Monday, January 10, 2005

Any Trope Freaks Out There?

I mean tropes in the Donald C. Williams sense, not the lit-crit sense. I won't explain what tropes are but merely pose two questions that have to do with the compresence relation that supposedly bundles tropes into ordinary concrete particulars. I will assume that trope theory is a one-category ontology according to which everything is either a trope or a construction from tropes. It follows that the compresence relation is a trope.

1. Is compresence a dyadic relation? Or is it polyadic? Suppose tropes T1, T2, and T3 are compresent. Are there two compresence tropes, one that connects T1 and T2, and a second that connects T2 to T3? Or is there one triadic compresence trope that connects T1, T2, and T3? Is the picture this: T1-C1-T2-C2-T3, or this: C(T1, T2, T3)? What are the pros and cons of either approach?

2. Suppose that compresence is dyadic. Since compresence is an equivalence relation, it is transitive. So if T1 is compresent with T2, and T2 with T3, then it follows that T1 is compresent with T3. Should be conclude that the compresence of T1 and T3 is an "ontological free lunch" (Armstrong) that supervenes upon the other two compresence relations, or is it "an addition to being" and thus a separate compresence trope? Does the bundle in question contain five tropes or six?

And what about reflexivity? If T1 is compresent with T2, then T1 is compresent with itself -- but surely there is no need for a separate compresence trope to bind T1 to itself.