Montague Semantics (1973) › Limitations and Challenges

Despite its theoretical elegance, Montague's framework faced substantial practical and theoretical limitations. The most obvious was coverage: Montague's fragments covered only tiny portions of English. Extending them to handle the full breadth of natural language.idioms, metaphors, ellipsis, discourse anaphora, intonation, word order variations.required enormous effort. Each new phenomenon demanded new syntactic rules, new semantic rules, new type assignments, new logical operators. The framework provided principles for how extensions should work, but implementing them consumed decades of research.

The intensional logic Montague employed, while powerful, was computationally expensive. Evaluating expressions in possible worlds semantics required considering multiple worlds, computing truth values in each, and combining results through modal operators. For real-time natural language understanding systems, this computational burden proved prohibitive. Even determining whether a simple inference was valid could require exploring exponentially many models. Researchers developed restricted logical formalisms.decidable fragments of intensional logic with better computational properties.but these restrictions limited expressiveness.

The framework's treatment of context and pragmatics remained underdeveloped. Montague focused on semantic content.truth conditions.but much of meaning in natural language derives from context and use. What "I" refers to depends on who's speaking; what "now" means depends on when it's uttered; what "here" picks out depends on spatial context. While Montague's possible worlds framework could theoretically handle these indexicals by including speaker-time-location parameters in models, the framework provided no systematic account of how context determined these parameters. Similarly, pragmatic phenomena like implicature, presupposition, and speech acts received minimal treatment.

Ambiguity, though Montague's framework could represent it formally, remained computationally problematic. Ambiguous sentences had multiple derivations, each producing a different semantic interpretation. But natural language sentences were often spectacularly ambiguous.structurally ambiguous at multiple levels, lexically ambiguous with multiple word senses, scope-ambiguous with different quantifier readings. A realistic parser might generate dozens or hundreds of interpretations for a single sentence. Determining which interpretation was intended required pragmatic reasoning, world knowledge, and context.resources beyond what the formal framework provided.

The relationship between logical form and conceptual structure raised deeper questions. Montague assumed that natural language meanings could be adequately captured by intensional logic.truth conditions, possible worlds, functions, and sets. But many cognitive linguists and psychologists argued that human conceptual representations were richer and more structured: concepts organized in frames, schemas, prototypes, mental models. Logical forms seemed too austere to capture the full richness of meaning. This tension between logical and cognitive approaches to semantics would drive much subsequent debate in linguistic theory.