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Ling 98A: the Meaning of Negation (Week 2)

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Ling 98A: the Meaning of Negation (Week 2) Ling 98a: The Meaning of Negation (Week 2) Yimei Xiang [email protected] 24 September 2013 1 Review 1.1 Negation in propositional logic • Truth table of negation; propositional logic • Some tautologies in propositional logic are not valid in natural languages 1.2 Oppositions • Contrary opposition vs. contradictory opposition • Defining oppositions with laws: – Law of Non-Contradiction (LNC): :(f ^ :f) – Law of Excluded Middle (LEM): f _:f • Three tricky issues: – Non-existent subjects – Scope ambiguity of negation – Metalinguistic negation • Categorical term-based logic of Aristotle – S(ubject)-P(redicate) form, a given P can be either affirmed or denied of a given S. – Two negations (neither of the following two is a propositional operator) ∗ Predicate denial: S is not (not-)P ∗ Term negation: S is not-P – When the given subject doesn’t exist, any affirmation about this subject is False and any denial is True. – Square of opposition ∗ Four corners: A, E, O, I ∗ Three types of oppositions: contradictories, contraries and subcontraries 1 Ling 98a: The Meaning of Negation (Week 2) 1.3 Presuppositions • Presuppositions – Presupposition triggers – Presuppositions vs. entailments/ implicatures – Presupposition projection ∗ Negation ∗ Conditionals ∗ Epistemic modals ∗ Interrogatives 2 Presuppositions (cont.) 2.1 Presupposition accommodation • A presupposition of a sentence must normally be part of the common ground of the utterance context (the shared knowledge of the interlocutors) in order for the sentence to be felicitous. This process of an addressee assuming that a presupposition is true (even in the absence of explicit information that it is), is called presupposition accommodation. • If the presupposition is not properly accommodated (namely, the truth of the presupposition is not satisfied in the CG), then we say there is a presupposition failure. (1) a. # John’s daughter is coming, and John doesn’t have a daughter. b. # If John’s daughter is coming, then we will have a party tonight. Although John doesn’t have a daughter. • A pragmatic approach (Heim 1983, a.o.) • A semantic approach (three-valued logic): If one of a sentence’s presuppositions is not True, then the sentence is neither True nor False, but has a third truth value ‘#’. (Strawson) (2) p is a presupposition of f (viz. fp) iff whenever p is not True, f is #. p fp 1 1 or 0 0 # Appendix: representative three-valued logical systems (Gamut 1 section 5.5.2) 2 Ling 98a: The Meaning of Negation (Week 2) 2.2 Presuppositions and negation • Presuppositions project under negation fp :fp 1 0 0 1 # # • However, in the following sentence, the presuppositions from the negative clause isn’t true. Why this sentence is still felicitous? (3) John’s daughter is not coming, since John doesn’t have a daughter. In other words, we need to address the dilemma between the following two observations: – The presupposition of f is projected in the negation of f. – The presupposition of f is defeasible in the negation of f. • Option 1: There are two kinds of negation in the extended Bochvar’s system: i. Internal/ presupposition-preserving negation: : ii. External/ presupposition-canceling negation: ∼ f :f ∼ f 1 0 0 0 1 1 # # 1 With internal negation, presuppositions are preserved and truth-value gaps arise when one or more of the presuppositions fail; with external negation, presuppositions are potentially re- moved or transformed into simple entailments and the sentence is bivalent. Selective Reading: Gamut 1 pp 188-189. • Option 2: Negation applies to an operator (assertion operator A) that has a meaning akin to “it is the case that/ it is true that ...”. (4) a. Not that John’s daughter is coming, (since John doesn’t have a daughter). b. Not that John has a daughter and his daughter is coming, (since he doesn’t have a daughter). fp Afp :Afp 1 1 0 0 0 1 # 0 1 Some characteristic properties of A (Beaver and Krahmer 2001): (5) a. If f presupposes p, then Afp is equivalent with Af ^ Ap. b. Af is equivalent with f, if f is defined. 3 Ling 98a: The Meaning of Negation (Week 2) • Global accommodation vs. local accommodation John’s daughter is not coming. – Global accommodation: John has a daughter and she is not coming. – Local accommodation: Not that [John has a daughter and she is coming] In-class Exercise 1: 1. Translate the sentences in (4) into propositional formulas and identify their truth conditions. (Omit the bracketed parts.) 2. Use truth tables to show the distinctions between fp, :Afp and A:fp. 3. The meta-assertion operator A and ∼ are interdefinable via :. Use truth tables to show the equivalent relations below. (6) a. ∼ f is equivalent to :Af. b. Af is equivalent to : ∼ f. 4 Ling 98a: The Meaning of Negation (Week 2) • Back to the original question: give an answer that differs from both Mary’s and John’s. Make sure that your answer cannot be simultaneously true with either of their answers. (15) Case 3 in Handout 1: – Mary: “Harry’s daughter is coming.” – John: “Harry’s daughter is not coming.” – You: “Harry doesn’t have a daughter.” In a three-valued logic, “not True” can be either False (0) or Neither (#); – a proposition with a presupposition can be either True, False or Neither; – a proposition without any presupposition is either True or False; When the presupposition “Harry has a daughter” is False (0), Mary’s answer will be Neither (#), while John’s answer is ambiguous. Can you tell what are the possible truth values of John’s answer? • In-class Exercise 2: There are many kinds of three-valued logical systems in the literature. Consider the Bochvar’s system below, for each of the following formulas, identify whether it is a tautology or not. Table 1: Truth table of the Bochvar’s system f y :f ∼ f f ^ y f _ y f ! y 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 # 0 0 # # # 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 # 1 1 # # # # 1 # 0 # # # # 0 # 0 # # # # # # 0 # # # (17) a. :(f ^ :f) b. ∼ (f^ ∼ f) c. ∼ (f ^ :f) d. :(f^ ∼ f) (18) a. f _:f b. f_ ∼ f (19) a. ::f $ f b. ∼∼ f $ f c. ∼ :f $ f d. : ∼ f $ f 5 Ling 98a: The Meaning of Negation (Week 2) 2.3 Another case of scope ambiguity: Neg-raising • “Neg-raising” (NR) is a phenomenon that the clause-mate negation of some sentence-embedding verb is intuitively interpreted as taking scope in the complement clause. (7) a. John doesn’t believe that it is raining. b. John believes that it isn’t raining. • Bartsch (1973): an NRP gives rise to an excluded middle (EM) homogeneity inference, sug- gesting that the subject is opinionated about the truth or falsity of the complement clause. (8) a. John believes that it is raining. belf b. John has a opinion as to whether it is raining. belf _ bel:f In a negative context, an NR reading (9c) is derived as a logical consequence of the negative assertion (9a) and the EM presupposition (9b). (9) a. John doesn’t believe that it’s raining. :belf b. John has an opinion as to if it’s raining. belf _ bel:f c. John believes that it isn’t raining. bel:f • Gajewski (2005, 2007): EMs are soft presuppositions that are lexically specified for NRPs. • A non-NR reading arises if there is a stress on the negative auxiliary. Gajewski (2007): negation takes scope over the A-operator. (10) a. John DOESN’T think that it is raining. b. 6! John thinks it isn’t raining. c. : A [John believes that it is raining] 6 Ling 98a: The Meaning of Negation (Week 2) 3 Implicatures 3.1 Conventional implicatures • Conventional implicatures are implications that are triggered by linguistic meaning. • Conventional implicatures are different from ordinary entailments in two ways: (i) the exact content of what is implied is not readily made explicit; (ii) the content of the implication does not seem at issue in the way that truth-conditional content standardly is. In-class Exercise 3: Only one of the first two sentences implies (11c), which one it is? Does it also entail (11c)? (11) a. Johni is an English man, but hei is cowardly. b. Johni is an English man, and hei is cowardly. c. John’si being cowardly is somehow unexpected or surprising in light of hisi being English. • Karttunee, Peters a.o. argue that conventional implicatures are conventionally presupposed. 7 Ling 98a: The Meaning of Negation (Week 2) 3.2 Conversational implicatures • Conversational implicatures are implications relying on more than the linguistic meaning. They are derived on the basis of conversational principles and assumptions. • Conversational principles: – Principle of cooperation (Grice [1967]1989: 26) Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk in which you are engaged. – Conversational maxims: (12) a. QUALITY: Try to make your contribution one that is true. i. Do not say what you believe to be false. ii. Do not say that for which you lack evidence. b. QUANTITY: i. Make your contribution as informative as is required (for the current pur- poses of the exchange). ii. Do not make your contribution more informative than is required. c. RELATION: Be relevant. d. MANNER: Be perspicuous. i. Avoid obscurity of expression. ii. Avoid ambiguity. iii. Be brief. (Avoid unnecessary prolixity.) iv. Be orderly. A conversational implicature is NOT a logical consequence of a sentence, but it is logical consequence of the assumption that the speaker in uttering the sentence is conforming to the conversational maxims.
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