A Matemática como linguagem analítica em R. Carnap

Logical empirism, which the metaphysical and seeks to discover the truth about the world exclusively through the natural sciences, owes its name two of its basic tenets, namely: the view that the solution of a philosophical problem requires a logical analysis of the languages in which the problem is stated, and that therefore logic plays a central role in philosophy, and the empiricist principle that any significant theory which is not of a purely logical or mathematical character must be testable by reference to empirical evidence. Carnap’s work provides, among other thing, a precise elaboration of, and a broad theoretical basis for these tenets and it develops the technical tools for the pursuit of philosophy as logical analysis. R. Carnap shall see that he furnished instruments for deduction, that is, for the transformation of formulations of factual and contingent knowledge. However, logic and mathematics not only supply rules for transformation of factual sentences but they themselves contain sentences of a different non-factual kind. On this article I explain the linguistic sense to Mathematics, and the philosophical foundations. However the logic language plays a very important role to the logical foundations of mathematics and Mathematics is to analytic language according to R. Carnap.