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Thursday, April 07, 2016

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That was superbly heuristic, Bill.

Yes, regardless of nomenclature – materia signata, materia formata, materia secundo prima – matter must be part of the ontological picture. Yet for trope theory, matter is the elephant in the room. To admit its presence would be to introduce another category into the one-category ontology of trope theory. But if there are to be concrete objects, properly endowed with impenetrability, there must be matter: that is, concrete objects must be hylomorphic. As one philosopher said, you can’t hold properties (or property particulars, particularized properties, abstract particulars, or property instances).

In my opinion, that lump of bronze cannot properly be construed as a trope. As (particularized) properties, tropes are interpenetrable and predicable. The lump of bronze is impenetrable and impredicable. Moreover, the lump of bronze is a bearer of properties, whereas no trope is a bearer of (first-order) properties. In my view, trope theory ignores matter. It abstracts properties from the object, subjects them to compresence, and then claims to have constituted the object out of tropes alone. The type of abstraction involved is one of those cited in your prior post, “Sense of ‘Abstract’ with a Little Help from Hegel”: “it is to abstract from the full reality of thing in order to focus on one of its determinations.” Heil concurs: “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” (2015, 119).

Trope theory attempts to enmatter tropes. As Maurin indicates, it renders them hylomorphic, composed of matter and form: “. . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance.” As Heil suggests, in the ontological project of D.C. Williams, the father of trope theory, “[t]he role of substances is to be filled by spatiotemporally ‘concurrent’ particularized properties” (2015, 119). Just as, according to Windelband, Leucippus [with his atomism] “shatters in pieces the world-body of Parmenides, and scatters its parts through infinite space” (1901, 48), so Williams shatters in pieces the Aristotelian substance, scattering properties (suitably refurbished as tropes), each of them qualifying, in Maurin’s view, as a “kind of substance.” Thus the trope becomes an ontological factotum, fulfilling two roles at once.

The insistence on ignoring matter leads trope theory to equivocation regarding parts and properties. Of course, properties and (physical) parts are distinct. The former can co-occupy a given region without limit, as with your recent example of the red dot – the site of at least three compresent tropes: red, circular, and extended. The latter (that is, parts) cannot co-occupy a given region. Instead of compresence, their aggregation entails juxtaposition. However, in constituting the object by compresent tropes (each of which is merely a property particular or particularized property), trope theory vainly attempts to achieve a concrete, material object, endowed with ontological independence. But it cannot do so. Parts are not properties. Parts combine mereologically to constitute that of which they are parts. They are not parasitic on the object they constitute. In contrast, in the conventional view of the relation between substance and property, as Campbell indicates, “[t]ropes are at best parasitic” (1981, 479). MacDonald concurs: “Independence was associated here with permanence, the sort of feature that substances or continuants have while events, accidents, etc., have, at best, only in a derivative sense, in virtue of being parasitic on substances” (2012, 19). In this context, I would like to requote Simons observation that 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).

I note that, when giving examples of tropes, trope theorists always refer to immaterial properties, like colour, shape, contour, weight, and so on. This comes out very clearly in Simons’ account of an airplane (also quoted earlier):

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)

An airplane constituted solely by immaterial tropes such as weight, length, shape would never fly. In my opinion, one-category trope theory does not fly either.

Something more now about that lump of bronze. How did it get shaped? If, for the sake argument, we agree that the lump can qualify as a trope, what transformed it from a lump (which it must be to enter into compresence) to a statue? We cannot say that some trope or group of tropes transformed the lump, because tropes as abstract properties are causally inert.

I think that two types of abstraction are behind trope theory. The first is one of those you mention: detaching one aspect from a totality or whole and focusing on it to the exclusion of the others and the whole to which they pertain. The second type of abstraction behind trope theory is one not included in your extremely instructive discussion. I refer to the type of abstraction which detaches, from a group of particulars, some trait or feature common to all of them. Hegel refers to this as the “operation of abstracting and collecting together what is common to the objects . . . .” Inwood characterizes it as “forming concepts by abstracting from those respects in which a group of individuals differ from each other and retaining those features which they have in common” (2002, 366-67). Whitehead elaborates: “There are simplicities connected with the motion of a bar of steel which are obscured if we refuse to abstract from the individual molecules and there are certain simplicities concerning the behaviour of men which are obscured if we refuse to abstract from the individual peculiarities of particular specimens” (1978, 16-17).

In my opinion, trope theory, by means of the first type of abstraction cited in the preceding paragraph, abstracts properties from the object or concrete particular, construes them as tropes, and combines them in compresence. All these tropes, in virtue of both their own nature and the operation of abstraction which detaches and collocates them, are immaterial. Of necessity, the object constituted (or reconstituted) by this compresence of abstract(ed) tropes, is an immaterial object, not a material one.

This point can be reinforced by consideration of the second type of abstraction mentioned earlier: detaching a feature common to many particulars. In this case, with regard to the compresent tropes, the feature common to all of them is compresence. Each one is together with all the others. Thus compresence itself is an abstraction of abstractions. How can a material object result from that?

>>In my opinion, that lump of bronze cannot properly be construed as a trope.<<

I don't think anyone would say that. I was suggesting above that the lump might be taken to be a bundle of tropes. A bundle of tropes is not a trope. The immateriality of individual tropes does not entail the immateriality of trope bundles.

Still, I think we agree that trope theory is incoherent, chiefly for the reason that little or no sense can be attached to the notion of an item that is indissolubly both a property and a substance, a predicable item and an impredicable item.

But how, then, is the trope-bundle pertaining to the lump to be related to the trope-bundle pertaining to the statue? And how can the required relation be related to its own relata without invoking Bradley's Regress?

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