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Giuliano Torrengo
Universita del Piemonte Orientale

Van Inwagen and Cross Temporal Relations

In Temporal parts and Identity across time, Van Inwagen makes two points questioning the intelligibility of the notion of temporal part. Firstly, we cannot simply take temporal parts as the referents of expressions such as ‘the book on the table at t’. Temporal expressions should be taken as applied to the verb (or the whole sentence). In a sentence such as

(1) The book on the table at t is clean

the only referring expressions is ‘the book on the table’, which refers to a three-dimensional object that t has the property of being clean.

Secondly, temporal qualifications are on a par with “perspective” qualifications such as ‘viewed full-face’, or, more generally, with qualifications that we may express through objective relative clauses such as ‘when he is drunk’ in

(2) Philip, when he is drunk, is rash

However, at a closer look these two claims seem to be at odd, at least when we consider relational statements. Objective relative clauses need not to take sentence-wide scope. This is why we can have an objective clause for each noun-phrases of a relational statement, and in such cases the most sensible option is to take them as having the noun phrases themselves as scope. Van Inwagen solves this tension by denying altogether that relations may be cross-temporally instantiated. He focuses mainly on the relation of identity. Consider

(3) The book, which is on the table at t, is identical with the book, which is on the table at t'

Temporal qualifications can be read as on a par with “perspective” qualifications because descriptions involving temporal expressions, such as ‘the book on the table at t’, can always be expanded in descriptions containing verb(s), such as ‘the book, which is on the table at t’. Thus, we can read (3) as a straightforward identity claim, rather than a cross-temporal one.

However, this strategy cannot be applied smoothly to relations other than identity in cross-temporal claims. Suppose a t on the table there is a, a perfectly clean book, and on the shelf there is b, a pretty dirty book. I start reading a eating pizza, while someone starts cleaning up b. At t', when a is pretty dirty and b is fairly clean, I remove b from the table and put a instead.

(4) The book that was on the table at t was cleaner than the book that is on the table at t'

is a true sentence in a transparent context, but if in (16) we substitute ‘that book that is on the table at t'’ with ‘that book that was on the shelf at t’––two expressions referring to b––we would get a false statement. Nor is of any use simply to deny that such contexts are not transparent. The point is that if the noun phrases refer to a three-dimensional object, and temporal expressions cannot be used for the time of evaluation of the whole sentence, cross-temporal sentences won’t get the right semantic analysis.

Van Inwagen’s way out is to eliminate “ordinary” cross-temporal relations in a slightly different way than relations of identity through time. In cases such as (4) is not just that the relation is not cross-temporally instantiated, it is rather that no relation between books is ascribed. Claims that looks like relating two objects at different times should be construed as claims about tenseless (or at any rate non cross-temporal) relations between two properties that the objects instantiate at different times, in conjunction with ascriptions of properties to the terms at distinct times. The book is dirtier than the book was, because its present state is one of less cleanness than its past state.

However, not all cases fit well into this model. The problem is that recasting every relational sentence in that way amounts to treating every relation as it were “internal”, namely reducible to non-relational properties of the relata. But it seems clear that certain relations are external, namely non thus reducible. And many––if not all––of them can be cross-temporally instantiated. I conclude Van Inwagen strategy for dismissing identity across-time and the notion of temporal parts thereby fires back as soon as we look at cases of cross-temporal relations other than identity.