A fixed-point problem for theories of meaning

Bibliographic Data

ID10810212
AuthorsNancy Dahl (0000-0001-9157-594X, Lund University, corresponding author)
Year2022
Volume200
Issue1
Publication date2022-02-01
Open AccessYes
TypeARTICLE
VenueSynthese (JOURNAL)
Journal identifiersISSN: 0039-7857 • E-ISSN: 1573-0964
PublisherSpringer Science and Business Media LLC (PUBLISHER)
DOI10.1007/s11229-022-03559-4
OpenAlexW4213208649
LanguageEN
Citations received2
References cited15

In this paper I argue that it’s impossible for there to be a single universal theory of meaning for a language. First, I will consider some minimal expressiveness requirements a language must meet to be able to express semantic claims. Then I will argue that in order to have a single unified theory of meaning, these expressiveness requirements must be satisfied by a language which the semantic theory itself applies to. That is, we would need a language which can express its own meaning. It has been well-known since Tarski that theories of meaning whose central notion is truth can’t be expressed in a language which they apply to. Here, I develop Quine’s formulation of the Liar Paradox in grammatical terms and use this to extend Tarski’s result to all theories of meaning. This general version of the paradox can be formalised as a special case of the Lawvere Fixed-Point Theorem applied to a categorial grammar. Taken together with the initial arguments, I infer that a universal theory of meaning is impossible and conclude the paper with a brief discussion on what alternatives are available

Epistemology · Grammar · Linguistics · Meaning (existential) · Metaphysics · Philosophy of language · Philosophy of science · Quine · Semantic theory of truth · Computer Science · Historical Linguistics and Language Studies · Logic, Reasoning, and Knowledge · Mathematics · Philosophy · Philosophy and Theoretical Science

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