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Wednesday, March 30, 2016


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Is it a bird? Is it a plane? No, it’s Mighty Metaphysician! What a thrill to watch Bill in full philosophical flight! I rise and applaud. Yet one passage blocks my progress toward full understanding.

Bill says that “[a] trope is not a property instance on one clear understanding of the latter.” But many philosophers insist that a trope is a property instance, including Bill himself in Section 7 of his superb article on Divine Simplicity in the Stanford Encyclopedia of Philosophy: “It [the trope] is a property-instance, an indissoluble unity of a property and itself as instance of itself.” Concurring philosophers include Lowe (1998, 78, 196), Denkel (1996, 172), Ellis (2001, 25), Heil (2015, 114), and MacDonald (2005, 250). On my own feeble analysis, a trope is indeed a property instance, but not of the garden variety. More precisely, a trope is a property self-instantiation or self-exemplification. Bill makes a similar observation in Section 7 of that Divine Simplicity article: “Given that a redness trope is a redness, it is predicable of itself.” Let’s look at this matter and its consequences more closely. We can begin with the distinction that Garcia draws between “a singly-characterizing property” and “a singly-charactered object” (2015, 133). As he indicates, “a trope is a singly-characterizing property (133). This means, of course, that a trope is not itself characterized by its own characterizing property. For example, a trope of redness is not itself red, nor is a trope of sphericity itself spherical. Yet Bill states that “a redness trope is red . . . by being (a bit of) redness.” This inevitably suggests that the redness trope, a characterzing property, is itself characterized by its own property. Somehow, the trope has changed from a property, understood as an abstract, non-spatio-temporal particular, to a concrete, spatio-temporal particular. That is, somehow the trope has changed from being unextended to being extended (as a little bit of red). Here we should note that Bill himself elsewhere reminds us that both “properties” and “extensionless points” are “unextended” (1992, 517). So a question arises. How did the redness trope change in this fashion? Certainly not by ordinary instantiation, because such instantiation requires something in which to be instantiated and, according to the one-category ontology of trope theory, all we have are tropes or particularized properties. To say that the trope is instantiated by the sole object having that property would be a mistake, because the object or concrete particular consists entirely of (compresent) tropes. The only remaining alternative, therefore, is self-instantiation or self-exemplification: the redness trope becomes a little bit of redness by exemplifying itself. To interpolate Smith’s formula (in a commentary on Vallicella 1992), a trope is “not exemplifiable by anything other than” itself (2013, 94). Thus a metaphysical entity becomes a physical one. But not so fast. The trope does not do this on its own. Etiquette requires that tropes concur or compresent in a trope-bundle, which in turn constitutes the object or concrete particular to which it pertains. Thus, the trope-bundle entails the concurrence or compresence of trope self-exemplifications. But from this it follows that object itself is a self-exemplification and not an object simpliciter. In other words, the object as concrete particular is an exemplification of itself as an abstract particular. At this point I fall down the rabbit hole. Perhaps I dug it myself.

Thank you for the comments, Eric, and for getting me back thinking about this topic.

>>Bill says that “[a] trope is not a property instance on one clear understanding of the latter.” But many philosophers insist that a trope is a property instance, including Bill himself in Section 7 of his superb article on Divine Simplicity in the Stanford Encyclopedia of Philosophy: “It [the trope] is a property-instance, an indissoluble unity of a property and itself as instance of itself.”<<

Philosophy is magnificent in aspiration but miserable in execution. Part of what makes it miserable is terminological fluidity. Almost every term in philosophy is used in different ways by different philosophers. 'Trope' and 'property instance' are prime examples. As I explained 'trope' and 'property instance' above, a trope is not a property instance. That other philosophers conflate the terms is irrelevant.

Do you have the complete bibliographical data for Garcia's article? He seems to have no understanding of trope theory if he in fact says or implies that >> For example, a trope of redness is not itself red, nor is a trope of sphericity itself spherical.<<

That can't be right. Right now I am staring at a red rubber ball. I see the redness of the ball. (If I didn't, how would I know, as I do know, that the ball is red?) On trope theory the redness I see (the exact shade of redness) is a particular, not a universal. The redness of a second rubber ball of the same shade of red is numerically distinct from the redness of the first ball.

It should be obvious that these redness tropes are themselves red. After all, they are open to visual inspection. Each is a visible bit of redness.

Anyone who doesn't understand this does not understand trope theory. So let's discuss this point and this point alone until we come to agreement. In every short exchanges.

Here is the Garcia reference: Robert K. Garcia, “Is trope theory a divided house? In The Problem of Universals in Contemporary Philosophy. Edited by Gabriele Galluzzo and Michael J. Loux (Cambridge UP, 2015). 133-155.

The core of his discussion concerns the distinction between something which is a characteristic (that is, a property) and something which is charactered (that is, the object): “[T]here is the concept of something which is charactered but not itself a property or characteristic. I will call the latter the concept of an object” (140). Hence, “it is in virtue of having a trope (troper) that an object is charactered in some way” (133). In summary, “The basic difference between tropes and tropers can be put as follows: If the sphericity of an object is a troper, then the sphericity is itself spherical; if the sphericity of an object is a trope, then the sphericity is not itself spherical. In effect, a troper is a singly-charactered object, whereas a trope is a singly-characterizing property” (133).

When you look at the redness of the red rubber ball, what do you see: the trope as a characterizing property or the object as charactered by the property?

Thanks for the reference. I wonder if someone can send me a pdf of Garcia's paper. As I recall, he commented here some years back.

This seems a bizarre and unnecessary terminology. Garcia seems to alluding to the distinction mentioned above between a trope as a property and a trope as a (junior) substance or object. On standard trope theory -- which alone is under discussion here -- the sphericity of a ball is at once both a property of the ball and a particular in its own right.

That's the theory. Whether it is coherent is a further question.

>>When you look at the redness of the red rubber ball, what do you see: the trope as a characterizing property or the object as charactered by the property?<<

When I look at a red ball - red all over -- I literally (with my eyes) see red at the ball or on the ball. I see red where the ball is. The point I have just made is purely phenomenological, and thus pre-theoretical. It does not entail trope theory. Nor does it entail the theory that what I see is literally a universal. The phenomenological datum is consistent with both theories. If I were an adherent of trope theory I would say what I see is a trope as a property of the ball and also as an ontological part of the ball that is itself red.

In other words, if the redness of the ball is a trope, then this redness is at once both a property of the ball and a constituent of the ball, a proper constituent that is itself red.

Perhaps I can see where Garcia is coming from, with his distinction between the trope as a singly-characterizing property and a troper (that is, the feature corresponding to the instance of the trope) as a singly-charactered object. MacDonald epitomizes the conventional view of the distinction between the characterizing property and the characterized thing: “We tend to suppose on the basis of it that although substances possess properties they are distinct from them. They are, so to speak, things characterized, rather than things that characterize” 2005, (82). Conventionally in metaphysics, things have properties, and they have them through exemplification. MacDonald confirms: “[O]n the standard way of construing the relation between a thing and its properties, a thing has a property by exemplifying it” (2005, 221). In the Aristotelian dispensation, for example, “the instances instantiate the properties” (2005, 237). Here the property is the characteristic, and the characteristic, metaphysically speaking, is a necessary, unextended, and non-spatio-temporal entity. We don’t see properties, in this sense. The property of sphericity is not itself spherical. But through exemplification or instantiation, a property as a characteristic correspondingly (that is, in accordance with its own attribute) characterizes the object in which it inheres. The property of sphericity characterizes the object as spherical.

But this model gets skewed in trope theory, where the object is nothing more than a bundle of tropes, and the distinction between a thing and its properties breaks down. Let’s see how this happens. To begin with, as a bundle theory, trope theory, in MacDonald’s formulation, “reduces substances to their properties” (2005, 82). But this reduction, I submit, both invokes and fudges conventional distinction, discussed above, between a property and its instantiation. On the one hand, tropes are properties, and hence are unextended. But on the other hand, tropes are property-instances, and hence are extended. Let’s see how MacDonald formulates this. First, her remark about tropes as properties: “[T]tropes are ‘particularized properties’, such as this redness, this roundness, and so on: properties that are as particular as the particular things that they constitute” (2005, 238). Next her remark about tropes as instantiations: “What it suggests is not that individual substances, such as apples, are literally constituted by abstract entities such as the property, red. Rather, it suggests that they are constituted by the particular instantiations of, or instances of those properties – what we might call ‘particularized properties’, or tropes, such as redness-in-place-p-at-time-t” (2005, 89).

We reach now the issue that baffles me and opens up the rabbit hole. According to trope theory, objects (concrete particulars) are constituted by the compresence of tropes (abstract particulars or particularized properties). But how are we to construe this compresence? Do tropes first congregate as properties, and then change into property instances? Of course, this sounds deliberately absurd. But what is the correct way of construing compresence? Remember, the distinction between a property and its instantiation. Properties are abstract attributes, like roundness and sphericity. For sure, they do not themselves exemplify their own attributes. But on instantiation they do. When thinking of trope compresence, are we therefore to postulate that an appropriately configured spherical contour and an appropriately extended red combine to constitute the trope-bundle of a ball? What has happened to properties as such – those entities without extension? And how do properties (those unextended entities) get transformed into property-instances (those extended features) without anything in which to inhere?

Really, this dispensation seems more like Arts & Crafts then metaphysics to me. Let’s make a red ball. We’ll take a nice instance of extended redness, attach it to a nice instance of rounded contour, add some other constituent tropes, and voilà! Let’s play tennis. You hit the ball back to me! But wait. I can anticipate, from your initial entry, how you might respond. “A trope is not a property instance on one clear understanding of the latter,” you wrote. Instead, according to Maurin, a trope “can be adequately categorized both as a kind of property and as a kind of substance.” Therefore, as you also wrote, “a trope is what it has,” and what it has is its own nature as itself: this bit of characterized substance.

Yet the equivocation in trope theory between the trope as property and the trope as substance makes no sense whatsoever to me. It does, as you note, bypass the problem of instantiation, but in so doing it also bypasses the distinction between abstract and concrete. Down the rabbit hole I go.

>>We reach now the issue that baffles me and opens up the rabbit hole. According to trope theory, objects (concrete particulars) are constituted by the compresence of tropes (abstract particulars or particularized properties). <<

That's right. Just bear in mind that 'abstract' in this context does not mean 'non-spatio-temporal.' Bear in mind also that 'particularized properties' may be misleading. The idea is that properties occur in reality only as particulars (unrepeatables). Thus there is no need for properties to be particularized; they are always already particulars. Thus I prefer to say that tropes are properties construed or "assayed" (a bit of jargon from G. Bergmann) as particulars. I prefer not to say that tropes are particularized properties. And when I use 'property' I mean that word pre-theoretically.

>>But how are we to construe this compresence? Do tropes first congregate as properties, and then change into property instances?<<

No. Please read carefully what I wrote immediately above.

>>Of course, this sounds deliberately absurd. But what is the correct way of construing compresence?<<

Compresence is an equivalence relation (reflexive, symmetrical, and transitive)that connects every trope in a trope bundle to every other one in that bundle.

>>Remember, the distinction between a property and its instantiation. Properties are abstract attributes, like roundness and sphericity.<<

No. Here is where you are going wrong. Note first that there is no instantiation in trope theory (standard trope theory as a one-category ontology). A concrete particular (a red ball) does not instantiate any tropes and no trope instantiates any trope. Nor does a trope in a class of exactly resembling tropes instantiate anything. Class membership is not instantiation. And neither is compresence. For one thing, compresence is symmetrical while instantiation is not.

Furthermore, how are you using 'abstract'?

>>For sure, they [roundness and sphericity] do not themselves exemplify their own attributes.<<

This is right if you are speaking of non-spatio-temporal multiply instantiable properties. But there is no place for such properties in trope theory. Don't forget: TT is a one-category ontology. Everything is a trope or a construction from tropes.

>>But on instantiation they do.<<

Again, one cannot speak of instantiation *strictu dictu* on trope theory. A trope is not the result of the instantiation of a multiply instantiable platonic property by a concrete individual. It is a sui generis item.

>>When thinking of trope compresence, are we therefore to postulate that an appropriately configured spherical contour and an appropriately extended red combine to constitute the trope-bundle of a ball?<<

Yes -- along with other tropes.

>> What has happened to properties as such – those entities without extension? And how do properties (those unextended entities) get transformed into property-instances (those extended features) without anything in which to inhere?<<

Again, you seem not to be grasping the fundamental idea behind trope theory as a one-category ontology. On trope theory there are no unextended (non-spatio-temporal) properties. TT is a moderate nominalism. It is nominalistic in that it holds that everything is a particular: there are no universals (repeatables). It is moderate as opposed to extreme because properties on trope theory are extralinguistic.

Furthermore, unextended properties don't need to get transformed into property instances since there are no swuch properties, ande because tropes are not property instances.

You want to construct tropes out of something more basic; but the whole idea is that there is nothing more basic than tropes. Again, it is a one-category ontology and the members of that category are tropes.

Please note that I am merely explaining trope theory, not advocating it. On my view it is incoherent.

Thank you very much, Bill. Your comment was extremely helpful. Might I respond off the cuff?

One sticking point concerns trope self-instantiation. In the DDS article, you appear to affirm it: “It [the trope] is a property-instance, an indissoluble unity of a property and itself as instance of itself.” But in your most recent comment, you explicitly deny it: “no trope instantiates any trope.” Yet, many commentators whom I have earlier cited refer to tropes as property instances, and we know that, as MacDonald states, “instances instantiate the properties” (2005, 237). Right now, from what you just wrote, it seems to me that tropes are being treated as reified properties, such that sphericality, for example, becomes this spherically contoured extension and redness becomes this redly coloured extension, and so on.

The temptation to construe a trope as a reified property is further provoked by Maurin’s conflation of property and substance in the passage you quoted: “. . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance.” This conflation sets up an aporia for me, blocking my passage toward understanding.

To begin with, if the trope property is also a substance, do we not here have a two-category ontology, not a one-category ontology? Or can trope theory have its cake and eat it too?

Second, the conflation of property and substance seems to violate the distinction between these two types of entity. Loux, for example, cites “a long tradition (one stemming from Aristotle) in which the term ‘substance’ is used in contrast with the term ‘attribute,’ so that substances are particulars than can exemplify attributes, but cannot themselves be exemplified” (1978, 107). Lowe points to a related distinction between substance and property: “Thus a substance is often conceived to be an object which does not depend for its existence upon anything else. Again, properties are often said to depend for their existence upon the objects which possess them” (1998, 137). So in the context of this well-established metaphysical convention, how can property and substance coincide?

Perhaps we are unwittingly drafting a book entitled Trope Theory for Dummies, with me as the dummy.


Let's not worry about the misleading things I and others have written in various publications. The interesting questions are: What is trope theory? and Is it coherent?

Please note also that we must distinguish between ordinary language and philosophical terminology. 'Instantiation' is a piece of phil. terminology. I defined first-order instantiation as a two-termed asymmetrical relation that connects a concrete individual to a first-order property.

There is no room in trope theory for instantiation thus defined. So none of the following make sense on TT:

a. A red ball instantiates a redness trope.
b. A redness trope instantiates the universal, redness.
c. This redness trope instantiates this sphericity trope.
d. This redness trope instantiates itself.

And the same goes for 'instance' used as a technical term, mutatis mutandis.

Do you agree?

Your excellent suggestion that we address both the content of trope theory and the question of its coherence points the way forward, in a manner recalling Husserl’s exhortation, “To the things themselves!” But a preliminary difficulty arises: how can trope theory – the real trope theory – be detached – or abstracted (!) – from the “misleading things written in various publications”? To begin with, as Maurin states in her admirable SEP article, the only proposition that trope theorists are obliged to agree on is that there are tropes: “Apart from this very thin core assumption—that there are tropes—different trope theories need not have very much in common.” Indeed, Garcia refers to trope theory as “a divided house.” And if trope theory is incoherent, then the house in question might suffer the same fate as Poe’s House of Usher!

As a result of this dissension and diversity, right now I really do not know what a trope is, according the extant trope theory. For example, the father of trope theory, D.C. Williams, in that inaugural article (1953, rpt 1997) distinguishes between “gross” and “finer” or “abstract” parts in an object (such as one of those lollipops), assigning the term, “trope,” to the latter. Daly encapsulates the confusion entrained by this typology: “But then it is unclear what the rationale is for saying that certain parts are tropes, and that certain other parts are not. It is unclear how “fine” or “abstract” a part must be for it to qualify as a trope” (142). I fall down the rabbit hole when Williams declares that “[a] whole soul or mind, if is not a unique immaterial substance on its own, is a trope” (rpt. 1997, 124). Climbing out is not aided by his companion claim: “Thus a cat and the cat’s tail are not tropes, but a cat’s smile is a trope, and so is the whole whose constituents are the cat’s smile plus her ears and the aridity of the moon” (1997, 115).

And then (but the list could extend indefinitely), there is Armstrong’s admonition: “Form and volume are therefore best considered not as tropes in their own right at all. Real tropes are qualities-of-a-formed-volume. The distinctions we can make between color, shape, and size are distinctions in thought to which correspond no distinction in reality” (1992, rpt. 1997,137). Here two problems arise: (a) the now familiar one concerning what is a trope and (b) ambiguity regarding whether tropes are phenomenal or mind-independent entities. Regarding the former, the dispute whether form is a trope constitutes a good example of dissension among trope theorists. Armstrong declares that form is not a trope, whereas Garcia (in that chapter cited earlier) says that it is (citing the example of sphericity). Regarding the latter problem (tropes as phenomenal or mind-independent, Maurin views them as mind-independent. But according to many other analyses, they seem not to be. Indeed, Maurin’s appeal to Husserl’s phenomenology when explicating tropes tends to tip the scale toward the phenomenal side, as does the recurrent reference, throughout trope literature, to the colour, red.

So if one of our goals is to address the question, “What is trope theory?” how can we proceed? Is the question now not “What is trope theory? but “What should trope theory be?”

Obviously, we can't proceed profitably unless we focus on one version of TT such as standard TT as a one-category ontology.

I note that you didn't answer my question above.

Yes, I now agree that tropes do not involve instantiation. Your explication is extremely illuminating, and dispels much confusion. Trettin supports it:

A trope is an individual quality. It is individual in that it is unique and not repeatable, although it will have various degrees of similarity to other individuals. What a trope conveys is its particular quality or individual nature. Thus, a trope of redness resembles another trope of redness, because each of them respectively is the individual redness it is. In accordance with K. Campbell, I propose that the individuality of tropes is basic and unanalyzable (Campbell 1990, p. 69). Tropes, as I conceive of them, are not particular accidents or modes of something. Nor are they property instances. These conceptions make use tacitly or explicitly of some entities which do the particularizing or which have to be instantiated. (2000, 283-84)

Simons also avoids the notion of instantiation, but by different means. He views (some) tropes as “particularized ways” (1994, 565) – a notion that seems very close to Lowe’s notion of modes (which I shall now quote):

A mode is a particular way something is. For instance, a solid material object, such as a rubber ball, will be shaped in a particular way and coloured in a particular way at any given time. Its being shaped in that way – say, spherically, with such-and-such a radius of curvature – is a mode of the ball, and its being coloured in that way – say, redly, with such-and-such a hue – is likewise a mode of the ball. (Lowe, 1998, 78)

By the term, “particularized ways,” Simons means “how something is”:

How something is is something about it, but not a part of it. Examine all the parts of a complex artifact, like an airplane. You will find its wings, its radar systems, its engines, its ailerons, etc., down to smaller parts like bolts, rivets, transistors, and bits of cable. You will not find its being 1005 tonnes in weight among them. Parts is one thing, properties another (and properties of parts something else again). (Simons, 1994, 563)

Thus, according to Simons, tropes are not things, but of things: “But they are not THING-like, if by that we mean substance-like. They are not res, they are rei or rerum” (1994, 565, upper case in original).

Now we reach one source of my confusion: the problem of thing-construction. In the passage quoted above, Simons distinguishes parts from properties. But how do (properly bundled) properties and only properties (in the one-category ontology of trope theory) constitute things (concrete particulars)? Ujvári distinguishes between abstract and concrete parts (terminology in trope theory can be ambiguous and contradicting), such that “Napoleon’s forelock does not quality as a trope, although it is particular and is a part of Napoleon, while his posture does qualify as a trope” (2012, 59). But again, how does the compresence of tropes as abstract particulars constitute a concrete particular?

Might we consider the example of a tomato? There is the tomato on the kitchen counter. How do tropes, duly bundled, constitute that tomato? I know that one trope will account for its redness, another for its weight, another for its size, another for its shape, another for its taste or flavour, another for its firmness. But how do we get a tomato that we can eat? No doubt there is a textural consistency trope for the pulp. Yet I still don’t know how we get the tissue, if I might call it that, of the tomato. Do we invoke something like “the property of having this pulp,” for example? Maurin’s example of the constituting of a ball doesn’t help me. Duly compresencing “a red-trope, a round-trope, and a soft-trope . . . so as to form a bundle (e.g. this ball)” comprising ” this redness, this roundness and this softness” does not seem to be enough to construct a ball that we can throw (2002, 133). What am I missing here? The SEP article on D.C. Williams does not resolve my quandary: “In Williams's scheme, each of these [i.e. concrete particulars] consists in a compresent cluster of tropes—the particular thing's particular shape, size, temperature, and consistency, its translucency, or acidity, or positive charge, and so on” (original emphasis).

If tropes are the alphabet of being, how do they manage to constitute a bowl of alphabet soup?


I agree with Trettin. That's the way I see it.

Lowe is talking about items that are rather like Aristotelian accidents. As I argue before, tropes should not be conflated with Aristotelian accidents.

One of the central questions here is whether there is any sense of 'part' according to which it would make sense to say that a property of a thing is a part of it. One thing is clear: bolts, nuts, resistors, capacitors, bits of wire and their physical parts are certainly not properties of the things they are parts of.

I still don’t understand how tropes constitute a concrete tomato! Can you dispel my incomprehension? I would be deeply grateful for enlightenment. Otherwise, I am just spinning my wheels.

Regarding that Lowe quotation concerning modes, I cited it because, out of context, it provided a perfect paraphrase of Simons’ notion of “particularized ways.” In fact, in rejecting the notion of tropes, Lowe views his own notion of “modes” as a substitute for and improvement on it: “As an example of non-objects I would cite modes – the items that other philosophers have variously called “tropes,” “property instances,” “particular qualities,” or “individual accidents” (1998, 78).

You would, I think, very much like Márta Ujvári, The Trope Bundle Theory of Substance: Change, Individuation and Individual Essence (2012). She sheds more light on trope theory, but still does not answer my question about the tomato. She too, by the way, rejects the notion that tropes are property instances, and construes tropes instead as property particulars: “[A] trope can be identified as a property particular that belongs to a concrete particular” (2012, 18).

Ujvári does attempt to answer my question about the tomato in two ways: (a) with respect to the epistemology of the object and (b) with respect to the ontology of the object. Regarding the first, she claims that, epistemologically speaking, an object is known through its qualities: “[A] substance, epistemologically speaking, is nothing for us but a bunch of qualitative features. In this way there arises a top-down conceptual necessity proceeding from the existing entity to its constituting items” (2012, 141). Regarding the second, she adroitly exploits the abstractness of tropes as a means of establishing the concreteness of the object they compresently constitute. Tropes belong to the ontological category of abstracta because, as “a quality instance” (oops, she used that forbidden term, “instance), they cannot, unlike individual substances, support a qualitative manifold (2012, 17). BUT through their compresence, tropes as abstracta constitute the qualitative manifold which is the concrete object:

[I]t is shown that the individuation of concrete individual substances is independent, in crucial respects, from the fact that they are construed as bundles of tropes. For, concrete individual substances are the bearers of qualitative manifolds qua qualitative manifolds, while each constituting abstract trope encompasses only one qualitative feature. Bearing a manifold of qualitative features is one criterion of concreteness implying also independence. Thus, the concrete individual substances have the emergent property of independence even if they are construed as bundles of tropes (2012, 9).

I have many more questions about tropes. But the most pressing of them concerns how trope theory accounts for the constitution of an actual object.

With respect to the distinction between parts and properties, Simons draws attention to it in the passage quoted at greater length in my preceding comment: “How something is is something about it, but not a part of it” (1994, 563). Denkel emphatically corroborates: “Properties are not parts” (1996, 40). He continues: “Thus parts cannot exist in an interpenetrated fashion without sharing some of their parts, whereas the elements of a bundle do so without every sharing any of their own parts.” However, according to Lowe, trope theory blurs the distinction between properties and parts: “By the same token, the trope theorist’s thesis that things such as rubber balls and leaves are 'bundles' of tropes can be seen as involving a confusion between properties and parts. A particular redness is not a part of a red rubber ball, as the trope theorist would have it – not even a 'dependent' part – but is, rather, something predicable of the ball" (1998, 208). Heil blends the two terms, properties and parts, in this passage: “If you are attracted to the idea that objects are bundles of properties, if you are suspicious of ‘substrata,’ you will want properties themselves to be particulars. One difficulty is in understanding properties as parts that add up to objects” (2105, 120). Heil also suggests that Williams fuses properties and parts: “Properties, considered as tropes, are, as Williams says, parts of objects in the sense that they make up or compose objects: objects are nothing more than collections, or sums, or ‘bundles’ of tropes” (2015, 131). Garica refers to properties as “metaphysical parts”: "And, a concrete object is charactered as it is in virtue of having properties as metaphysical parts” (2015, 135). By the way, in PTE, you draw an excellent distinction between whole and part: “A proper part of a whole is distinct from the whole of which it is a part, yet the whole cannot exist without the part. The whole is ontologically dependent upon its parts, but not vice versa” (2009, 219).


Ujvari's book is available at ASU and I will snag it before long. Thanks again for bringing it to my attention. Her 'property particular' is a felicitous phrase.

Could we summarize your main difficulty by saying that you cannot see how there could be any sense of 'part' according to which the properties of things are parts of it?

If yes, then you are a nonconstituent ontologist in my PTE sense. But this has its own extremely vexing problems. Did you see my critique of van Inwagen on this?

I am presently writing a post on the various senses of 'abstract.' This term has been insufficiently clarified.

But now I have to suit up for a hike in the Superstition Wilderness and after that the old man has to take a nap and so I may not get that entry posted today.

Thanks again for the intriguing discussion and the references. I plan to respond to your latest long missive as well in which you mention John Hospers whose book I too used as an undergraduate.

Hi Bill,

But properties are distinct from parts.

Regarding the various senses of "abstract," the following list, just compiled, might be useful:

Definitions of “Abstract”

Ujvári (2012): Regarding the category of abstracta, she offers three criteria: (i) their existence depends upon the existence of those things to which they belong, (ii) they cannot bear a manifold of qualitative features, and (iii) “what they are instances of, are properties featuring the substance only from one aspect. Thus they are not concrete in the sense of comprising all features of the substance” (66).

MacDonald (2005): “Further, they hold that universals, unlike concrete things, are such that many of them can be either in the same place at the same time or exemplified in the same place at the same time (and so are abstract)” (224). “Second, properties and relations of abstract objects may need to be acknowledged. But such objects have no spatio-temporal location and so they cannot instantiate Aristotelian universals, there being nowhere for such universals to be” (238). “On one way of understanding it, the properties that constitute substances are understood to be abstract universal things. They are abstract in the sense that many of them can be in the same place at the same time (as when, for example, the properties of being red and being round are both in the same place as the red round ball currently sitting on my desk), and universal in that they can be exemplified in many places at the same time, as when, for example, both the red ball and the red cup on my desk exemplify one and the same property, red. These entities, such as red and round, are different from the things that exemplify or instantiate them, things like red, round apples. When we say such things as ‘the [end 88] property, green, is not the property, red, although both are colour properties’, we are talking about properties as abstract universal things” (88-89).

Vallicella: (1992) “Causally inert” (551).

Denkel (1996): “interpenetrable”: “For the Tropes View the fact of inherence presents a major problem calling for explanation; we need to know why invariably interpenetrable abstract properties locate themselves tightly within compresences without falling apart” (187).

Universal: “Conversely, anything abstract is universal and, perhaps with the exception of entities such as sets and numbers, mind-dependent” (188).

Mellor and Oliver, 1997: “Sets are usually taken to be abstract entities, by which…is usually meant that they lack causes, effects and spatio-temporal location” (23).

Williams 1953, rpt. 1997: Re: Abstract: “One of them is the use of the “abstract” to mean transcending individual existence, as a universal essence, or Platonic idea is supposed to transcend it (121). At its broadest the ‘true’ meaning of ‘abstract’ is partial, incomplete, or fragmentary, the trait of what is less than its including whole” (122).

Campbell: 1981, rpt. 1997: Concrete vs. Abstract: “. . . an item is abstract if it is got before the mind by an act of abstraction, that is, by concentrating attention on some, but not all, of what is presented. A complete material body, a shoe, ship, or lump of sealing wax, is concrete; all of what is where the shoe is belongs to the shoe – its color, texture, chemical composition, temperature, elasticity, and so on are all aspects or elements included in the being of the shoe. But these features or characteristics, considered individually, e.g. the shoe’s color or texture, are by comparison abstract” (126).

Lowe 1998: “Both electrons and parts of stuff are concrete entities, that is, entities which exist in space and time (by contrast with abstract entities such as numbers and sets” (77). “an ‘abstract’ entity is one which exists in neither space nor time” (180).

Heil (2015): On abstraction: “A particular billiard ball’s sphericality is abstract, not in the sense of its falling short of being fully ‘concrete,’ but in the sense that its ‘separation’ from the ball is a matter of abstraction, Locke’s ‘partial consideration,’ an exercise of our capacity for considering the ball’s shape as distinct from considering its color or considering the ball itself. The idea is not that, in abstracting, we manufacture abstracta; abstraction (partial consideration) is what enables us to apprehend abstracta” (119).

Vallicella: (2002): “Tropes are particularized properties or abstract particulars: the particular smell of this coffee, the shape of that cup, the purple of yonder mountain. 'Abstract' here does not mean non-spatio-temporal, but partial or incomplete” (221.

Lowe (2002): “Rather, the implication of calling tropes ‘abstract’ in this sense is that , unlike ‘concrete’ objects that possess them, they are ontologically dependent entities which are incapable of existence ‘separately’ from such concrete objects” (367).

I have just read your outstanding explication of the term, "abstract." I shall re-read and ponder, then read again. Meanwhile, might I submit a little more on the problem of compresent tropes constituting a concrete particular?

The Emperor’s Clothes Revisited or Trope Theory Interrogated

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” (2105, 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.”

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?

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? 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 later, 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.

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