This paper offers a new theory of donkey anaphora that does not include any dynamic component. Even if the approach is not dynamic, it retains a key aspect of the dynamic tradition, namely the view that information states include not just factual information about the world, but also information about discourse referents, e.g., variables. It also makes crucial use of plural assignment functions (sets of standard assignments, cf. van der Berg 1996; Nouwen 2003; Brasoveanu in Linguist Philos 31: 129–209, 2008). Unlike dynamic approaches, sentences are evaluated as true or false relative to a pair (w, G), where w is a possible world and G is a plural assignment, with no reference to contexts or information states, and compositional semantics does not refer in any way to context update. In order to predict adequate meanings and felicity conditions, I combine two ingredients that have been used to account for presupposition projection, namely trivalence (Peters 1979, Beaver and Krahmer 2001) and Schlenker’s Transparency Condition (Schlenker 2007, 2008a). Two ideas play a crucial role in the proposal. First, a sentence such as ‘She<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$_x$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mi>x</mi> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> came’ comes with the presupposition that the variable x is “valued” and denotes an atomic individual, which means that every atomic assignment in G maps x to the same atomic value. Second, I adopt Mandelkern’s witness condition (Mandelkern’s 2022): an existential statement such as ‘Someone<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$_x$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mi>x</mi> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> came’ is undefined in (w, G) if it is classically true in w but G does not map x to a witness of the existential statement. Importantly, undefinedness is not equated with presupposition failure (e.g., even though ‘Someone<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$_x$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mi>x</mi> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> came’ can be undefined, it is in fact never a presupposition failure). Rather, presupposition projection is governed by Schlenker’s Transparency Condition (Schlenker 2007, 2008a): the presupposition ‘x is valued and atomic’ should be redundant in the syntactic position in which ‘She<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$_x$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mi>x</mi> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> came’ occurs. At the end of the paper, I discuss well-known ambiguities with donkey sentences (weak vs. strong, existential vs. universal readings) and show how they can be addressed in my system. The theory is presented here as a non-standard semantics for first-order logic, rather than a fragment of a natural language. Free variables are the counterparts of syntactically unbound pronouns, and existential quantifiers those of singular indefinites.

Trivalence and transparency: a non-dynamic approach to anaphora

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2026年4月25日

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Benjamin Spector

摘要

This paper offers a new theory of donkey anaphora that does not include any dynamic component. Even if the approach is not dynamic, it retains a key aspect of the dynamic tradition, namely the view that information states include not just factual information about the world, but also information about discourse referents, e.g., variables. It also makes crucial use of plural assignment functions (sets of standard assignments, cf. van der Berg 1996; Nouwen 2003; Brasoveanu in Linguist Philos 31: 129–209, 2008). Unlike dynamic approaches, sentences are evaluated as true or false relative to a pair (w, G), where w is a possible world and G is a plural assignment, with no reference to contexts or information states, and compositional semantics does not refer in any way to context update. In order to predict adequate meanings and felicity conditions, I combine two ingredients that have been used to account for presupposition projection, namely trivalence (Peters 1979, Beaver and Krahmer 2001) and Schlenker’s Transparency Condition (Schlenker 2007, 2008a). Two ideas play a crucial role in the proposal. First, a sentence such as ‘She $_x$ $_{x}$ came’ comes with the presupposition that the variable x is “valued” and denotes an atomic individual, which means that every atomic assignment in G maps x to the same atomic value. Second, I adopt Mandelkern’s witness condition (Mandelkern’s 2022): an existential statement such as ‘Someone $_x$ $_{x}$ came’ is undefined in (w, G) if it is classically true in w but G does not map x to a witness of the existential statement. Importantly, undefinedness is not equated with presupposition failure (e.g., even though ‘Someone $_x$ $_{x}$ came’ can be undefined, it is in fact never a presupposition failure). Rather, presupposition projection is governed by Schlenker’s Transparency Condition (Schlenker 2007, 2008a): the presupposition ‘x is valued and atomic’ should be redundant in the syntactic position in which ‘She $_x$ $_{x}$ came’ occurs. At the end of the paper, I discuss well-known ambiguities with donkey sentences (weak vs. strong, existential vs. universal readings) and show how they can be addressed in my system. The theory is presented here as a non-standard semantics for first-order logic, rather than a fragment of a natural language. Free variables are the counterparts of syntactically unbound pronouns, and existential quantifiers those of singular indefinites.