By Laurence R. Horn
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Additional resources for A Natural History of Negation
B. c. d. e. Christ Christ Christ Christ Christ is immortal. lives forever. 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.
Absence of negation: (30) a. He's staying. b. He's not leaving. to the inventory established by Apuleius (27a, b), Frege (28c, d, e), and Ayer (29a, b), points out that the traditional criteria for negativity-the presence of a negative particle, its appearance in a specified syntactic location, and so forth-apply only to sentences, not to statements or propositions. 34 In fact, for Kissin, there is no such animal as a negative statement or proposition. AFFIRMATION (AFFIRMATIVE) refers to what people do with sentences; its opposite number is DENIAL.
Thus, even a singular proposition like Socrates est homo must be negated as Non Socrates est homo,rather than the far more natural Socrates non est homo. Abelard's uniform treatment of propositional negation yields the following pairs of contradictories: (20) omnis homo est albus (every man is white) quidam homo est albus (some man is white) Socrates est albus homo est albus «a) man is white): non omnis homo est albus non quidam homo est albus non Socrates est albus non homo est albus Consistency has been achieved-at the cost of naturalness.