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Discourse dynamics, pragmatics, and indefinites

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Notes

  1. 1.

    Whether the change in context affects the truth or merely the acceptability of (3) depends one one’s view of predicates like flat.

  2. 2.

    It’s a little weird to think of untokened discourses as dynamic; it is more precise to think of tokened discourses as dynamic and untokened discourses as things that would be dynamic if they were tokened.

  3. 3.

    This is not an entirely accurate characterization of static semantics, since static semantics includes views in which contents encode more than merely truth conditions, such as structured views of content. The point is that static contents are not things that act directly on contexts.

  4. 4.

    See chapter 1 of Lewis (2011) for arguments for this point.

  5. 5.

    While the present paper concentrates on basic, unembedded cases of indefinites, in other work (Lewis (2011)) I show how my account can be extended to cases of indefinites embedded under operators and quantifiers.

  6. 6.

    This is not to argue that no dynamic semantic account can be right, but that this family of accounts cannot be right.

  7. 7.

    This description glosses over considerable formal differences between the views. These differences are not relevant for the present project.

  8. 8.

    I take file cards to be equivalent to other concepts that do the same work, such as discourse referents or discourse entities. I prefer the file card metaphor because the terminology involves no temptation to confuse file cards with real objects in the world, contrary to the unfortunate term discourse referent. Anyone who prefers working in a discourse referent framework should feel free to substitute discourse referent for file card throughout. By adopting Heim’s metaphor of a file card, I do not intend to take on any of the details of file change semantics.

  9. 9.

    One standard example of such a view is Dynamic Predicate Logic (Groenendijk and Stokhof (1991)). The interested reader is encouraged to look at the Appendix for a somewhat formal comparison between DPL and an implementation of the view I present informally in § 3.

  10. 10.

    In general, sentences with pronouns encode an instruction to update a particular file card; just which file card depends on the association of a pronoun with a particular antecedent, which is determined before the semantic machinery does its thing. How this association takes place is itself an interesting topic, but is beyond the scope of the present work.

  11. 11.

    On certain formal implementations, this amounts to the indefinite semantically binding the pronoun. See the Appendix for more details.

  12. 12.

    After formulating these examples, I was pleased to discover that Szabo (2000) also notes an example of this kind:

    1. (10)

      The detective ordered a Martini. As soon as the waiter left he knew that something was wrong. Then he realized what it was. He had just ordered a Martini from a waiter who looked exactly like the murderer he was after. (p. 37)

    Szabo also uses this as evidence that novelty is pragmatic, but offers neither further argument for this fact, nor a pragmatic derivation of novelty.

  13. 13.

    One thing the proponent of a semantic account of novelty might say in these cases is that they involve the merging of file cards. Multiple file cards can be merged into one during the course of a conversation if it is revealed that what were being treated as distinct objects under discussion are actually satisfied by one and the same object in the world. For example, suppose we are discussing Mark Twain and Samuel Clemens, unaware that they are in fact the same individual. If at some point someone informs the conversational participants that they are one and the same person, the file card for Mark Twain and the one for Samuel Clemens are merged into one. So someone might suggest that what is going on in the summary uses is that a new file card for the indefinite description is in fact being introduced, but then immediately merged with the relevant old one. I think this explanation of the summary cases fails for several reasons. There is nothing jarring about the cases. Unlike the case in which it is explicitly conveyed in the conversation that we have been mistakenly treating one object as two, there is nothing here to provoke a pragmatic repair of the context. Furthermore, a merging solution seems to be an ad hoc treatment of the intuitive data. Phenomenologically speaking, there is nothing in the summary cases that feels like the paradigmatic cases of merging file cards (as in the Mark Twain/Samuel Clemens case). Merging saves a technical notion of novelty by sacrificing the file card picture’s ability to capture what is intuitively going with the objects under discussion (i.e. that there is one object under discussion in the summary cases, not two). An account of discourse dynamics that captures what ordinary people take to be going on in conversations is preferable to an account that makes technical distinctions that don’t intuitively connect to what is going on in real life conversations.

  14. 14.

    p. 65 fn. 59. Though clearly a case of non-novelty, this doesn’t seem like the same sort of example as the summary cases. Introductory and summary uses of indefinites are not intended to exhaustively cover all possible uses of indefinites.

  15. 15.

    Another case of non-novelty for indefinites, called the requantification problem, occurs when giving a focus sensitive or presupposition sensitive semantics for adverbs of quantification. These semantics require that some indefinites pick up old file cards. For more discussion see Rooth (1995), Krifka (2001), and von Fintel (1994).

  16. 16.

    E.g., this is the approach of Krifka (2001) and Farkas (2002).

  17. 17.

    See Grice (1989) pp. 39, 44. It seems that Grice himself actually misspeaks when he writes about generalized conversational implicatures. While generalized implicatures are supposed to work just like particularized ones in that they are derived from the content of an utterance, Grice writes that they are associated with “a certain form of words in an utterance”. (p. 37) He must mean, rather, that the implicature is normally associated with the content of utterances containing a certain form of words.

  18. 18.

    For example, suppose I am on the phone with you and I am in New York City and you are in Florida. If I say “it’s raining”, the default interpretation is that it’s raining in New York City. But I can cancel that interpretation by explaining that I was watching TV and saw that it is raining where you are in Florida, which is what I meant to express.

  19. 19.

    See for example Thomason (1990), Levinson (1983), Leech (1983), Harnish (1976), and Davis (1998) for some criticisms of Gricean derivations of implicature.

  20. 20.

    p. 330

  21. 21.

    It should be noted that some people disagree with this assessment, and think the only element that needs to be represented in the context is the common ground, i.e. the set of propositions mutually presumed by the conversational participants. Since the common ground represents everything that is presumed by the conversational participants, it will include information about the conversation itself, such as which objects are under discussion. Therefore, in principle, there should be some way to translate what I say here into an account that has only the common ground in the context. However, I do not think it is a fruitful way of thinking of things and so will not pursue it further here.

  22. 22.

    Discourse plans are distinct from domain plans in that the latter is a plan regarding a task aside from the conversation, while the former is a plan for the conversation itself. The two can of course be related—my plan for the conversation might be intricately involved with achieving my domain plan—but they are nevertheless distinct. For example, suppose we are having a conversation about going to see a movie together tonight. I might have a domain plan to go see an action film; I might have a discourse plan (part of which is) to enter the topic of action films onto the conversational context. Clearly the discourse plan here is aimed to play a part in achieving my domain plan, but they are not the same plan. See Grosz and Sidner (1990) and Litman and Allen (1990) for further discussion on discourse vs. domain plans.

  23. 23.

    Local plans might also be thought of a subplans, or elements of an overall plan. I am remaining neutral for now on the nature of plans.

  24. 24.

    A speaker might have a weaker sort of plan, one that constrains the possible plans for the conversation rather than determining one particular future course, even in the short term. For example, a speaker might mention several places and continue to talk about one of them depending on what her interlocutor replies.

  25. 25.

    At least in part—I leave it open that there are other ways in which the conversational context is updated; for example, updating with the fact that a goat just walked into the room is not a matter of recognizing anybody’s plans. I will not be concerned with these other ways in the present paper.

  26. 26.

    Thomason argues that plan recognition should replace Grice’s conversational maxims, but I think it is better seen as compatible with Grice’s project.

  27. 27.

    In “Logic and Conversation”, Grice suggests that some generalized conversational implicatures associated with sentences containing indefinites are a result of the maxim of quantity. I think this explanation fails in this case, because one of the alternatives to using an indefinite is using a proper name, and the two cannot be placed in an informativity scale, thus making it impossible to apply the maxim of quantity.

  28. 28.

    See Grice (1989) pp. 31–32. Grice’s two examples are each in their own way relevantly analogous and disanalogous to the derivation I give below. The reader should not take any details of these specific derivations as features of my view. The point is only that Grice seemed to think relevance and perspicuity often join together in generating implicatures.

  29. 29.

    p .6

  30. 30.

    Recall that I am not assuming that these expressions are conventionally associated with familiarity, but merely that they have the ability to pick out familiar objects.

  31. 31.

    Robin Jeshion (pc.) suggested there might also be something like a scalar implicature going on here, since the content of the sentence is neutral as to the number of women potentially under discussion, and so we might expect to get a numerically neutral file card, i.e. one that is not specifically singular or plural, rather than a singular file card. I think this is a perfectly natural addition to the pragmatic derivation. I am also open to the idea that it is in fact a neutrally numbered file card that gets added and the fact that only a singular pronoun is licensed is a grammatical, and not a semantic or a pragmatic, constraint. At this point, I am not sure how to decide between the two explanations.

  32. 32.

    On the static view, how the pronoun gets its value from the file card is a matter of the semantics of the pronoun. The present account is compatible with various views on the subject. I explore one formal account—treating the pronoun as a free variable—in the Appendix.

  33. 33.

    Planning to talk about an object under discussion is not the only area in which speakers may have a range of plans rather than a specific plan in mind. Other examples include specificity resolution for questions and the interpretation of epistemic modals. (See von Fintel and Gillies (2008)).

  34. 34.

    On some views of structured propositions such as that of King (2007), (18) and (16a) do not have the same content. On such a view, existential sentences are only those that explicitly contain an existential term like some or a. On this view, the novelty implicature runs entirely off content, though the explanation is otherwise the same.

  35. 35.

    This is not to preclude the possibility of adding new file cards based on the perceptual environment or by accommodation. Under certain circumstances, I do think file cards can be added by accommodation. I will turn to some such cases shortly. File cards are also added for things salient in the perceptual environment of a conversation. For example, to borrow a well-known example from Stalnaker, if a goat walks into the room during our conversation, we all note that a goat walked into the room and record that fact. In our current terminology that amounts to adding a file card for the goat that walked in.

  36. 36.

    For example, see Roberts (2003). This sort of position is generally motivated by a desire to account for the familiarity requirement on definites in the face of data that demonstrates that definite descriptions can be used without explicitly introduced antecedents. The position is also not entirely fruitful, since there are just as many examples of definite descriptions felicitously used where the existence of the object in question is not entailed by the context. For example, while the position on file cards may solve the problem for cases like “I went out for dinner last night. The waiter was rude.”, it doesn’t solve the problem for cases like “I went out for dinner last night. The salmon was divine.”. Restaurants almost always have waiters, but they do not almost always have salmon.

  37. 37.

    In Roberts (ms), she argues that the file cards that are actually tracked by the conversational participants are just a limited subset of all the file cards available in the context, the file cards that are relevant to the current question(s) under discussion.

  38. 38.

    The implicature appears to be detachable in the case of one or more, but I take this to be mere appearance. Utterances containing the locution one or more do not appear to license singular anaphora, despite the fact that they are truth-conditionally equivalent to claims containing indefinites. One would expect given my account that they do introduce a new file card and license subsequent anaphora. However, it seems that the lack of felicitous singular anaphora is a grammatical constraint quite independent from anything discussed here. Utterances containing one or more do in fact introduce a new file card, but it’s one that licenses plural anaphora. (A complete account of anaphora involves positing something like plural file cards anyway.) While “One or more women walked in. #She sat down.” is bad, “One or more women walked in. They sat down.” is fine, despite the first sentence’s non-committance as to whether there is one or multiple women. Even if one takes one or more to have the same semantic value as a, some, and at least one, it is undeniable that the former takes a plural noun and requires plural agreement on the verb, while the latter take singular nouns and require singular agreement. Thus it should come as no surprise that the former takes a plural pronoun while the latter take singular ones.

  39. 39.

    In some of the summary uses, such as (25b), the sentence doesn’t add any information, but rather registers the speaker’s surprise. While it is not straightforwardly an informational update, it still intuitively clear how such a statement is relevant to the set of file cards, since it comments on an existing card in the set. Such cases are probably more acceptable if repeating the known information helps to answer a question under discussion. The connection between objects under discussion and questions under discussion is an interesting one, but pursuing it is beyond the scope of the present work.

  40. 40.

    The example is originally due to Barbara Partee, and discussed in Heim (1982), Kamp (1988), and Groenendijk and Stokhof (1999), among others.

  41. 41.

    There are other replies to this example on behalf of traditional semantics. For example, Stalnaker (1998) argues that one can account for the difference based on the referential intentions of the speakers. See chapter 4 of Lewis (2011) for arguments against a referential intentions account of anaphora on indefinites.

  42. 42.

    This is not to say that a dynamic semanticist could not offer an explanation, but to claim that there is no explanation that stems naturally from the family of dynamic semantic views considered in § 2.

  43. 43.

    These examples are from Heim (1982).

  44. 44.

    See for example Evans (1977), Neale (1990) and King (1994), among others.

  45. 45.

    See in particular Stalnaker (1978) for more discussion on the pragmatic motivations of this update.

  46. 46.

    I present the rule based on the simple case for purposes of perspicuity. The general rule for ∃ xϕ is a little more complicated to define.

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Acknowledgments

Thanks are due to Josh Armstrong, Andy Egan, Thony Gillies, Gabe Greenberg, Robin Jeshion, Michael Johnson, Jeff King, Ernie Lepore, Eliot Michaelson, Sarah Moss, Jason Stanley, Will Starr, Catherine Wearing, the members of the Rutgers philosophy of language work-in-progress group, and the participants at the Bellingham Summer Philosophy Conference 2011 for helpful comments and discussion. Earlier drafts of this work also benefited from the comments of audience members at the Rutgers Center for Cognitive Science semantics discussion group and the Rutgers Philosophy Department graduate student colloquium. All mistakes are of course my own.

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Correspondence to Karen S. Lewis.

Appendix: DPL and PL+D

Appendix: DPL and PL+D

In order to get a sense of how my view compares to the dynamic semantic views described in § 2, I will compare a standard example of such a dynamic semantics with a simple formal implementation of my view. The dynamic semantics I will look at is Dynamic Predicate Logic (henceforth DPL, Groenendijk and Stokhof (1991)). I will compare it with static, ordinary first order predicate logic augmented with the pragmatic view argued for in this paper, a system I call Predicate Logic plus Dynamics (PL+D ). First order predicate logic is almost certainly not the best logic for capturing natural language semantics. I mean to endorse neither of these systems as the ultimate examples of their genre. However, they serve as convenient illustrative examples, since most readers are familiar with predicate logic, and we need not look at a more complicated logic to capture the point I wish to make.

DPL

The syntax of DPL is that of ordinary first order predicate logic, and so I will not review it here. A DPL model is a standard model for predicate logic, a pair 〈D , F〉, where D is a non-empty set of individuals, and F is an interpretation function. Contexts are sets of assignment functions, which are total functions from variables to individuals in the model. Semantic values on this formulation of DPL are relations between input and output assignment functions, but this is equivalent to stating them in terms of functions from contexts to contexts (from sets of assignment functions to sets of assignment functions). See Groenendijk and Stokhof (1990) for a detailed discussion of this equivalence. Here are the semantic clauses relevant to the examples discussed in this paper. (I suppress reference to a model since it shouldn’t cause any confusion for the present examples. I use the letters g, h, and k for arbitrary assignment functions.)

DPL semantics (relevant clauses)

  1. 1.

    \( \begin{aligned}{\left[\kern-0.15em\left[ t \right]\kern-0.15em\right]_g} &= g(t)\,\hbox{if t is a variable}\\ &= F(t)\,\hbox{if t is a constant}\end{aligned} \)

  2. 2.

    \(\left[\kern-0.15em\left[ Rt_1\ldots t_n \right]\kern-0.15em\right] = \{\langle g,h \rangle|\;h = g\; \& \;\langle \left[\kern-0.15em\left[ t_1 \right]\kern-0.15em\right]_h\ldots \left[\kern-0.15em\left[ t_n \right]\kern-0.15em\right]_h \rangle \in F(R) \}\)

  3. 3.

    \( \left[\kern-0.15em\left[ \phi \wedge \psi \right]\kern-0.15em\right] = \{\langle g,h \rangle|\;\exists k: \langle g,k \rangle \in \left[\kern-0.15em\left[ \phi \right]\kern-0.15em\right] \,\&\, \langle k,h \rangle \in \left[\kern-0.15em\left[ \psi \right]\kern-0.15em\right] \}\)

  4. 4.

    \(\left[\kern-0.15em\left[ \exists x \phi \right]\kern-0.15em\right] = \{\langle g,h \rangle |\;\exists k : k[x]g \,\& \,\langle k,h \rangle \in \left[\kern-0.15em\left[ \phi \right]\kern-0.15em\right] \}\)

Let’s work through example (4), repeated here, and its (D)PL translation:

  1. (31)

    a. A woman walked in.

    b. She ordered lunch.

  2. (32)

    a. ∃x(woman(x) ∧ walked.in(x))

    b. ordered.lunch(x)

DPL treats discourses as conjunctions of the sentences in the discourse. Given the definition of conjunction, this amounts to finding the semantic value of the first sentence of the discourse, and using the output assignment functions of that sentence as the input functions to the second sentence in the discourse. So let’s just go sentence by sentence. Plugging (32a) into the semantic clause for existentials, we get \(\{\langle g,h \rangle|\;\exists k : k[x]g \,\&\, \langle k,h \rangle \in \left[\kern-0.15em\left[ woman(x) \wedge walked.in(x) \right]\kern-0.15em\right] \}\). This result will be much more perspicuous if we first reduce the last part (the semantic value of woman(x) ∧ walked.in(x)). This is a conjunction, so we apply clause 3, which guarantees that the output assignments of the first conjunct serve as the input to the second. Since each conjunct is an atomic formula, the formulas act as tests on the input context, passing through only those assignment functions from the input that assign x to something in the interpretation of the appropriate predicate. Since we’re dealing with all atomic formulas, for which in each input-output assignment function pair the output is identical to the input, we need not worry about going through the steps of calculating the value of the conjunction. After applying clauses 3, then 2, and then 1 inside the existential, we now have \(\{\langle g,h \rangle|\;h[x]g \,\&\,h(x)\; \in F(woman) \,\&\, h(x)\in F(walked.in)\}\). Now it’s easy to see what the existential does. (In fact, all the extra steps we just took are because the definition must apply in the general case in which there may be another quantifier inside the scope of the existential.) An existential is an assignment shifter—it takes each of the assignment functions in the input and returns all of those that differ at most from it in that they assign x to an individual in the interpretation of woman and walked.in. The output context of (32a), therefore, is the set of x-variants of the input context that assign x to a woman who walked in. The output context of (32a) serves as the input to (32b), which, as an atomic formula, tests the context, allowing through just those assignment functions that assign x to something in the interpretation of ordered.lunch. The result is that the final output context contains all and only assignment functions that assign x to a woman who walked in and ordered lunch.

The discourse is true if and only if the output context is not empty, that is, there is at least one woman who walked in and ordered lunch. Thus DPL succeeds in giving the intuitively right truth conditions for the discourse and accounting for both novelty and licensing. We can think of the assignment functions as recording information about the objects under discussion. Changes to the assignment functions reflect changes in information about objects under discussion. As outlined above, the CCP of an indefinite resets the potential value of a particular variable. This is what accounts for novelty—x is treated like a brand new variable, with which no previous information is associated. At the same time, it explains licensing. Though the pronoun is not syntactically bound by the indefinite, on this view it is semantically bound: the indefinite shifts the assignment functions and it is this new set of assignment functions relative to which the pronoun is interpreted. Finally, changing the context so that it includes only assignment functions that assign x to something in the interpretation of ordered.lunch is tantamount to updating the relevant file card with that information.

PL+D

PL+D is just ordinary first order predicate logic augmented with two pragmatic principles. It is intended to cover the same fragment of English as DPL. Models and contexts are defined in the same way as for DPL. Strictly speaking, treating contexts as sets of assignment functions doesn’t exactly match the informal description of contexts employed in this paper. I’ve said we are taking a context to be a set of file cards, but this implies that each assignment function represents a file card, which it clearly doesn’t. Technically, a more appropriate formal implementation of a file card is as a set of (partial) assignment functions, and so our formal contexts should be sets of sets of assignment functions. I will suppress this complication for present purposes, since the simpler version offers a better comparison with DPL, and still captures information about objects under discussion, even if the context is not strictly speaking a set of file cards. (One can think of the set of partial assignment functions for each variable as the file cards.) Following the ordinary Tarskian interpretation of predicate logic, the semantic value of formulas in PL+D are sets of truth-making assignment functions. A formula is true (relative to a model) iff its denotation is not empty.

PL +D semantics (relevant clauses)

  1. 1.

    \( \begin{aligned}{\left[\kern-0.15em\left[ t \right]\kern-0.15em\right]_g} &= g(t)\,\hbox{if t is a variable}\\ &= F(t)\,\hbox{if t is a constant}\end{aligned} \)

  2. 2.

    \(\left[\kern-0.15em\left[ Rt_1\ldots t_n \right]\kern-0.15em\right] = \{ g | \langle \left[\kern-0.15em\left[ t_{1}\right]\kern-0.15em\right]_{g}\ldots \left[\kern-0.15em\left[ t_{n}\right]\kern-0.15em\right]_{g} \rangle \in F(R) \}\)

  3. 3.

    \(\left[\kern-0.15em\left[ \phi \wedge \psi \right]\kern-0.15em\right] = \{g|g \in \left[\kern-0.15em\left[ \phi \right]\kern-0.15em\right] \,\&\, g \in \left[\kern-0.15em\left[ \psi \right]\kern-0.15em\right] \}\)

  4. 4.

    \(\left[\kern-0.15em\left[ \exists x \phi \right]\kern-0.15em\right] = \{g|\exists k : k[x]g \,\&\, k \in \left[\kern-0.15em\left[ \phi \right]\kern-0.15em\right] \}\)

In addition, there are two pragmatically motivated operations that relate utterances to contexts. One adds the truth-conditional content of an utterance to the context, and is formally modeled as set intersection. Intersective updates apply to every utterance: they take the truth-conditional content of an utterance (the set of truth-supporting assignment functions) and intersect them with the input context, thereby outputting only those assignment functions that are compatible with the information conveyed by the utterance. I did not give a pragmatic motivation for intersection in the present paper, but it is already recognized by dynamic and static semanticists alike that this is easily done.Footnote 45 In brief, the explanation is as follows. One of the central goals of a conversation is to convey information. The conversational context encodes the mutual presumptions of the conversational participants, leaving as open possibilities anything compatible with the presumed information. Once an assertion has been accepted, it is only rational to eliminate all the possibilities that conflict with the information conveyed by the assertion. Given our assumptions about the nature of contexts and contents, the formal operation that models this is intersection.

The other pragmatic update adds a new file card to the context. Adding a new file card is modeled as a function that takes all the assignment functions in the input context and returns all the x-variants (or, more generally, variants for the appropriate variable) that assign x to an object with the properties predicated of x in the logical form of the utterance. As the reader can probably already guess, this update is pragmatically triggered when a sentence containing an indefinite in an introductory context is uttered. The function that returns the appropriate x-variants of assignment functions is the formal operation that represents what we’ve been informally glossing as adding a new file card. If we are modeling information about objects under discussion in terms of assignment functions, then updates regarding the objects under discussion must be modeled as changes to the assignment functions.

PL+D pragmatic updates

Where C is the input context, P is the content of an arbitrary assertion, and H is an arbitrary predicate, the 2 pragmatic updates are:

  1. 1.

    C[P] = C ∩ P (Truth-conditional update)

  2. 2.

    C[∃xHx]Footnote 46 = \(\bigcup\limits_{g \in C}\,\{ h|\;h[x]g \,\&\, h(x) \in F(H) \}\) (New file card update)

Let’s see how PL+D explains (32). Conversational participants always update the context with the informational content of an assertion (by intersection). The content of (32a) is the set of assignment functions such that for each assignment function, there exists at least one x-variant that assigns x to a woman who walked in. If there is such an object in the model, this will amount to the denotation being the set of all assignment functions. The intersective update, therefore, has no effect on the input context. (32a), as an existential, also triggers the second pragmatic update. The function for adding a new file card takes the input context and returns all the x-variants of each assignment function that assign x to a woman who walked in. So after semantically and pragmatically processing (32a), the context is in the same state as after the semantic processing of the same sentence according to DPL. (32b) will trigger the normal intersective update. Its content is the set of assignment functions that assign x to something that ordered lunch. Since all the the assignment functions in its input context assign x to a woman who walked in, the resulting output context will include only assignments that assign x to a woman who walked in and ordered lunch. The final output context is therefore the same one DPL predicts, and intuitively the correct one; the assignment functions record the information that there is at least one object that is a woman, and walked in, and ordered lunch.

I have been glossing over one complication of PL+D . The problem with treating pronouns as straightforward free variables in a static semantics is that formulas containing free variables do not get the truth conditions we really want. The set of assignment functions (32b) determines, for instance, is the set of all assignment functions that assign x to an object that ordered lunch, and so the sentence would be true so long as something in the model ordered lunch. This may or may not be a bad consequence, depending on one’s take of the data. This may just be the correct way of modeling the truth conditions of a pronominal sentence out of context. But within a context, we want a sentence containing a pronoun to pick out a subset of these assignment functions. In (32), this is the set of assignment functions that assign x to a woman who walked in. This is easily fixed, however, by making the semantic clause for pronouns sensitive to the assignment functions in the input context. This is an intuitive way to model the fact that pronouns are anaphoric—they must look to something prior for their value. Moreover, dynamic and static semanticists alike agree that it is perfectly acceptable to have context-sensitive expressions in a static semantics. It is the context-affecting nature of certain expressions that make some people think we need a dynamic semantics. If we want to leave the semantic clause for free variables alone (say, because we want to employ free variables for something other than the translation of pronouns), we can always introduce a new sort of symbol for translating the pronoun into the logic that acts as a context-sensitive free variable. I propose we translate pronouns as lower case p’s (loosely following Dekker (2004)) with alphabetical subscripts that connect them to the variable associated with their antecedents. For example, (32b) would be translated as follows:

  1. (33)

    ordered.lunch(p x )

And the semantic clause for such phrases would be:

$$ \left[\kern-0.15em\left[ Rp_x\ldots p_z \right]\kern-0.15em\right] = \{g \in C | \langle \left[\kern-0.15em\left[ x \right]\kern-0.15em\right]_g\ldots\left[\kern-0.15em\left[ z \right]\kern-0.15em\right]_g \rangle \in F(R)\} \hbox{(where C is the input context)} $$

PL+D offers analogous explanations of novelty and licensing to DPL, though pragmatically instead of semantically explained. Adding a new file card resets the x-values of the assignment functions in the context (like the semantic value of an existential in DPL); this accounts for novelty. It also outputs all the x-variants of the input assignment functions; it is this new context relative to which the anaphoric pronoun is interpreted, thus accounting for licensing. Whereas in DPL we saw something we thought of as semantic binding, in PL+D , we can think of the relationship between indefinite and pronoun as pragmatic binding. A sentence containing an indefinite pragmatically triggers the assignment functions in the context to be set up in a way such that when the information conveyed by a pronominal sentence is added to the context, the pronoun receives the correct interpretation.

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Lewis, K.S. Discourse dynamics, pragmatics, and indefinites. Philos Stud 158, 313–342 (2012). https://doi.org/10.1007/s11098-012-9882-y

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Keywords

  • Scalar Implicature
  • Conversational Context
  • Dynamic Semantic
  • Discourse Referent
  • File Card