annot be predicated of the
same man in the same relation; but there are many middling men, of whom
neither can be predicated on the whole. For the comparison of
quantities, again, we have three correlative terms,
'greater--equal--less,' and none of these is the contradictory of either
of the others. In fact, the contradictory of any term is one that
denotes the sum of its co-ordinates (Sec. 6); and to obtain a
contradictory, the surest way is to coin one by prefixing to the given
term the particle 'not' or (sometimes) 'non': as 'wise, not-wise,'
'human, non-human,' 'greater, not-greater.'

The separate word 'not' is surer to constitute a contradictory than the
usual prefixes of negation, 'un-' or 'in-,' or even 'non'; since
compounds of these are generally warped by common use from a purely
negative meaning. Thus, 'Nonconformist' does not denote everybody who
fails to conform. 'Unwise' is not equivalent to 'not-wise,' but means
'rather foolish'; a very foolish action is not-wise, but can only be
called unwise by meiosis or irony. Still, negatives formed by 'in' or
'un' or 'non' are sometimes really contradictory of their positives; as
'visible, invisible,' 'equal, unequal.'

Sec. 8. The distinction between Positive and Negative terms is not of much
value in Logic, what importance would else attach to it being absorbed
by the more definite distinction of contradictories. For contradictories
are positive and negative in essence and, when least ambiguously stated,
also in form. And, on the other hand, as we have seen, when positive and
negative terms are not contradictory, they are misleading. As with
'wise-unwise,' so with many others, such as 'happy-unhappy'; which are
not contradictories; since a man may be neither happy nor unhappy, but
indifferent, or (again) so miserable that he can only be called unhappy
by a figure of speech. In fact, in the common vocabulary a formal
negative often has a limited positive sense; and this is the case with
unhappy, signifying the state of feeling in the milder shades of
Purgatory.

When a Negative term is fully contradictory of its Positive it is said
to be Infinite; because it denotes an unascertained multitude of things,
a multitude only limited by the positive term and the _suppositio_; thus
'not-wise' denotes all except the wise, within the _suppositio_ of
'intelligent beings.' Formally (disregarding any _suppositio_), such a
negative term stands for all possible terms except