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Auteur: Laurence HORN

The Singular Square: Contrariety and double negation from Aristotle to Homer

Abstract/Résumé: Centuries before inspiring the post-Aristotelian square of opposition relating the quantified statement types in (1), Aristotle himself (in the Prior Analytics, Chapter 46) defined the SINGULAR square as illustrated in (2), in which two distinct varieties of negation are distinguished corresponding to contradictory (O-vertex) and contrary (E-vertex) opposition. (1) All F is G ———No F is G A E | | | | I O Some F is G——Some F is not G (2) F is G————F is not-G A E | | | | I O F isn't not-G——F isn't G MAXCONTRARY is the natural language conspiracy by which a contradictory negation ¬p with apparent sentential or wide scope tends to strengthen to a contrary, ©p. Evidence includes: (i) the diachronic strengthening of formal contradictories (O values) to contrary (E) meanings, as when "Il ne faut pas partir", lit. = 'It is not necessary to leave', is re-interpreted as 'one must not-leave' (ii) the cross-linguistic prevalence of prohibitives, dedicated E-valued markers, often expressed by apparent O structures ('not-want', 'not-must') (iii) the "neg-raising" construal of negation outside the scope of (some) propositional attitude predicates (e.g. "I don't believe that p") as inside the embedded clause ("I believe that not-p"). (iv) the inference from a formally contradictory negation of an unmarked positive value, whether affixal ("x is unfair/unhappy") or clausal ("x isn't fair/happy"), to a contrary, either as an online R-based implicature (Horn 1984, 1989) or conventionalized in the lexical semantics. (v) the interpretation of negated plural definites ("The children aren't sleeping") or bare plurals ("Lions don't have manes") as contraries rather than simple contradictories of the corresponding affirmatives ("The children are sleeping"; "Lions have manes"). The other major goal of this study is to recruit the Singular Square to inform an explanatory account of the seemingly illogical behavior of "logical" double negation. Just as the Law of Excluded Middle sometimes applies where it "shouldn't", resulting in pragmatic disjunctions between semantic contraries (reading "p v ©p" as an instance of "p v ¬p"), the Law of Double Negation sometimes fails to apply where it "should", as when "not impossible" seems weaker than "possible", when those who are not not friends aren't quite friends. When a double negation is understood as ¬©p rather than ¬¬p, the middle between p and not not p is unexcluded.