By Laurence R. Horn
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Extra resources for A Natural History of Negation
1 Negation and the Legacy of Aristotle 33 Negation within the predicate phrase of a sentence constitutes for Frege either a necessary nor a sufficient criterion for producing a negative judg~ent: 'A negation may occur anywhere in a sentence without making the thought indubitably negative' (1919: 125). If the notion 'negative judgment' is not simply a linguistic concept (identifiable with the negative sentence) illegitimately smuggled into philosophical discourse, its deployment is at best premature (in the absence of clear diagnostics for cases like those in (28) and at worst pointless, resulting in 'endless disputes, carried on with the greatest subtlety, and nevertheless essentially sterile' (Frege 1919: 125-26).
Predicate denial-in which the entire predicate is negated-results in contradictory negation. Predicate term negation-in which a negative verb is affirmed of the subject-results in a contrary affirmation. Thus, there is strictly speaking no EXTERNAL, propositional negation as such, but two syntactically and semantically distinct types of INTERNAL negation. Propositional negation originated with the Stoics. While Aristotle and his followers of the Peripatetic school practiced a term logic, using term .
Given the principle of existential import for all and only affirmative sentences, the version of the square employed by Buridan and others would translate into modern notation as follows (Moody 1953:51-52): (22) 3xFx A A---------E \fx(Fx ~ Gx) ~(3x)(Fx A Gx) 1----------0 3x(Fx A Gx) ~(3x)Fx v 3x(Fx A ~Gx) 28 Negation and Opposition in Classical Logic For Aristotle, as we have seen, a singular proposition has existential import if it is affirmative (S is (not-)P) but not if it is negative (S is not (not-)P).