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, we may deny that a leaf is green on one side without being bound to affirm that it is not-green on the other.  But in the same relation a leaf is either green or not-green; at the same time, a stick is either bent or not-bent.  If we deny that A is greater than B, we must affirm that it is not-greater than B.

Whilst, then, the principle of Contradiction (that ’of contradictory predicates, one being affirmed, the other is denied ’) might seem to leave open a third or middle course, the denying of both contradictories, the principle of Excluded Middle derives its name from the excluding of this middle course, by declaring that the one or the other must be affirmed.  Hence the principle of Excluded Middle does not hold good of mere contrary terms.  If we deny that a leaf is green, we are not bound to affirm it to be yellow; for it may be red; and then we may deny both contraries, yellow and green.  In fact, two contraries do not between them cover the whole predicable area, but contradictories do:  the form of their expression is such that (within the suppositio) each includes all that the other excludes; so that the subject (if brought within the suppositio) must fall under the one or the other.  It may seem absurd to say that Mont Blanc is either wise or not-wise; but how comes any mind so ill-organised as to introduce Mont Blanc into this strange company?  Being there, however, the principle is inexorable:  Mont Blanc is not-wise.

In fact, the principles of Contradiction and Excluded Middle are inseparable; they are implicit in all distinct experience, and may be regarded as indicating the two aspects of Negation.  The principle of Contradiction says:  B is not both A and not-A, as if not-A might be nothing at all; this is abstract negation.  But the principle of Excluded Middle says:  Granting that B is not A, it is still something—­namely, not-A; thus bringing us back to the concrete experience of a continuum in which the absence of one thing implies the presence of something else.  Symbolically:  to deny that B is A is to affirm that B is not A, and this only differs by a hyphen from B is not-A.