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 | |  Scope and Derivational History | |
A well known example of scope ambiguity is Every man loves a woman. Is there only one woman involved (e.g. mother Mary), or does every man love a different woman? The sentence has no lexically ambiguous words, and there are no syntactic arguments to assign them more than one constituent structure. How to account for the ambiguity?In Montague 1973, the scope ambiguity is dealt with by providing for the sentence two different derivations. On the reading that every has wide scope, the sentence is produced from every manand loves a woman. On the reading that only one woman is involved, the sentence is obtained from Every man loves him1. The him1 is an artifact, a placeholder, or, one might say, a syntactic variable. A special kind of rule, called a ‘quantifying-in rule’, will replace this him1 by a noun phrase or a pronoun (in case there are more occurrences of this placeholder). The placeholder corresponds with a logical variable that becomes bound by the semantic counterpart of the quantifying-in rule. For the sentence under discussion, the effect of the application of the quantifying-in rule to a woman and Every man loves him1 is that the desired sentence is produced and that the quantifier corresponding with a woman gets wide scope. When we would depict its derivation as a tree, this tree would be larger than the constituent structure of the sentence due to the introduction and later removal of him1.This quantifying-in rule is used by Montague for other phenomena as well. An example is co-referentiality: Mary loves the man whom she kissed is obtained from He1 loves the man whom he1 kissed. And the de re reading of John seeks a unicorn is obtained from a unicorn and John seeks him1.Many researchers did not like this analysis in which powerful syntactic rules and artificial symbols (him1) are used. Below we consider two strategies to remedy.The first strategy was to deny the ambiguity. Some linguists have argued that the scope order is the same as the surface order; this is known as ‘Jackendoff's principle’ (Jackendoff 1972). But there are sentences where this does not work. Others said that it is sufficient only to obtain the weakest reading (every wide scope), and that the stronger reading is inferred when additional information is available. But there are sentences for which the different scope readings are logically independent, as in Every woman loves one man.The second strategy was to capture the ambiguity in another way than by the quantifying-in rules. Historically the first method was to put the interpretations of the noun phrases in a store from which these interpretations could be retrieved when needed: different stages of retrieving correspond with differences in scope. One might see this as a grammar in which the direct correspondence between syntax and semantics has been relaxed. The method is called ‘Cooper Store’, after the author who proposed this (Cooper 1983). A later proposal is DRT (= discourse representation theory), where representations are used to account for such ambiguities (van Eijck & Kamp 1997).A recent method is by means of ‘lifting rules’ (see Sect. 3.3): the meaning of a noun-phrase is ‘lifted’ to a more abstract level, and different levels yield different scope readings (see Hendriks 2001 and Jacobson 2014).Even if the role of derivational history can be avoided for scope and co-referentiality, other phenomena remain for which derivational histories have a role. An example is John wondered when Alice said she would leave. This is ambiguous between John asking for the time of leaving, or for the time of saying. So the sentence is ambiguous, even though there are no arguments for assigning to it more than one constituent structure. Pelletier (1993) presents this sentence and others, and says: ‘In order to maintain the Compositionality Principle, theorists have resorted to a number of devices which are all more or less unmotivated (except to maintain the Principle): Montagovian “quantifying-in” rules, traces, gaps, […].’ Pelletier's objection can be appreciated if one assumes that meaning assignment is directly linked with constituent structure. But, as explained in Section 1.2, this is not the case. The derivation specifies which rules are combined in which order, and this derivation constitutes the input to the meaning assignment function. The constituent structure is determined by the output of the syntactic rules, and different derivation processes may generate one and the same constituent structure. In this way, semantic ambiguities are accounted for. One should not call something ‘constituent structure’ if it is not intended as such, and next refute it because it does not have the desired properties.The distinction between a derivation tree and a constituent tree is made in several theories of grammar. In Tree Adjoining Grammars (TAG's) the different scope readings of the sentence about loving a woman differ in the order in which the noun-phrases are substituted in the basic tree. A classical example in Chomskyan grammar is The shooting of the hunters was bloody, which is ambiguous between the hunters shooting, or the hunters being shot at. The two readings come from two different sources: one in which the hunters is the subject of the sentence, and one in which it is the object.3. Philosophical Aspects 3.1 From Frege to IntensionsFrege (1892) introduced the distinction between ‘sense’ and ‘reference’. It has been said that Montague followed this distinction, and that ‘intension’ coincides with ‘sense’. But that is not correct. Let us first consider Frege's argumentation. It concerns The Greeks did not know that the morning star is the evening star. During classical antiquity, it had not yet been discovered that both the morning star and the evening star are the planet Venus. We would, however, not like to analyze the sentence as stating that the Greeks did not know that Venus is the same as Venus, i.e. that they did not recognize an obvious truth. Frege's theory is that in ordinary contexts the expression the morning star denotes its referent (a celestial object), but in indirect contexts it denotes something different that is called ‘its sense’. This notion includes not only the referent, but also the way in which one refers to an object. Since referring to a celestial object by the morning star differs from referring to it by the evening star, the sentence The morning star is the evening star does not express an analytic truth.Frege's approach was abandoned because it was not really satisfactory. It introduced an ambiguity of the of the phrase the morning star, whereas it is not a lexical ambiguity: there is no sentence that has different readings due to that phrase. Nevertheless, Frege associated with that expression two denotations. The situation gets even worse: Carnap (1947) noted that under Frege's approach we would also need the ‘sense of a sense’ etc. Consequently, Frege's approach requires an infinite hierarchy of semantic denotations (and that for an expression which never gives rise to the ambiguity of a sentence). Carnap proposed another formalization of the same idea, but in which with one expression only one denotation is associated. Montague (1970c, 233) introduced with his ‘intensional logic’ a variant of this idea. The difference with Frege (one denotation for an expression, instead of infinitely many) was possible due to two novelties (see Montague 1970a, 217–218): ‘descriptive phrases do not denote individuals’, and ‘the denotation of a sentence is not a truth-value’.For an more elaborated discussion, see Janssen 2011; for information on the history of intensional logic, see Montague 1970b (145). 3.2 CompositionalityFor Montague the principle of compositionality was not a subject of deliberation or discussion, because for him, as a mathematical logician, it was the only way to proceed. He describes his method in side remarks with phrases like ‘following Tarski’, or ‘following Frege’, without ever calling it a principle. Later authors identified the Principle of Compositionality as the cornerstone of Montague's work. The reason was that discussions arose, and an investigation of the foundations of Montague grammar was asked for.It has been claimed that Montague himself did not work compositionally in the case of pronouns. This is, however, not the case. In order to explain the compositional nature of his treatment of pronouns, both Janssen (1997) and Dowty (2007) explain how variables are interpreted in logic; we follow their explanations. Consider the following clauses from the traditional Tarskian interpretation of predicate logic.[list="margin-top: 0.5em; color: rgb(26, 26, 26); font-family: serif; font-size: 16.5px; line-height: 21px; background-color: rgb(255, 255, 255);"] [*]⟦ϕ ∧ ψ⟧ g = 1 if and only if ⟦ϕ⟧ g = 1 and ⟦ψ⟧ g = 1[*]⟦∀ xϕ⟧ g = 1 if and only if for all h ∼ xg holds ⟦ϕ⟧ h = 1[/list] The first clause says: ϕ ∧ ψ is true when using assignment g if and only if ϕ and ψ are true when the assignment g is used. In the second clause assignments h are introduced (by ∼x g) which are equal to g except maybe for the value they assign to variable x. Montague uses the same format, with the difference that besides g he also has i, the time of reference and j, the possible world, as superscripts.In the formulation of the clauses there is nothing which can be pointed at as ‘the meaning’, in fact it is a definition of truth with g and h as parameters. So how is it possible that this (and Montague's work) are compositional?The answer requires a shift in perspective. The meaning of a formula ϕ, shortly M(ϕ), is the set of assignments for which the formula is true. Then the first clause says that M(ϕ ∧ ψ) = M(ϕ) ∩M(ψ), so a simple set-theoretic combination on the two meanings is performed. And M(∀xϕ) = {h ∼xg∣g ∈ M(ϕ)}, which can be described as: extend the set M(ϕ) with all x-variants. Likewise, in Montague semantics the meaning of an expression is a function which has as domain the triples .Is it possible to achieve compositionality for natural language? Obvious candidates for counterexamples are idioms, because their meanings seem not to be built from their constituting words. However, Westerståhl (2002) presents a collection of methods, varying from compound basic expressions, to deviant meanings for constituting parts. Janssen (1997) refutes several other counterexamples that are put forward in the literature.How strong is compositionality? Mathematical results show that any language can be given a compositional semantics, either by using an unorthodox syntax (Janssen 1997) or by using an unorthodox semantics (Zadrozny 1994). However their proofs are not helpful in practice. Hodges (2001) showed how a given compositional semantics for a fragment can be extended to a larger language.Among formal semanticists one can find the following attitudes towards compositionality (nearly the same list is given in Partee 1996):[list="margin-top: 0.5em; color: rgb(26, 26, 26); font-family: serif; font-size: 16.5px; line-height: 21px; background-color: rgb(255, 255, 255);"] [*]Compositionality is a basic methodological principle; any proposal should obey it. Janssen(1997) and Jacobson(2014) are adherents of this position. [*]Compositionality is a good method, but other methods can be used as well. For instance formal meaning representation can be used in an essential way. An example is DRT (discourse representation theory, Kamp 1981). [*]Compositionality is an ideal, but a proposal need not to satisfy it. [*]It is an empirical issue whether compositionality can be achieved. See Dowty 2007 for a discussion. [/list] An extensive discussion of compositionality is given in Janssen 1997, and in the entry oncompositionality (Szabó 2007). | |
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