By Laurence R. Horn
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Extra resources for A Natural History of Negation
But any statement can be so used (Ayer  1963: 38). In the end, the difference between affirmative and negative statements is reduced to one of approach: 'A statement is negative if it states that an object lacks a certain property rather than stating that it possesses the complementary property: a statement is negative if it states that a certain property is not instantiated, rather than stating that the complementary property is universally instantiated (Ayer  1963: 61). But it is by no means clear that this criterion, or its subsequent winnowing via Ayer's notion of specificity-by which the negative statement will always be the less specific member of a pair of contradictories-can be successfully defended.
The straightforward translations of the classical propositional forms into standard first-order quantificationallogic work out as follows: 'v'x(Fx ~ Gx) (23) A: All Fs are G I: Some Fs are G 3x(Fx A Gx) (= at least one F is G) E: No Fs are G 'v'x~(Fx A Gx) [or the equivalent ~3x(Fx A Gx)] 0: Some Fs are not G, 3x(Fx A ~Gx) [or the equivalent Not every F is G ~'v'x(Fx ~ Gx)] It will be noticed that no distinction is drawn here between the roles of subject and predicate; F and G are merely two different predicate names.
Alongside the standard binary connectives in the Stoic inventory of truth-functional propositional operators figures the one-place negative connective. ; cf. Sullivan 1967: 41-42)-distinguished three varieties of negation, none of them corresponding exactly to Aristotle's predicate denial: (17) a. DENIAL (arnetikon), composed of a 'denying particle' and a predicate: No one is walking. (steretikon), formed from an atomic proposition by reversing the predicate: This man is unkind. (cf. Aristotle's predicate term negation) c.
A Natural History of Negation by Laurence R. Horn