Linguistics and Philosophy

, Volume 4, Issue 2, pp 259–309 | Cite as

Ambiguity and quantification

  • Ruth M. Kempson
  • Annabel Cormack


In the opening sections of this paper, we defined ambiguity in terms of distinct sentences (for a single sentence-string) with, in particular, distinct sets of truth conditions for the corresponding negative sentence-string. Lexical vagueness was defined as equivalent to disjunction, for under conditions of the negation of a sentence-string containing such an expression, all the relevant more specific interpretations of the string had also to be negated. Yet in the case of mixed quantification sentences, the strengthened, more specific, interpretations of some such positive string are not all of them necessarily implied to be false if the corresponding negative sentence-string is asserted. On the contrary, as we saw in section 6, a negative sentence-string can be used to deny one of the more specific interpretations of the corresponding positive string without also denying other weaker interpretations of that same string. One might therefore argue that the only empirical evidence availble for assessing quantified sentences suggests clearly that these sentence-strings are ambiguous. Indeed logicians, many of whom restrict their attention to propositions, MUST recognise logical ambiguity at this point. For the contextualisation of the negative sentences in section 6 showed that it was possible to assert the falsity of some proposition P expressed by the sentence S while asserting a further proposition which was compatible with the truth of S. However the corresponding conclusion that such sentence-strings are sententially ambiguous is not a necessary conclusion for the linguist: for the alternative account of postulating a single semantic representation plus a set of semantic procedures is also compatible with the negation evidence. Moreover we have seen independent reasons for thinking that if sentential ambiguity is assumed to be in one-to-one correspondence with what we should now call logical ambiguity, a considerable body of generalisations is lost. For the maximal ambiguity account, it should be recalled, is committed to assigning at least thirteen distinct propositions and hence thirteen distinct sentence outputs for every sentence-string containing no more than two quantifiers, for three out of the four interpretations originally outlined in this paper can be understood with each numeral taken either in an ‘exactly’ sense or in an ‘at least’ sense. Moreover there is no explanation of why just these interpretations are available-they are merely an arbitrary list, no more connected than are the two interpretations of John saw her duck, with no reason to predict that the ambiguity would carry over from language to language. If then it is granted that an ambiguity account fails to capture appropriate generalisations, only two alternative accounts of mixed quantification sentence-strings remain viable-an analysis proposing an initial co-ordinate logical form like the logical form III, which is the strongest form compatible with each of the propositional interpretations of sentence-string Two examiners marked six scripts, and the radically weak form in which only existential quantification (both over sets and over members of those sets) is invoked. Since there are strong arguments to suggest that the procedures which both analyses require are semantic, there seems no reason not to adopt the radical vagueness account, with its considerably greater simplicity.

Throughout this comparison of alternative analyses, we have restricted the discussion to the theoretical mechanisms required by any one of the possible alternatives to predict the full range of uses of mixed quantification sentences. In selecting the vagueness analysis,53 we are forced to the conclusion that the traditional conception of truth conditions is correct: truth conditions are stated over proposition, and not (or at least not solely) over sentences. The semantic representation proposed for mixed quantification sentence-string is only an entailment of the truth conditions of each of its interpretations, but it does not fully specify any one of these. While philosophers will not find this result disconcerting, the linguist faces the conclusion that the semantic generalisations to be made about sentence meaning cannot be stated directly in terms of truth conditions, despite the recent assumptions in much linguistic semantics that this is so.54 However if the vagueness analysis is even in outline correct, then the philosopher too is required to recognise that the level of proposition is not the only level required in a semantic theory of natural language if the general properties of quantified sentences are to be explained.55

The semantic model which we are thus advocating as essential if all the requisite generalisation about the interpretation of natural-language sentence-strings are to be captured, is one in which for every sentence output of the grammar, there is a two-level semantic characterisation-a semantic representation of the sentence, and a semantic specification of each of the propositions which that sentence may express, with rules stating explicitly the nature of the relations between the two. The semantic component of a formal linguistic model will, then, have to incorporate three different types of rule: rules mapping syntactic structures onto semantic representations (involving interaction with the lexicon), semantic transformations-viz. the various procedures, and filters. With this model to hand, we can now see how the interaction between the linguistic characterisation of a sentence and logical ambiguity is entirely systematic. Ambiguity in the logical sense arises from interaction between each of the three available components of the grammar and phonology: (i) from the lexicon with a mapping of unrelated lexical items onto the same phonological sequence;56 (ii) from the syntactic component with distinct syntactic mappings for a single phonological string; (iii) from the semantic component with distinct semantic transformations for a single phonological string. Within this model, it does not arise from syntax-semantics mapping rules. Both lexical ambiguity and syntactic ambiguity give rise to arbitrary, unrelated pairs. Only in the case of the semantic transformations do we get systematic, or non-arbitrary, logical ambiguity. If the model suggested by our analysis is to be convincing, this pattern should apply throughout the data. We would therefore predict that any case of systematic non-arbitrary ambiguity will have a characterisation like that assigned to quantifiers here, in terms of an initial single semantic representation and procedures operating upon that representation.


Truth Condition Semantic Representation Lexical Ambiguity Sentential Ambiguity Semantic Component 
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Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Ruth M. Kempson
    • 1
  • Annabel Cormack
    • 1
  1. 1.School of Oriental & African StudiesUniversity of LondonLondonUK

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