Sattig on Endurantism and Property Abstraction

I am currently working on a review of Thomas Sattig's book: The Language and Reality of Time (Oxford UP, 2006) for Notre Dame Philosophical Reviews. This is a preview.

As the views are standardly characterized, endurantism is the view that objects persist by being fully present at different times, whereas perdurantism is the view that objects persist by having temporal parts at different times. On the most popular version of the latter view, temporal parts just are spatio-temporal regions. Endurantists insist that objects are never identical to spatio-temporal regions.

Sattig develops a new endurantist view according to which objects persist by being fully present at different spatio-temporal regions. Moreover, objects have properties at times insofar as the spatio-temporal regions they occopy at those times have these properties simpliciter. This view has some unexpected consequences, for example that spatio-temporal regions can be female, be happy, be married, be conscious, believe that it is raining, feel that the room is too hot, be mad at their spouse, and so forth.

Sattig does a very good job explaining why these unexpected consequences of his view are not counter to our intuitions (the explanation turns on the fact that spatio-temporal regions, on his view, do not have the properties at times)

However, Sattig notices a problem for his view: property abstraction. Consider the following sentences:

(1) John is happy
(2) John is such that he is happy
Or: John has the property of being a thing x such that x is happy

Property abstraction is widely regarded as a valid move. But, as Sattig observes, it appears to make trouble for his view. Consider:

(3) At t, John is identical to John.

By property abstraction, we get:

(4) At t, John is such that he is identical to John.
Or: at t, John has the property of being a thing x such that x is identical to John.

But if John has this property at t, then the spatio-temporal region he occupies at t has the property of being a thing x such that x is identical to John simpliciter. But surely only John can be identical to John.

Sattig notes that the problem of property abstraction is a problem, not just for his account, but also for perdurantism. He then offers the following solution.

Property abstraction -- e.g., the move from (1) to (2), or the move from (3) to (4) -- is indeed valid, but it is trivially valid. For (2) just has the same logical form as (1), and (4) just has the same logical form as (2). In other words, (2) and (4) are pleonastic paraphrases of (1) and (3).

I think, however, that this way of viewing property abstraction is problematic. Consider the following sentence:

(5) Every one of the students is happy

(5) contains a partitive noun phrase that embeds a definite description. By property abstraction we get:

(6) The students are such that every one of them is happy.
Or: The students X are such that every one of X is happy.

But it is widely agreed that sentences like (5) have the logical form given by (6). To arrive at the logical form of (6), we need property abstraction. Property abstraction reflects genuine syntactical movement. Since there is plenty of evidence for the syntactical movement in question, there is also plenty of evidence against the view that the logical form of (4) is very different from its surface form.