Propositional attitudes

Transcription

1 Propositional attitudes Readings: Portner, Ch What are attitude verbs? We have already seen that verbs like think, want, hope, doubt, etc. create intensional environments. For example, (1a) and (1b) don t jointly entail (1c). (1) a. The most powerful wand is the Elder Wand. b. Lockhart thinks that his wand is the most powerful wand. c. Lockhart thinks that his wand is the Elder Wand. Such verbs indicate that their subject holds a certain mental state, or attitude, regarding the proposition denoted by the embedded sentence. So we call such verbs (propositional) attitude verbs. We ll focus on attitude verbs that encode belief (such as think or doubt) and desire (such as want and hope). 2. Possible world semantics for attitude verbs 2.1. Motivating possible world semantics for attitude verbs Parallels with modals There are obvious similarities between modal verbs and attitude verbs: (2) a. Hermione might be in the library. In some of the speaker s belief worlds, Hermione is in the library. b. Ron must do his homework. In all worlds where all obligations are fulfilled, Ron does his homework. c. Harry thinks that Hermione is in the library. In all of Harry s belief worlds, Hermione is in the library. d. Molly wants Ron to do his homework. In all of Molly s desire worlds, Ron does his homework Issues with a possible-world-free analysis Consider the following sentences: (3) a. Little Emma thinks there is a monster under her bed. b. Little Emma wants to find a unicorn. Trying to give a semantics to (3a) without possible worlds quickly gets us into trouble (similar reasoning applies to (3b)): (4) a. x.monster(x) Think(e, Under(x, b)) Problem: we commit to the existence of monsters. 1

2 b. Think(e, x.monster(x) Under(x, b)) Problem: if we treat the second argument of Think extensionally, then it denotes a truth value, in which case (3b) is equivalent to any sentence attributing any belief that has the same truth value to little Emma. We thus need to treat the complement of think intensionally, as a set of possible worlds Fleshing out the possible-world-based analysis We resort once again to accessibility relations: The accessibility relations of belief attitude verbs deliver worlds that are compatible with what the subject believes at the world of evaluation. The accessibility relations of desire attitude verbs deliver worlds in which all the subject s desires are fulfilled. Every attitude verbs we ve looked at so far has imposes requirements on all the worlds delivered by the accessibility relation, i.e., they come with universal quantificational force (express modal necessity). (5) x believes p = 1 iff Acc bel (x) p x believes p is true iff the set of worlds compatible with x s beliefs is a subset of p (6) x wants p = 1 iff Acc boul (x) p x wants p is true iff the set of worlds compatible with x s desires is a subset of p Let s look at an example. Let B stand for There is a monster under little Emma s bed, and R for There is a monster on little Emma s roof. Now let s assume the model in (7) where w 0 is the world of evaluation and the arrows point to the worlds accessible from w 0 : (7) w 0 B, R w 1 B, R w 2 B, R w 3 B, R The sentence (3a) (Little Emma thinks there is a monster under her bed) is true in (7), because B holds in all accessible worlds, but we don t commit to the existence of monsters in the actual world. We can now also capture the fact that (8a) and (8b) don t jointly entail (8c), since the tallest building in NYC will pick out different referents in the world of evaluation and in little Emma s belief worlds: (8) a. The tallest building in NYC is One World Trade Center. b. Little Emma thinks that her house is the tallest building in NYC. c. Little Emma thinks that her house is One World Trade Center. 2

3 In-class Exercise 1 Given the model in (9), for each of the accessibility relations in (10), determine whether the sentence (2c) is true under that accessibility relation. (9) w 0 (world of evaluation) : Hermione is not in the library, Snape is angry. w 1 : Hermione is not in the library, Snape is not angry. w 2 : Hermione is in the library, Snape is angry. w 3 : Hermione is in the library, Snape is not angry. (10) worlds accessible from w 0 : a. w 0, w 1, w 2, w 3 b. w 0, w 2, w 3 c. w 2, w 3 d. w 2 Now do the same thing for the model in (11), the accessibility relations in (12), and the sentence in (2d). (11) w 0 (world of evaluation) : Ron doesn t do his homework, Snape is angry. w 1 : Ron doesn t do his homework, Snape is not angry. w 2 : Ron does his homework, Snape is angry. w 3 : Ron does his homework, Snape is not angry. (12) worlds accessible from w 0 : a. w 1, w 2, w 3 b. w 2, w 3 c. w Logical consequences of the modal analysis of attitude verbs Because the set of one s belief worlds in which p holds is necessarily a subset of the set of all the worlds in which p holds, the analysis proposed above also has some logical consequences: Consequence 1 If x believes/wants p is true, and p contradicts q, then x believes/wants q is false. Consequence 2 If x believes/wants p is true, and p entails q, then x believes/wants q is also true. As a special case: if x believes/wants p is true, and p and q are semantically equivalent, then x believes/wants q is also true. Sometimes these consequences are correct. For example, if Harry thinks that Hermione is in the library, it follows that he doesn t think that Hermione is not in the library. But as we will see, sometimes those consequences are incorrect. 3

4 3. Issues with the possible-world-based analysis of attitude verbs 3.1. Problems of Consequence 1: gradability of desire The simplistic view from section 2.2 cannot handle contradictory desires; thus, assuming that Hermione can t both go home and stay at Hogwarts for Christmas, Consequence 1 from 2.3 predicts that Hermione can t have both desires in (13): (13) a. Hermione wants to go home for Christmas to see her parents. b. Hermione wants to stay at Hogwarts for Christmas to study in peace. Let s see why that s the case: Let G stay for the intension of Hermione goes home and S for the intension of Hermione stays at Hogwarts. Because Hermione can t do both, the sets G and S are disjoint: G S =. (13a) requires that Acc boul (h) G, and (13b) requires that Acc boul (h) S. The only way that can be the case is if Acc boul (h) =. Similarly, the simplistic view can t account for sentences like this: (14) a. Hermione wants to go home for Christmas more than she wants to stay at Hogwarts. b. Hermione wants to go home for Christmas as much as she wants to stay at Hogwarts. In other words, the simplistic view doesn t take into account the gradable nature of desire. We could solve the issues above by imposing orderings on the sets of worlds delivered by desire-related accessibility relations, so that some worlds are better than other Problems of Consequence 2: undesirable entailments Let s look at some examples when the prediction that x believes/wants p entails x believes/wants q whenever p entails q is empirically wrong. For example, since p always entails p q, we incorrectly predict that (15a) entails (15b): (15) a. Harry believes that Gryffindor won. b. Harry believes that Gryffindor or Slytherin won. Another example. The two sentences in (16) are mathematical truths and thus necessarily true in all possible worlds: (16) a. Two plus two is four. b. The square root of is 245. Thus, if one believes (16a), under the view developed in 2, they should also believe (16b). However, (17a) can be true without (17b) being true: (17) a. Emma knows that two plus two is four. b. Emma knows that the square root of is

5 Yet another example. Under the analysis of names as rigid designators, if two names refer to the same individual, they have the same denotation. For example, the names Cicero and Tully refer to the same individual, thus, the sentences in (18) are semantically equivalent: (18) a. Cicero was a great orator. b. Tully was a great orator. However, the sentences in (19) don t seem to be semantically equivalent (imagine that Emma doesn t know that Cicero and Tully are two different names for the same person): (19) a. Emma believes that Cicero was a great orator. b. Emma believes that Tully was a great orator Possible solution: take form into account One direction towards a solution is to say that sometimes the form of a sentence matters: (20) a. Emma s beliefs can be represented by the sentence Cicero was a great orator. b. Emma s beliefs can be represented by the sentence Tully was a great orator. The move in (20), however, takes us beyond standard truth-conditional, compositional semantics, so it is not uncontroversial. What you need to know Key notions: verbs (propositional) attitude verbs, desire attitude verbs, belief attitude Answers to the following questions: What problems does an analysis of attitude verbs without possible worlds run into? What are some issues with desire and belief attitude verbs that arise under the simplistic view from section 2, and what are some possible directions for resolving them? Skills: Informally describe the truth conditions of sentences with desire and belief attitude verbs under the simplistic view from section 2 (e.g., x believes that p is true iff in all x s belief worlds p is true). Given a model and an accessibility relation, determine if a given sentence containing a desire or belief attitude verb is true or false. 5