304
PETER CAWS
As anybody who has taught logic knows, this kind of simple move can
drive otherwise intelligent people to panic. The argument runs as follows:
if
x
is equal to
x
-
(y - y),
as the premise asserts, then it can be sub–
stituted for
x
-
(y - y)
wherever that expression occurs, according to
the rule. The expression occurs on the right hand side of the premise
itself; substituting
x
for it there yields the required identity. But why,
the bewildered reader asks, prove that
x
=
x?
Isn't it obvious?-certainly
more so than
x
=
x
-
(y
-
y)?
And to this the only answer is that we
have left the domain in which the luxury of the ordinary-language "ob–
vious" can
be
indulged. Now we are doing logic, and we follow the
rules, one step at a time. For most people this requires a real effort at
simplemindedness, a kind of heroic return to innocence, and this may
be the reason why otherwise simpleminded men are sometimes so good
at logic.
Quine, however, cannot be counted in this group. He can be simple
when the business in hand requires it, either because of the stepwise
character of the work itself or because of the need for lucid exposition,
but when it is a question of the place of logic in philosophy, or of the
strategy for achieving certain logical ends or of the implications for
human understanding of results arrived at in logic, he is capable of as
much philosophical complexity as the ordinary-language philosophers
themselves. The point is to understand what logic is about, when doing
it to do it rigorously, and when doing something else to know what
that
is about and how it is appropriately to be done. Logic does not
exist for the better formulation of ordinary locutions like "every," "all,"
"if ... , then ..."; it substitutes its own locutions for these in certain
specialized uses, for example, those of mathematics and science, with a
view to "maximizing algorithmic facility" (to return to the review of
Strawson from which we started). The whole apparatus is to be judged
in terms of its success in coping with experience; even the most funda–
mental logical laws are not to be considered sacrosanct, although their
great generality does confer on them a kind of privilege, so that it is
hard to imagine the kind of empirical revelation that would make us
abandon them.
The development of the technical apparatus of logic has uncovered
some surprising difficulties in the symbolic formulation of truth, diffi–
culties which might never have emerged from discussion in ordinary
language. The most celebrated of these are the incompleteness proof,
due to Godel, and a series of paradoxes starting with Russell's. These
form the subject of the title essay of
The Ways of Paradox,
in which, of
all the papers collected here, Quine's clarity and patience in exposition
