2
Logic and Conversation
It
is a commonplace
of
philosophical logic
that
there are, or appear
to be, divergences in meaning between, on the one hand, at least some
of
what
I shall call the formal
devices,
1\,
V,
:J,
('t/x), (3x),
(LX)
(when these are given a standard twovalued
interpretation)and
,
on the other,
are taken to be their analogues or counterparts in
natural
languagesuch
expressions as
not, and, or,
if,
all, some
(or
at
Least
one), the.
Some logicians may at some time have wanted to
claim
there are in fact no such divergences; but such claims, if
made at all, have been somewhat rashly made, and those suspected of
making them have been subjected to some pretty rough handling.
Those who concede
such divergences exist adhere, in the main,
to one
or
the other of two rival groups, which I shall call the formal
ist and the informalist groups. An outline of a
not
uncharacteristic
formalist position may be given as follows: Insofar as logicians are
concerned with the formulation of very general patterns of valid
inference, the formal devices possess a decisive advantage over their
natural counterparts. For it will be possible to construct in terms of
the formal devices a system of very general formulas, a considerable
number of which can be regarded as,
are closely related to,
pat

terns of inferences the expression of which involves some or all of the
devices: Such a system may consist of a certain set of simple formulas
must be acceptable if the devices have the meaning that has been
assigned to them,
and
an indefinite number of further formulas, many
of which are less obviously acceptable
each of which can be
shown to be acceptable if the members of the original set are accept
able. We have, thus, a way
handling dubiously acceptable patterns
of inference, and if, as is sometimes possible, we can apply a decision