One might think, given the above, that the tables have turned in favour of the worm theorist. This is not so, however, for worm theory fails quite quickly too, once one looks at the details.
The key features of worm theory are that referring expressions pick out worms, and worms possess properties by virtue of their parts possessing them. This motivates the following two examples of semantic values, where ’<’ stands for the parthood relation:
• JJoanK=Joan
• JlaughsK=λx.∃y y<x and y laughs.
The entry for names is simple: a name simply refers to the whole worm which the object is. The entry for predicates is slightly more involved: it takes a worm, and returns true provided that worm hasapart which has the property in question. This existentiality in the semantic value, we will see, can be used to derive a problem for the worm theorist. For tensed cases, it appears that a straightforward quantificational treatment will work, initially. We’ll posit covert temporal variables, and amend the semantic value as so:
• JlaughK=λt.λx.∃y y<x and y exists at t and y laughs.
We can note that it will sail through our problematic sentence above:
• PASTt1PASTt2Kant lived(t1) and died(t2)
For Kant to satisfy the first predicate is for him to have a part existing at t1 which possesses the property living, and for him to satisfy the second is for him to have a part existing at t2 which possesses the property dying. If we assume the domains of the quantifiers are restricted in such a way that the domain of the second quantifier contains only later moments than that of the first, we’ll get the right result.
So things look good. But the worm theorist will fall to a problem almost the oppo- site of that which afflicts the stage theorist. Imagine we’re talking about the night of Kant’s death. Then the following is bad, and indeed necessarily bad:
(136) Kant was both alive and dead
And the reason it’s necessarily bad is that we’re attributing incompatible properties to one and the same thing. But its worm theoretic logical form will be:
• PASTt1Kant be both alive(t1) and dead(t1)
And for it to be true there has to be a time in the salient past–the night of Kant’s death– such that he satisfies both predicates. And to satisfy the first is to have a living part existing then, while to satisfy the second is to have a dead part existing then. But the following scenario verifies this: on the night of his death, Kant is alive from 7pm-11pm, and dead from 11.01pm to 12.00am. So the sentence, which sounds necessarily false, is possibly true for the worm theorist. And that’s a misprediction. And it’s almost a converse problem in the following sense: for the stage theorist, we have problems when we wish to speak about two different stages, but have only one name around to speak about them. By contrast, the worm theorist’s problem is that sometimes sen- tences are bad because they attribute to one and the same thing inconsistent properties. But because the semantic value for predicates for the worm theory involves existen- tially quantifying over parts, we don’t get this guarantee: one part can verify one of the predicates, while another can verify the other. One of the goals, then, of a four dimensional semantics will be to navigate the Scylla and Charybdis we’ve just seen.
5.4
Conclusion
So much the worse, one might think, for stage theory and for worm theory, and thus for four dimensionalism. Should we stick with three dimensionalism? I think that would be overly hasty. The next section, building on all that has come before, shows how to develop a new sort of four dimensional semantics.
Stage Semantics
6.1
Introduction
Let’s recap what we’ve seen so far. We have seen some good, if far from conclusive, reasons to opt for four dimensionalism, construed broadly in the sense that persistence is a matter of temporal parts, in the debate about the metaphysics of persistence. And we’ve also seen so good, if far from conclusive, reasons to opt for predicativism in the debate about the semantics of names.
However, we have seen that both of these theories face problems. The stage and worm theorist have problems with semantics, while the predicativist’s postulation of a covert definite is empirically inadequate in several ways. My aim in this chapter is to solve these problems in one swoop by developing a predicativist semantics that doesn’t require the positing of any covert article, and which takes seriously the existence of stages by holding that the extension of a disambiguated name is a predicate which has stages in its extension; ’Barack Obama’ stands for all of Barack’s stages.
The former part of the view requires a different understanding of the syntax/semantics interface, and I’ll adopt a verion of Pietroski’s (Pietroski, 2005) conjunctivism, accord- ing to which a sentence like ’Joan swims’ is a conjunction of predicates with variables bound by an obligatory covert sentence-level existential quantifier. However, this is not
asingularquantifier. The reason for this is that many, indeed probably most, predicates
are what Hawley calls ’lingering’: they are satisfied not by a single stage, but by some stages taken together. For example, a single stage can’t satisfy ’eat a banana’: that takes the co-operation of a series of stages. To capture this, I will hold that the sentence-level existential is apluralquantifier.
Moreover, this in turn requires, or at least suggests, that to treat natural language quantified noun phrases like ’every book’ will require something more than singular quantification, and indeed I will suggest that this is so: natural language quantifica- tion crucially involves higher levels of reference and quantification, of the sort called
superplural.
There are several reasons why one should be interested in such a project; let me remind the reader of, or introduce them to, them. Firstly, as we have seen in chapter four, with regard to four dimensional, and two with regard to predicativism, existing theories have problems and I claim this view can solve them. Secondly, in the spirit of pluralism, one may as well let many semantic flowers bloom, and try to work out the details of non-standard formal semantics, to see what interesting properties they have. Thirdly, it’s interesting to note that most semantic theorising in the tradition of quan- tified modal logic has a notably three dimensional flavour: objects exist at different times (and worlds), and predicates’ extensions are time (and world) relative (Lewis’s counterpart theoretic semantics is to some extent a counterexample to this: this is more clear with regard to worlds). It’s thus an oversight that alternative systems haven’t
been considered, especially given the importance the notion of rigidity has played in guiding our theorising about reference, and the different verdicts stage theory and en- durantism give about temporal rigidity (as has already been seen in chapters two and four). Fourthly, if one bought the stuff about metaphysical externalism in chapter three, and one believes in four dimensionalism, then a four dimensional semantics is some- thing one ought not only merely explore, but which one has to try to pursue, because if stages are in our environment, they must show up in the semantic facts.
So that’s the rough shape of the view, and some motivation for exploring it. The plan for the chapter is as follows. In the next section, I’ll expand a bit on the précis given above, introducing the idea of conjunctivist semantics, and showing the need for the default quantifier to be plural. Following that, I will review some reasons for think- ing that plural and superplural reference are bona fide semantic phenomena. Along the way I will present a new argument defending the legitimacy of the latter. Having done so, I will be able to present my account of quantification and various other con- structions. The section following that will present some interesting consequences of the view which we have landed on, and the also consider and reply to some objections.