It was probably present to the mind
of Aristotle, though he misconceives its real extent of operation,
and makes it subservient to his still more comprehensive
classification of the different contemporaneous agencies (regular and
irregular) which he supposes to pervade the Kosmos.
In the treatise before us, he next proceeds to state what collocation
of the negative particle constitutes the special or legitimate
negation to any given affirmation, or what are the real forms of
proposition, standing in contradictory opposition to certain other
forms, so as to make up one _Antiphasis_.[22] The simplest
proposition must include a noun and a verb, either definite or
indefinite: _non homo_ is a specimen of an indefinite noun--_non
currit_, of an indefinite verb. There must be, in any one
proposition, one subject and one predicate; even the indefinite noun
or verb signifies, in a certain sense, one thing. Each affirmation
comprises a noun, or an indefinite noun, with a verb; the special
corresponding or contradictory negation (making up the _Antiphasis_
along with the former) comprises a noun (or an indefinite noun) with
an indefinite verb. The simplest proposition is--
_Affirmative_. _Contradictory Negative_.
Est homo ... ... ... ... Non est homo.
Est non homo ... ... ... ... Non est non homo.
Here are only two pairs of antithetic propositions, or one
quaternion. The above is an indefinite proposition (which may be
either universal or not). When we universalize it, or turn it an
universal proposition, we have--
_Affirmative_. _Contradictory Negative_.
Est omnis homo ... ... ... Non est omnis homo.
Est omnis non homo ... ... Non est omnis non homo.
[Footnote 22: Aristot. De Interpr. p. 19, b. 5, seq.]
The above are specimens of the smallest proposition; but when we
regard larger propositions, such as those (called _tertii
adjacentis_) where there are two terms besides _est_, the collocation
of the negative particle becomes more complicated, and requires
fuller illustration. Take, as an example, the affirmative _Est justus
homo_, the true negation of this is, _Non est justus homo_. In these
two propositions, _homo_ is the subject; but we may join the negative
with it, and we may consider _non homo_, not less than _homo_, as a
distinct subject for predication, affirmative or negative. Farther,
we may attach _est_ and _non est_ either to _justus_ or to _non
justus_ as the predicate of the proposition, with either _homo_, or
_non homo_, as subject. We shall thus obtain a double mode of
antithesis, or two distinct quaternions, each containing two pairs of
contradictory propositions. The second pair of the first quaternion
will not be in the same relation as the second pair of the second
quaternion, to the proposition just mentioned, viz.--(A) _Est justus
homo_; with its negative, (B) _Non est justice homo_.[23]
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