Throughout his philosophical career, Carnap places the foundations of logic and mathematics at the center of his inquiries: he is concerned above all with the Kantian question “How is mathematics (both pure and applied) possible?” Although he changes his mind about many particular issues, Carnap never gives up his belief in the importance and centrality of this question, nor does he ever waver in his conviction that he has the answer: the possibility of mathematics and logic is to be explained by a sharp distinction between formal and factual, analytic and synthetic truth. Thus, throughout his career, Carnap calls for, and attempts to provide,

For Carnap, it is this foundation for logic and mathematics that is distinctive of logical – as opposed to traditional – empiricism. As he puts it in his “Intellectual Autobiography” (1963a, p. 47): “It became possible for the first time to combine the basic tenet of empiricism with a satisfactory explanation of the nature of logic and mathematics.” In particular, we can avoid the “non-empiricist” appeal to “pure intuition” or “pure reason” while simultaneously avoiding the naive and excessively empiricist position of J. S. Mill (Ibid.).