Further Reflections on Atheism 207empty of information about reality, then it would seem that no analytic
sentence can tell us what really exists. Or thus was Findlay’s idea.
Two things make us look back with some scepticism about all this line of
thought. First, there was Quine’s criticisms of the analytic–synthetic distinction.
At any rate if there are analytic propositions, they are ones of no philo-
sophical interest, for example, ‘No bachelors are married’. Secondly, it is
misleading to think that mathematics is logic. Even if first-order logic has
a tautological character this does not apply to set theory. As I remarked on
FE p. 39, Quine has pointed out three characteristics possessed by first-order
logic (with identity) but not by set theory and hence mathematics since all
classical mathematics can be expressed in or mapped on to set theory.
For Quine, the numbers π or e or trigonometric functions, for example,
are not to be believed in a priori. They are to be believed in because of their
indispensability in physics.^16 They seem to exist necessarilybecause they
are well entrenched in our system of beliefs – more deeply entrenched and
immune to theory revision than electrons or curved space–time. So perhaps
even assertions such as that there are infinitely many primes, or even that
there is a number greater than 9, are only as a matter of degree less contin-
gent than are the assertion of the existence of electrons and the like. For
Findlay’s disproof of the existence of God he needs to deny the possibility
of necessary existential statements. And yet there do seem to be such. For
example, ‘there are infinitely many primes’. Perhaps, however, we confuse
necessity with being eternal.
5 Further Reflections on Necessity and Theism
We have seen cause to question the idea that mathematics is tautological
or empty of ontological commitment. So the theist should do well to question
Findlay’s idea that necessity derives from linguistic convention only. To be
an adequate object of worship God would have to exist necessarily and his
attributes would belong to him with objective necessity too. This could not be
so if necessity was a mere matter of linguistic convention. Indeed, Findlay
even says that the Divine Existence would be a necessary matter if we had
made up our minds to speak theistically ‘whatever the empirical circumstances
turned out to be’. (We might suspect that many theists are like this: consider
the sailor who is saved from drowning and attributes his rescue to divine
intervention, despite his knowledge of all his shipmates who drown. This is
contrary to the Popperian methodology of looking for refutations rather than
verifications.) Findlay refers to those who like Spinoza think theistically merely
to give expression to a way of feeling about the universe, or perhaps to use the
term ‘God’ to ‘cover whatever tendencies towards righteousness and beauty