5.1.5 Montague's Approach to the Scope Problem

Of course, linguists soon became well aware of the fact that Montague Grammar had to do something about scope. Montague himself extended his formalism with an operation called quantifying in to remedy the problem.

Of course, linguists soon became well aware of the fact that Montague Grammar had to do something about scope. Montague himself extended his formalism with an operation called quantifying in to remedy the problem.

Basically, his idea was to postulate two alternative syntactic analyses of sentences like ``Every man loves a woman'':

1. The sentence is taken to consist of the NP ``Every man'' and the VP ``loves a woman''. This is the analysis we're used to. We already know that this analysis gives us the formula , where ``Every man'' has scope over ``a woman''.

2. Alternatively, the sentence is analysed in a way that may be paraphrased as ``A woman - every man loves her.''. (Of course ``her'' in this paraphrase refers to the woman introduced by the NP ``a woman''). For semantic construction, this means that the representation for the whole sentence is built by applying the translation of ``a woman'' to the translation of ``every man loves her''. This analysis yields the reading where ``a woman'' outscopes ``every man''.

To make the second analysis work, one has to think of a representation for the pronoun, and one must provide for linking the pronoun to its antecedent ``a woman'' later in the semantic construction process. Intuitively, the pronoun itself is semantically empty. Now Montague's idea essentially was to choose a new variable to represent the pronoun. Additionally, he had to secure that this variable ends up in the right place after -reduction.