34 J.J.C. Smart
Holmes smokes a pipe’ but that is within the context of fiction, in which
there is a pretence on the part of Conan Doyle and his readers that ‘Sherlock
Holmes’ does successfully name something.) If we are in doubt whether or
not God exists we should treat the word ‘God’ as a predicate, as in ‘the one
and only x such that x gods’. (To god might be to be omnipotent, omniscient
and benevolent.^61 )
It is true that we could use a non-standard logic such that names such
as ‘Zeus’ are allowed. In such a logic ‘exists’ could occur as a predicate. In
such a logic quantification (‘for all x’ and ‘there is an x’) would be what is
called ‘substitutional’. According to this ‘(∃x)Fx’ is true if for some name ‘a’
the sentence ‘Fa’ is true. Here there is no commitment to existence since
‘a’ might be, say, ‘Sherlock Holmes’. Contrast the (standard) ‘objectual’ quan-
tification, where ‘(∃x)Fx’ is true only if ‘Fx’ is true of (or ‘satisfied by’) some-
thing. The usual objection to substitutional quantification is that we get into
trouble with ‘all rabbits’ or ‘some rabbits’ since we do not have names for all
the rabbits. (And if we replace ‘rabbits’ by ‘real numbers’ it is even worse,
since it is mathematically impossible to have names for all real numbers. It is
impossible for finite sequences of symbols to be in one–one correlation with
the real numbers.)
It should be noted that in logic ‘(∃x)’ or ‘there is a’ must be understood
as tenseless. We could also take ‘exists’ as tenseless, too, and replace some
such idiom as ‘The old town hall no longer exists’ by ‘The old town hall exists
(tenseless) earlier than now’. We put tenses into the predicate and keep
‘There is a’ as tenseless. In what follows I shall use ‘exists’ as tenseless.
Still, allowing substitutional quantification, we could deal easily with such
a sentence as (to use an example of Jonathan Barnes’s) ‘(∃x) (Socrates vowed
a cock to x’) which is true (substitutionally) because it comes out true when
‘Asclepius’ is substituted for ‘x’.^62 (In standard logic, with objectual quanti-
fication, we would deal with the case differently, as perhaps ‘Socrates vowed-
true of himself “gives a cock to Asclepius” ’. Here there is no reference to
Asclepius, only the name ‘Asclepius’, as the quotation marks indicate.)
If we allow substitutional quantification ‘exists’ could be a predicate
in ‘God exists’. Even then the ontological argument does not work. We
might have the concept of a perfect being, and include ‘exists’, understood
substitutionally, as a predicate contributing to this concept. Nevertheless there
would still be the question of whether this concept is true of or applies to
anything. Note that ‘applies to anything’ brings us back to objectual quantifi-
cation. The ontological argument thus understood is circular and assumes
what it sets out to prove.
Barnes tries to show that ‘there is a’ and ‘exist’ are not equivalent. Some
of his examples involve intensional contexts, as with ‘The agents he named
under torture were found not to exist’. There are special problems here.