axiom (n.)

An application in LINGUISTICS of the general use of this term in the branch of logic known as axiomatics. It refers to a set of initial PROPOSITIONS (or axioms) which a theory assumes to be true. Further propositions (or ‘the-orems’) are then deduced from these by means of specific rules of inference (to which the term ‘transformational rule’ is sometimes applied). The full statement of an axiomatic system will contain a ‘syntax’, which determines the WELL-FORMEDNESS of its propositions, and a ‘vocabulary’, which lists the terms of the system. The application of these ideas in LINGUISTICS has come mainly from the influence of CHOMSKYAN ideas, concerning the FORMALIZATION of LANGUAGE, and is central to MATHEMATICAL linguistics. In PRE-GENERATIVE attempts at systematizing ideas about language, the weaker term POSTULATES was usually used. A specifically non-generative approach is axiomatic functionalism, a paradigm of enquiry developed in the 1960s by J(ohannes) W(ilhelmus) F(ranciscus) Mulder (b. 1919), in which linguistics is presented as a formal axiomatic-deductive system within a broad SEMIOTIC frame of reference. The approach applies a network of postulates, supporting definitions, and associated theorems to the structural analysis of core areas of language as well as to areas which are conventionally handled under other headings (such as PRAGMATICS).