Donkey sentences are sentences that contain a
pronoun
In linguistics and grammar, a pronoun (abbreviated ) 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 parts of speech, but some modern theorists would not c ...
with clear meaning (it is
bound
Bound or bounds may refer to:
Mathematics
* Bound variable
* Upper and lower bounds, observed limits of mathematical functions
Physics
* Bound state, a particle that has a tendency to remain localized in one or more regions of space
Geography
*B ...
semantically
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and compu ...
) but whose
syntactical role in the sentence poses challenges to
grammarians. Such sentences defy straightforward attempts to generate their
formal language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.
The alphabet of a formal language consists of sy ...
equivalents. The difficulty is with understanding how English speakers
parse
Parsing, syntax analysis, or syntactic analysis is the process of analyzing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar. The term ''parsing'' comes from Lat ...
such sentences.
Barker and Shan define a donkey pronoun as "a pronoun that lies outside the restrictor of a
quantifier or the if-clause of a
conditional, yet
covaries with some
quantificational element inside it, usually an
indefinite." The pronoun in question is sometimes termed a donkey pronoun or donkey
anaphora.
The following sentences are examples of donkey sentences.
*"" ("Every man who owns a donkey sees it") —
Walter Burley
Walter Burley (or Burleigh; 1275 – 1344/45) was an English scholastic philosopher and logician with at least 50 works attributed to him. He studied under Thomas WiltonHarjeet Singh Gill, ''Signification in language and culture'', Indian Inst ...
(1328),
*"Every farmer who owns a donkey beats it."
*"Every police officer who arrested a murderer insulted him."
History
Walter Burley
Walter Burley (or Burleigh; 1275 – 1344/45) was an English scholastic philosopher and logician with at least 50 works attributed to him. He studied under Thomas WiltonHarjeet Singh Gill, ''Signification in language and culture'', Indian Inst ...
, a medieval scholastic philosopher, introduced donkey sentences in the context of the theory of ''
suppositio'', the medieval equivalent of reference theory.
Peter Geach 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 "John Smith is not a lazy student" is a ...
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 ...
's proposal for a generalized formal representation of
quantification in
natural language.
His example was reused by
David Lewis (1975),
Gareth Evans (1977)
and many others, and is still quoted in recent publications.
Analysis of donkey sentences
The goal of
Montague grammar is to show how sentences of a natural language (like 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
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, w ...
,
as in the following simple example from Burchardt ''et al'':
: "A woman smokes." is translated as
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 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
is left
free in the predicate
.
:
It may be attempted to extend the
scope
Scope or scopes may refer to:
People with the surname
* Jamie Scope (born 1986), English footballer
* John T. Scopes (1900–1970), central figure in the Scopes Trial regarding the teaching of evolution
Arts, media, and entertainment
* Cinem ...
of the existential quantifier to bind the free instance of
, but it still does not give a correct translation.
:
This translation is incorrect since it is always true. Given any object to be substituted for
, substituting any non-donkey object for
makes the
material conditional
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q i ...
true (since its
antecedent is false), and so existential clause is true for every choice of
.
A correct translation into first-order logic for the donkey sentence seems to be
:
,
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, 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, unambiguou ...
.
It is unknown how natural language users are – apparently effortlessly – agreeing 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.
Kamp was born in Den Burg. He received a Ph.D. in UCLA Departmen ...
(1981) and
Irene Heim
Irene Roswitha Heim (born in Munich, Germany, on 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 i ...
(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 inclu ...
(DRT) and
file change semantics
File or filing may refer to:
Mechanical tools and processes
* File (tool), a tool used to ''remove'' fine amounts of material from a workpiece
**Filing (metalworking), a material removal process in manufacturing
** Nail file, a tool used to gent ...
(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
In formal semantics and philosophy of language, a definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is ''proper'' if X applies to a unique individual or o ...
. 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 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 inclu ...
(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 known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
.
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
In linguistics, a noun phrase, or nominal (phrase), is a phrase that has a noun or pronoun as its head or performs the same grammatical function as a noun. Noun phrases are very common cross-linguistically, and they may be the most frequently oc ...
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 known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
variables, but allows quantifiers in a
formula to bind variables in other formulae.
See also
*
*
*
*
*
*
References
Further reading
*
Abbott, Barbara
'Donkey Demonstratives'.''
Natural Language Semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
'' 10 (2002): 285–298.
*Barker, Chris. 'Individuation and Quantification'. ''
Linguistic Inquiry'' 30 (1999): 683–691.
*Barker, Chris. 'Presuppositions for Proportional Quantifiers'. ''
Natural Language Semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
'' 4 (1996): 237–259.
*Brasoveanu, Adrian. ''Structured Nominal and Modal Reference''.
Rutgers University
Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and was ...
PhD
dissertation, 2007.
*Brasoveanu, Adrian
'Uniqueness Effects in Donkey Sentences and Correlatives'''
Sinn und Bedeutung
In the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the ...
'' 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 (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
'' 4 (1996): 121–163.
*Cohen, Ariel. ''Think Generic!'' Stanford, California:
CSLI Publications
Stanford University has many centers and institutes dedicated to the study of various specific topics. These centers and institutes may be within a department, within a school but across departments, an independent laboratory, institute or center ...
, 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, UMass) is a public research university in Amherst, Massachusetts and the sole public land-grant university in Commonwealth of Massachusetts. Founded in 1863 as an agricultural college, ...
, 1995.
*
Evans, Gareth. 'Pronouns'. ''
Linguistic Inquiry'' 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'', the ScienceDirect collection of electronic journals, '' Trends'', ...
, 1999.
*
Harman, Gilbert. 'Anaphoric Pronouns as Bound Variables: Syntax or Semantics?' ''
Language
Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of ...
'' 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'' 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 statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...
, 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
Nissim Francez (Hebrew: נסים פרנסיז; born: 19 January 1944) is an Israeli professor, emeritus in the computer science faculty at the Technion, and former head of computational linguistics laboratory in the faculty.
Early life an ...
. '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 which, like the related term general linguistics, can be understood in different ways. Both can be taken as a reference to theory of language, or the branch of linguistics which inquires into the n ...
'' 15 (1989): 263–286.
*
Lewis, David. ''Parts of Classes'', Oxford:
Blackwell Publishing, 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 a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962.
History
The MIT Press traces its origins back to 1926 when MIT publish ...
, 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, e ...
'' 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'' is a 1960 work by the philosopher Willard Van Orman Quine, in which the author expands upon the line of thought of his earlier writings in ''From a Logical Point of View'' (1953), and reformulates some of his earlier arguments ...
''. Cambridge, Massachusetts:
MIT Press
The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962.
History
The MIT Press traces its origins back to 1926 when MIT publish ...
, 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 research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,07 ...
PhD
dissertation, 1994.
Notes
External links
The Handbook of Philosophical LogicDiscourse Representation TheorySEP 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 statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...
, 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
Pompeu Fabra University ( ca, Universitat Pompeu Fabra, UPF, ; es, link=no, Universidad Pompeu Fabra) is a public university located in the city of Barcelona, Catalonia in Spain. The university was created by the Autonomous Government of Catalo ...
, 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, 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 publisher. It was founded in 1836 by George Routledge, and specialises in providing academic books, journals and online resources in the fields of the humanities, behavioural science, education, law ...
, 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 is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer.
Cambridge University Pre ...
, 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)