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.
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