BOO KS
303
sification of a man who studied under Whitehead and has taken
pains to reject the two cardinal beliefs of the logical empiricists, namely
the analytic-synthetic distinction and phenomenalist reductionism (but
then later in the same review he is said to have "constructed single–
handed ... a position which has some general affinities with the ab–
solute idealism of F. H. Bradley"). The reason for this intractability in
classification is, I think, just that Quine has got on with his own work,
engaging in controversy only when provoked, and then not so much
in the role of an advocate as in that of an expert. What he is expert in
is, of course, logic, but empiricist logicians are not necessarily logical
empiricists.
What these books offer is a view of the expert at work.
Selected
Logic Papers
shows him actually doing logic;
The Ways of Paradox
shows him reflecting on the consequences of having done it. The great
thing about logic, as about any discipline in which there is a recognized
expertise with categorical judgments of success and failure, is that for
the most part there is no ambiguity about the task, and one can con–
centrate attention on the mastery and precision with which it is carried
out. ("I have omitted an appendix," says Quine of one of the
Selected
Papers,
"because, as Church showed me, it was wrong.") Not that
every problem in logic is straightforward-on the contrary; but once
taken, each step appears simple and "logical," as that term has come
to be understood in ordinary language. The technical papers are of
course full of technical terminology, so that they look to the untrained
and easily intimidated eye like a series of frightful complexities. To do
logic at any advanced level does indeed call for skill in handling com–
plexity, since a great deal hinges on which simple step to take next,
from which of the premises in hand, and so on. To understand it when
done is a different matter, and I am quite sure that what prevents many
people from understanding logic (apart from the psychological block
which may be induced by the symbolism itself) is not at all that it is
too complex, but that it is too simple.
Consider for example a derivation given by Quine in his paper
"A Method of Generating Part of Arithmetic Without Use of Intuitive
Logic"-a paper to be recommended to the neophyte because it requires
no knowledge of any algebraic operation except subtraction. At a very
early point it is required to move from the premise
x=x- (y-y),
by means of the rule
Given
a
=
/3,
put
a
for
/3
anywhere,
to the identity
x
=
x.
