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NON-NOMINAL QUANTIFICATION 33
treat a predicate or sentence as if it were a name referring to an object (1966). Prior agreed
with Quine that objectual quantification into predicate or name position would misrepresent
predicates and sentences as names, but whereas Quine thought all quantification must be
objectual Prior thought that non-objectual forms of quantification were possible:
quantification into nominal position is objectual, since nominal quantifiers generalise the
function of names, which is to refer to objects; but since predicates and sentences do not
name objects, predicate and sentential quantifiers do not quantify over objects (1971: 35).
Quine and Prior were both motivated in part by a suspicion of abstract objects, a suspicion
that was not shared by Peter Strawson. Like Prior, Strawson upheld the possibility of
quantification into non-nominal positions, but held that names and general terms alike
introduce or specify objects: the abstract noun ‘redness’ and the general term ‘red’ introduce
the same property of redness despite the difference in their grammatical categories (1997: 4–
6; 85–91). Quantification into general term position can therefore be regarded as objectual
along with quantification into the position of the abstract noun. 1
This, then, is one of the motivations for the objectual account of quantification into nonnominal
positions: it offers a non-substitutional treatment of non-nominal quantification that
respects differences of grammatical category whilst recognising that sentences and general
terms have something importantly in common with their nominalizations. Thus, Fraser
MacBride has defended the possibility of objectual quantification into predicate position on
the basis that the function of predicates may involve reference as well as description (2006a;
see also his 2006b). Wolfgang Künne has developed in detail an account of objectual
quantification into general term and sentence positions, both in his account of abstract
objects and in his quantificational theory of truth, although he has recently adopted an
account of quantification more in line with the argument of this paper (2003: 350–7; 2005;
2008a; 2008b; for his current position see his 2010). The theory of truth provides an
additional motivation for the objectual interpretation of non-nominal quantification, since it
would allow us to give a sententially quantified definition of the truth-predicate without
employing substitutional quantification, which many have argued is problematic and would
lead to circularity. Scott Soames has also remarked upon the advantages an objectual account
of sentential quantification would have for the theory of truth (1999: 41–8).
3. Objectual Non-Nominal Quantification
According to the approach under consideration we should understand non-nominal
quantification as quantification over objects. Quantification into general term position, for
example, may be regarded as quantification over properties. These properties are not,
however, referred to by the substituends of the variable but are instead ascribed by them.
Glock explains the position as follows:
By contrast to substitutional quantification, the variables have not just substituends
but also values, a range of objects with which they are associated, namely properties.
By contrast to [nominal] objectual quantification, the substituends of predicate
variables do not name these values (attributes), they ascribe them. (Glock 2003: 58)
Likewise, quantification into sentence position may be regarded as quantification over the
propositions which sentences might express. The truth-conditions of a quantification are then
given in terms of the values in the domain of the quantifier meeting certain satisfaction
conditions. Since Künne’s exposition remains the clearest and fullest I shall follow his
account.
1
Note that Strawson also defended the possibility of non-objectual quantification, which he thought was
the correct interpretation for adverbial generalisations. See his 1997b.