Montague Semantics (1973) › The Meaning Problem

Linguists and philosophers had long recognized that sentences have meanings.that "snow is white" means something different from "grass is green," and that both differ from "colorless green ideas sleep furiously." But what exactly did it mean for a sentence to "have a meaning"? Informal descriptions sufficed for many purposes: one could paraphrase, translate, or explain meanings without formalizing them. Yet this informality created problems. Without a precise notion of meaning, linguists couldn't rigorously test semantic theories, couldn't definitively determine when two sentences had the same meaning, and couldn't systematically predict the meanings of novel sentences from their parts.

The problem grew particularly acute when dealing with complex semantic phenomena. Consider quantification: "every student read some book" is ambiguous between two readings.one where there's a specific book all students read, another where each student read potentially different books. How could this ambiguity be formally represented and resolved? Consider intensional contexts: "John seeks a unicorn" doesn't require unicorns to exist, while "John finds a unicorn" does. What makes "seeks" different from "finds" in terms of existential commitment? Consider embedded clauses: "Mary believes that John left" has a different logical structure from "Mary believes John," involving a proposition rather than an individual. How could these structural differences be systematically captured?

Previous approaches to semantics had provided partial answers. The tradition of formal logic, descending from Frege, Russell, and Tarski, had developed sophisticated tools for analyzing mathematical and scientific language. First-order predicate logic could represent statements like "all men are mortal" as formal expressions whose truth could be evaluated in models. But logicians had largely restricted their attention to carefully controlled formal languages, avoiding the complications of natural language. When they did address natural language, they often dismissed problematic constructions as defective, needing reform rather than analysis.

Linguists, conversely, attended carefully to natural language data but lacked formal semantic tools. Generative semanticists in the late 1960s had attempted to collapse syntax and semantics, treating semantic representations as deep syntactic structures that transformed into surface forms. This approach generated productive research but faced conceptual difficulties: semantic representations looked suspiciously like logical formulas, yet the grammatical machinery of transformations seemed ill-suited to semantic composition. The relationship between syntactic structure and semantic interpretation remained unclear, more stipulated than explained.

What was needed was a bridge: a formal framework that could handle the full complexity of natural language meanings while maintaining mathematical rigor. The framework would need to specify exactly how complex meanings derived from simpler parts, handle ambiguity systematically, distinguish semantic from pragmatic phenomena, and provide a notion of meaning precise enough to support theoretical predictions and computational implementation. Montague set out to build precisely this bridge, bringing the tools of mathematical logic to bear on natural language semantics.