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Church Alonzo. Special Cases of the Decision Problem. In: Revue Philosophique de Louvain. Troisième série, tome 49, n°22, 1951. pp. 203-221.

Publisher Summary The purpose of this chapter is to regard a language as a set of primitive symbols and formation rules and—in some sense that it is not necessary to make definite—meanings for the expressions of the language. \The chapter concerns an old question relative to which developments have come to a conclusion or at least a pause. It is not true that opinions are agreed now. But the cessation of active development means that the matter can be summed up and even that some attempt may be made at adjudication. There are two senses in which it is maintained that logic is prior to mathematics. One of these, the stronger sense, is the doctrine that has come to be known as “logicism.” And the other, the weak sense, is the sense in which the standard postulational or axiomatic view of the nature of mathematics requires the priority of logic as being the means by which the consequences of a particular system of mathematical postulates are determined.