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2 of informativeness can be determined by entailment relations. The stronger term entails the weaker but New York Institute - St Petersburg 2007 not vice versa. All __ is a stronger [determiner] than Some __ because All ___ entails Some ___ while PROBLEM SET Some ___ does not entail All ___ (to say that All Italians like ice-cream logically implies [=entails] that P. Schlenker - Presupposition Some Italians like ice-cream; however, to say that Some Italians like ice-cream does not necessarily imply [=entail] that All Italians like ice-cream). Given the prominent role of scales, this kind of inference has been dubbed scalar implicature and has since become a paradigmatic case for the study of implicature in Exercise 1. the linguistic-pragmatic literature. This (...) analysis to not restricted to [determiners]. It can be applied to a host of scales (...). For In each of the following, determine whether b. is: examples, if a speaker uses the modal [=auxiliary] Might (as in Bill might be in the office), it implies [or (i) an entailment of a. rather: implicates -PS] that the speaker had reason not to say the stronger-sounding Must (as in Bill must (ii) a scalar implicature triggered by a. be in the office [note that the same reasoning would apply to Has to, as in: Bill has to be in the office. The (iii) a presupposition of a. experiment discussed below uses has to instead of must, but this does not affect the argument -PS]. Other (iv) none of the above scales can be applied to, but are by no means limited to, frequency (where the use of Sometimes excludes [You can give your answer without justification - this is just a practice exercise] Always), epistemic status1 (where the weaker Think __ implies [=implicates] that it is not the case that Know ___), and connectives (where P or Q indicates [=implicates] Not both P and Q). In each case, scales (1) a. John stopped smoking. range from less to more informative and the speaker's use of a less informative term implies [=implicates] b. John used to smoke. the exclusion of a more informative one. The present study has two goals. One is to establish that scalar implicatures are psychologically (2) a. There was a package on the table. real and common in reasoning scenarios. In addressing this goal, this work draws on theories of linguistic b. There was only one package on the table. pragmatics. To my knowledge there are no experimental studies that actually try to unravel the implicature process as described by contemporary linguistic-pragmaticists. It would be of obvious value to bring (4) a. At least 4 students came to the party experimental data to bear on their analyses. b. At least 3 students came to the party The second objective, which addresses the paper's experimental approach, is to establish how this class of weak scalar terms develops [in children -PS]. (...) I will argue that the explicit meaning of a weak (5) a. At least 4 students came to the party scalar term needs to be incorporated before any implicit meanings (i.e. implicatures) are determined. Thus, b. At least 5 students came to the party when a weak scalar term is employed (e.g. Some), its explicit meaning (e.g. at least one) must be the default before it undergoes implicit pragmatic modifications (e.g. at least one but not all). Given that the (6) a. Exactly half the students came to the party. explicit meanings of these terms are tantamount to standard logic's, across development one should find b. Not all students came to the party. indication of a consistent ordering in which logical meanings are preferred before implicit interpretations are. (7) a. Some students came to the party. How does one go about demonstrating the main developmental claim about implicatures b. Not all students came to the party experimentally? I begin by pointing to evidence from the developmental literature [=scientific literature concerned with children's cognitive development -PS] that shows that children's initial representations of (8) a. I respect the King of Moldova. relatively weak scalar terms appear logical in nature [=these representations include the meaning but not b. Moldova has a king. the scalar implicature -PS] before yielding to emergent pragmatic interpretations [=interpretations that include both the meaning and the scalar implicature -PS]. This intriguing finding has been uncovered in (9) a. Most students came to the party three independent studies. Smith (1980) shows that younger children (4- to 7-year-olds), while appearing b. More than 7 students came to the party rather competent overall with [determiners], 'overwhelmingly' treat Some as compatible with All on a task where children had to answer questions like 'Do some birds have wings?' This implies that the well-known (10) a. John knows that Mary is sick. pragmatic interpretation of Some (where Some is not compatible with All) arrives afterward. Similarly, b. Mary is sick. with respect to proposition connectives, Braine and Rumain (1981) presented evidence showing that deductively competent 7- and 9-year-old children favor a logical interpretation of Or (which can be Exercise 2. The Acquisition of Scalar Implicatures glossed as p or q and perhaps both) [in other words, these children favor an interpretation of Or with its normal meaning but without the associated scalar implicature -PS]. Adults on the same task were The following is an excerpt from 'When Children Are More Logical than Adults: Experimental equivocal [i.e. they hesitated between several interpretations -PS], though they tended to favor exclusive Investigations of Scalar Implicatures', an article by the psychologist Ira Noveck that appeared in the interpretations (...) [i.e. they favored an interpretation of p or q as: p or q but not both]. One other journal Cognition in 2001 (Cognition 78, 165-188). independent confirmation of this pragmatic effect comes from Paris (1973), whose data on disjunction (=on or) reveal the same developmental tendency as Braine and Rumain's. Thus, empirical findings [According to theories of scalar implicatures], 'when one utters a relatively weak term (e.g. Some), indicate that interpretations of weak scalar terms among children, who are otherwise competent, are it is an indication that the speaker chose not to articulate a more informative term from the same scale (e.g. initially logical in nature and, with age, become potentially pragmatic [i.e. start including scalar All). Presumably, the speaker does not know whether All is applicable or knows that it is not. Thus, implicatures -PS]. It should be noted that none of these authors anticipated such findings. uttering Some __ ___ implicates Not All __ __ (and Not all __ __ is logically equivalent to Some __ are not __ [example: Not all cats are black is logically equivalent to Some cats are not black -PS]. The scale 1 Epistemic = relating to knowledge. 3 4 If this developmental tendency - showing that pragmatic interpretations of weak scalar terms are consistently shown to increase subsequent to, and at the apparent expense of, logical meanings - can be Column 3: pointing to the Parrot + Bear Box generalized it would indicate the emergence of scalar implicature. It also leads to an unusual True if the implicature is not taken into account, for the same reasons as in Column 2. development curve in which young competent participants appear more logical than their older cohorts [=than the older children they are compared to -PS]. This leads to the paper's experiments. Column 4: pointing to the covered box. Experiment 1 tests participants' rendering of Might in a scenario that justifies two opposing The participants know that the covered box is either like the Parrot-Only box or like the Parrot- treatments, a logical interpretation (where Might is compatible with Must [note that in the experiment Bear Box. Either way there must be a parrot in the box. Hence: below, Must is replaced with Has to, but the argument is the same -PS]) and a pragmatic one (where Might (i) Without the implicature, There might be a parrot in the box is true is not compatible with Must [i.e. in the experiment below it is not compatible with Has to -PS]). The (ii) With the implicature, There might be a parrot in the box is false. scenario also allows for the evaluation of an exhaustive set of modal statements in order to see how implicature development takes place with respect to logical development. (...) Experiment 1: Might The paradigm in Experiment 1 is a reasoning scenario, but only as background for a puppet who utters an exhaustive series of modal statements [=statements involving might, has to, etc. -PS]. That is, modal statements expressing necessity, non-necessity, possibility, and impossibility are presented with respect to a visual scene. The scenario is described below. Consider three boxes. One is open and has a toy parrot and a toy bear in it (the Parrot + Bear Box), the second is open and has only a parrot (the Parrot-only Box), and the third stays covered (Box C). Participants are told that Box C has the same content as either the Parrot + Bear Box or the Parrot-only Box. The paradigm may be explained in terms of [Table 1] (...). Note (PS): Table 1 gives truth values for the statements without their implicatures. The table should be read as follows. Experimental Situation: The participants are shown a box with a parrot only, a box with a parrot and a bear, and a covered box about which the experimenter says: 'All I know is that this [pointing to the covered box] looks like this [pointing to the parrot only box] or like this 'pointing to the parrot + bear box'. First line: There has to be a parrot in the box. Column 2: pointing to the Parrot-only Box. The participant knows that there must be a parrot in this box, hence the sentence 'There has to be a parrot in the box' is true. The puppet presents each of eight statements and it is the child's task to say whether the puppet's claim is right or not. The critical statement that allows us to study implicature is There might be a Colum 3: pointing to the Parrot + Bear Box parrot in the box. On the one hand, if the participant adopts an explicit, logical interpretation of The participant knows that there must be a parrot in this box, hence the sentence 'There has to be a Might (where Might is compatible with Has to), one would expect an affirmative reply ('the puppet is parrot in the box' is true. right'). On the other hand, if the participant adopts a pragmatic, restrictive interpretation of Might [i.e. an interpretation of might __ with the implicature: ... but not has to ___ -PS] (where Might is not compatible Column 4: pointing to the covered box. with Has to) one would expect a negative reply ('the puppet is wrong') or at least some equivocation The participant knows that the covered box is either like the Parrot-only Box or like the Parrot- [=hesitation among two interpretations -PS]'. Bear Box. Either way there must be a parrot in the box. Hence 'There has to be a parrot in the box' is again true. Method Third line: 'There might be a parrot in the box' -Participants Column 2: pointing to the Parrot-only Box Thirty-two 5-year-olds, 20 7-year-olds, 16 9-year-olds and 20 adult native English speakers The participant knows that there must be a parrot in this box, hence the simple meaning of the participated in the study. The children's mean ages (...) were 5 years 5 months (...) [for the first group, sentence 'There might be a parrot in the box' [without the implicature] is true. (With the implicature the ranging from 5 years 1 month to 5 years 11 months -PS], 7 years 5 months [for the second group, ranging sentence would be interpreted as: 'There might be a parrots in the box and it's not the case there has to be a from 7 years 1 month to 8 years 0 otnhs -PS], and 9 years 4 months [for the third group, ranging from 9 parrot in the box, which given the information available is false). years 0 months to 9 years 5 months -PS]. Participants were recruited from Minneapolis and St. Paul in 5 6 Minnesota. Adults participated to fulfill requirements for the Introductory Psychology course at the Note that the 7- and 9-year olds are doing some rather sophisticated modal reasoning University of Minnesota. [=reasoning involving possibilities -PS] and they have no difficulty rejecting statements that appear wrong. A significant number of children detect logically wrong statements like There cannot be a bear -Materials and There does not have to be a parrot. Yet, these same children tend to agree with There might be a parrot. Their ability to detect wrong statements does not extend to those that would involve pragmatic Two opened boxes and one closed box were presented. One opened box contained a parrot and interpretations. Adults also detect when statements are wrong but their equivocality [=their hesitation -PS] another contained a parrot and a bear. Participants were told that the closed box had the same contents as surrounding There might be a parrot indicates that they are wary of its potential for two interpretations. ' one of the two open boxes (...). Participants then heard eight statements by a puppet named Wylbur. [These are the eight statements in Table 1.] Question 1. What is the scale relevant for the analysis of might? Results Analyses begin with an overview of children's reasoning abilities on this task. This way we can Question 2. In this experiment, why do adults tend to reject There might be a parrot in the box even determine the approximate age at which children show competence before I turn to the expression of though they systematically accept There might be a bear in the box ? interest, There might be a parrot in the box. Question 3. Given these data, what it the most plausible explanation of why 5-year-old children appear to behave more logically than adults? Question 4. Why do 9-year-olds appear to behave more logically than adults, but less logically than 5- and 7-year-olds? Exercise 3. Presupposition Projection in Heim’s theory Question 1. Consider the following contexts (for present purposes you may take them to be possible worlds): c1: There are exactly two students. They are all sick. c2: There is exactly one student. He is sick. c3. There are exactly two students. They are all healthy. c4. There is exactly one student. He is healthy. The Context Set is C ={c1, c2, c3, c4} The actual context is: c4 Table 2 shows participants' rates of correct evaluations in relation to each of the eight modal For each sentence S in (1)-(5), you should: statements across the four age groups. Participants' performance is of interest with respect to: a) compute C[S] (you need not give complete details -down to the lexical entries you posit- but you (1) chance - the probability is 0.5 that a child would be correct on any given statement; and should still say how you obtain your result). (2) developmental changes. b) compute the truth value of S in c4. The table shows that 5-year-olds are above chance levels in three of the eight conditions. This is an impressive rate of success, but it does not reveal that the 5-year olds have largely mastered the task. Note: you will assume that a sentence S has the value # in c4 if C[S]=#. Seven-year-olds answer correctly at rates that are above chance levels for seven out of the eight conditions and show the earliest signs of showing consistent mastery on the task. The same holds for 9-year-olds. (1) Both students are sick. That 7-year-olds should appear competent in modal reasoning abilities conforms to expectations based on the literature (...). (2) The student is healthy. Seven-year-olds' rate of logical interpretations with respect to There might be a parrot in the box (80%) is intriguing not only because they respond at rates that are significantly above chance (3) There is exactly one student and the student is healthy. levels but because they do so at a rate that is significantly higher than that of the adults (35%) (...). Most adults assume that the possibility that the parrot will be found in the hidden box is wrong because the (4) There are exactly two students and both students are healthy. expectation is that the parrot's presence in the hidden box is necessary. Nine-year olds look less like the 7- year-olds; 69% provide the logically correct answer. Nevertheless, the difference between the 9-year-olds (5) There are exactly two students or else the student is sick. and adults is [statistically] significant. (...) 7 8 -the implicature of p v q is the conjunction of the implicatures of p and the implicatures of q and ¬(p ! Question 2. q) Consider the sentence in (6): Example: the implicature of ((A v B) & C) is the conjunction of the implicature of (A v B) and of the implicature of C [by (ii)] (6) It is raining and both students are sick. C has no implicature [by (i)] The implicature of (A v B) is ¬(A ! B) [by (ii) and (i)] When (6) is uttered, we typically infer that there are exactly two students. Suppose that this is a In sum, the implicature of ((A v B) ! C) is: ¬(A ! B). presupposition of the sentence. Is this fact predicted by Heim's analysis (as presented in class)? Be very This appears to be correct. If I say ‘(Rick is a philosopher or he is a poet) and he is a musician’, it will precise, i.e. show in detail why it is or is not predicted that any Context Set in which the sentence is typically be understood that Rick isn’t both a philosopher and a poet. uttered felicitously (though not necessarily truly) is one in which there are exactly two students. (Big hint: Heim does not make the right predictions here.) Show that this procedure also derives the correct result for ((A v B) v C). Question 4. (Even more optional) Exercise 4. Implicature Projection (M. Simons; B. Schwarz) [Advanced and OPTIONAL; the Prove that the result can be generalized: for any natural number n!2, this procedure predicts that exercise presupposes a good knowledge of propositional logic] A1 v A2 v... v An implicates that at most one of A1, ..., An is true. Since A1 v A2 v... v An also asserts that at least one of A1, ..., An is true, the assertion together with the implicature will yield the result that exactly When one utters ‘Rick is a philosopher or he is a poet or he is a musician’, it is normally understood that one of A1, ..., An is true. Rick has exactly one of these occupations, although we also know that someone might be at the same Hint: use a proof by induction. time a philosopher, a poet and a musician. We explore how this observation could be derived. Notation: As in propositional logic, we abbreviate not as ¬, and as !, (inclusive) or as v. Question 1. Exclusive 'or'? Let us suppose first that ‘or’ is ambiguous, and has a variant (which you will symbolize as v) on which it is read as exclusive. Give the truth-table of v, and apply the truth table method to ‘((A v B) v C)’. Does this derive the result observed above? Justify your answer. Question 2. Inclusive ‘or’ with global computation of implicatures? Suppose now that ‘or’ is unambiguous, and always has the meaning of inclusive disjunction, which you will symbolize as ‘v’. Let us use the following abbreviations: A=’Rick is a philosopher’ B=’he is a poet’ C=’he is a musician’. Discuss the predictions of a theory based on scalar implicatures for the following sub-hypotheses: (a) (A " B) " C has a single scalar alternative: (A ! B) ! C (b) (A " B) " C has a single scalar alternative: (A v B) ! C (c) (A " B) " C has a single scalar alternative: (A ! B) v C (d) A " B) " C has as scalar alternatives all of (A ! B) ! C, (A v B) ! C, (A ! B) v C Question 3. Inclusive ‘or’ with local computation of implicatures? Let us now depart from the standard assumption that implicatures are computed by comparing entire sentences to other sentences that could have been uttered instead. Rather, we will assume that implicatures are computed locally in each subtree, in the following way (note that we restrict ourselves to a fragment that contains only conjunctions and disjunctions): (i) Atomic formulas don’t have implicatures. (ii) For any formulas p and q (whether atomic or not), -the implicature of p ! q is the conjunction of the implicatures of p and the implicatures of q