By Laurence R. Horn
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Additional info for A Natural History of Negation
LIb» from the closely related true proposition (lla) involving predicate denial: (II) a. Socrates is not ill. b. Socrates is not-ill. ) It should be borne in mind that for Aristotle and his Greek- and Latinwriting commentators, the distinction between affirming a negative term and denying a positive term (or predicate) was not signaled by hyphens or brackets but by word order-that is, syntactic scope. Thus the real contrast cited above 12 was, for the ancients, more literally that between (II'a, b):13 (II') a.
Is not immortal. is mortal. does not live forever. and try to give a coherent, non-ad hoc reply to the obvious question: 'Now which of the thoughts we have here is affirmative, and which is negative'? According to Peirce (extrapolating from his answer to a similar poser), the judgments corresponding to (28a, b, d) would count as affirmative and those corresponding to (28c, e) as negative, at least within the ancient and traditional model. 552), thereby begging the Fregean question. 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).
In addition to ordinary subject and predicate names we must therefore countenance INFINITE or INDEFINITE names, consisting of a term negation and the term it negates, for example, not-man, not-ill, not-recovers. , (lIb» from the closely related true proposition (lla) involving predicate denial: (II) a. Socrates is not ill. b. Socrates is not-ill. ) It should be borne in mind that for Aristotle and his Greek- and Latinwriting commentators, the distinction between affirming a negative term and denying a positive term (or predicate) was not signaled by hyphens or brackets but by word order-that is, syntactic scope.