(_b_) Formal Logic clearly will not quail before the charge of
uselessness. But on its own principles it ought to be consistent. But by
this test also, when it is rigorously judged by it, it fails completely.
Its inconsistencies are many and incurable. It cannot even be consistent
in its theory of the simplest fundamentals. It is found upon some
occasions to define judgment as that which may be _either_ true _or_
false; and upon others as that which is 'true' (formally)--_i.e._, it
cannot decide whether or not to ignore the existence of error.

(_c_) The Formal view of inference regards it as a 'paradox.' An
inference is required on the one hand to supply fresh information, and
on the other to follow rigorously from its premisses; it must, in a
word, exhibit both _novelty_ and _necessity_. It would seem, however,
that if our inference genuinely had imparted new knowledge, the event
must be merely psychological; for how can any process or event perturb,
or add to, the completed totality of truth in itself? On the other hand,
if the 'necessity' of the operation be taken seriously, the 'inference'
becomes illusory; for if the conclusion inferred is already contained
in the premisses, what sense is there in the purely verbal process of
drawing it out?

(_d_) Most glaringly inadequate of all, however, is the Formal doctrine
of 'Proof' contained in its theory of the Syllogism. A Formal or verbal
syllogism depends essentially on the ability of its Middle Term to
connect the terms in its conclusion. If, however, the Middle Term has
not _the same_ meaning in the two premisses, the syllogism breaks in
two, and no 'valid' conclusion can be reached. Now, whether in fact any
particular Middle Term bears the same meaning in any actual reasoning
Formal Logic has debarred itself from inquiring, by deciding that actual