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