206 J.J.C. Smart
of necessity is that of ‘logical necessity’. According to Findlay, contemporary
philosophical views that all propositions that have necessary truth are
necessary because ‘tautologous’. Remember that he was writing about half a
century ago.
A word of explanation here. ‘Tautology’ since Wittgenstein’sTractatus
Logico-Philosophicushas been used by logicians to refer to sentences of
propositional logic that can be validated by the method of truth tables.
Elementary logic (first-order logic with identity) is better characterized as a
certain body of logical truths. (Wittgenstein did try to assimilate truths of
first-order logic containing words such as ‘all’ and ‘some’ by exhibiting them
as made up of infinite conjunctions and disjunctions, which is in effect what
has come to be called ‘substitutional quantification’. This can be objected
to in various ways which I shall pass over here.^13 We need quantification in
theobjectualsense which carries ontic commitment, and is the best way of
construing ‘there is a’.)
At the time he wrote this article, Findlay thought of logic very widely.
Its tautologous character of emptiness of information about the world was
extended to so-called analyticsentences, which are made true purely by the
meanings of the words and other expressions in them. This is in contrast to
empirical sentences. These are made true or false not only by the meanings of
the words in them (if ‘tall’ meant ‘short’ the sentence, ‘The Eiffel Tower is
tall’ would be false but by the facts of the case). There was also some running
together of the term ‘a priori’ with the term ‘necessary’. The former is an
epistemological one, whereas the other is (or is meant to be) a semantic one.
However, there was another confusion as a legacy from the Vienna Circle,
a confusion between truth and verification, and in the case of mathematics
between truth and provability. (Even though Tarski had shown a clear dis-
tinction between the two, in intuitionist philosophy of mathematics of
Brouwer and others the conflation of truth and provability seems to have
been a motivating factor.)
There was also an unfortunate legacy from Bertrand Russell. He claimed
to derive mathematics from logic. He had also been persuaded by the young
Wittgenstein that logic was tautological. So he lost the youthful joy that he
had once had from mathematics, which he had supposed to be the explora-
tion of a beautiful shining world of Platonic entities. It was sad to think that
pure mathematics was just a matter of finding more and more complicated
ways of saying nothing.^14
This, then, gives some necessary background information about the frame
of mind that was current when Findlay wrote his refutation of theism.^15
If necessity was analyticity, God could not have his attributes essentially,
because ‘God is omnipotent’, etc. would be true purely by our linguistic
convention. Nor could God’s existence be necessary. If analytic sentences are