I will examine from a logical point of view several conditions, formulated by Dummett, for a contextual definition to be considered legitimate as a “permissible means of introducing an expression” into a Fregean formal language. To this purpose, I will introduce an abstract framework in which all relevant notions are expressed in terms of a primitive relation of logical consequence, along a tradition started by Tarski in the thirties of the last century.

I will examine the mutual relationship between the different Frege-Dummett conditions and, in particular, I will prove a mathematical result about a weakening of the “uniqueness of solution” requirement parenthetically suggested by Dummett in the following passage taken from "Frege: Philosophy of Language" (1981, 2nd ed., p. 653):

"(We might, however, relax the requirement of a unique solution in cases in which different solutions would still yield the same truth-value for each sentence in which the expression was going to occur.)"

I will next use the interpretation of the first-order fragment of Frege’s classical logic into the standard Tarskian semantics to contrast Dummett’s suggestion with the standard theory of definitions centred around Beth’s definability theorem.