metaphysically perfect language might well be right. I appealed to the notion of a
natural expression when formulating the doctrine that there are modes of being. In a
metaphysically perfect language, every expression is a perfectly natural expression.
On my view, a metaphysically perfect language will contain multiple quantifiers.
Given a commitment to multiple fundamental quantifiers, it is natural to hold
that there are distinct sets of variables associated with these quantifiers. That is, the
metaphysically perfect language is multi-sorted.^51 For each set of variables, there will
be a maximal set of terms that are their possible substitution-instances. These sets
need not overlap.
Secondly, the metaphysically perfect language will contain two kinds of predicates,
intra-categorialpredicates andinter-categorialpredicates. An intra-categorial predi-
cate is such that it can meaningfully prefix only terms from exactly one maximal set
of terms. An inter-categorial predicate can meaningfully prefix terms from more than
one maximal set, but for each such predicate there will be syntactic rules governing
how that predicate can combine with these terms. Whether a predicate is an intra-
categorial predicate or an inter-categorial predicate is as much a function of its logical
form as whether that predicate is, for example, a one-place or two-place predicate.
The logical form of a predicate is shown by the range of open sentences one can
construct with the predicate.“x 1 is to the left ofx 2 ”is an open sentence in which the
predicate“is to the left of”appears.“x 1 is to the left of”fails to be an open sentence.
On the view under consideration, thesortof variables matters as much as the number
of variables. One can begin with an open sentence, replace a variable of one sort with
a variable of another sort, and end with something that fails to be an open sentence.
So, for example,“x 1 is to the left ofn 1 ”fails to be an open sentence, since“n 1 ”is not a
variable of the right sort.
One makes ametaphysical category mistakewhen one constructs a pseudo-
sentence by either prefixing an intra-categorial predicate to some terms from the
wrong maximal set of terms (or to variables from the wrong class) or by prefixing an
inter-categorial predicate to some terms in violation of the syntactic rules of the
metaphysically perfect language.
This is a bit abstract. An example should help. Suppose that the correct ontology
has two ontological categories:individualandset. There is a fundamental quantifier,
“ (^9) ind,”that ranges over all and only individuals, and a fundamental quantifier,“ (^9) set,”
that ranges over all and only sets. Associated with thefirst quantifier are the variables
“x 1 ...xn”and associated with the second are“s 1 ...sn.”
(^51) Turner (2010) explicitly discusses multi-sorting, but, as I did in McDaniel (2009b), opts to focus on a
version of ontological pluralism that makes use of single-sorted variables. He also briefly indicates that one
nice feature of multi-sorting is the possibility of explaining category mistakes. Norton (1977: 62–5)
extensively discusses Carnap’s use of a multi-sorted language to make what are intuitively categorial
distinctions; see also Norton (1977: 101–2, 154–6).