Oxford Studies in Metaphysics - Vol. 1

By Dean W. Zimmerman | Go to book overview

1. Tensed Quantifiers

David Lewis

Some of our idioms of quantification embed verbs, e.g ‘there is’, ‘there exists’. When they do, those verbs can be tensed, forming what I shall call tensed quantifiers. There are past-tensed quantifiers, e.g. ‘there was’, ‘there has been’, ‘there existed’. There are future-tensed quantifiers, e.g. ‘there will be’, ‘there is going to exist’. There are tensed quantifiers with compound tenses, ‘there had existed’, or ‘there will have been’. And sometimes, at least, the unmarked quantifier phrase ‘there is’ or ‘there exists’ acts as a present-tensed quantifier.

Some of us are four-dimensionalists. We think that things are spread out through time just as they are through space. Our most inclusive domain of quantification—disregarding, for now, ‘abstract’ entities and unactualized possibilia—consists of past, present, and future things. We four-dimensionalists have a ready-made way to understand tensed quantifiers: the tenses mark restrictions of the quantifiers to subdomains of that most inclusive domain. They impose a restriction, perhaps, to past things; or to future things; or to present things; or to things that are past from some contextually definite point in the past. Or they may impose a restriction to things that will at some future time be past—which is no restriction at all.1

(All four-dimensionalists agree that the unmarked idioms of quantification sometimes are present-tensed, and carry a restriction to present things. Some four-dimensionalists think, rightly in my view, that sometimes instead the unmarked idioms carry no restriction. They may be used to quantify over the entire domain of past, present, and future things. But other four-dimensionalists may insist that the unmarked quantifiers invariably carry a restriction to present things, so

© Estate of David K. Lewis, 2002

I thank John Bigelow, M. J. Cresswell, Allen Hazen, Mark Johnston, Lloyd Humberstone,
Gideon Rosen, Ted Sider, Michael Smith, Dean Zimmerman, and the audience at the
Australasian Association of Logic conference, 1999, for valuable comments.

1 Except in certain structures of two-way branching time.

-3-

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