Was sollen wir tun? Was dürfen wir glauben? - bei DuEPublico ...

The Ineliminability of Non-Nominal
Quantification
David Dolby
Objectual interpretations of non-nominal quantification seems to offer a non-substitutional
treatment of quantification which respects differences of grammatical category in the object
language whilst only employing nominal quantification in the metalanguage. I argue that the
satisfaction conditions of such interpretations makes use concepts that must themselves be
explained through non-nominal quantification. As a result, the interpretation misrepresents
the structure of non-nominal quantification and the relationship between nominal and nonnominal
forms of generality.
1. Introduction
Natural language appears to contain expressions of generality in various syntactic categories:
English has not only the (typically) nominal ‘something’, but also adverbial forms such as
‘somehow’ and ‘somewhere’. Nevertheless, many philosophers, following Quine, have claimed
that all genuine quantification is nominal: quantifiers and variables range over a domain of
objects which are named by their substituends. Since supposed non-nominal quantifications
quantify into positions which do not name, there is no domain of objects for the quantifier to
range over: they are at best substitutional quantifications—conveniently abbreviated nominal
quantifications over linguistic items—and not generalisations about the extra-linguistic world
(Quine 1970: 91–4; Inwagen 2004: 124). The most significant opponent to this position was
Arthur Prior, who argued that predicate and sentence generalisations are genuinely
quantificational although they involve no domain of objects: indeed, he suggested that any
attempt to reduce non-nominal quantification to objectual quantification must fail, since in
any interpretation of a quantifier we cannot avoid employing the very form of quantification
we seek to explain (1971: 31–47). Positions similar to his have been developed by Christopher
Williams (1981), Philip Hugly and Charles Sayward (1996), and Timothy Williamson (1999).
Recently, philosophers have become more willing to accept the legitimacy of non-nominal
quantification. However, it is often proposed pace Prior that the quantifiers should be given
an interpretation in terms of a domain of objects, such as properties or propositions—those
associated with the substituends by some semantic relation other than naming (Strawson
1997a; Soames 1999, Künne 2003, 2008a; Glock 2003; Rosefeldt 2008). I shall claim that
such an account will inevitably appeal to non-nominal generalisation, either explicitly or
implicitly, in its statement of truth-conditions, and thereby obscures the relationships that
hold between non-nominal quantified sentences and their parts and between nominal and
non-nominal forms of generality.
2. Quantification and Reference
Questions about quantification are closely related to questions about reference and syntax.
Indeed, Quine argued that nominal positions in a sentence are precisely those which are open
to quantification. He thought that to quantify into predicate or sentence position would be to