Having had my say about what is known in the trade as Occam's Razor, and having secured some welcome agreement with the proprietor of Beyond Necessity in the combox of the aforelinked post, I am now ready to address the meat of Richard Hennessey's response to my three-post critique of what I took to be his theory of accidental predication.
There is no need to stray from our hoary example of accidental predication: 'Socrates is seated.' I took Hennessey to be saying that in a true accidental predication of this simple form subject and predicate refer to exactly the same thing. If they didn't, the sentence could not be true. Here is how Hennessey puts it:
Let us take the proposition “Socrates is sitting” or the strictly equivalent “Socrates is a sitting being.” The referent of the subject term here is the sitting Socrates and that of the predicate term is one and the same sitting Socrates. . . . only if the referent of the “Socrates” and that of the “sitting” of “Socrates is sitting” are identical can it be true that Socrates is actually the one sitting.
Since Hennessey uses the word 'identity' we can call this an identity theory of accidental predication: in true predications of this sort, the referent of the subject term and the referent of the predicate term are identical, and this identty is what insures that the predication is true. If so, then the same goes for all other true predications which are about Socrates. So consider 'Socrates is standing' which is the logical contrary (not contradictory) of 'Socrates is sitting.' These sentences cannot both be true at the same time, but they can be true at different times. Suppose we ask what the truth-maker is in each case. Given that subject and predicate terms refer to exactly the same thing, namely, Socrates, it follows that in each case it is Socrates and Socrates alone that is the truth-maker of both sentences. When he is sitting, Socrates makes-true 'Socrates is sitting' and when he is standing Socrates makes-true 'Socrates is standing.'
What I do not understand, however, is how these obviously different sentences, which differ in their truth-conditions, can have one and the same entity as truth-maker. The same problem does not seem to arise for such essential predications as 'Socrates is human.' For there is no time when he is not human, and (this is a distinct modal point), at every time at which he is human he is not possibly such as to be nonhuman. In the case of essential predications an identity theory may be workable. Perhaps we can say that Socrates himself is the truth-maker of 'Socrates is human,' 'Socrates is rational,' and Socrates is animal.'
In the case of accidental predications, however, it seems definitely unworkable. This is because different accidental predications about Socrates need different truth-makers. It is not Socrates, but Socrates' being seated that is the truth-maker of 'Socrates is seated' and it is not Socrates, but Socrates' standing that is the truth-maker of 'Socrates is standing.'
Without worrying about what exactly the italicized phrases pick out (facts? states of affairs? tropes?), one thing seems crystal clear: there cannot be a strict identity of, e.g., the referent of 'Socrates' and the referent of 'seated.' And since there cannot be a strict identity, there must be some difference between the referents of the subject and predicate terms. Hennessey seems to show an appreciation of this in his response (second hyperlink above):
If we tweak the [B.V.] passage a bit, we can, it strikes me, improve the thesis about the referencing at work in the sentence “Socrates is sitting” so that it offers a more satisfactory support of the neo-Aristotelian thesis of anti-realism in the theory of universals, one indeed getting along “without invoking universals.” First, let us speak of “particular property” instead of “particularized property,” for the latter expression suggests, at least to me, that the property would be, prior to some act of particularization, a universal and not a particular. Let us then accept, but with a precision, Bill’s statement that “‘sitting’ refers to a particularized property (a trope),” saying instead that while the “Socrates” in our statement refers to Socrates, the person at present sitting, the “sitting” primarily refers to Socrates, the person at present sitting, and also co-refers to the particular property of sitting that inheres in Socrates. (An alternative terminology might have it that the “Socrates” in our statement denotes Socrates and the “sitting” primarily denotes Socrates, still the person sitting, and also connotesthe property of sitting that inheres in Socrates; come to think of it, I believe I recall having read, long ago, a similar distinction in the Petite logique of Jacques Maritain, a book which I no longer have, thanks to a flooded basement.)
This is definitely an improvement. It is an improvement because it tries to accommodate the perfectly obvious point that there must be some difference or other between the worldly referents of the subject and predicate terms in accidental predications. Hennessey is now telling us that 'Socrates' in our example refers to exactly one item, Socrates, while 'sitting' refers to two items, Socrates and the particular property (trope, accident) seatedness which inheres in Socrates.
But Hennessey is not yet in the clear. For I will now ask him what the copula 'is' expresses. It seems he must say that it expresses inherence. He must say that it is because seatedness inheres in Socrates that 'Socrates is seated' is true. Now inherence is an asymmetrical relation: if x inheres in y, then it is not the case that y inheres in x. But there is no sameness relation (whether strict identity, contingent identity, accidental sameness, Castaneda's consubstantiaton, etc) that is not symmetrical. Thus if x is in any sense the same as y, then y is (in the same sense) the same as x. Therefore, Hennessey's bringing of inherence into the picture is at odds with his claims of identity. Inherence, being asymmetrical, is not a type of identity or sameness. So why the talk of identity in the first passage quoted above?
Why does Hennessey say that 'seated' refers primarily to Socrates but also to the particular property seatedness? Why not just say this: 'Socrates' refers to the primary substance (prote ousia) Socrates and nothing else; 'is' refers to the inherence relation or nexus and nothing else; 'seated/sitting' refers to the particular property (trope, accident) seatedness and nothing else. This would give him what he wants, a theory of predication free of universals.
But this is not what Hennessey says. He is putting forth some sort of identity theory of predication. He thinks that in some sense the subject and predicate terms refer to the very same thing. He tells us that 'seated' refers both to a substance and to an accident. The upshot is that Hennessey has given birth to a hybrid theory which I for one do not find intelligible.
Here is the question he needs to confront directly: what, in the world, makes it true that 'Socrates is seated' (assuming of course that the sentence is true)? Here is a clear answer: the sentence is true because seatedness inheres in Socrates. But then of course there can be no talk of the identity of Socrates and seatedness. They are obviously not identical: one is a substance and the other an accident. The relation between them, being asymmetrical, cannot be any sort of sameness relation.
The other clear answer which, though clear, is absurd is this: the sentence is true because 'Socrates' and 'seated' refer to the very same thing with the result that the copula expresses identity. Now this is absurd for the reasons given over several posts. This was his original theory which he has wisely moved away from.
Instead of plumping for one of these clear theories, Hennessey gives us an unintelligible hybrid, a monster if you will, as we approach Halloween.