Model-theoretic semantics applied to natural language attempts to account for human reason without taking human beings into account at all. The assumption that the mind is a mirror of nature allows model-theoretic semanticists to bypass the mind altogether. Where model theory appears to make sense, it does so by incorporating into model aspects of commonsense folk theories about the world, as in the case of the Barwise-Perry (1984) account of seeing [...]. Our commonsense folk theory of colors has red as a property of objects, and so it seems intuitively correct when model-theoretic semantics treats red as a one-place predicate holding of objects in the world. But this is not a correct description of the world. It is a correct description of human folk theory.
- Lakoff (1987), a pag.206

A model-theoretical semantics consists of a model structure and rules for mapping the symbols of the deductive system into elements of that model structure. The most typical kind of model structure consists of a set of entities and various other set-theoretical constructions-sets of entities, sets of n-tuples of entities, etc. Strictly speaking, the models are also meaningless. They are just structures with entities and sets. The only structure they have is set-theoretical structure. [...] The models are understood as “giving meaning” to the sentences. All that means is that sentences are associated with a model. Everything-the sentences, the models, and the pairings-is completely precise. No problems of human understanding get in the way.
- Lakoff (1987), a pag.222

Model theoretic semantics tries to use truth (that is, satisfaction in a model) and reference to define meaning. In model-theoretic semantics, the meaning of a sentence (the whole) is identified with its truth conditions in every possible situation. And the meaning of the terms (the parts) is identified with their referents in every possible situation. But truth underdetermines reference in model theory. Preserving the truth of sentences across models does not mean that the reference of the parts, while still preserving truth for the whole in every interpretation. But if sentence meaning is defined in terms of truth, and if the meaning of terms is defined in terms of reference, then one can change the “meaning” of the parts while preserving the “meaning” of the whole sentence.
- Lakoff (1987), a pag.235

Model-theoretic semantics can no longer be bolstered by the claim that it uses an appropriate mathematics. Quite the reverse. The mathematics it has been using is inconsistent with the requirements for a theory of meaning. No clearly and unequivocally “reasonable” method has been demonstrated so far that avoids the inconsistency. At present, the mathematical considerations argue against model-theoretic semantics, nor for it.
- Lakoff (1987), a pag.256