyzable in terms of sets or classes of exactly resembling tropes.

Neat, eh?

Now here is my question. Trope theory was advertised as a one-category ontology.  Don't we now have two categories, a category of tropes and a category of sets?

"There is no commitment to sets.  All the furry tropes resemble each other.  Furriness the universal is just the furry tropes."

I don't think this is a good answer.  For I could press: the furry tropes taken distributively or taken collectively?  Obviously, they must be taken collectively.  But then we are back to sets.

How then would a trope theorist answer my (non-rhetorical) question?

Cat and mouse:

 

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The Emperor’s Clothes Revisited or Trope Theory Interrogated

The following is a comment by Eric Levy in a recent trope thread.  My responses are in blue.

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Might I revert to the problem of compresent tropes constituting a concrete particular? Heil well formulates it: “One difficulty is in understanding properties as parts that add up to objects” (2015, 120). The whole business seems to me riddled with equivocation, epitomized by Maurin’s formulation: “. . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance.”

BV:  We agree, I think, that standard trope theory is trope bundle theory, a one-category ontology.  This version of the theory alone is presently under discussion.  John Heil puts his finger on a very serious difficulty.  I would add that it is a difficulty not only for trope bundle theory but for every bundle theory including the theory that ordinary particular are bundles or clusters of universals, as well as for Hector Castaneda's bundle-bundle theory.  On Castaneda's theory, an ordinary particular at a time is a synchronic bundle of "consubstantiated" "guises" with a particular over time being a "transubstantiated" diachronic bundle of these synchronic bundles.

Intellectual honesty requires me to say that the theory I advance in PTE also faces Heil's difficulty.  For on the view developed in PTE, ordinary concrete particulars are facts or states of affairs along Bergmannian-Armstrongian lines.  On this theory Socrates is not a bundle but a concrete truth-making fact which has among its ontological constituents or parts his properties.

Generalizing, we can say that the difficulty Heil mentions is one for any constituent ontology that assays properties as ontological parts of the things that, as we say in the vernacular, 'have them.'

Anna-Sofia Maurin is entirely right in her explanation of trope theory but as far as I know she would not admit that Heil's difficulty really is one.

For example, on the one hand, properties are immaterial and interpenetrable abstracta. On the other hand, these immaterial and interpenetrable abstracta somehow constitute, through compresence, an enmattered, impenetrable object. Let us consider a red rubber ball and then a bronze statue. There is the rubber ball – the triumphant consequence of compresent tropes. One trope is to be construed, as we earlier agreed, as an appropriately extended red or redness. Another trope is to be construed as an appropriately diametered spherical contour. Another trope – the hardness trope – is to be construed as an appropriately calibrated resistance to deformation. But then we reach the rubber trope; for we are talking about a red rubber ball. What are we to posit here: an amorphous chunk of rubber appropriately qualified by its compresent fellows? How does trope theory account for the rubber in the red rubber ball?

BV:  Excellent question(s), Eric.  Well, the chunk or hunk of rubber cannot be amorphous -- formless -- for then it would be materia prima rather than what it is, materia signata.  It is after all a hunk of rubber, not of clay, and indeed a particular hunk of rubber, not rubber in general.  The parcel of rubber is formed matter, hence not prime matter.  It is this matter, not matter in general.  Your question, I take it, is whether this rubber could be construed as a trope in the way that this redness and  this hardness can be construed as tropes.  The latter are simple property particulars.  But this rubber is not simple, but a hylomorphic compound.  So it would appear that this rubber cannot be construed as a trope.

Even if the property of  being rubbery could be construed as a trope, it is hard to see how the stuff, rubber, could be construed as a trope.  For tropes are simple while stuffs are hylomorphic compounds -- prime stuff aside.  Tropes are formal or akin to forms while stuffs are matter-form compounds.  Mud is muddy.  But the muddiness of a glob of mud would seem to be quite different from the  stuff, mud.  

My desk is wooden.  The property of being wooden is different from the designated matter (materia signata) that has the form of a desk.  Harry is hairy.  He has hair on his back, in his nose, and everywhere else.  He is one hairy dude.   His hair is literally a part of him, a physical part.  His being hairy, however, is a property of him.  If this property is a trope, then it is (i) a property particular that is (ii) an ontological part of Harry.  But then what is the relation between the ontological part and the physical part?  Can a clear sense be attached to 'ontological part'?   As has often been noted, ontological parts are not parts in the sense of mereology.

Here  then is one question for the trope theorist:  How do you account for the designated matter of a material thing?  Is it a trope or not?   How could a trope theorist deal with matter?  A trope theorist might say this.  "There is no matter ultimately speaking.  It is form 'all the way down.'  A hunk of rubber is not formed matter.  For this matter is either prime matter, which cannot exist, or just a lower level of form."

A second question:  if tropes are immaterial, how can bundling them 'add up' to a material thing? A trope theorist might respond as follows. 

You are assuming that there are in ultimate reality irreducibly material things.  On trope theory, however, material things reduce to systems of compresent tropes.  So, while individual tropes are immaterial, a system of compresent tropes is material in the only sense that stands up to scrutiny.  We trope theorists are not denying that there are material things, we are telling you what they are, namely, bundles of compresent tropes.  Material things are just bundles of immaterial tropes.  The distinction between the immaterial and the material is accommodated by the distinction between unbundled and bundled tropes.  And while it is true that individual tropes interpenetrate, that is consistent with the impenetrability of trope bundles.  Impenetrability is perhaps an emergent feature of trope bundles.

Now let’s move to the bronze statue. What does trope theory do with the bronze? This is, after all, a bronze statue. Is bronze, then, a trope or “property particular” of the statue? And if so, how are we to construe this trope? Is it material or immaterial?

BV:  A trope theorist might be able to say that there are two trope bundles here, the lump of bronze and the statue.  Lump and Statue are arguably two, not one, in that they have different persistence conditions.  Lump exists at times when Statue doesn't.  So they are temporally discernible.  They are also modally discernible.  Even if in the actual world Lump and Statue exist at all the same times, there are possible worlds in which Lump exists but Statue does not. (Of course there are no possible worlds in which Statue exists and Lump does not.)

And to what do we assign the trope of shape: the bronze or the statue? As Lowe point out, “the bronze and the statue, while the former composes the latter, are exactly the same shape. Do they, then, have numerically distinct but exactly coinciding shapes . . .” (1998, 198)? Or does the shape as form pertain to just one candidate? Lowe suggests that the shape, as form, belongs or pertains to the statue, not the bronze, and that the property concerned is “the property of being a statue of such-and-such a shape,” not the property of the statue’s particular shape. The reason for this distinction is that the form (being a statue of such-and-such a shape) is identified with the statue itself.

In this example, in the context of trope theory, how can there be a property, “being a statue of such-and-such a shape,” when the statue itself is constituted? Trope theory cannot account for this property, because trope theory cannot distinguish between the shape of the bronze and the shape of the statue. It cannot make this distinction because, as you point out in PTE, in trope theory there is no distinction between compresence and the existence of the object (Vallicella 2002, 87). One of the tropes in that compresence can be a shape trope, of course. But it cannot be the trope of “being a statue of such-and-such a shape,” because, in the wacky world of trope theory, the statue itself must be constituted before it can be a statue of such-and-such a shape. In other words, no trope in the compresent bundle can be the trope of “being a statue of such-and-such a shape,” because, until the tropes compresent, there cannot be a statue. This is what happens in a one-category ontology that recognizes only property particulars. If there were a trope of “being a statue of such-and-such a shape,” it would have to qualify the statue after the statue had been constituted.

BV:  The last stretch of argumentation is not clear to me.  Please clarify in the ComBox.

Related articles

Senses of 'Abstract' with a Little Help from Hegel

Tropes as Truth-Makers? Or Do We Need Facts?

A Question About Tropes

Senses of 'Abstract' with a Little Help from Hegel

For Eric Levy, who 'inspired' me to dig deeper into this material.

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Keith Campbell and others call tropes abstract particulars.  But what is it for something to be abstract?  It may be useful to sort out the different senses of 'abstract' since this term and its opposite 'concrete' are thrown around quite a lot in philosophy.  I propose that we distinguish between ontic and epistemic uses of the word. 

Ontic Senses of 'Abstract'

a. Non-spatio-temporal.  The prevalent sense of 'abstract' in the Anglosphere is:  not located in space or in time.  Candidates for abstract status in this sense: sets, numbers, propositions, unexemplified universals.  The set of prime numbers less than 10 is nowhere to be found in space for the simple reason that it is not in space.    If you say it is, then tell me where it is. The same holds for all sets as sets are understood in set theory.   (My chess set is not a set in this sense.)  Nor are sets in time, although this is less clear: one could argue that they, or rather some of them, are omnitemporal, that they exist at every time. That {1, 3, 5, 7, 9} should exist at some times but not others smacks of absurdity, but it doesn't sound absurd to say that this set  exists at all times. 

This wrinkle notwithstanding, sets are among the candidates for abstract status in the (a) sense.

The same goes for numbers.  They are non-spatio-temporal.

If you understand a proposition to be the Fregean sense of a declarative sentence from which all indexical elements, including tenses of verbs, have been extruded, then propositions so understood are candidates for abstract status in sense (a).

Suppose perfect justice is a universal and suppose there is no God. Then perfect justice is an unexemplified universal.  If there are unexemplified universals, then they are abstract in the (a) sense.

This (a) criterion implies that God is an abstract object.  For God, as classically conceived, is not in space or in time, and this despite the divine omnipresence.  But surely there is a huge different between God who acts, even if, as impassible, he cannot be acted upon, and sets, numbers, propositions and the like that are incapable of either acting or being acted upon.  And so we are led to a second understanding of 'abstract' as that which is:

b. Causally inert.  Much of what is abstract in the (a) sense will be causally inert and thus abstract in the (b) sense.  And vice versa.  My cat can bite me, but the set having him as its sole member cannot bite me.  Nor can I bite this singleton or toss it across the room, as I can the cat.  Sets are abstract  in that they cannot act or be acted upon.  A less robust way of putting it:  Sets cannot be the terms of causal relations.  This formulation is neutral on the question whether causation involves agency in any sense. 

God and Kantian noumenal agents show that the first two criteria come apart.  God is abstract in the (a) sense but not in the (b) sense.  The same goes for noumenal agents which, as noumenal, are not in space or time, but which, as agents are capable of initiating causal event-sequences. 

It may also be that there are items that are causally inert but located in space and time.  (Spatio-temporal positions perhaps?)

So perhaps we should spring for a disjunctive criterion according to which the abstract is that which is:

c. Non-spatio-temporal or causally inert.  This would imply that God and Socrates are both concrete.

d. On a fourth construal of 'abstract'  an item is abstract just in case it is incomplete.  To get a sense of what I am driving at, consider the following from Hegel's essay Who Thinks Abstractly?

A murderer is led to the place of execution. For the common populace he is nothing but a murderer. Ladies perhaps remark that he is a strong, handsome, interesting man. The populace finds this remark terrible: What? A murderer handsome? How can one think so wickedly and call a murderer handsome . . . .

This is abstract thinking: to see nothing in the murderer except the abstract fact that he is a murderer, and to annul all other human essence in him with this simple quality.

The murderer is not just a murderer; he is other things besides: a father, a son, a husband, a handsome devil, a lover of dogs, a strong chess player . . . .  In general, the being of anything that actually exists cannot be reduced to one of its qualities.  To acquiesce in such a reduction is to think abstractly: it is to abstract from the full reality of thing in order to focus on one of its determinations.  But here we should distinguish between legitimate abstraction and vicious abstraction.  What Hegel is railing against is vicious abstraction.

Now I am not interested here in explaining Hegel.  I am using him for my purposes, one of which is to pin down a classical as opposed to a Quinean sense of 'abstract.'  Accordingly, an abstract entity in the (d) sense   is an entity that is got before the mind by an act of abstraction.  But please note that if epistemic access to an entity is via abstraction, it does not follow that the entity is a merely intentional object.  What I am trying to articulate is a fourth ontic sense of 'abstract,' not an epistemic/doxastic/intentional sense.  It could well be that there are incomplete entities, where an entity is anything that exists.  (As I use 'item,' an item may or may not exist, so as not to beg the question against the great Austrian philosopher Alexius von Meinong.)

We have now arrived at the sense of 'abstract' relevant to trope theory.  Here is a red round spot on a white piece of paper.  When I direct my eyes to the spot I see red, a particular shade of red.  That is a datum.  On the trope theory, the red that I see is a particular, an unrepeatable item.  It is not a universal, a repeatable item.  Thus on trope theory the red I see is numerically distinct from the red I see when I look at a numerically different spot of the same (exact shade of ) color. 

It is important to realize that one cannot resolve the question whether properties are particulars or universals phenomenologically.  That I see red here and also over there does not show that there are two rednesses.  For the phenomenological datum is consistent with redness being a universal that is located into two different places and visible in two different places.  Phenomenology alone won't cut it in philosophy; we need dialectics too.  Husserl take note!

There are philosophers who are not bundle theorists who speak of tropes.  C. B. Martin is one.  I do not approve of their hijacking of 'trope,' a term introduced by D. C. Williams, bundle theorist.  I am a bit of a prick when to comes to language.  Technical words and phrases ought to be used with close attention to their provenience.  It rankles me when 'bare particular' is used any old way when it is a terminus technicus introduced by Gustav Bergmann with a precise meaning.  Read Bergmann, and then sling 'bare particular.'

On standard trope theory, trope bundle theory, the spot -- a concrete item -- is a system of compresent tropes. It is just a bundle of tropes. There is no substratum that supports the tropes: the spot just is compresent tropes.  Furthermore, the existence of the spot is just the compresence of its tropes.  Since the spot exists contingently, the tropes are compresent contingently.  That implies that the compresent tropes can in some sense 'be' without being bundled.  (Note that tropes are bundled iff they are compresent.)  For if there were no sense in which the tropes could 'be' without being bundled, then how could one account for the contingency of a give trope bundle? 

Now if tropes can be without being bundled, then they are not products of abstraction:  they are not merely intentional items that arise before our minds when we abstract from the other features of a thing.  When I consider the redness of the spot, I leave out of consideration the roundness.  On trope theory this particular redness  really exists whether or not I bring it before my mind by a process of abstraction.  Tropes are thus incomplete entities, not incomplete intentional objects.  They are in no way mind-dependent.  They have to be entities if they are to be the ultimate ontological building blocks of ordinary concrete particulars such as our  round, red spot.

An abstract item in the (d) sense, then, is an incomplete entity.  It is not complete, i.e.,  completely determinate.  For example, a redness trope is a a property assayed as a particular.  It is the ontological ground of the datanic redness of our spot and it is this by being itself red.  Our redness trope is itself red. But that is all it is: it is just red.  This is why it is abstract in the (d) sense.  Nothing can be concrete if it is just red.  For if a concretum is red, then it is either sticky or non-sticky (by the Law of Excluded Middle) and either way a concrete red thing is either red sticky thing or a red non-sticky thing.

The Epistemic Sense of 'Abstract'

I have already alluded to this sense according to which an item is abstract iff it is brought before the mind by an act of abstraction and is only as a merely intentional object.

At this point I must take issue with my esteemed coworker in these ontological vineyards, J. P. Moreland.  He writes, ". . . Campbell follows the moderate nominalist tendency of treating 'abstract' as an epistemic, and not ontological, notion." (Universals, p. 53)  I don't think so.  The process of abstracting is epistemic, but not that which is brought before the mind by this process.  So I say that 'abstract' as Campbell uses it is an ontological or ontic notion.  After all, tropes or abstract particulars as Campbell calls them are not mere products of mental abstraction: they are mind-independent building blocks of everything including things that existed long before minds made the scene.

Related articles

Is Hegel Guilty of 'Epochism'?

The Marxist roots of Islamic extremism

A Question About Tropes

In a Philosophical Conversation, Three's a Crowd

Is Anything Real Self-Identical?

Trope Troubles: An Exercise in Aporetics with the Help of Professor Levy

Eric P. Levy, an emeritus professor of English at the University of British Columbia, has been much exercised of late by trope theory and other questions in ontology.  He has been sharing his enthusiasm with me.   He espies 

. . . an apparent antinomy at the heart of trope theory. On the one hand, tropes are logically prior to objects. But on the other hand, objects (or, more precisely, the trope-bundles constituting objects) are logically prior to tropes, because without objects tropes have nowhere to be – without objects (or the trope-bundles constituting objects) tropes cannot be. Moreover, as has I hope been shown, a trope cannot be in (or constitute) any object or trope-bundle other than that in which it already is.

How might a trope theorist plausibly respond to this?  Can she?

What are tropes?

It is a 'Moorean fact,' a pre-analytic datum, that things have properties.  This is a pre-philosophical observation.  In making it we are not yet doing philosophy.  If things have properties, then there are properties.  This is a related pre-philosophical observation.  We begin  to do philosophy when we ask: given that there are properties, what exactly are they?  What is their nature?  How are we to understand them?  This is not the question, what properties are there, but the question, what are properties?  The philosophical question, then, is not whether there are properties, but what properties are.

On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on the standard  bundle version of trope theory) or by being a substratum in which a redness trope inheres (on a nonstandard theory which I will not further discuss). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ 'Has' and cognates are words of ordinary English: they do not commit us to ontological theories of what the having consists in.  So don't confuse 'a has F-ness' with 'a instantiates F-ness.'  Instantiation is a term of art, a terminus technicus in ontology.  Or at least that is what it is in my book.  More on instantiation in a moment.

Thus a redness trope is red, but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness.

It is therefore inaccurate to speak of tropes as property instances.  A trope is not a property instance on one clear understanding of the latter.  First-order instantiation is a dyadic asymmetrical relation: if a instantiates F-ness, then it is not the case that F-ness instantiates a.  (Higher order instantiation is not asymmetrical but  nonsymmetrical.  Exercise for the reader: prove it!)  Suppose the instantiation relation connects the individual Socrates here below to the universal wisdom in the realm of platonica.  Then a further item comes into consideration, namely, the wisdom of Socrates. This is a property instance.  It is a particular, an unrepeatable, since it is the wisdom of Socrates and of no one else. This distinguishes it from the universal, wisdom, which is repeated in each wise individual.  On the other side, the wisdom of Socrates is distinct from Socrates since there is more to Socrates that his being wise.  There is his being snubnosed, etc.  Now why do I maintain that a trope is not a property instance? Two arguments. 

Tropes are simple, not complex.  (See Maurin, here.)  They are not further analyzable.  Property instances, however, are complex, not simple.   'The F-ness of a'  --  'the wisdom of Socrates,' e.g. -- picks out a complex item that is analyzable into F-ness, a, and the referent of 'of.'  Therefore, tropes are not property instances.

A second, related,  argument.  Tropes are in no way proposition-like.  Property instances are proposition-like as can be gathered from the phrases we use to refer to them.  Ergo, tropes are not property instances. 

One can see from this that tropes on standard trope theory, as ably presented by Maurin in her SEP entry, are very strange items, so strange indeed that one can wonder whether they are coherently conceivable at all by minds of our discursive constitution.  Here is one problem.

How could anything be both predicable and impredicable?

Properties are predicable items.  So if tropes are properties, then tropes are predicable items.  If the redness of my tomato, call it 'Tom,'  is a trope, then this trope is predicable of Tom. Suppose I assertively utter a token of 'Tom is red.'  On one way of parsing this we have a subject term 'Tom' and a predicate term '___ is red.'  Thus the parsing: Tom/is red.  But then the trope would appear to have a proposition-like structure, the structure of what Russell calls a propositional function.  Clearly, '___ is red' does not pick out a proposition, but it does pick out something proposition-like and thus something complex.  But now we have trouble since tropes are supposed to be simple.  Expressed as an aporetic triad or antilogism:

a. Tropes are simple.
b. Tropes are predicable.
c.  Predicable items are complex.

The limbs of the antilogism are each of them rationally supportable, but they cannot all be true. The conjunction of any two limbs entails the negation of the remaining one.  Thus the conjunction of (b) and (c) entails ~(a).

We might try to get around this difficulty by parsing 'Tom is red' differently, as: Tom/is/red.  On this scheme, 'Tom' and 'red' are both names.  'Tom' names a concrete particular whereas 'red' names an abstract particular.  ('Abstract' is here being used in the classical, not the Quinean, sense.)   As Maurin relates, D. C. Williams, who introduced the term 'trope' in its present usage back in the '50s, thinks of the designators of tropes as akin to names and demonstratives, not as definite descriptions. But then it becomes difficult to see how tropes could be predicable entities. 

A tomato is not a predicable entity.  One cannot predicate a tomato of anything.  The same goes for the parts of a tomato; the seeds, e.g., are not predicable of anything.  Now if a tomato is a bundle of tropes, then it is a whole of ontological parts, these latter being tropes.  If we think of the tomato as a (full-fledged) substance, then the tropes constituting it are "junior substances." (See D. M. Armstrong, 1989, 115) But now the problem is: how can one and the same item -- a trope --  be both a substance and a property, both an object and a concept (in Fregean jargon), both impredicable and predicable?  Expressed as an aporetic dyad or antinomy:

d. Tropes are predicable items.
e. Tropes are not predicable items.

Maurin seems to think that the limbs of the dyad can both be true:  ". . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance."  If the limbs can both be true, then they are not contradictory despite appearances.

How can we defuse the apparent contradiction in the d-e dyad?  Consider again Tom and the redness trope R.  To say that R is predicable of Tom  is to say that Tom is a trope bundle having R as an ontological (proper) part.  To say that R us impredicable or  a substance is to say that R is capable of independent existence..  Recall that Armstrong plausibly defines a substance as anything logically capable of independent existence.

It looks as if we have just rid ourselves of the contradiction.  The sense in which tropes are predicable is not the sense in which they are impredicable.  They are predicable as constituents of trope bundles; they are impredicable in themselves. Equivalently, tropes are properties when they are compresent with sufficiently many other tropes to form trope bundles (concrete particulars); but they are substances in themselves apart from trope bundles as the 'building blocks' out of which such bundles are (logically or rather ontologically) constructed.

Which came first: the whole or the parts?

But wait!  This solution appears to have all the advantages of jumping from the fying pan into the fire, or from the toilet into the cesspool. (I apologize to the good professor for the mixture and crudity of my metaphors.)  For now we bang up against Levy's Antinomy, or something like it, to wit:

f. Tropes as substances, as ontological building blocks, are logically prior to concrete particulars.
g. Tropes as properties, as predicable items, are not logically prior to concrete particulars.

This looks like a genuine aporia.  The limbs cannot both be true.  And yet each is an entailment of standard trope theory.  If tropes are the "alphabet of being" in a phrase from Williams, then they are are logically prior to what they spell out.  But if tropes are unrepeatable properties, properties as particulars, then a trope cannot exist except as a proper ontological part of a trope bundle, the very one of which it is a part.  For if a trope were not tied to the very bundle of which it is a part, it would be a universal, perhaps only an immanent universal, but a universal all the same. 

Furthermore, what makes a trope abstract in the classical sense of the term is that it is abstracted from a concretum.  But then the concretum comes first, ontologically speaking, and (g) is true.

Interim conclusion: Trope theory, pace Anna-Sofia [what a beautiful aptronym!] Maurin, is incoherent. But of course we have only scratched the surface. 

Picture below, left-to-right:  Anna-Sofia Maurin, your humble correspondent, Arianna Betti, Jan Willem Wieland. Geneva, Switzerland, December 2008.  It was a cold night.

 

Related articles

Armstrong, Quine, Universals, Abstract Objects, and Naturalism

Peter van Inwagen, "A Theory of Properties," Exposition and Critique

Atheism and Ontological Simplicity: A Retraction and a Repair

God and Mann: Divine Simplicity and Property-Instances

God, Simplicity, and Tropes

Tropes as Truth-Makers? Or Do We Need Facts?

In a Philosophical Conversation, Three's a Crowd

A Question About Tropes

EL: I have been reading with great pleasure and enlightenment certain sections of your superb work, A Paradigm Theory of Existence: Onto-Theology Vindicated. Your skill and poise in framing and unfolding your argument, your marvelous dexterity with rebuttal of adversarial views, and your insistence that existence remain at the center of metaphysical inquiry instead of being reduced to an afterthought – or cast out of the mind altogether – reward and refresh the reader.

BV:  Thanks for the kind words.  The book snagged some favorable reviews from Hugh McCann, Panayot Butchvarov, and others.  But the treatment it received at Notre Dame Philosophy Reviews was pretty shabby.  Kluwer sent the then editor Gary Gutting a copy and he sent it to a reviewer who declined to review it.  So I requested that the copy be returned either to me or Kluwer so that it could be sent elsewhere.  Gutting informed me that the reviewer had sold the book.  So the reviewer accepted an expensive book to review, decided not to review it, and then sold it to profit himself.     A person with a modicum of moral decency would first of all not agree to have a book sent to him if he had no intention of reviewing it.  But if he finds that for some reason he cannot review it, then he ought to return it.  The book is the payment for the review; it is wrong to keep a book one does not review after one has agreed to review it.

EL: My question concerns your statement, in A Paradigm Theory of Existence, that tropes “float free” (221). Is this correct?

BV:  It depends on what 'float free' means.  Here is what I said in PTE, 221-222:

Tropes differ from Aristotelian accidents in that they do not require the support of a substratum.  They 'float free.'  They need individuation ab extra as little as they need support ab extra:  they differ numerically from each other without the need of any constituent to make them differ.  In that respect they are like bare particulars except of course that they are not bare.  Each is a nature. Each is at once and indissolubly a this and a such.  Tropes are the "alphabet of being" (D. C. Williams), the rock bottom existents out of which all else is built up.  Ordinary, concrete particulars are bundles or clusters of these abstract particulars.  Thus Socrates is a bundle of tropes, a system of actually compresent tropes, and to say that he is pale is to say that a pale trope is compresent with other tropes comprising him.

Therefore, to say that tropes 'float free' is to say that they are unlike Aristotelian accidents in at least two ways. 

First,  they do not require for their existence a substratum in which to inhere.  An accident A of a substance S cannot exist except 'in' a substance, and indeed, 'in' S, the very substance of which it is an accident.  To exist for an accident is to inhere.  But to exist for a trope is not to inhere.  That is what it means to say that tropes do not need support ab extra.  They stand on their own, ontologically speaking.  Otherwise they wouldn't constitute the "alphabet of being" in Donald C. Williams' felicitous phrase. 

If an ordinary particular, my coffee cup say, is a bundle of compresent tropes, then surely there must be a sense in which the tropes are ontologically prior to the bundle, and a corresponding sense in which the bundle is ontologically posterior to the constituent tropes.  This is obvious from the fact that my cup is a contingent being.  In trope-theoretic terms what this means is that the tropes that compose my cup might not have been compresent.  The possible nonexistence of my cup is then the possible non-compresence of its constituent tropes.  The tropes composing my cup could have existed without the cup existing, but the cup could not have existed without those tropes existing. Crude analogy: the stones in my stone wall could have existed without the wall existing, but the wall -- that very wall -- could not have existed without the stones existing.

But this is not to say tropes can exist on their own apart from any bundle.  It could be that they can exist only in some bundle or other but not necessarily in the bundle in which they happen to be bundled.  The perhaps infelicitous 'float free' need not be read as implying that tropes can exist  unbundled.  By the way, here is where the crude analogy breaks down.  The stones in my wall could have existed in a wholly scattered state.  But presumably the tropes composing my cup could not have existed unbundled.

Second, tropes, unlike accidents, do not need something external to them for their individuation, or rather ontological differentiation.  What makes two accidents two rather than one?  The numerical difference of the substances in which they inhere.  The metaphysical ground of the numerical difference of A1 and A2 -- both accidents -- is the numerical difference of the primary substances in which they inhere.  But tropes need nothing external to them to ground their numerical difference from one another. 

Example.  My cats Max Black and Manny Black are asleep by the fire. Each is warm, both metabolically, and by the causal agency of the fire.  Consider only the warmth in each caused by the fire.  Assume that the degree of warmth is the same.  If warmth is either an Aristotelian accident or a trope then it is a particular (an unrepeatable, non-instantiable) item, not a universal.  On either theory,  each cat has its own warmth.  But what makes the two 'warmths' two?  What is the ground of their numerical difference?  On the accident theory, it is the numerical difference of the underlying substances, Max and Manny.  On the trope theory, the two warmths are just numerically different: they are self-differentiating.

EL:  I understand that tropes are self-individuating, each being a numerically distinct, particularized, and unrepeatable quality. As Maurin explains,  “To a trope theorist, therefore, the fact that each particular redness (each trope) is such that it resembles every other particular redness is a consequence of the fact that each particular redness is what it is and nothing else” (2002, 57). But I don’t understand how tropes “float free.”

BV:  I believe I have just given a satisfactory explanation of what 'floats free' means in this context.   I would agree, however, that 'floats free' is not a particularly happy formulation.

EL:  Your clarification would be keenly appreciated. When reading about trope theory, I sometimes feel that I’ve fallen down a rabbit hole.  Then you need some music therapy.

BV:  If you want from me a defense of the coherence and tenability of trope theory, that I cannot provide.  I suspect that every philosophical theory succumbs in the end to aporiai.  And that goes for the theories I propose in PTE as well. 

EL:  On the one hand, tropes (abstract particulars) are logically prior to things (concrete particulars), because through their compresence tropes bring things into existence.

BV: Right.

EL:  On the other hand, things are logically prior to tropes because, lacking existential independence, tropes are only through compresence in the thing they constitute.

BV:  Not quite.  Tropes are only when compresent in some bundle or other.  But this is not to say that tropes composing my coffee cup could not have existed in other bundles.

EL: Indeed, Lowe argues that trope theory “fall[s] into a fatal circularity which deprives both tropes and trope-bundles of well-defined identity-conditions altogether” (1998, 206).

BV: What is the title of the book or article? 

The following view is fatally circular. An ordinary particular is a system of compresent tropes.  Its existence is just the compresence of those tropes.  The tropes themselves  exist only as the relata of the compresence relation within the very same ordinary particular.

To avoid this circularity one could say what I said above:  while tropes cannot exist apart from some bundle or other, there is no necessity that the tropes composing a given bundle be confined to that very bundle.  Saying this, one would grant some independence to the trope 'building blocks.' But then the problem is to make sense of this independence.

Suppose that in the actual world trope T1 is a constituent of Bundle B1, but that there is a merely possible world W in which T1 is a constituent of bundle B2.  But then T1 threatens to turn into a universal, a repeatable item.  For then T1 occurs in two possible worlds, the actual world and W.

Related articles

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A Question About God and Existence

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Time Trouble

Atheism and Ontological Simplicity: A Retraction and a Repair

Chad McIntosh spotted the sloppiness in something I posted the other day.  A retraction is in order. And then a repair.

A Retraction

I wrote,

The simple atheist -- to give him a name -- cannot countenance anything as God that is not ontologically simple.  That is, he buys all the arguments classical theists give for the divine simplicity.  It is just that he finds the notion of an ontologically simple being incoherent.  He accepts, among others, all of Plantinga's arguments on the latter score.  His signature argument runs as follows:

1. If God exists, then God is simple.
2. Nothing is or can be simple.
Therefore
3. God does not exist.

First of all, one could be a simple atheist (simplicity atheist) as I have defined him without holding that nothing is ontologically simple.  Surely there is nothing in the nature of atheism to require that an atheist eschew every ontologically simple item.  And the same goes for the character I called the ontic theist, Dale Tuggy being an example of one.  Surely there is nothing in the nature of ontic theism, according to which God is not ontologically simple, to require that an ontic theist eschew every ontologically simple item. 

Second, while Alvin Plantinga does argue against the divine simplicity in Does God Have a Nature? (Marquette UP, 1980)  he does not (as I recall without checking) argue that nothing is ontologically simple.

There is no little irony in my sloppiness inasmuch as in my SEP entry on the divine simplicity I adduce tropes as ontologically simple items to soften up readers for the divine simplicity:

We have surveyed some but not all of the problems DDS faces, and have considered some of the ways of addressing them. We conclude by noting a parallel between the simplicity of God and the simplicity of a popular contemporary philosophical posit: tropes.

Tropes are ontologically simple entities. On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on one version of trope theory) or by being a substratum in which a redness trope inheres (on a second theory). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ Thus a redness trope is red , but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness. In this respect it is like God who is what he has. God has omniscience by being (identical to) omniscience. Just as there is no distinction between God and his omniscience, there is no distinction in a redness trope between the trope and its redness. And just as the simple God is not a particular exemplifying universals, a trope is not a particular exemplifying a universal. In both cases we have a particular that is also a property, a subject of predication that is also a predicable entity, where the predicable entity is predicated of itself. Given that God is omniscience, he is predicable of himself. Given that a redness trope is a redness, it is predicable of itself. An important difference, of course, is that whereas God is unique, tropes are not: there is and can be only one God, but there are many redness tropes.

Not only is each trope identical to the property it has, in each trope there is an identity of essence and existence. A trope is neither a bare particular nor an uninstantiated property. It is a property-instance, an indissoluble unity of a property and itself as instance of itself. As property, it is an essence; as instance, it is the existence of that essence. Because it is simple, essence and existence are identical in it. Tropes are thus necessary beings (beings whose very possibility entails their actuality) as they must be if they are to serve as the ontological building blocks of everything else (on the dominant one-category version of trope theory). In the necessity of their existence, tropes resemble God.

If one can bring oneself to countenance tropes, then one cannot object to the simple God on the ground that (i) nothing can be identical to its properties, or (ii) in nothing are essence and existence identical. For tropes are counterexamples to (i) and (ii).

A Repair

Matters are quickly set right if I 'simply' ascribe to the simplicity atheist the following less committal argument:

1. If God exists, then God is simple.
2*. God cannot be simple.
Therefore
3. God does not exist.

To the ontic theist we may ascribe:

2*. God cannot be simple.
~3. God exists.
Therefore
~1. It is not the case that if God exists, then God is simple.

Question 1: Has anyone ever argued along the lines of the simplicity atheist?  Have I stumbled upon a new argument here? 

Question 2:  Can you think of any non-divine ontologically simple items other than tropes?

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Evil as it Appears to Theists and Atheists

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Pre-Print: Peter van Inwagen, Existence: Essays in Ontology

The following review article is scheduled to appear later this year in Studia Neoscholastica.  The editor grants me permission to reproduce it here should anyone have comments that might lead to its improvement.

REVIEW ARTICLE

William F. Vallicella

 Peter van Inwagen, Existence: Essays in Ontology, Cambridge University Press, 2014, viii + 261 pp.

This volume collects twelve of Peter van Inwagen's recent essays in ontology and meta-ontology, all of them previously published except one, “Alston on Ontological Commitment.” It also includes an introduction, “Inside and Outside the Ontology Room.” It goes without saying that anyone who works in ontology should study this collection of rigorous, brilliant, and creative articles. One route into the heart of van Inwagen's philosophical position is via the theory of fictional entities he develops in chapter 4, “Existence, ontological commitment, and fictional entities.”

 Fictional Entities

One might reasonably take it to be a datum that a purely fictional item such as Sherlock Holmes does not exist. After all, most of us know that Holmes is a purely fictional character, and it seems analytic that what is purely fictional does not exist. Van Inwagen, however, demurs:

The lesson I mean to convey by these examples is that the nonexistence of [Sherlock] Holmes is not an ontological datum; the ontological datum is that we can use the sentence 'Sherlock Holmes does not exist' to say something true. (105)

So, while many of us are inclined to say that the nonexistence of Holmes is an ontological datum in virtue of his being a purely fictional entity, one wholly made up by Sir Arthur Conan Doyle, van Inwagen maintains that Holmes exists and that his existence is consistent with his being purely fictional. One man's datum is another man's (false) theory! To sort this out, we need to understand van Inwagen's approach to ficta.

Comments on "On the Individuation of Tropes"

What follows is a paper by a reader, posted with his permission, together with some comments of mine.  I will make my comments as time permits and not all in one session.  Others are invited to add their comments in the ComBox.

On the Individuation of Tropes

Introduction

Trope theorists see their view as a happy middle ground between nominalism and universalism. It is not too hot or too cold; it’s just right. It does not scandalously posit entities that are said to be simultaneously in multiple places, like universalism. And, at least at first blush, it does not seem to be plagued by an appeal to a primitive notion of resemblance, like some prominent versions of nominalism.

BV: 'Universalism' is used in more than one way in ontology alone.  So I would like to see a definition of this term right at the outset of the paper.  I take it that universalism as here intended is the doctrine that there are universals.  But what exactly are universals?  Here too a definition would be helpful.  And please note that a commitment to universals does not bring with it a commitment to entities that are wholly present in multiple places.  For example, van Inwagen thinks of properties as universals but, eschewing as he does constituent ontology, does not view them as present in the things that have them.

One distinction that needs to be made is that between transcendent and immanent universals.  A transcendent (immanent) universal is one that can (cannot) exist unexemplified.  A second needed distinction is between universals that enter into the  structure of the things that have them and those that don't.  Call the first constituent universals; call the second nonconstituent universals.  The two distinction-pairs cut perpendicular to each other yielding four combinatorially possible views according to which properties are: (a) transcendent non-constituent universals (Peter van Inwagen, e.g., if we leave aside haecceities); (b) immanent non-constituent universals (e.g., R. Grossmann); (c) immanent constituent universals (e.g., G. Bergmann, D. Armstrong); (d) transcendent constituent universals.

 

Tropes as Truth-Makers? Or Do We Need Facts?

Here is a white cube.  Call it 'Carl.'  'Carl is white' is true.  But Carl, though white, might not have been white. (He would not have been white had I painted him red.) So 'Carl is white' is contingently true.  There is no necessity that Carl be white.  By contrast, 'Carl is three-dimensional' is necessarily true.  It is metaphysically necessary that he be three-dimensional.  Of course, the necessity here is conditional:  given that Carl exists, he cannot fail to be three-dimensional.  But Carl might not have existed.  So Carl is subject to a two-fold contingency, one of existence and one of property-possession.  It is contingent that Carl exists at all -- he is not a necessary being -- and with respect to some of his properties it is contingent that he has them.  He exists contingently and he is white contingently.  Or, using 'essence' and 'accident,' we can say: Carl is a contingent being that is accidentally white but essentially three-dimensional.  By contrast, the number 7 is a necessary being that accidentally enjoys the distinction of being Poindexter's favorite number, but is essentially prime.

Some truths need truth-makers.  'Carl is white' is one of them.  Grant me that some truths need truth-makers.  My question is this: Can a trope do the truth-making job in a case like this or do we need a concrete fact?

Carl is white.  That is given.  Some say that (at least some of) the properties of particulars are themselves particulars (unrepeatables).  Suppose you think along those lines. You accept that things have properties -- Carl, after all, is white extralinguistically -- and therefore that there are properties, but you deny that properties are universals.  Your nominalism is moderate, not extreme.  Suppose you think of Carl's whiteness as a trope or as an Husserlian moment or as an Aristotelian accident. (Don't worry about the differences among these items.)  That is, you take the phrase 'Carl's whiteness' to refer, not to the fact of Carl's being white, which is a complex having Carl himself as a constituent, but to a simple item: a bit of whiteness.  This item depends for its existence on Carl: it cannot exist unless Carl exists, and, being particular, it cannot exist in or at any other thing such as Max the white billiard ball.  Nor is it transferrable: the whiteness of Carl cannot migrate to  Max. 

The truth-maker of a truth is an existing thing in virtue of whose existence the truth is true.  Why can't Carl's whiteness trope be the truth-maker of 'Carl is white'?  That very trope cannot exist unless it exists 'in' Carl as characterizing Carl.  So the mere existence of that simple item suffices to make true the sentence 'Carl is white.'  Or so it seems to some distinguished philosophers.

If this is right, then there is no need that the truth-maker of a truth have a sentence-like or proposition-like structure.  (For if a proposition-like truth-maker is not needed in a case like that of Carl the cube, then presumably there is no case in which it is needed.) A simple unrepeatable bit of whiteness has no internal structure whatsoever, hence no internal proposition-like structure.  A concrete fact or state of affairs, however, does: Carl's being white, for example, has at a bare minimum a subject constituent and a property constituent with the former instantiating the second.

My thesis is not that all truth-makers are proposition-like, but that some are.  Presumably, the truth-maker of 'Carl is Carl'  and 'Carl exists' is just Carl.  But it seems to me that the truth-maker of 'Carl is white' cannot be the particular whiteness of Carl.  In cases like this a simple item will not do the job.  Why not?

1. If it is legitimate to demand an ontological ground of the truth of a truth-bearer, whether it be a sentence or a proposition or a judgment or whatever, then it is legitimate to demand an ontological ground of the contingency of the truth of a truth-bearer.  If we have a right to ask: what makes 'Carl is white' true, then we also have a right to ask: What makes 'Carl is white' contingently or accidentally true as opposed to essentially true?  Truth and contingent truth are not the same.  And it is contingent truth that needs explaining.  If a truth-bearer is necessarily true, it may be such in virtue of its logical form, or because it is true ex vi terminorum; in either case it is not clear that the is any need for a truth-maker.  Does 'Bachelors are male' need a truth-maker?  Not as far as I can see.  But 'Tom is a bachelor' does.  Unlike David Armstrong, I am not a truth-maker maximalist.  See Truthmaker Maximalism Questioned.

2. The trope Carl's whiteness can perhaps explain why the sentence 'Carl is white' is true, but it cannot explain why it is accidentally true as opposed to essentially true.  For the existence of the trope is consistent  both with Carl's being essentially white and Carl's being accidentally white.  If F is a trope, and F exists, then F is necessarily tied to a concrete individual (this is the case whether one is a trope bundle theorist or a trope substratum theorist like C. B. Martin), and so the concrete indiviual exists and is characterized by F.  But this is so whether the concrete individual is essentially F or accidentally F.

3. To explain the contingency of a contingent truth it is not enough that the truth-maker be contingent; there must also be contingency within the truth-maker.  Or so it seems to me.  The fact theory can accommodate this requirement.  For in the fact of Carl's being white, the fact itself is contingent, but so also is the connection between Carl and whiteness.   Carl and whiteness can exist  without the fact existing.  (This assumes that whiteness is a universal)  The contingency of the connection of the constituents within the fact accounts for the contingency of the truth of 'Carl is white.'  But no trope is contingently connected to any concrete individual of which it is the trope. 

Peter van Inwagen's Trouble with Tropes

Concerning tropes, Peter van Inwagen says, "I don't understand what people can be talking about when  they talk about those alleged items."  (Existence: Essays in Ontology, Cambridge UP, 2014, p. 211.)  He continues on the same page:

Consider two tennis balls that are perfect duplicates of each other.  Among their other features, each is 6.7 centimeters in diameter, and the color of each is a certain rather distressing greenish yellow called "optical yellow."  Apparently, some people understand what it means to say that each of the balls has its own color -- albeit the color of one is  a perfect duplicate of the color of the other.  I wonder whether anyone would understand me if I said that each ball had its own diameter -- albeit the diameter of one was a perfect duplicate of the diameter of the other.  I doubt it.  But one statement makes about as much sense to me as the other -- for just as the diameter of one of the balls is the diameter of the other (6.7 centimeters), the color of one of the balls is the color of the other (optical yellow).

Although van Inwagen couches the argument in terms of what does and does not make sense to him, the argument is of little interest if he is offering a merely autobiographical comment about the limits of his ability to understand.  And it does seem that he intends more when he says that he doubts whether anyone would understand the claim that each ball has its own diameter.  So I'll take the argument to be an argument for the objective meaninglessness of trope talk, not just the PvI-meaninglessness of such talk:

1. It is meaningful to state that each ball has its own color if and only if it is meaningful to state that each ball has its own diameter.

2. It is not meaningful to state that each ball has its own diameter.

Therefore

3. It is not meaningful to state that each ball has its own color.

Therefore

4. Talk of tropes is meaningless.

The argument is valid, and (1) is true. But I don't see why we should accept (2).  So I say the argument is unsound.

I am not defending the truth of trope theory, only its meaningfulness.  I am maintaining that trope theory is a meaningful ontological proposal and that van Inwagen is wrong to think otherwise.

It is given that the two tennis balls have the same diameter.  But all that means is that the diameter of ball A and the diameter of ball B have the same measurement, 6.7 cm.  This fact  is consistent with there being two numerically distinct particular diameters, the diameter of A and the diameter of B. 

What's more, the diameters have to be numerically distinct.  If I didn't know that the two balls were of the same diameter, I could measure them to find out.  Now what would I be measuring?  Not each ball, but each ball's diameter.   And indeed each ball's own diameter, not some common diameter.   I would measure the diameter of A, and then the diameter of B.  If each turns out to be 6.7 cm in length, then we could say that they have the 'same diameter' where this phrase means that A's diameter has the same length as B's diameter.  But again, this is consistent with the diameters' being numerically distinct.

There are two diameters of the same length just as there are two colored expanses of the same color:  two yellownesses of the same shade of yellow.  So I suggest we run van Inwagen's argument in reverse.  Just as it is meaningful to maintain that the yellowness of A is numerically distinct from the yellowness of B, it is meaningful to maintain that the diameter of A is numerically distinct from the diameter of B.  Looking at the two balls we see two yellownesses, one here, the other there.  Similarly, measuring the balls' diameter,  we measure two diameters, one here, the other there. 

Again, this does not show that trope theory is true, but only that it makes sense.  It makes as much sense as van Inwagen's proposal according to which optical yellow is an abstract property exemplified by the two balls.

Related articles

Van Inwagen on the Univocity of 'Exists'

A Second Van Inwagen Argument for the Univocity of 'Exists'

'Something is Self-Identical' Cannot Translate 'There are Objects': Another Argument Against the Thin Theory

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

Zygotic Division: Was I Once a Zygote?

 

God, Simplicity, and Tropes

A reader asks,

In your Stanford Encyclopedia of Philosophy divine simplicity article you draw a helpful  comparison toward the end between trope theory and divine simplicity. However it left me wondering in what way the claim that 1) God is simple differs from the claim that 2) God is just a trope of divinity?

Excellent question.  But can I answer it?  Here is what I said in the SEP entry:

Tropes are ontologically simple entities. On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on one version of trope theory) or by being a substratum in which a redness trope inheres (on a second theory). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ Thus a redness trope is red, but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness. In this respect it is like God who is what he has. God has omniscience by being (identical to) omniscience. Just as there is no distinction between God and his omniscience, there is no distinction in a redness trope between the trope and its redness. And just as the simple God is not a particular exemplifying universals, a trope is not a particular exemplifying a universal. In both cases we have a particular that is also a property, a subject of predication that is also a predicable entity, where the predicable entity is predicated of itself. Given that God is omniscience, he is predicable of himself. Given that a redness trope is a redness, it is predicable of itself. An important difference, of course, is that whereas God is unique, tropes are not: there is and can be only one God, but there are many redness tropes.

Not only is each trope identical to the property it has, in each trope there is an identity of essence and existence. A trope is neither a bare particular nor an uninstantiated property. It is a property-instance, an indissoluble unity of a property and itself as instance of itself. As property, it is an essence, as instance, it is the existence of that essence. Because it is simple, essence and existence are identical in it. Tropes are thus necessary beings (beings whose very possibility entails their actuality) as they must be if they are to serve as the ontological building blocks of everything else (on the dominant one-category version of trope theory). In the necessity of their existence, tropes resemble God.

If one can bring oneself to countenance tropes, then one cannot object to the simple God on the ground that (i) nothing can be identical to its properties, or (ii) in nothing are essence and existence identical. For tropes are counterexamples to (i) and (ii).

In the SEP article I was merely trying to "to soften up the contemporary reader for the possible coherence of DDS . . . by adducing some garden variety examples of contemporary philosophical posits that are ontologically simple in one or more of the ways in which God is said to be simple."  I was not suggesting that God is a divinity trope.

But perhaps this suggestion can be developed.  Perhaps God can be usefully viewed as analogous to a trope, as a divinity trope. One thing is clear and must be borne in mind.  God is a stupendously rich reality, the ne plus ultra of absoluteness, transcendence, and alterity.  He cannot easily be brought within the human conceptual horizon.  If you are not thinking of God in these terms, you are probably thinking like an atheist, as if God is just one more being among beings. God, however, is nothing like that famous piece of (hypothetical) space junk, Russell's teapot. 

Given the divine transcendence and absoluteness, one cannot expect God to fit easily into any presupposed ontological framework  developed for the purpose of understanding 'sublunary' items.  God is not a trope among tropes any more than he is a substance among substances or a concrete particular among concrete particulars. Two points. First, there are indefinitely many redness tropes, but there cannot be indefinitely many divinity tropes.  If God is a trope, then he is an absolutely unique trope.  Second, no concrete 'sublunary' item is identical to a single trope.  (I trust my astute readers understand my use of 'sublunary' here.) Many tropes enter into the constitution of any ordinary particular.  But if God is a trope he must be absolutely unitary, enfolding all of his reality in his radical unity. So 'trope' needs some analogical stretching to fit the divine reality.

To answer the reader's question, God cannot be a trope among  tropes.  But an analogical extension of the trope conception in the direction of deity may be worth pursuing.

Related articles

What Exactly is an Ontological Constituent?

E. J. Lowe on the Distinction Between Constituent and Relational Ontology

Reply to Ken Hochstetter on Divine Simplicity

Relational Ontology, Constituent Ontology, and Divine Simplicity

Tropes

Donald Cary Williams

Radde-Gallwitz on Divine Simplicity

Trope Simplicity and Divine Simplicity Compared

I concluded my Stanford Encyclopedia of Philosophy entry on the divine simplicity with an attempt at softening up the contemporary reader for the possible coherence of the doctrine of divine simplicity  by adducing some garden variety examples of contemporary philosophical posits that are ontologically simple in one or more of the ways in which God is said to be simple. I gave the example of tropes.  One might of course proceed in the opposite direction by tarring tropes with a close cousin of the (alleged) absurdity of the  doctrine of divine simplicity.  You decide whether there is anything to my comparison:

Tropes are ontologically simple entities. On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on one version of trope theory) or by being a substratum in which a redness trope inheres (on a second theory). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ Thus a redness trope is red , but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness. In this respect it is like God who is what he has. God has omniscience by being (identical to) omniscience. Just as there is no distinction between God and his omniscience, there is no distinction in a redness trope between the trope and its redness. And just as the simple God is not a particular exemplifying universals, a trope is not a particular exemplifying a universal. In both cases we have a particular that is also a property, a subject of predication that is also a predicable entity, where the predicable entity is predicated of itself. Given that God is omniscience, he is predicable of himself. Given that a redness trope is a redness, it is predicable of itself. An important difference, of course, is that whereas God is unique, tropes are not: there is and can be only one God, but there are many redness tropes.

Not only is each trope identical to the property it has, in each trope there is an identity of essence and existence. A trope is neither a bare particular nor an uninstantiated property. It is a property-instance, an indissoluble unity of a property and itself as instance of itself. As property, it is an essence, as instance, it is the existence of that essence. Because it is simple, essence and existence are identical in it. Tropes are thus necessary beings (beings whose very possibility entails their actuality) as they must be if they are to serve as the ontological building blocks of everything else (on the dominant one-category version of trope theory). In the necessity of their existence, tropes resemble God.

If one can bring oneself to countenance tropes, then one cannot object to the simple God on the ground that (i) nothing can be identical to its properties, or (ii) in nothing are essence and existence identical. For tropes are counterexamples to (i) and (ii).

Bradley's Regress and the 'Adicity' of Compresence: Is it Dyadic, Triadic, or N-Adic?

This is an addendum to Trope Theory Meets Bradley's Regress.  In that paper I touched upon the question whether the compresence relation is dyadic or not, but did not delve into the matter in any depth.  Now I will say a little more with the help of George Molnar's excellent discussion in Powers: A Study in Metaphysics (Oxford 2003), pp. 48-51.  Molnar draws upon Peter Simons, "Particulars in Particular Clothing: Three Trope Theories of Substance (Philosophy and Phenomenological Research, September 1994, 553-575), which I have also consulted.