 But why stop at arithmetic? If logical analysis could illuminate the foundations of mathematics by showing how the axioms of arithmetic could all be derived from pure logic by substitution of synonyms, perhaps it could also illuminate the foundations of the rest of our knowledge by showing how its claims could similarly be derived from some kind of combination of logic and experience. Such was the hope and program of Logical Positivism (see Logical Empiricism) championed by, e.g., Moritz Schlick, A.J. Ayer and, especially, Rudolf Carnap from about 1915 in Vienna and Berlin to well into the 1950s in England and America. Of course, such a proposal did presume that all of our concepts were somehow “derived” either from logic or experience, but this seemed in keeping with the then prevailing presumptions of empiricism, which, they assumed, had been vindicated by the immense success of the empirical sciences.