208 J.J.C. Smart
are actually included in the make up of our world’. Indeed, many theists can
feel in this way, say, on a beautiful summer’s day in a hilly pastoral landscape.
The clear-headed atheist will nevertheless scorn to cover up this ontological
atheism with misleading religious language.
G.E. Hughes, in a spirited reply,^17 challenges Findlay’s appeal to what he
called ‘the modern mind’ with its conventionalist notion of necessity, which
now after half a century seems a bit old-fashioned, at least because of Findlay’s
assimilation of pure mathematics to pure logic, and even conventionalism
about pure logic has come to look at least questionable, indeed ever since
Quine’s article ‘Truth by Convention’^18 published in 1935 and long rather
neglected. Hughes concludes reasonably enough that even if Findlay were
right about logic and mathematics this would merely show that if we say that
‘God exists’ is a necessary proposition, then we cannot be using ‘exists’ in
quite the same way as that in which we say that tables and chairs exist.
As against Hughes we should not too readily agree that ‘exist’ is ambiguous
other than in obvious cases as when we use ‘exist’ to mean ‘still be alive’ (or
even ‘barely alive’). ‘Exist’ is just the existential quantifier ‘there is a’. Assume
also that in ‘there is a’ we make ‘exist’ tenseless. Tensed qualifications ‘in the
past’ or ‘in the future’ or ‘now’ can be put in separately. Tenses are highly
contextual: what a tensed sentence says depends on its time of utterance. So
we could always keep the quantifier itself tenseless and we need to do so in
mathematics where temporal modifications are not apposite.
Now ‘necessary’ need not mean ‘logically necessary’. ‘Necessarily’ is equi-
valent to ‘not possibly not’ and there are many sorts of possibility: logical
possibility, but also physical possibility (being in accordance with the laws of
nature), moral possibility (being in accordance with the principles of moral-
ity), and so on. It would seem that necessity and possibility can be dealt with
on the minimalist lines suggested by Quine’s ‘Necessary Truth’, as mentioned
in FE p. 37.
On this account ‘There is prime number between 18 and 20’ is a necessary
proposition if it follows from contextually agreed background assumptions.
What would these be? Are they Peano’s axioms? Surely one was sure of there
having to be a prime number between 18 and 20 long before knowing Peano’s
axioms. One just satisfies oneself, by considering all numbers greater than 1
and less than 20 (actually the procedure can be shortened) and making sure
that they do not divide into 19. Still some rules of arithmetic must be sup-
posed and they function as background assumptions.
Those who are satisfied with this minimalist account of necessity
may also not be satisfied with Quine’s form of Platonism, that we should
believe in mathematics because mathematics is part and parcel of well-tested
physical theories. We believe in the Platonic entities through the hypothetico-
deductive method of science, so that there is no need to postulate any