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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204 J.J.C. Smart<br />
Notice that if we restrict the term ‘logic’ to quantifiers ‘every’ <strong>and</strong> ‘some’<br />
together with variables ‘x’, ‘y’, etc. (so we have ‘for every x’ <strong>and</strong> ‘for some x’,<br />
etc.) <strong>and</strong> predicate letters ‘F’, ‘S’, etc., <strong>and</strong> also the predicate ‘is identical with’,<br />
which in a finite vocabulary is eliminable, talk of possible worlds is outside<br />
logic because we have the constant ‘w’ ranging over worlds <strong>and</strong> the constant<br />
predicate ‘in’ as ‘in world w’. Of course the modal logician who objected to<br />
possible worlds semantics might take ‘necessarily’ <strong>and</strong> ‘possibly’ as unanalysed<br />
primitives, but then there would be obscurity in their use. Quine has objected<br />
plausibly to quantified modal logic, that is, using ‘necessarily’ or ‘possibly’<br />
within the scope of a quantifier (‘all’ or ‘some’). I side with Quine here but it<br />
is commonly thought that Saul Kripke has made modal logic respectable with<br />
his notion of ‘rigid designator’. A rigid designator refers to the same object<br />
in every possible world. This involves built-in essentialism, which we can<br />
avoid in David Lewis’s counterpart theory. In counterpart theory we have a<br />
distinction between (say) Julius Caesar in world one, <strong>and</strong> Julius Caesar in<br />
world two (one crossed the Rubicon, perhaps, <strong>and</strong> the other didn’t). Essentialism<br />
is optional only. We could say that crossing the Rubicon was an<br />
essential property of Caesar if the counterpart of Caesar in every possible<br />
world crossed the Rubicon.<br />
Compare time. If we think in terms of space–time we see ourselves as a<br />
long space–time worm: one second of our life corresponds to 186,300 miles.<br />
A person stage is one bit of this long worm. One person stage of the whole<br />
person may be thin <strong>and</strong> a later person stage may be fat. So in a sense the<br />
whole person in w is thin at t 1, <strong>and</strong> fat at t 2, but the temporal stage at t 1 is<br />
thin simpliciter <strong>and</strong> the later stage at t 2 is fat simpliciter. I can illustrate the<br />
matter by referring to my excellent colleague, John Bigelow. John is a presentist,<br />
thinks that only the present moment is real. I retort that I don’t like to think<br />
that such a fine person as he is should be only instantaneous. But I shall now<br />
leave the murky matter of technical modal logic itself <strong>and</strong> consider a conception<br />
about logic as that of truths which are true by linguistic convention.<br />
Here I shall discuss the interesting supposed disproof of theism that<br />
I mentioned on FE p. 69. Fifty years or so ago, especially in Oxford <strong>and</strong><br />
Cambridge, with influences from Wittgenstein <strong>and</strong> earlier from the Vienna<br />
Circle, a rather wide notion of logic was current, the idea being that logic,<br />
<strong>and</strong> even mathematics, was analytic or true by linguistic convention. All sorts<br />
of supposedly analytic propositions were subsumed under logic. (Wittgenstein<br />
himself deviated from this a bit, holding that mathematics consisted of<br />
invention rather than discovery.) From this Findlay devised an argument<br />
for atheism. Since Quine’s criticisms of the analytic–synthetic distinction<br />
<strong>and</strong> his demarcation of logic proper from set theory (<strong>and</strong> hence in effect<br />
mathematics), the bounds of logic are now better understood, even by those<br />
not fully in agreement with Quine. However, it will be instructive to look in