Sentence Relations and TruthSemanticsChapter 4Sentence Relations1. a. My brother is a bachelor.b. My brother has never married. 2. a. The anarchist assassinated the emperor.b. The emperor is dead.3. a. My brother has just come from Rome.b. My brother has never been to Rome4. a. The mayor of Manchester is a woman.b. There is a mayor of Manchester. 5. a. Ireland is Ireland.b. Rich people are rich.6. a. ?He is a murderer but he’s never killed anyone.b. ?Now is not now.a and b are synonymous.a entails b.a contradicts b.a presupposes b.a and b are contradictions.a and b are tautologies.Logic and Truth The tools of logic can help us to represent sentence meaning.13. Modus ponens (긍정식)a. If Arnd left work early, then he is in the pub.b. Arnd left early.c. Arnd is in the pub.14. Modus tollens (부정식)a. If Arnd has arrived, then he is in the pub.b. Arnd is not in the pub.c. Arnd has not arrived.premisesconclusion15. Hypothetical syllogisma. If Arnd is in the pub, then he is drinking beer.b. If Arnd is drinking beer, then he is drinking Guinness.c. If Arnd is in the pub, then he is drinking Guinness.16. Disjunctive syllogisma. Arnd is in the public bar or he is in the lounge.b. Arnd isn’t in the public bar.c. Arnd is in the lounge.Truth A part of logic is a concern for the truth of statements and whether truth is preserved or lost by putting sentences into different patterns. Truth means a correct descriptions of states of affairs in the world; truth is empirical (or contingent) because we have to have some access to the facts of the world to know whether a statement is true or not.17. My father was the first man to visit Mars.Truth Value Truth value- a sentence’s being true or false Truth conditions- the facts that would have to obtain in reality to make a sentence true or false19. a. Your car has been stolen.b. Your car has not been stolen.20. a. p 21. p ¬p(negation)b. ¬p T FF Tlogical formsConnectives: and22. a. The house is on fire.b. The fire brigade are on the way.c. The house is on fire and the fire brigade are on the way.23. p q p∧q (conjunction)T T TT F FF T FF F F The study of the truth effects of connectives are called propositional logic.Connectives: or24. p q p∨q (disjunction; inclusive or)T T TT F TF T TF F F25. I’ll see you today or tomorrow.26. p q p∨eq (disjunction; exclusive or)T T FT F TF T TF F F27. You will pay the fine or you will go to jail.  ‘but not both’Connectives: if… then28. p q p  q (material implication)T T TT F FF T TF F T29. If it rains, then I’ll go to the movies. p is a sufficient condition for q (rain will cause me to go) but not a necessary condition (other things might take me go; it might snow!)`antecedentconsequentConnectives: if… then Material implication captures some but not all aspects of our use of if . . . then.30. If Patricia goes to the party, the Emmet will go too. A natural implication of sentence 30 is that Emmet is going because Patricia is. What if Patricia isn’t going?Connectives: if… then32. a. If I were an ostrich, then I would be a bird.b. If I were an ostrich, then I would not be a bird.Because p is false here, both 32a and 32b have to be true according to the truth table. This is against our intuitions.The material implication relation does not fit our use of counterfactuals.Connectives: if and only if (iff)33. p q p ≡ q (biconditional↔)T T TT F FF T FF F T  (pq) ⋀ (qp)34. We’ll leave if and only if we’re forced to. p is a necessary condition for q, i.e. p is the only possible cause for q. Plausible translation of our use of counterfactuals such as 30.To sum up, statements have a truth value; this truth value depends on a correspondence to facts; and different ways of connecting statements have different effects on the truth value of the compounds produced.Types of Truth Semantic distinction (depending the meaning of the words within them)• Analytic truth- follows from the meaning relations within the sentence. e.g. My father is my father.• Synthetic truth- depends on the accordance with the facts of the world. e.g. My father has been to Mars. Mogadishu is Hamar. Necessarily true, but can be a posterioriTwo names for the same city, the capital of SomaliaTypes of Truth42. a. Either Germany will win the World Cup or Germany won’t win it. Either p or not-pb. If Germany are champions and Brazil are runners-up then Germany are champions. if p and q then pd. If Germany beat Brazil then Brazil lose to Germany.  If G X B then B Y G.; truth relies on the individual lexical relations (beatand lose) Sentences can be analytically true because of the behaviour of logical words or because of the meaning of individual nouns and verbs.Logical wordsEntailment52. a. The anarchist assassinated the emperor.b. The emperor died.53. Entailment defined by truth:p entails q when the truth of the first guarantees the truth of the second, and the falsity of the second guarantees the falsity of the first.55. Composite truth table for entailmentp qT  TF  T or FF  FT or F  TEntailment58. The Etruscans built this tomb.59. This tomb was build by Eratuscans.60. Composite truth table for synonymyp qT  TF  FT  TF  F64. Mr. Jones stole my car. 65. Mr. Jones did not steal my car.63. Contradictionp qT  FF  TT  FF  TParaphrases; mutual entailmentcontradictionPresupposition66. a. He’s stopped turning into a werewolf every full moon.b. He used to turn into a werewolf every full moon.67. a. Her husband is a fool.b. She has a husband. a presupposes b entailment vs. implicature (sensitive to facts about the context)?Presupposition as a truth relation Sentences are views as external objects73. Step 1: If p is true then q is true.Step 2: If p is false then q is still true.Step 3: If q is true, p is either true or false.74. A First Truth table for presuppositionp qT  TF  TT or F  TComposite truth table for entailmentp qT  TF  T or FF  FT or F  TPresupposition as a truth relation75. a. I saw my father today.b. I didn’t see my father todayc. I saw someone today. (a entails c)76. a. The mayor of Liverpool is in town.b. The mayor of Liverpool isn’t in town.c. There is a mayor of Liverpool. (a presupposes c) Negating the presupposing sentence does not affect the presupposition, whereas negating an entailing sentence destroys the entailment.Presupposition as