The syntactic approach

pp. 34-44

in: Paul Gochet, Outline of a nominalist theory of propositions, Berlin, Springer, 1980

Abstract

Let us briefly recall what one understands by the term "axiomatic definition". The axioms of a discipline contain primitive terms. They allow any interpretation compatible with the truth of the axioms in which they occur. By the same token they exclude other interpretations. One may thus, with Tarski, assimilate axioms to propositional functions and primitive terms to variables. Axioms effect a sorting-out among the objects that belong to the domain constituting the value-range of these variables; they select the classes of those objects of which they are true. It is this power of selection, of delimitation, that one associates with definition.