Pronouns and their antecedents

Heim 1982, Kamp 1988, a.o.

1. Andrew has a child.
   She is at school.

2. Andrew is a parent.
   # She is at school.

3. Exactly one of the ten balls is not in the bag.
   It is under the sofa.

4. Exactly nine of the ten balls are in the bag.
   # It is under the sofa.

Aboutness

• The requirement for an indefinite antecedent is sometimes called the Formal Link Condition.

• The dynamic view: Content is influenced not just by what is said, but how it is said (Kamp 1981, Heim 1982).

• In talking, we keep track not just of information concerning how things are, but also referential information concerning what/who the speaker intended to refer to.

  • An utterance of “Andrew has a child” is about a child of Andrew’s in a way that “Andrew is a parent” is not.
  • Another way of saying the same thing: “Andrew has a child” introduces a discourse referent (Karttunen 1969)

The dynamic perspective

• Dynamic semantics enriches conversational contexts with referential information concerning intended reference (Irene Heim’s notion of a file).

• Part of the dynamic thesis is that uttering a sentence with an indefinite changes the referential information in the conversational context in a special way.

• Sentences with pronouns are sensitive to referential information in a way which other expressions aren’t.

• Dynamic semantics provides an elegant account of the aboutness properties of sentences with indefinites.
  • Dynamic semantics has a problem however: the behaviour of anaphora in complex sentences motivates a theory in which individual lexical items are in charge of referential information flow.

Where we’re going

• We’ll begin by touring data concerning possible anaphoric dependencies between indefinites and pronouns taken for granted in orthodox dynamic theories — the accessibility generalizations.
• We’ll lay out some problems and tensions for the accessibility generalizations, concluding that:
  • Orthodox dynamic semantics isn’t classical enough.
  • We need to take into account the role of pragmatics in anaphoric licensing.
• The goal will be a dynamic semantics in which referential information is passed uniformly from left-to-right.
  • The resulting theory will be rather permissive - we’ll restrict it in the pragmatic component.

Conjunction

5. A linguist walked in, and she sat next to a philosopher.
   He yawned.

6. # She walked in, and a linguist sat down.

Conditionals

7. If a linguist is here, she’s sitting next to a philosopher.
   # He yawned.

Negation

8. It’s not the case that a linguist is here.
   # She yawned.

Disjunction

9. # Either a linguist is here, or she’s smoking outside.

10. Either a linguist is here, or it’s raining.
    # She’s smoking outside.

Context change potentials

DS puts the lexicon in charge of regulating referential information flow.

(Schlenker 2006 a.o. make the same point wrt. presupposition projection.)

An alternative take

To be developed today:

• Taking the accessibility generalizations to be indicative of the semantic contribution of the logical connectives precludes a principled account of referential information flow.
• The accessibility generalizations are empirically flawed; accessibility is sensitive to contextual factors.
• The main point: the logical connectives are exactly what they seem to be - truth-functional operators - referential information flows uniformly from left-to-right.

Double negation

11. Frank doesn’t own no shirt. It’s in the closet.

12. It’s not the case that Frank doesn’t own any shirt. It’s in the closet.

Bathroom disjunctions

13. Either there isn’t a bathroom, or it’s upstairs.

• Referential information destroyed in an initial disjunct can be resurrected in a subsequent disjunct (observation due to Barbara Partee).

• N.b. this intuitively parallels presupposition projection facts (Beaver 2001):

14. Either Sam never smoked, or he stopped smoking.

Groenendijk & Stokhof disjunctions

15. Either we’re interviewing a linguist, or we’re interviewing a philosopher.
    (Either way) she’s waiting outside.

Anaphora and contextual entailment

• The final issue is, in my opinion, the most telling of all.

16. A: Either it’s a weekday, or Gabe baked a cake.
    B: It’s Saturday afternoon.
    A: Then, it’s cooling on the windowsill!

Beyond disjunction

Recall that conditionals are also (claimed to be) externally static.

17. A: If it’s the weekend, then Gabe baked a cake.
    B: It’s Saturday afternoon.
    A: Then, it’s cooling on the windowsill!

Take-away points

• Double-negation suggests we want a theory that is more classical than, e.g., orthodox DS.
• Bathroom disjunctions tell us that disjunction isn’t straightforwardly internally static; referential information can be transmitted between disjuncts.
• G&S disjunctions tell us that disjunction isn’t straightforwardly externally static; referential information can be passed further.
• Anaphora and contextual entailment tells us that pragmatic factors have a role to play in regulating the availability of subsequent anaphora.

A logical substrate

We’ll develop a theory of anaphora based on the following ideas:

• The core semantic value of a sentence is a (trivalent) truth-value; referential information is computed in tandem with this logical substrate.
• The logical connectives operate exclusively on the logical substrate.
  • Referential information is passed from left-to-right uniformly.
  • Incrementality in anaphoric processing is achieved by flipping a single “switch” throughout the grammar.

Enriching the dynamic notion of content

• Assignments are a store of referential information; they tell us how to fix the value of variables (i.e., pronouns).
• Sentences express functions from assignments (the input) to sets of assignment-truth-value pairs (the outputs) (Charlow 2014, 2019).
  • Another way of thinking about this: output assignments are polarized.
  • Whence talk of a ‘logical substrate’.
• Sentences containing neither indefinites nor pronouns polarize the input according to truth-conditional content.

Pronouns and the third truth-value

• Sentences with pronouns polarize the input assignment \(g\) depending on truth at \(g\).
• We’ll assume that assignments are partial; namely, an assignment \(g\) may not deliver a value for a particular index \(n\).

• Our trivalent logical substrate is starting to do some work.

Indefinites and indeterminacy

• We’ll use sets to model the idea that indefinites extend the input assignment indeterministically (following G&S).
  • Another way of thinking about this — indefinites introduce alternatives.

• What’s important here is that, due to the logical substrate, we distinguish between:
  • referential information introduced when there is a verifier (the input is extended indeterministically).
  • referential information introduced when there is no verifier (the input remains unchanged).

Illustration i

18. \(⟦\text{A}^1\text{ triangle is in the circle.}⟧^{[]}\)

\[ = \begin{cases} \{(⊤,[x]) \mid x\text{ is a triangle in the circle}\}\\ \{(⊥,[])\}\qquad\color{gray}{\text{there is no triangle in the circle}} \end{cases} \]

\[ = \{(⊤,[\color{red}{Δ}]),(⊤,[\color{blue}{Δ}])\} \]

Illustration ii

19. \(⟦\text{A}^1\text{ triangle is in the circle.}⟧^{[]}\)

\[ = \begin{cases} \{(⊤,[x]) \mid x\text{ is a triangle in the circle}\}\\ \{(⊥,[])\}\qquad\color{gray}{\text{there is no triangle in the circle}} \end{cases} \]

\[ = \{(⊥,[])\} \]

Comparison with first-generation Dynamic Semantics

• If there is a witness for the existential statement, then the true-paired outputs are equivalent to what is delivered by first-generation dynamic theories, such as Groenendijk & Stokhof’s (1991) Dynamic Predicate Logic.
• If there is no witness for the existential statement, the output is just the input assignment paired with false.
• In first-generation theories however, if there is no witness then the output set is simply empty; here we crucially keep track of both positive and negative referential information.

Payoff #1: negation

• Remember, one of the core foundations of the current approach: logical operators are truth-functional.
• Negation is lifted through the dynamic scaffolding, and applies pointwise to the contained truth-values.

• N.b. referential information survives, but it’s false-tagged.

Double negation

• Since negation is truth-functional, applying another negation will flip the polarities again.

• A doubly negated sentence conveys the same referential information as its positive counterpart!

Interlude: Strong Kleene

• Before we proceed much further, a remark is due on the semantics we’ll assume for the logical connectives.

  • Recall that a foundational assumption of the current approach is that logical operators are truth-functional; but we have three truth values (\(⊤,⊥,\#\)) to consider, not just two, which opens up a number of possibilities.

• The interpretation schema we’ll adopt for the logical connectives is Kleene’s strong logic of indeterminacy; (i.e., Strong Kleene).

• This is the logic that naturally emerges if we take \(\#\) to stand in for uncertainty whether true or false.

Strong Kleene conjunction

• In Strong Kleene, conjunctive sentences are:
  • true if both conjuncts are true,
  • false if either conjunct is false.
  • I.e., strong Kleene conjunctions have conjunctive verification conditions and disjunctive falsification conditions.

Strong Kleene disjunction

• In Strong Kleene, disjunctive sentences are:
  • true if either disjunct is true,
  • false if both disjuncts are false.
  • I.e., strong Kleene disjunctions have disjunctive verification conditions and conjunctive falsification conditions.

On explanatory adequacy

• The Strong Kleene entries for the connectives don’t need to be stipulated but rather reify how we ordinarily reason about uncertainty.

• An independent reason to think that Strong Kleene is a reasonable foundation: I agree with Rothschild (2017, p1) that “[…] when the dust has settled, this remains the simplest viable treatment of presupposition projection on the market.”

• Important: the Strong Kleene logic underlying the analysis here is completely symmetric; there is no room for asymmetries or incrementality in the logical substrate.

  • Compare, e.g., George (2007, 2008, 2014) who incrementalizes the logic in order to account for asymmetries in presupposition projection.

Lifting the logical operators

• In order to lift binary logical operators into a dynamic setting, we’ll adopt much the same strategy as with negation.
  • The truth-functional operator applies pointwise to the values in the logical substrate.
  • This time, we have two sets of outputs to worry about - the referential information ouputed by the first junct as passed in as the input to the second.

• Some details for the more technically-minded. For any two-place truth-functional operator \(\mathbf{R}\):

• N.b. Charlow (2014, 2019) reifies this algorithm in the compositional semantics via a regime of type-shifters; the current approach can be spelled out in these terms too.

A note on architecture

• Our algorithm relies on the assumption that the semantics can see the order of the juncts.

• This has important architectural ramifications regarding the information visible to the semantics.

Payoff 2: Dynamic conjunction

• Applying this algorithm to \(∧^s\) gives us something equivalent to DPL conjunction wrt positive referential information.
  • We can see this most clearly if we just compute the positive extension (\(⟦.⟧_+\); the referential information paired with \(\color{red}{⊤}\)).

• Conjunction is asymmetric despite a symmetric logical substrate.
• N.b., when we take into account the possibility of either conjunct being false the predictions diverge from orthodox DS. We’ll come back to this when we discuss the pragmatics.

Payoff 3: Bathroom disjunctions

20. Either there isn’t a\(^1\) bathroom, or it\(_1\)’s upstairs.

• In plain English, we can compute the positive referential information conveyed by the disjunctive sentence by:
  • passing the positive referential information of the first disjunct into the second, and gathering all of the outputs, positive or otherwise.
  • passing the outputs of the first disjunct (positive or otherwise) into the second, and retaining just the positive outputs.
• For our purposes, the second clause is important: we can pass the negative ouputs of the first disjunct into the second, and if there are positive outputs we dynamically verify the disjunctive sentence.

• Because of how negation works, if there is a bathroom (\(b\)), this will be stored in the negative information conveyed by the first disjunct “there isn’t a bathroom”:

• The false-tagged assignment licenses a pronoun in the subsequent sentence, which will be paired with true if there is indeed a bathroom upstairs:

21. Either there isn’t a bathroom, or it’s upstairs.
    # It is very clean.

The dynamic connective par excellence

• One way of thinking about what we’re doing: we take DPL conjunction to be the dynamic connective par excellence, and generalize it.
  • Referential information is always piped between juncts (from left-to-right), and can in principle be passed further.

22. Either a\(^1\) linguist is here or it’s raining.
    # She\(_1\)’s smoking outside.

• Just how bad is this result? In the next section i’ll argue that, in stating accessibiliy generalizations, we haven’t been paying enough attention to the pragmatic component.
• Once we understand some of the independently motivated pragmatic constraints on asserting complex, sentences, we’ll be in a position to understand apparent external staticity.
  • A move foreshadowed by the contextual entailment facts.

Pragmatics via Stalnaker and Heim

• In order to keep things simple, we’ve been operating in a purely extensional setting.

• To return to one of the themes explored at the beginning of this talk, we’d like a theory which addresses both worldly, and referential information.

• Following Heim (1982), we’ll treat the context set (which we’ll write as \(C\)), as a set of world-assignment pairs.

• Before anything has been uttered, every world in \(C\) is simply paired with the initial assignment \([]\).

Intensionalization

• We can mechanically intensionalize our theory by adding a world parameter to our interpretation function.
  • outputs are now truth-value/world/assignment triples

Stalnaker’s bridge

• We update \(C\) with a sentence \(ϕ\) (\(C[ϕ]\)) by evaluating \(ϕ\) wrt each world-assignment pair in \(C\), and retaining the true-tagged outputs.

• Stalnaker’s bridge (von Fintel 2008) demands that for assertion of \(ϕ\) to be successful, \(ϕ\) cannot be undefined at any point in \(C\).

• A direct consequence: a sentence with a pronoun indexed \(n\) carries a referential presupposition that \(n\) is defined.

Indefinites and updates

Some things that fall out automatically:

• Updating \(C\) with an existential statement results in a new context-set that licenses the referential presupposition of a subsequent coindexed pronoun.

• A witness to the existential statement is a necessary but not sufficient condition for licensing subsequent anaphora; using an indefinite is crucial.

A pragmatic constraint on disjunction

• We now have everything we need to understand apparent external staticity with disjunction

• We can independently observe that an utterance “P or Q” is only felicitous if P and Q are both real possibilies wrt the context set.

  • \(C\) shouldn’t entail the truth or falsity of either disjunct.

23. # Either someone was in the audience or the event was a disaster.

Accounting for external staticity

• \(\color{#20A5BA}{w_{ad}}\): \(a\) was in the audience; the event was a disaster.
• \(\color{#20A5BA}{w_{a¬d}}\): \(a\) was in the audience; the event was successful.
• \(\color{#20A5BA}{w_{∅d}}\): Nobody was in the audience; the event was a disaster.
• \(\color{#20A5BA}{w_{∅¬d}}\): Nobody was in the audience; the event wasn’t a disaster.

• Knock out the final world (\(\color{#20A5BA}{w_{∅¬d}}\)).
• Extend assignments paired with \(a\)-worlds with \(a\) (\(\color{#20A5BA}{w_{ad}}\),\(\color{#20A5BA}{w_{a¬d}}\)).
• Fail to extend the assignment paired with \(\color{#20A5BA}{w_{∅d}}\).

\[ \left\{\begin{aligned}[c] &(\color{#20A5BA}{w_{ad}},\color{#10A778}{[]})\\ &(\color{#20A5BA}{w_{a¬d}},\color{#10A778}{[]})\\ &(\color{#20A5BA}{w_{∅d}},\color{#10A778}{[]})\\ &(\color{#20A5BA}{w_{∅¬d}},\color{#10A778}{[]})\\ \end{aligned}\right\}\left[\begin{aligned}[c] &\text{someone}^1\text{ was in the audience}\\ &\text{or the event was a disaster} \end{aligned}\right] \]

\[ = \{(\color{#20A5BA}{w_{ad}},\color{#10A778}{[a]}),(\color{#20A5BA}{w_{a¬d}},\color{#10A778}{[a]}),(\color{#20A5BA}{w_{∅d}},\color{#10A778}{[]})\} \]

• Note that the resulting context set is not one in which the presupposition of a subsequent pronoun will be licensed.
  • This reflects the fact that a witness for the existential statement is not contextually entailed post-assertion!
  • We therefore get the appearance of external staticity - this does not however motivate saying anything special about the dynamics of disjunction. Moreover, our system doesn’t allow us to say anything special.

Addressing the role of contextual entailment

• The explanation for anaphora and contextual entailment falls out straightforwardly.
  • After using an indefinite, if a witness for the existential statement is subsequently contextually entailed, we predict anaphora to be possible.
• For example, a subsequent utterance might knock out the problematic world assignment pair:

24. A: Either someone was in the audience or the event was a disaster.
    B: The event wasn’t a disaster.
    A: In that case, I hope she enjoyed it!

Disjunctive subordination

25. Each linguist [met with a philosopher or read a philosophy paper]

26. They each [found her interesting or couldn’t understand it]

Negating conjunctions

27. It’s not the case that [anyone walked in and they sat down].
    # They remained standing.

G&S disjunctions

28. Either we’re interviewing a\(^1\) linguist
    or we’re interviewing a\(^1\) philosopher.

• The presupposition of a subsequent co-indexed pronoun will be satisfied, exactly because G&S disjunctions contextually entail a witness.
• It’s crucial that the indefinites in each disjunct are co-indexed (this has interesting consequences for Heim’s novelty condition - ask me about this in the Q&A).

Internal staticity and Hurford disjunctions

29. # Either a linguist is here, or she’s smoking outside.

Simons’ observation

30. # Either someone is in the audience,
    or the person in the audience is sitting down.

• In other words, if the presupposition of the second disjunct is satisfied, in entails the first.
• This is a special case of Hurford’s constraint (HC): a disjunction is odd if one disjunct entails the other.

Hurford’s constraint in a dynamic setting

31. # Someone\(^1\) is in the audience, or she\(_1\) is sitting down.

The bottom line

• We’ve achieved a dynamic semantics which is up-front about what exactly it stipulates.
  • Concretely, the locus of stipulation is in the statement of the algorithm for passing referential information, which we stipulate passes information from left-to-right.
• The idea is that there is a single switch which gives rise to incrementality in anaphoric processing; this isn’t localized to the lexical entries of individual connectives.
  • This makes a clear predictions with respect to acquisition, and cross-linguistic uniformity with respect to referential information flow.

• In developing a more principled theory of anaphora, what we’ve learned is that the literature has essentially been mistaken in taking the accessibility generalizations at face value.
  • In order to maintain a parsimonious semantic theory, due care needs to be taken to address the role of pragmatic factors.
  • Developing an understanding of the pragmatics of referential information is essential in order to improve on our understanding of the semantic component.
• As we’ve seen, it’s possible to retain some of the appealing aspects of dynamic semantics - such as the dynamic notion of content - while improving upon the stipulative nature of extant dynamic theories.

Acknowledgments

I’m deeply grateful to Simon Charlow, Keny Chatain, Enrico Flor, Danny Fox, Matthew Gotham, Julian Grove, Nathan Klinedinst, Matt Mandelkern, and Yasu Sudo for feedback which greatly improved this work.

I’d also like to thank audiences at Rutgers, NYU, and LENLS 17 for their feedback.

Ext 1: Donkey anaphora

• Although material implication doesn’t give a realistic semantics for conditionals, it’s interesting to consider what this system predicts when we apply our algorithm for logical connectives.
  • Unlike orthodox dynamic semantics, we systematically predict so-called “weak” or “existential” truth-conditions for donkey sentences (Kanazawa 1994, Chierchia 1995); ask me more about this in the Q&A.
  • Such readings are attested, but strong readings must be derived via some kind of strengthening mechanism.

Ext 2: Generalized quantifiers and modal subordination

• This is necessary in order to develop a principled account of donkey anaphora which doesn’t face the proportion problem.

32. Maybe there is no bathroom and maybe it is upstairs.