From tropes to the Trinity

Suppose that each cat has its own catness trope, each dog has its own dogness trope, and so on: each thing has its own essence trope. Thus, whenever we have two cats, we have two individuals—understood as bare particulars, bundles, substances, composite wholes, or in some other way—and two catnesses. Now, the question comes: When we say "There are two cats", is the content that

1. There are two individuals each of which is a cat, or that
2. There are two catnesses?

Whenever one is true, so is the other. Moreover, both statements are pretty natural. On a reference magnetism semantics on which the contents of our assertions are determined by charity plus naturalness, the choice between (1) and (2) will be a close one. In fact, it may be so close that it may be indeterminate whether "There are two cats" means (1) or (2). If naturalness favors either reading, it seems to favor (2) slightly, I think. So the choice between (1) and (2) will be a close one, and the answer will be either indeterminate or in favor of (2).

Likewise, does "Felix" refer to the individual or the catness? If the former, then "Felix sits" has the content that this individual has a sitting trope, and if the latter, then "Felix sits" has the content that this catness is coinstantiated with a sitting trope. Again, both candidates are pretty close to as natural. So again, the question whether names refer to individuals or their essence tropes will be a close one on reference magnetism, and maybe the answer will be indeterminate.

Suppose now that by a miracle there came to be two cat individuals that had the very same catness trope. Why not, after all? There doesn't appear to be anything logically contradictory about the supposition. After all, Siamese twins may share a heart. Why can't they share a trope as well?

So now you assign names, Felix and Tiger, and you say: "Felix is not Tiger." While it may have been indeterminate, or at least was close, whether ordinary cat names referred to catnesses or individuals, in the case at hand there is no indeterminacy or closeness. Charity now requires that at least these two names refer to the individuals, not the shared catness, since there is but one shared catness.

But while it is clear that we should say that Felix is not Tiger, it is less clear whether we should say that there are two cats. It is tempting to argue that Felix is a cat, Tiger is a cat, Felix and Tiger are two, so there are two cats. Certainly, there are two each of which is a cat. But are there two cats? Remember that it was indeterminate or close whether in general "There are two cats" referred to a duality of individuals or a duality of catnesses. If it should turn out to have in general referred to a duality of catnesses, then we should say "There is one cat". But even if it was indeterminate whether "There are two cats" refers to a duality of individuals or catnesses, we might reasonably in this very exceptional case settle on duality of catnesses. There is also a significant consideration in favor of describing the case by saying "There is one cat": it lets one say that there is exactly one catness trope per cat.

But now suppose we have three individuals, the Father, the Son and the Holy Spirit, who have one divinity trope. Then charity will make us say that the Father, the Son and the Holy Spirit are three individuals. Should we say that they are three Gods or that they are one God? If in ordinary cases we take counting to go with essence tropes, then we unambiguously have to go for the "one God" reading. If in ordinary cases, counting is indeterminate between individuals and their essence tropes, then we might in the case at hand simply reasonably resolve the ambiguity by speaking in the "one God" way, which then lets us say, as appears right, that there is exactly one divinity trope per God.

I am not defending this exact theory of the Trinity. One needs to be very cautious talking of individuals that have divinity due to divine simplicity. But I think something like the above is Aquinas' story.