Limitations of Formal (Logical) Semantics



According to the received view formal semantics applies to natural (ordinary) language to some extent only. It is so because natural language is inherently indefinite, in particular, its expressions are ambiguous, vague and admits departures from syntactic rule. Moreover, intensional contexts occur in ordinary language – it results in limitations of the principle of compositionality. The ordinary conversation appeals to various principles, for instance, Grice’s maxims which exceed logical formalism. Thus, ordinary language cannot be fully formalized. On the other hand, if L is a formal language, its metalanguage ML, must be partially informal – for instance, it contains, terms of ordinary mathematics, especially set theory. Even, if, for instance, due to the technique of aritmetization, ML can be represented in ML, such a representation is only local. In fact, this view can be derived from some Tarski’s remarks on the role played by natural language. It is usually assumed that the universality of natural language, is the source of troubles associated with antinomies. It is so and this circumstance requires a solution, for example by distinguishing levels of language. However, even, if antinomies are excluded, what is informal is prior with respect to what is formal. It shows that formal semantics has limitations even with respect to formalized languages.

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