Definition

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A statement about the content of a linguistic expression (ideally based on rules of formal logic). Viewed formally, every scientific definition is a relation of equivalence that consists of an unknown entity to be defined (=definiendum) and a known entity that is used to define (=definiens). The following types of definition and their respective rules of formation are relevant for linguistic and scientific descriptive methods. (a) Real definitions: the definition of an object or of a concrete concept by indicating the genus G (=genus proximum) and the specifying type trait T (=differentia specifica), e.g. A plosive is a consonant that is formed by stopping and releasing two articulators. In traditional logic general rules must be taken into consideration: a definition must encompass the essence of the concept being defined; it may be neither negative nor circular; the defining concepts G and T must be sufficiently clear and sharply delineated. (b) Operational (or genetic) definitions are a special type of real definition that indicate on the basis of which method a concept ‘emerges’ or is verifiable, e.g. the definition Constituents are syntactic units that can be permutated within a sentence ( operational procedures). (c) Nominal definitions: in contrast to a real definitions, which have to do with objects and concrete characteristics, nominal definitions involve designating objects and abstract characteristics, i.e. names, concepts, or linguistic expressions. They are statements that represent a relation of synonymy between the definiens and the (initially meaningless) definiendum. A necessary condition for a concrete nominal definition is that the definiens and the definiendum are expressions of the same category. In particular, variables not found in the definiendum must not be found in the definiens. Explicit definitions are those definitions in which the definiendum next to the sign being defined only contains variables but not already defined logical symbols and the like. Such explicit definitions have the character of abbreviations, i.e. a complex state of affairs is denoted by an abbreviation. With this, the demand for the eliminability of the defined expressions is simultaneously taken into account, i.e. the reducibility of all statements to the basic concept and the axioms. (d) Inductive definitions serve to characterize a class that, as a rule, has an infinite number of objects, by means of a set B of basic elements and a number of linking rules or operations. In grammar theory the set of well-formed (=grammatical) expressions of a language L is typically defined inductively.

So, for example, the inductive definition of a well-formed expression (abbreviated ‘WFE’) in propositional logic L reads: (i) every propositional variable A is a WFE of L; (ii) if E is an expression of language L, then not-E is an expression of L; (iii) if E₁ and E₂ are expressions of L, then E₁ E₂, E₁ E₂, E₁→ E₂, E₁↔E₂ are also expressions of L; (iv) no expression in L is a WFE, unless it is generated by (i), (ii), or (iii); (v) recursive definitions ( recursive rules); (vi) for extensional vs intensional definitions extension, intension.

Bierwisch, M. and M.Kiefer, 1969. Remarks on definition in natural language. In F.Kiefer (ed.), Studies in syntax and semantics. Dordrecht. 55–79.

Borsodi, R. 1967. The definition of definition: a new linguistic approach to the integration of knowledge. Boston, MA.

Haas, W. 1955. On defining linguistic units. TPS 1954. 54–84.

Kutschera, F.V. and A.Breitkopf. 1971. Einführung in die moderne Logik. Freiburg.

Robinson, R. 1954. Definition. Oxford.

Schnelle, H. 1973. Sprachphilosophie und Linguistik: Prinzipien der Sprachanalyse a priori und a posteriori. Reinbek.

Petöfi, J.S. (ed.) 1978. Logic and the formal theory of natural language: selective bibliography. Hamburg.

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