towards the greater goal of providing necessary and sufficient conditions for meta-
physical possibility.
One tempting move is to distinguish between positive category mistakes and
negative category mistakes. A positive category mistake is a sentence that (i) ascribes
a property to an object (or a relation to some objects) and (ii) has no translation into
the metaphysically perfect language. A negative category mistake is the negation of a
positive category mistake. Now state that all positive category mistakes are necessar-
ily false and all negative category mistakes are necessarily true, or at least are true in
any world in which the object in question exists.
This tempting move is too crude. There’s the question about what to say about
sentences with predicates such as“non-charged.”Consider,“this set is non-charged.”
It’s true, and yet it seems that it will lack a translation into the metaphysically perfect
language as well. The idea is that the translation of“charged”into metaphysically
perfect language is a predicate that is explicitly typed, i.e., an intra-categorial predi-
cate in the sense defined above. So the translation of “non-charged”into the
metaphysically perfect language should be the result of prefixing this typed predicate
with predicate-negation, and therefore the result should be another typed predicate.^54
This is assuming that the metaphysically perfect language has a negation operator that
can attach to predicates; it might not, for if it does, it will contain complex predicates
that express less than perfectly natural properties! (We could refine the idea of a
metaphysically perfect language by saying that it is one in which all simple expressions
correspond to perfectly natural entities if they correspond to anything at all.) It looks
like then we should classify“this set is non-charged”as a positive category mistake, and
accordingly hold that it is necessarily false, even though it is true!
Alternatively, it might be that one function of the predicate-negation operator in
the metaphysically perfect language is to remove type-restrictions: if this is so, then
prefixing this operator to an intra-categorial predicate would result in producing an
inter-categorial predicate. Things would be a bit easier if this were the case.
The metaphysically perfect language can’t say some of the things our imperfect
language can, and this is the source of the difficulty we are facing here. I do not take
the lack of“expressive power”to be a defect of this language, since the things it can’t
say are not worth saying, at least not in what van Inwagen (2014) calls“the ontology
room.”And the metaphysically perfect language is not the appropriate language to
use outside this room. But perhaps we should consider a Wittgensteinian move,
and distinguish between what the metaphysically perfect language cansay—that is,
what propositions can be expressed via it—and what that language canshow.^55
(^54) See Magidor (2013: 95–9) for a relevant discussion of a similar problem for some treatments of
category mistakes in natural language. 55
The distinction between what a language can say and what it can only show comes from Wittgenstein
(1966). But interestingly, McManus (2013: 668–9) suggests that to understand some of the later
Heidegger’s thought about being and its modes, it might be useful to make a similar distinction.