Robert Pasternak (2018), “Thinking Alone and Thinking Together” Minghui Yang 1. Distributive versus non-distributive readings of attitude ascriptions w There are two possible ways to interpret a sentence containing plural NP. w Distributive reading: the predicate is applied to each of the individual members of the “group” designated by the NP. Under this reading, each of the individuals designated by the NP must instantiate the relevant property. e.g. Alexis and Brian are running entails Alexis is running . w Non-distributive/collective reading: the predicate is only applied to the “group” understood as a whole. e.g. Alexis and Brian ate a whole pie does not entail Brian ate a whole pie . 1.1 Distributive reading of attitude ascriptions w Attitude ascriptions usually take distributive readings: (1) a. Alexis and Brian think that Cass left. b. Alexis and Brian want Cass to leave. c. Alexis and Brian wish that Cass had left. d. Alexis and Brian regret that Cass didn’t leave. w Sentence (1a) entails: (1a*) Alexis believes that Cass left, and Brian believes that Cass left. w Similarly, (1b)-(1d) entail that both Alexis and Brian have the desire, wish and regret, respectively. 1.2 Non-distributive reading of attitude ascriptions w Attitude verbs can also take non-distributive readings, as illustrated in the following case: Case: Sam owns a construction company and has six clients, none of whom know of the others’ existence. She has convinced each client that she would build a house for him. In reality, she is a con artist and built no houses at all. (2) (In total,) Sam’s six clients think she built six houses for them. Intuition: (2) is true in the context.
w The story has made it clear that none of the clients have the belief that Sam will build six houses. Thus a distributive reading of (2) would render it false. w Moreover, (2) cannot be explained away by appealing to de re , since the following sentence is also false: (3) There are six houses that Sam’s six clients think she built for them. w Thus, sentence (2) must have a non-distributive reading. 1.3 “Conjunction” versus “Disjunction” 1.3.1 Collective beliefs obtained by conjunction w What would be a non-distributive reading of (2)? A natural thought: Each of the six clients believes that Sam will build one house. Now their beliefs could somehow be “added up” conjunctively into one “cumulative” belief that Sam will build six houses. Notes: (i) “Cumulative” beliefs are not mental states proper. (ii) Conjoining “Sam will build a house for client i” (i = 1-6) six times will get you a house-count of six only if all instances of “for client i” are non-overlapping (i.e. if house x is for client i, then it is not for client j where i ≠ j). This assumption is tacit in the story. w One more example that confirms the “conjunction” intuition: Case: Paul just got married, and his cousins Arnie and Beatrice, who have never met, just caught wind of it. Arnie suspects that Paul’s husband is rich, and has no other relevant opinions. Beatrice thinks he’s a New Yorker, and has no other relevant opinions. (4) Paul’s cousins think he married a rich New Yorker. Intuition: Sentence (4) is true. w None of Paul’s cousins individually has the belief that Paul married a rich New Yorker. Thus we are once again forced into a non-distributive reading of (4). w The most straightforward way to account for the truth of (4) once again appeals to conjunction : the conjunction of Arnie’s belief and Beatrice’s belief is that Paul’s husband is a rich New Yorker . 1.3.2 Collective beliefs obtained by disjunction w There are cases in which the conjunction strategy doesn’t work, for instance: Case: Paul just got married, and his cousins Arnie and Beatrice, who have never met, just caught wind of it. Arnie thinks that Paul married a rich Marylander, while Beatrice thinks he married a poor New Yorker.
(5) Paul’s cousins think he married a rich New Yorker. (6) Paul’s cousins think he either married a rich Marylander or a poor New Yorker. Intuition: Sentence (5) is false, sentence (6) is true. w It seems that we are adding things up by disjunction this time. w Quibble: maybe we are not forced into read (6) collectively in the first place. Indeed, if we adopt a distributive reading of (6) instead, we would also predict that (6) is true. Note: Here we need the additional assumption that beliefs of Arnie and Beatrice are suitably closed under entailment. The assumption is significant from an epistemological perspective, but tacit and ubiquitous in semantics. w To rule out the distributive reading, we consider yet another case: Case: Paul has three cousins, Arnie, Beatrice, and Kate. Arnie and Beatrice’s beliefs are as in the original wedding scenario: rich and New Yorker, respectively, and otherwise agnostic. Kate, like Beatrice, is not opinionated about Paul’s husband’s wealth, but she thinks he’s from Iowa, not New York. (7) Paul’s cousins think he married a rich man from either New York or Iowa. Intuition: (7) is true. w Our intuition in (7) is not compatible with the suggestion that the attitude ascription should be read distributively: Arnie is not committed to Paul’s husband’s being from New York or Iowa, while Beatrice and Kate are not committed to Paul’s husband’s being rich. Thus the distributive reading would render (7) false. And yet (7) seems true. w So we are committed to a collective reading of (7). 1.3.3 Separating conjunctive and disjunctive cases w Question: what separates conjunctive cases from disjunctive cases? Tentative answer: when the individual beliefs of group members are compatible , we add them up by conjunction ; otherwise we add them up by disjunction . w To flesh out a little more details of this: The conjunction case seems relatively uncontroversial. When we have a bundle of individual beliefs that are consistent, we simply conjoin them together. The case in which the bundle of beliefs are inconsistent, however, deserves more scrutiny. Suppose we have a set of individual beliefs {P, Q, R} where P is consistent with both Q and R but Q is inconsistent with R. {P, Q, R} is an inconsistent set. But we don’t want the cumulative belief to be (P or Q or R), the straightforward disjunction of all the relevant beliefs--it seems too weak! What we really want, as illustrated by (7), is rather:
(P and (Q or R)) w What is the way to do this? Pasternak has discussed two accounts. Due to the limited time, however, I shall talk about only one of them, i.e. the “premise negotiation” analysis. 2. Background: semantics of “believe” (and “think”) w The lexical entry of “believe”: (8) [[believe]] ! = λp.λe. ∀ w ∈ Dox(e)[p(w)] (9) [[Arnie believes that Paul married a rich man]] ! = 1 iff ∃ e [Exp(e) = a ∧ ∀ w ∈ Dox(e)[rich-man(w)]] w Transcribe (9) into plain English: in any possible world compatible with Arnie’s doxastic state (which is designated by the event-variable e ), Paul married a rich man. w Exp (e) is the function that returns the subject of the doxastic state e. w Ordinary doxastic states have only one subject. But we may introduce “cumulative” doxastic states (notification: 𝑓 " ⊔ 𝑓 # ) which has multiple subjects. Accordingly we extrapolate the definition of Exp (e) to allow plural subjects like x ⊔ y . (10) [[Paul’s cousins believe that p]] ! = 1 iff ∃ e[Exp(e) = a ⊔ b ∧ ∀ w ∈ Dox(e)[p(w)]] We may just define x ⊔ y as the mereological sum of x and y. But what is 𝑓 " ⊔ 𝑓 # ? It must be w generated from individual doxastic states 𝑓 " and 𝑓 # . For now we introduce an operation J as a placeholder for this operation: (11) Dox(e) = J({Dox(e’)) | e’ ∈ Atm(e)}) where Atm(e) is defined as the set of individual doxastic states that compose e. 3. Premise negotiation 3.1 Motivating ideas w The basic idea of premise negotiation is to “make the most of it” even in a pessimistic situation. Suppose you have a list of obligations to fulfill. When the list is consistent (i.e. it is possible to fulfill them all), the way to “make the most of it” is to fulfill all of them. But what if the list is inconsistent? In this case it is not possible to fulfill all of the listed obligations. Yet it still makes sense to ask them to fulfill their obligations as much as possible . What does this mean? Let’s consider a concrete example: Say, that the person is asked to pick out a card. The relevant obligations are (i) picking out a diamond (D), (ii) picking out a queen (Q) and (iii) picking out a king (K).
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