Donkey sentence

Insemantics,adonkey sentenceis a sentence containing apronounwhich is semanticallyboundbut syntactically free. They are a classic puzzle informal semanticsandphilosophy of languagebecause they are fullygrammaticaland yet defy straightforward attempts to generate theirformal languageequivalents. In order to explain how speakers are able to understand them, semanticists have proposed a variety of formalisms including systems ofdynamic semanticssuch asDiscourse representation theory.Their name comes from the example sentence "Every farmer who owns a donkey beats it", in which thedonkey pronounacts as a donkey pronoun because it is semantically but not syntactically bound by the indefinitenoun phrase"a donkey". The phenomenon is known asdonkey anaphora.

Examples

The following sentences are examples of donkey sentences.

• Omne homo habens asinum videt illum.( "Every man who owns a donkey sees it" ) —Walter Burley(1328),De puritate artis logicae tractatus longior
• Every farmer who owns a donkey beats it.
• If a farmer owns a donkey, he beats it.
• Every police officer who arrested a murderer insulted him. "

Analysis of donkey sentences

The goal offormal semanticsis to show how sentences of anatural languagesuch asEnglishcould be translated into a formal logical language, and so would then be amenable to mathematical analysis. FollowingRussell,it is typical to translateindefinite noun phrasesusing anexistential quantifier, as in the following simple example from Burchardtet al:

"A woman smokes." is translated as$\exists x\,({\text{WOMAN}}(x)\land {\text{SMOKES}}(x))$

The prototypical donkey sentence, "Every farmer who owns a donkey beats it.", requires careful consideration for adequate description (though reading "each" in place of "every" does simplify the formal analysis). The donkey pronoun in this case is the wordit.Correctly translating this sentence will require using auniversal quantifierfor the indefinite noun phrase "a donkey", rather than the expected existential quantifier.

The naive first attempt at translation given below is not a well-formed sentence, since the variable$y$is leftfreein the predicate${\text{BEAT}}(x,y)$.

$\forall x\,({\text{FARMER}}(x)\land \exists y\,({\text{DONKEY}}(y)\land {\text{OWNS}}(x,y))\rightarrow {\text{BEAT}}(x,y))$

It may be attempted to extend thescopeof the existential quantifier to bind the free instance of$y$,but it still does not give a correct translation.

$\forall x\,\exists y\,({\text{FARMER}}(x)\land {\text{DONKEY}}(y)\land {\text{OWNS}}(x,y)\rightarrow {\text{BEAT}}(x,y))$

This translation is incorrect since it is already true if there exists any object that is not a donkey: Given any object to be substituted for$x$,substituting any non-donkey object for$y$makes thematerial conditionaltrue (since itsantecedentis false), and so existential clause is true for every choice of$x$.

A correct translation into first-order logic for the donkey sentence seems to be

$\forall x\,\forall y\,(({\text{FARMER}}(x)\land {\text{DONKEY}}(y)\land {\text{OWNS}}(x,y))\rightarrow {\text{BEAT}}(x,y))$,

indicating that indefinites must sometimes be interpreted as existential quantifiers, and other times as universal quantifiers.

There is nothing wrong with donkey sentences: they are grammatically correct, they are well-formed and meaningful, and their syntax is regular. However, it is difficult to explain how donkey sentences produce their semantic results, and how those results generalize consistently with all other language use. If such an analysis were successful, it might allow a computer program to accurately translate natural language forms intological form.It is unknown how natural language users agree – apparently effortlessly – on the meaning of sentences such as the examples.

There may be several equivalent ways of describing this process. In fact,Hans Kamp(1981) andIrene Heim(1982) independently proposed very similar accounts in different terminology, which they calleddiscourse representation theory(DRT) andfile change semantics(FCS), respectively.

Theories of donkey anaphora

It is usual to distinguish two main kinds of theories about the semantics of donkey pronouns. The most classical proposals fall within the so-calleddescription-theoretic approach,a label that is meant to encompass all the theories that treat the semantics of these pronouns as akin to, or derivative from, the semantics ofdefinite descriptions.The second main family of proposals goes by the namedynamic theories,and they model donkey anaphora – and anaphora in general – on the assumption that the meaning of a sentence lies in its potential to change the context (understood as the information shared by the participants in a conversation).

Description-theoretic approaches

Description-theoretic approaches are theories of donkey pronouns in which definite descriptions play an important role. They were pioneered byGareth Evans's E-type approach,which holds that donkey pronouns can be understood as referring terms whose reference is fixed by description.

For example, in "Every farmer who owns a donkey beats it.", the donkey pronoun "it" can be expanded as a definite description to yield "Every farmer who owns a donkey beats the donkey he/she owns." This expanded sentence can be interpreted along the lines of Russell'stheory of descriptions.

Later authors have attributed an even larger role to definite descriptions, to the point of arguing that donkey pronouns have the semantics,and even the syntax,of definite descriptions. Approaches of the latter kind are usually calledD-type.

Discourse representation theory

Donkey sentences became a major force in advancingsemanticresearch in the 1980s, with the introduction ofdiscourse representation theory(DRT). During that time, an effort was made to settle the inconsistencies which arose from the attempts to translate donkey sentences intofirst-order logic.

The solution thatDRTprovides for the donkey sentence problem can be roughly outlined as follows: The common semantic function of non-anaphoricnoun phrasesis the introduction of a newdiscourse referent,which is in turn available for the binding of anaphoric expressions. No quantifiers are introduced into the representation, thus overcoming the scope problem that the logical translations had.

Dynamic Predicate Logic

Dynamic Predicate Logic models pronouns asfirst-order logicvariables,but allows quantifiers in aformulato bind variables in other formulae.

History

Walter Burley,a medieval scholastic philosopher, introduced donkey sentences in the context of the theory ofsuppositio,the medieval equivalent of reference theory.

Peter Geachreintroduced donkey sentences as acounterexampletoRichard Montague's proposal for a generalized formal representation ofquantificationinnatural language.His example was reused byDavid Lewis(1975),Gareth Evans(1977)and many others, and is still quoted in recent publications.

See also

• Epsilon calculus– Extension of a formal language by the epsilon operator
• Garden-path sentence– Sentence that starts in a way that a reader's likely interpretation will be wrong
• Generic antecedent– Representatives of classes in a situation in which gender is typically unknown
• Lambda calculus– Mathematical-logic system based on functions
• Montague grammar– Approach to natural language semantics
• Singular they– Gender-neutral English pronoun

Further reading

• Abbott,Barbara.'Donkey Demonstratives'.Natural Language Semantics10(2002): 285–298.
• Barker, Chris. 'Individuation and Quantification'.Linguistic Inquiry30(1999): 683–691.
• Barker, Chris. 'Presuppositions for Proportional Quantifiers'.Natural Language Semantics4(1996): 237–259.
• Brasoveanu, Adrian.Structured Nominal and Modal Reference.Rutgers UniversityPhDdissertation,2007.
• Brasoveanu, Adrian.'Uniqueness Effects in Donkey Sentences and Correlatives'.Sinn und Bedeutung12(2007):1.
• Burgess, John P.'E Pluribus Unum:Plural Logic and Set Theory',Philosophia Mathematica12(2004): 193–221.
• Cheng, Lisa LSandC.-T. James Huang.'Two Types of Donkey Sentences'.Natural Language Semantics4(1996): 121–163.
• Cohen, Ariel.Think Generic!Stanford, California:CSLI Publications,1999.
• Conway, L. and S. Crain. 'Donkey Anaphora in Child Grammar'. InProceedings of the North East Linguistics Society(NELS)25.University of Massachusetts Amherst,1995.
• Evans, Gareth.'Pronouns'.Linguistic Inquiry11(1980): 337–362.
• Geurts, Bart.Presuppositions and Pronouns.Oxford:Elsevier,1999.
• Harman, Gilbert.'Anaphoric Pronouns as Bound Variables: Syntax or Semantics?'Language52(1976): 78–81.
• Heim, Irene.'E-Type Pronouns and Donkey Anaphora'.Linguistics and Philosophy13(1990): 137–177.
• Just, MA.'Comprehending Quantified Sentences: The Relation between Sentencepicture and Semantic Memory Verification'.Cognitive Psychology6(1974): 216–236.
• Just, MA and PA Carpenter. 'Comprehension of Negation with Quantification'.Journal of Verbal Learning and Verbal Behavior10(1971): 244–253.
• Kadmon, N.Formal Pragmatics: Semantics, Pragmatics, Presupposition, and Focus.Oxford: Blackwell Publishers, 2001.
• Kamp, Hansand Reyle, U.From Discourse to Logic.Dordrecht: Kluwer, 1993.
• Kanazawa, Makoto.'Singular Donkey Pronouns Are Semantically Singular'.Linguistics and Philosophy24(2001): 383–403.
• Kanazawa, Makoto. 'Weak vs. Strong Readings of Donkey Sentences and Monotonicity Inference in a Dynamic Setting'.Linguistics and Philosophy17(1994): 109–158.
• Krifka, Manfred.'Pragmatic Strengthening in Plural Predications and Donkey Sentences'. InProceedings from Semantics and Linguistic Theory(SALT)6.Ithaca, New York:Cornell University,1996. Pages 136–153.
• Lappin, Shalom. 'An Intensional Parametric Semantics for Vague Quantifiers'.Linguistics and Philosophy23(2000): 599–620.
• Lappin, Shalom andNissim Francez.'E-type Pronouns, i-Sums, and Donkey Anaphora'.Linguistics and Philosophy17(1994): 391–428.
• Lappin, Shalom. 'Donkey Pronouns Unbound'.Theoretical Linguistics15(1989): 263–286.
• Lewis, David.Parts of Classes,Oxford:Blackwell Publishing,1991.
• Lewis, David. 'General Semantics'.Synthese22(1970): 18–27.
• Moltmann, Friederike. 'Unbound Anaphoric Pronouns: E-Type, Dynamic and Structured Propositions Approaches'.Synthese153(2006): 199–260.
• Moltmann, Friederike. 'Presuppositions and Quantifier Domains'.Synthese149(2006): 179–224.
• Montague, Richard.'Universal Grammar'.Theoria26(1970): 373–398.
• Neale, Stephen.Descriptions.Cambridge:MIT Press,1990.
• Neale, Stephen. 'Descriptive Pronouns and Donkey Anaphora'.Journal of Philosophy87(1990): 113–150.
• Partee, Barbara H.'Opacity, Coreference, and Pronouns'.Synthese21(1970): 359–385.
• Quine, Willard Van Orman.Word and Object.Cambridge, Massachusetts:MIT Press,1970.
• Rooij, Robert van.'Free Choice Counterfactual Donkeys'.Journal of Semantics23(2006): 383–402.
• Yoon, Y-E.Weak and Strong Interpretations of Quantifiers and Definite NPs in English and Korean.University of Texas at AustinPhDdissertation,1994.

External links

• The Handbook of Philosophical Logic
• Discourse Representation Theory
• Introduction to Discourse Representation Theory
• SEP Entry
• Archive of CSI 5386 Donkey Sentence Discussion
• Barker, Chris.'A Presuppositional Account of Proportional Ambiguity'.InProceedings of Semantic and Linguistic Theory(SALT)3.Ithaca, New York:Cornell University,1993. Pages 1–18.
• Brasoveanu, Adrian.'Donkey Pluralities: Plural Information States vs. Non-Atomic Individuals'.InProceedings of Sinn und Bedeutung11.Edited by E. Puig-Waldmüller. Barcelona:Pompeu Fabra University,2007. Pages 106–120.
• Evans, Gareth.'Pronouns, Quantifiers, and Relative Clauses (I)'.Canadian Journal of Philosophy7(1977): 467–536.
• Geurts, Bart.'Donkey Business'.Linguistics and Philosophy25(2002): 129–156.
• Huang, C-T James.'Logical Form'.Chapter 3 inGovernment and Binding Theory and the Minimalist Program: Principles and Parameters in Syntactic Theoryedited by Gert Webelhuth. Oxford and Cambridge:Blackwell Publishing,1995. Pages 127–177.
• Kamp, Hans.'A Theory of Truth and Semantic Representation'.In J. Groenendijk and others (eds.).Formal Methods in the Study of Language.Amsterdam: Mathematics Center, 1981.
• Kitagawa, Yoshihisa.'Copying Variables'.Chapter 2 inFunctional Structure(s), Form and Interpretation: Perspectives from East Asian Languages.Edited by Yen-hui Audrey Li and others.Routledge,2003. Pages 28–64.
• Lewis, David.'Adverbs of Quantification'.InFormal Semantics of Natural Language.Edited by Edward L Keenan. Cambridge:Cambridge University Press,1975. Pages 3–15.
• Montague, Richard.'The Proper Treatment of Quantification in Ordinary English'.In KJJ Hintikka and others (eds).Proceedings of the 1970 Stanford Workshop on Grammar and Semantics.Dordrecht: Reidel, 1973. Pages 212–242.