does
not concern itself. To realise this is to understand more clearly the
limitations of Formal Logic.

In common speech, to deny a quality of anything is by implication to
attribute to it some other quality of the same kind. Let any man tell
me that "the streets of such and such a town are not paved with wood,"
I at once conclude that they are paved with some other material. It
is the legitimate effect of his negative proposition to convey this
impression to my mind. If, proceeding on this, I go on to ask: "Then
they are paved with granite or asphalt, or this or that?" and he turns
round and says: "I did not say they were paved at all," I should be
justified in accusing him of a quibble. In ordinary speech, to deny
one kind of pavement is to assert pavement of some kind. Similarly, to
deny that So-and-so is not in the Twenty-first Regiment, is to
imply that he is in another regiment, that he is in the army in some
regiment. To retort upon this inference: "He is not in the army at
all," is a quibble: as much so as it would be to retort: "There is no
such person in existence".

Now Logic does not take account of this implication, and nothing has
contributed more to bring upon it the reproach of quibbling. In Logic,
to deny a quality is simply to declare a repugnance between it and the
subject; negation is mere sublation, taking away, and implies nothing
more. Not-_b_ is entirely indefinite: it may cover anything except
_b_.

Is Logic then really useless, or even misleading, inasmuch as it
ignores the definite implication of negatives in ordinary thought
and speech? In ignoring this implication, does Logic oppose this
implication as erroneous? Does Logic shelter the quibbler who
trades upon it? By no means: to jump to this conclusion were a
misunderstanding. The fact only is that nothing beyond the logical
Law of Contradiction needs to be assumed for any of the processes
of Formal Logic. Aristotle required to assume nothing more for his
syllogistic formulae, and Logic has not yet included in its scope any
process that requires any further assumption. "If not-_b_ represent
everything except _b_, everything outside _b_, then that A is _b_, and
that A is not-_b_, cannot both be true, and one or other of them must
be true."

Whether the scope of Logic ought to be extended is another question.
It seems to me that the scope of Logic may legitimately be extended so
as to take account both of the positive implication of n