Donkey Sentence
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semantics Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...
, a donkey sentence is a sentence containing a
pronoun In linguistics and grammar, a pronoun (Interlinear gloss, glossed ) is a word or a group of words that one may substitute for a noun or noun phrase. Pronouns have traditionally been regarded as one of the part of speech, parts of speech, but so ...
which is semantically bound but syntactically free. They are a classic puzzle in formal semantics and
philosophy of language Philosophy of language refers to the philosophical study of the nature of language. It investigates the relationship between language, language users, and the world. Investigations may include inquiry into the nature of Meaning (philosophy), me ...
because they are fully
grammatical In linguistics, grammaticality is determined by the conformity to language usage as derived by the grammar of a particular speech variety. The notion of grammaticality rose alongside the theory of generative grammar, the goal of which is to formu ...
and yet defy straightforward attempts to generate their
formal language In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also c ...
equivalents. In order to explain how speakers are able to understand them, semanticists have proposed a variety of formalisms including systems of
dynamic semantics Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sentence amounts to knowing when it is true; in dyna ...
such as
Discourse representation theory In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT inc ...
. Their name comes from the example sentence "Every farmer who owns a donkey beats it", in which "it" acts as a donkey pronoun because it is semantically but not syntactically bound by the indefinite
noun phrase A noun phrase – or NP or nominal (phrase) – is a phrase that usually has a noun or pronoun as its head, and has the same grammatical functions as a noun. Noun phrases are very common cross-linguistically, and they may be the most frequently ...
"a donkey". The phenomenon is known as donkey anaphora.


Examples

The following sentences are examples of donkey sentences. * ("Every man who owns a donkey sees it") — Walter Burley (1328), *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 of formal semantics is to show how sentences of a
natural language A natural language or ordinary language is a language that occurs naturally in a human community by a process of use, repetition, and change. It can take different forms, typically either a spoken language or a sign language. Natural languages ...
such as English could be translated into a formal logical language, and so would then be amenable to mathematical analysis. Following Russell, it is typical to translate indefinite noun phrases using an
existential quantifier Existentialism is a family of philosophy, philosophical views and inquiry that explore the human individual's struggle to lead an Authenticity (philosophy), authentic life despite the apparent Absurdity#The Absurd, absurdity or incomprehensibili ...
, as in the following simple example from Burchardt ''et al'': : "A woman smokes." is translated as \exists x \,( \text(x) \land \text(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 word ''it''. Correctly translating this sentence will require using a
universal quantifier In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every", or "given an arbitrary element". It expresses that a predicate can be satisfied by e ...
for 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 left free in the predicate \text(x,y) . : \forall x\, (\text (x) \land \exists y \,( \text(y) \land \text(x,y)) \rightarrow \text(x,y)) It may be attempted to extend the scope of the existential quantifier to bind the free instance of y , but it still does not give a correct translation. : \forall x \,\exists y\, (\text (x) \land \text(y) \land \text(x,y) \rightarrow \text(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 the
material conditional The material conditional (also known as material implication) is a binary operation commonly used in logic. When the conditional symbol \to is interpreted as material implication, a formula P \to Q is true unless P is true and Q is false. M ...
true (since its antecedent is 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 (x) \land \text(y) \land \text(x,y)) \rightarrow \text(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 into
logical form In logic, the logical form of a statement is a precisely specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unamb ...
. 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 Johan Anthony Willem "Hans" Kamp (born 5 September 1940) is a Dutch philosopher and Linguistics, linguist, responsible for introducing discourse representation theory (DRT) in 1981. Biography Kamp was born in Den Burg. He received a Ph.D. in UC ...
(1981) and
Irene Heim Irene Roswitha Heim (born October 30, 1954) is a linguist and a leading specialist in semantics. She was a professor at the University of Texas at Austin and UCLA before moving to the Massachusetts Institute of Technology in 1989, where she is Pr ...
(1982) independently proposed very similar accounts in different terminology, which they called
discourse representation theory In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT inc ...
(DRT) and file 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-called ''description-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 of definite descriptions. The second main family of proposals goes by the name ''dynamic 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 by Gareth 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's
theory of descriptions The theory of descriptions is the philosopher Bertrand Russell's most significant contribution to the philosophy of language. It is also known as Russell's theory of descriptions (commonly abbreviated as RTD). In short, Russell argued that the ...
. 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 called ''D-type''.


Discourse representation theory

Donkey sentences became a major force in advancing
semantic Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...
research in the 1980s, with the introduction of
discourse representation theory In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT inc ...
(DRT). During that time, an effort was made to settle the inconsistencies which arose from the attempts to translate donkey sentences into
first-order logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over ...
. The solution that DRT provides for the donkey sentence problem can be roughly outlined as follows: The common semantic function of non-anaphoric
noun phrase A noun phrase – or NP or nominal (phrase) – is a phrase that usually has a noun or pronoun as its head, and has the same grammatical functions as a noun. Noun phrases are very common cross-linguistically, and they may be the most frequently ...
s is the introduction of a new discourse 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 as
first-order logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over ...
variables, but allows quantifiers in a
formula In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwe ...
to bind variables in other formulae.


History

Walter Burley, a medieval scholastic philosopher, introduced donkey sentences in the context of '' supposition theory'', the medieval equivalent of reference theory.
Peter Geach Peter Thomas Geach (29 March 1916 – 21 December 2013) was a British philosopher who was Professor of Logic at the University of Leeds. His areas of interest were philosophical logic, ethics, history of philosophy, philosophy of religion and ...
reintroduced donkey sentences as a
counterexample A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "student John Smith is not lazy" is a c ...
to
Richard Montague Richard Merritt Montague (September 20, 1930 – March 7, 1971) was an American mathematician and philosopher who made contributions to mathematical logic and the philosophy of language. He is known for proposing Montague grammar to formalize th ...
's proposal for a generalized formal representation of quantification in
natural language A natural language or ordinary language is a language that occurs naturally in a human community by a process of use, repetition, and change. It can take different forms, typically either a spoken language or a sign language. Natural languages ...
. His example was reused by David Lewis (1975), Gareth Evans (1977) and many others, and is still quoted in recent publications.


See also

* * * * * *


References


Further reading

* Abbott, Barbara
'Donkey Demonstratives'.
''
Natural Language Semantics Semantics is the study of linguistic meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction between sense and referenc ...
'' 10 (2002): 285–298. * Barker, Chris. 'Individuation and Quantification'. ''
Linguistic Inquiry ''Linguistic Inquiry'' is a peer-reviewed academic journal in generative linguistics published by the MIT Press The MIT Press is the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambri ...
'' 30 (1999): 683–691. * Barker, Chris. 'Presuppositions for Proportional Quantifiers'. ''
Natural Language Semantics Semantics is the study of linguistic meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction between sense and referenc ...
'' 4 (1996): 237–259. * Brasoveanu, Adrian. ''Structured Nominal and Modal Reference''.
Rutgers University Rutgers University ( ), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of three campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's C ...
PhD dissertation, 2007. * Brasoveanu, Adrian
'Uniqueness Effects in Donkey Sentences and Correlatives'
'' Sinn und Bedeutung'' 12 (2007):1. * Burgess, John P. ' ''E Pluribus Unum'': Plural Logic and Set Theory', ''Philosophia Mathematica'' 12 (2004): 193–221. * Cheng, Lisa LS and C.-T. James Huang
'Two Types of Donkey Sentences'.
''
Natural Language Semantics Semantics is the study of linguistic meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction between sense and referenc ...
'' 4 (1996): 121–163. * Cohen, Ariel. ''Think Generic!'' Stanford, California: CSLI Publications, 1999. * Conway, L. and S. Crain. 'Donkey Anaphora in Child Grammar'. In ''Proceedings of the North East Linguistics Society'' (NELS) 25.
University of Massachusetts Amherst The University of Massachusetts Amherst (UMass Amherst) is a public land-grant research university in Amherst, Massachusetts, United States. It is the flagship campus of the University of Massachusetts system and was founded in 1863 as the ...
, 1995. * Evans, Gareth. 'Pronouns'. ''
Linguistic Inquiry ''Linguistic Inquiry'' is a peer-reviewed academic journal in generative linguistics published by the MIT Press The MIT Press is the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambri ...
'' 11 (1980): 337–362. * Geurts, Bart. ''Presuppositions and Pronouns''. Oxford:
Elsevier Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell (journal), Cell'', the ScienceDirect collection of electronic journals, ...
, 1999. * Harman, Gilbert. 'Anaphoric Pronouns as Bound Variables: Syntax or Semantics?' ''
Language Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and signed language, signed forms, and may also be conveyed through writing syste ...
'' 52 (1976): 78–81. * Heim, Irene
'E-Type Pronouns and Donkey Anaphora'.

Linguistics and Philosophy
' 13 (1990): 137–177. * Just, MA. 'Comprehending Quantified Sentences: The Relation between Sentencepicture and Semantic Memory Verification'. ''
Cognitive Psychology Cognitive psychology is the scientific study of human mental processes such as attention, language use, memory, perception, problem solving, creativity, and reasoning. Cognitive psychology originated in the 1960s in a break from behaviorism, whi ...
'' 6 (1974): 216–236. * Just, MA and PA Carpenter. 'Comprehension of Negation with Quantification'. ''Journal of Verbal Learning and Verbal Behavior'' 10 (1971): 244–253. * Kadmon, N. ''Formal Pragmatics: Semantics, Pragmatics, Presupposition, and Focus''. Oxford: Blackwell Publishers, 2001. * Kamp, Hans and Reyle, U. ''From Discourse to Logic''. Dordrecht: Kluwer, 1993. * Kanazawa, Makoto
'Singular Donkey Pronouns Are Semantically Singular'.

Linguistics and Philosophy
' 24 (2001): 383–403. * Kanazawa, Makoto. 'Weak vs. Strong Readings of Donkey Sentences and Monotonicity Inference in a Dynamic Setting'.
Linguistics and Philosophy
' 17 (1994): 109–158. * Krifka, Manfred. 'Pragmatic Strengthening in Plural Predications and Donkey Sentences'. In ''Proceedings from Semantics and Linguistic Theory'' (SALT) 6. Ithaca, New York:
Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...
, 1996. Pages 136–153. * Lappin, Shalom. 'An Intensional Parametric Semantics for Vague Quantifiers'.
Linguistics and Philosophy
' 23 (2000): 599–620. * Lappin, Shalom and Nissim Francez. 'E-type Pronouns, i-Sums, and Donkey Anaphora'.
Linguistics and Philosophy
' 17 (1994): 391–428. * Lappin, Shalom. 'Donkey Pronouns Unbound'. ''
Theoretical Linguistics Theoretical linguistics is a term in linguistics that, like the related term general linguistics, can be understood in different ways. Both can be taken as a reference to the theory of language, or the branch of linguistics that inquires into the ...
'' 15 (1989): 263–286. * Lewis, David. ''Parts of Classes'', Oxford:
Blackwell Publishing Wiley-Blackwell is an international scientific, technical, medical, and scholarly publishing business of John Wiley & Sons. It was formed by the merger of John Wiley & Sons Global Scientific, Technical, and Medical business with Blackwell Publis ...
, 1991. * Lewis, David. 'General Semantics'. ''Synthese'' 22 (1970): 18–27. * Moltmann, Friederike. 'Unbound Anaphoric Pronouns: E-Type, Dynamic and Structured Propositions Approaches'. ''Synthese'' 153 (2006): 199–260. * Moltmann, Friederike. 'Presuppositions and Quantifier Domains'. ''Synthese'' 149 (2006): 179–224. * Montague, Richard. 'Universal Grammar'. ''Theoria'' 26 (1970): 373–398. * Neale, Stephen. ''Descriptions''. Cambridge:
MIT Press The MIT Press is the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambridge, Massachusetts. The MIT Press publishes a number of academic journals and has been a pioneer in the Open Ac ...
, 1990. * Neale, Stephen. 'Descriptive Pronouns and Donkey Anaphora'. ''
Journal of Philosophy ''The Journal of Philosophy'' is a monthly peer-reviewed academic journal on philosophy, founded in 1904 at Columbia University. Its stated purpose is "To publish philosophical articles of current interest and encourage the interchange of ideas, es ...
'' 87 (1990): 113–150. * Partee, Barbara H. 'Opacity, Coreference, and Pronouns'. ''Synthese'' 21 (1970): 359–385. * Quine, Willard Van Orman. ''
Word and Object ''Word and Object'', philosopher Willard Van Orman Quine's most famous work, expands on ideas in ''From a Logical Point of View'' (1953) and reformulates earlier arguments like his attack on the analytic–synthetic distinction from " Two Dogmas ...
''. Cambridge, Massachusetts:
MIT Press The MIT Press is the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambridge, Massachusetts. The MIT Press publishes a number of academic journals and has been a pioneer in the Open Ac ...
, 1970. * Rooij, Robert van
'Free Choice Counterfactual Donkeys'.
'' Journal of Semantics'' 23 (2006): 383–402. * Yoon, Y-E. ''Weak and Strong Interpretations of Quantifiers and Definite NPs in English and Korean''.
University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public university, public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 stud ...
PhD dissertation, 1994.


Notes


External links


The Handbook of Philosophical Logic

Discourse Representation Theory



SEP Entry


* Barker, Chris
'A Presuppositional Account of Proportional Ambiguity'.
In ''Proceedings of Semantic and Linguistic Theory'' (SALT) 3. Ithaca, New York:
Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...
, 1993. Pages 1–18. * Brasoveanu, Adrian
'Donkey Pluralities: Plural Information States vs. Non-Atomic Individuals'.
In ''Proceedings of Sinn und Bedeutung'' 11. Edited by E. Puig-Waldmüller. Barcelona: Pompeu Fabra University, 2007. Pages 106–120. * Evans, Gareth. 'Pronouns, Quantifiers, and Relative Clauses (I)'. ''Canadian Journal of Philosophy'' 7 (1977): 467–536. * Geurts, Bart
'Donkey Business'.

Linguistics and Philosophy
' 25 (2002): 129–156. * Huang, C-T James
'Logical Form'.
Chapter 3 in ''Government and Binding Theory and the Minimalist Program: Principles and Parameters in Syntactic Theory'' edited by Gert Webelhuth. Oxford and Cambridge:
Blackwell Publishing Wiley-Blackwell is an international scientific, technical, medical, and scholarly publishing business of John Wiley & Sons. It was formed by the merger of John Wiley & Sons Global Scientific, Technical, and Medical business with Blackwell Publis ...
, 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 in ''Functional Structure(s), Form and Interpretation: Perspectives from East Asian Languages''. Edited by Yen-hui Audrey Li and others.
Routledge Routledge ( ) is a British multinational corporation, multinational publisher. It was founded in 1836 by George Routledge, and specialises in providing academic books, academic journals, journals and online resources in the fields of the humanit ...
, 2003. Pages 28–64. * Lewis, David
'Adverbs of Quantification'.
In ''Formal Semantics of Natural Language''. Edited by Edward L Keenan. Cambridge:
Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...
, 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. {{Formal semantics Pronouns Quantifier (logic) Semantics Formal semantics (natural language)