§ 129. A positive and a negative term, which have the same matter,
must exhaust the universe between them, e.g. 'white' and 'not-white,'
since, according to the law of excluded middle, everything must be
either one or the other. To say, however, that a thing is 'not-white'
is merely to say that the term 'white' is inapplicable to it.
'Not-white' may be predicated of things which do not possess extension
as well as of those which do. Such a pair of terms as 'white' and
'not-white,' in their relation to one another, are called
Contradictories.
§ 130. Contrary terms must be distinguished from
contradictory. Contrary terms are those which are most opposed under
the same head. Thus 'white' and 'black' are contrary terms, being the
most opposed under the same head of colour. 'Virtuous' and 'vicious'
again are contraries, being the most opposed under the same head of
moral quality.
§ 131. A positive and a privative term in the same matter will always
be contraries, e.g. 'wise' and 'unwise,' 'safe' and 'unsafe': but
contraries do not always assume the shape of positive and privative
terms, but may both be positive in form, e.g. 'wise' and 'foolish,'
'safe' and 'dangerous.'
§ 132. Words which are positive in form are often privative in
meaning, and vice versâ. This is the case, for instance, with the word
'safe,' which connotes nothing more than the absence of danger. We
talk of a thing involving 'positive danger' and of its being
'positively unsafe' to do so and so. 'Unhappy,' on the other hand,
signifies the presence of actual misery. Similarly in Latin 'inutilis'
signifies not merely that there is no benefit to be derived from a
thing, but that it is _positively injurious_. All such questions,
however, are for the grammarian or lexicographer, and not for the
logician. For the latter it is sufficient to know that corresponding
to every term which signifies the presence of some attribute there may
be imagined another which indicates the absence of the same attribute,
where it might be possessed, and a third which indicates its absence,
whether it might be possessed or not.
§ 133. Negative terms proper are formed by the prefix 'not-' or
'non-,' and are mere figments of logic. We do not in practice require
to speak of the whole universe of objects minus those which possess a
given attribute or collection of attributes. We have often occasion to
speak of things which might be wise and are not, but seldom, if ever,
of all things other than wise.
§ 134. Every privative attributive has, or may have, a corresponding
abstract term, and the same is the case with negatives: for the
absence of an attribute, is itself an attribute. Corresponding to
'empty,' there is 'emptiness'; corresponding to 'not-full' there may
be imagined the term 'not-fulness.'
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