position that _Every man is
liable to error_? It seems pedantic to demand a separate proposition
that _Fallible is liable to error_. But, on the other hand, the
insidious substitution of one term for another speciously identical, is
a chief occasion of fallacy. How if we go on to argue: therefore, _Every
man is apt to blunder, prone to confusion of thought, inured to
self-contradiction_? Practically, the substitution of identities must be
left to candour and good-sense; and may they increase among us. Formal
Logic is, no doubt, safest with symbols; should, perhaps, content itself
with A and B; or, at least, hardly venture beyond Y and Z.

Sec. 5. The principle of Contradiction is usually written symbolically,
thus: _A is not not-A_. But, since this formula seems to be adapted to a
single term, whereas we want one that is applicable to propositions, it
may be better to write it thus: _B is not both A and not-A_. That is to
say: _if any term may be affirmed of a subject, the contradictory term
may, in the same relation, be denied of it_. A leaf that is green on one
side of it may be not-green on the other; but it is not both green and
not-green on the same surface, at the same time, and in the same light.
If a stick is straight, it is false that it is at the same time
not-straight: having granted that two angles are equal, we must deny
that they are unequal.

But is it necessarily false that the stick is 'crooked'; must we deny
that either angle is 'greater or less' than the other? How far is it
permissible to substitute any other term for the formal contradictory?
Clearly, the principle of Contradiction takes for granted the principle
of Identity, and is subject to the same difficulties in its practical
application. As a matter of fact and common sense, if we affirm any term
of a Subject, we are bound to deny of that Subject, in the same
relation, not only the contradictory but all synonyms for this, and also
all contraries and opposites; which, of course, are included in the
contradictory. But who shall determine what these are? Without an
authoritative Logical Dictionary to refer to, where all contradictories,
synonyms, and contraries may be found on record, Formal Logic will
hardly sanction the free play of common sense.

The principle of Excluded Middle may be written: _B is either A or
not-A_; that is, _if any term be denied of a subject, the contradictory
term may, in the same relation, be affirmed_. Of course, w