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Donkey Anaphora Lancaster View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by MPG.PuRe In: Simon Botley and Tony McEnery (eds.) (1998). New Approaches to Discourse Anaphora: Proceedings of the Second Colloquium on Discourse Anaphora and Anaphor Resolution (DAARC2). Lancaster University Centre for Computer Corpus Research on Language, Vol. 11. Pp. 212–221. Towards a discourse-semantic account of donkey anaphora Pieter A.M. Seuren 1 Donkey anaphora: the problem Donkey anaphora is a form of pronominal or nominal anaphora which cannot be adequately rendered in the language of modern predicate calculus as devised by Russell at the start of this century. The problem of donkey anaphora consists precisely in the inability of modern predi- cate calculus to account for it, and is thus entirely theory-dependent. Sentences containing such anaphoric expressions are known as donkey sentences, after Geach’s little but influential book Reference and Generality of 1962, where the relevant example sentences all involve mention of donkeys. One may surmise that Geach had taken his cue from the English nominalist philosopher Walter Burleigh, who lived from ±1275 till after 1344, even if Geach does not refer to him but merely speaks (1962:116) of ‘another sort of medieval example’. In Burleigh (1988:92), which was probably written around 1328, one finds the example:1 (1) Omnis homo habens asinum videt illum (every man owning a donkey sees it) Obviously, the modern problem of donkey anaphora could not be known to Burleigh, as Russellian predicate calculus did not exist in his day. Burleigh’s problem was of an entirely different nature. Having noticed first that there exist what we now call quantifier-bound pronouns, as in: (2) Nobody expected that the dog would bite him (them) and having stated that such pronouns may never take as antecedent a constituent of the same clause (‘propositio categorica’), he presents (1) as an apparent counterexample, since the pro- noun illum (‘it’) takes as antecedent asinum (‘a donkey’), which stands under the same finite verb (videt) and is thus in the same clause. He then solves this problem by observing that the antecedent of illum, i.e. asinum, is not a main constituent of the same clause but a constituent of a subordinate predication, i.e. habens asinum (‘owning a donkey’). Geach’s treatment of (1) and similar cases in his (1962) is, on the whole, rather circum- stantial and not always entirely perspicuous, due, it seems, to his double perspective of medieval and modern theories of reference. But one must give him credit for having seen, or at least intuited, the relevance of cases like (1) in the light of modern predicate calculus. Upon reading Geach (1962), logicians and philosophers of language quickly saw the point and have since treated the donkey anaphora problem as a serious threat to the status of modern predicate calculus as a means of rendering and analysing the meanings of all natural language sentences. The reason why the language of modern predicate calculus (LPC) is unable to render donkey anaphora lies in the fact that LPC, in so far as it remains purely extensional (i.e. al- lows for substitution of co-referring terms salva veritate), knows only two kinds of argument terms for predicates: constant or referring terms, which refer to a precisely defined and actually existing entity or set of entities, and bound variables. In fact, the first category, that of referring terms, came under attack early on in the piece. In his (1905) Russell tried to tackle the riddle of reference to non-existing entities, as in his celebrated example sentence The present king of France is bald. He did so by dissolving definite descriptions into an extistential quantifier and a few propositional functions containing the variable bound by it. The American philosopher Quine, in his Word and Object (1960:181-6), supported and generalized Russell’s analysis of definite terms, proposing that the regimented ‘canonical’ form of sentences, which displays just their logical properties without the clutter accrued from the impure conditions of usage, should contain no referring expressions at all, so that all statements about the world could be expressed with the help of the two standard quantifiers and propositional functions containing the variables bound by them. Hence his slogan: ‘To be 1 I owe this reference to Joachim Ballweg. 213 is to be the value of a variable’. A systematic application of this program of ‘elimination of singular terms’ should, in Quine’s eyes, provide answers to all the many problems connected with reference. Later on, when Kripke proposed his analysis of proper names as rigid designators (Kripke 1972), mainstream philosophy of language and formal semantics allowed proper names back in as the only admissible class of referring expressions in the semantic analysis of sentences. On the whole, the main burden of reference came to lie with the bound variables. Yet, with or without Russell’s analysis of definite descriptions, or Quine’s program of elimination of singular terms, or Kripke’s analysis of proper names, LPC still remains unable to cater for donkey anaphora. Let us have a look at the details. Donkey anaphora in its simplest form, as diagnosed by Geach, occurs in sentences of the following types: (3)a. If Smith owns a donkey, he feeds it b. Every farmer who owns a donkey feeds it c. Either Smith owns no donkey, or he feeds it The pronoun it in these sentences cannot be rendered in LPC as a constant or referring term, since, in the semantics standardly provided with LPC, these sentences must be considered true in worlds not containing any donkeys at all (in which case the clause containing the troublesome pronoun it no longer counts for the truth calculus). So the it must be rendered as a bound variable. However, as is shown in (4a-c), the normal and most straightforward translation method of natural language sentences into LPC leads to trouble: (4)a. ∃x[Donkey(x) ∧ Own(Smith,x)] → Feed(Smith,?) b. ∀y[Farmer(y) ∧ ∃x[Donkey(x) ∧ Own(y,x)] → Feed (y,?)] c. ¬ ∃x[Donkey(x) ∧ Own(Smith,x)] ∨ Feed(Smith,?) The problem is, obviously, that the variable x, which one would like to see in the position of the question mark in (4a-c), is not allowed to occur there because it falls outside the scope of the (existential) quantifier binding it. Quine (1960) shows no awareness of the donkey anaphora problem. He does, however, deal with a similar problem posed by sentences of the type (1960:138): (5) If any member contributes, he gets a poppy If the word any is taken to represent the existential quantifier, the pronoun he is left stranded, or, as Quine says (1960:139), ‘left high and dry’: (6) ∃x[Member(x) ∧ Contribute(x)] → Get a poppy(?) Quine then proposes not to use the existential quantifier and get the universal quantifier to do all the work, stipulating that ‘by a simple and irreducible trait of English usage’, every always takes the smallest and any the largest possible scope. This proposal was used later to solve the problem of the stranded variables in cases like (4a-c). The idea was to translate (3a-c) with the help of the universal quantifier only: (7)a. ∀x[Donkey(x) → [Own(Smith,x) → Feed(Smith,x)]] b. ∀x∀y[[Donkey(x) ∧ Farmer(y) ∧ Own(y,x)] → Feed (y,x)]] c. ∀x[Donkey(x) → [¬ Own(Smith,x) ∨ Feed(Smith,x)]] This does indeed eliminate the scope problem raised by (4a-c). There are, however, other problems that now raise their head. First, one wonders why natural language chooses to use surface structure representatives of the existential quantifier (a donkey, no donkey), allowing unbound variables to dangle, clearly without any problem for natural interpretation processes. In other words, one wonders what could justify the sudden change in the translation or map- ping relation between the logical and the grammatical form of the sentences involved. Secondly, Quine forgot to mention that in a sentence like If John has bought something, I’ll take it away the same scope problem occurs for it as in If John has bought anything, I’ll take it away. But he does not put forward the daring proposal to treat the word some as a re- presentative of the universal quantifier. Thirdly, and perhaps most seriously, Quine’s universal quantifier ploy fails to work in certain other, less simple cases, in particular those where the clauses in question are placed under different sentential operators. Consider, for example, the following sentences: (8)a. If it’s a bad thing that Smith owns a donkey, it’s a good thing he feeds it b. Every farmer who is thought to own a donkey is expected to feed it c. Either Smith no longer owns a donkey, or he still feeds it Now try Quine’s ploy. Any form of binding the pronoun it under the universal quantifier results in an analysis that is incompatible with what the sentence in question means. Consider 214 such binding for (8a-c). The only way of binding it under the spurious universal quantifier is to place the quantifier over the whole structure, as in (9a-c), respectively: (9)a. ∀x[Donkey(x) → [BAD[Own(Smith,x)] → GOOD[Feed(Smith,x)]]] b. ∀x∀y[[Donkey(x) ∧ Farmer(y) ∧ THOUGHT[Own(y,x)]] → EXPECTED[Feed (y,x)]] c. ∀x[Donkey(x) → [NO LONGER[Own(Smith,x)] ∨ STILL[Feed(Smith,x)]]] (9a), however, fails because it is gratuitously true if there are no donkeys, whereas (8a) cannot be true in such a case.
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