How Composition Could be Identity

How Composition Could be Identity 10
lation, there are (2 n − 1) 2 propositions predicating it of some objects and
some objects (in order).
Let us turn to language. Consider expanding first-order grammar to
include plural complex terms (corresponding, e.g., to ‘John and Paul’) and
an apparatus of plural quantification (corresponding to the apparatus in
‘There are some things such that . . . they . . . ’). Suppose that outweigh expresses
a relation in a language with the expanded grammar. Consider the
sentence
John and Paul outweigh Mary.
(imagine that Mary is a large guitar amplifier). If we avail ourselves only
of metaphysical ideas appropriate for a classical first-order framework,
this sentence presents a logico-semantic problem. Whereas the distributive
reading of the plural predication reasonably can be thought of as expressing
(when true) a conjunction of two atomic facts, the collective reading
must be approached differently.
I suggest that we think of the collective reading as expressing (if true)
the fact that the outweighing relation holds between John and Paul (collectively,
not each), on the one hand, and Mary, on the other. The outweighing
relation involved is the very same two-place relation that is involved
in the fact that John outweighs Ringo. It is a “two-place” relation, but more
than one thing can (simultaneously, so to speak) fill one of its places. The
collective mode of predication is what connects (one of the blank spots of)
the relation with John and Paul.
This conception has a great advantage over conceptions on which what
is really going on in this case involves a three-place relation (or three-place
instance or determinate of a multigrade relation). 11
Suppose we think of ‘outweigh’ as here expressing a three-place relation,
that holds among John, Paul, and Mary. Then
John, Paul, and George (collectively) outweigh Mary.
would involve a different, four-place, relation, and
Some men (collectively) outweigh Mary.
11 The term ‘multigrade relation’ seems to come from Leonard and Goodman [5]. A
multigrade relation can apply as if it had any number of blank spots. But what exactly
does this mean? Most attempts to make this out have focussed on formal logic and semantics,
rather than metaphysics, as in [8] and [13].
DRAFT