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