 David Hilbert placed the axiomatic tradition in mathematics on a formalist footing by eliminating the requirement of a fixed meaning for primitive terms such as ’points’ and ’lines’ except holistically and implicitly, in the set of axioms or definitions in which they appear. Hilbert extended the application of his program of axiomatics from geometry and arithmetic to physics. Gottlob Frege, followed by A.N. Whitehead and Bertrand Russell, sought to place mathematics, or at least arithmetic, on firm and rational principles of logic, which now included a theory of relations and was to provide a comprehensive and unifying foundation. The reductionist ideal was fatally criticized by Kurt Gödel. Russell, having replaced idealist monism with perceptual atomism, next put the new logical framework to epistemological use in the scientific program of logical construction of objects of experience and thought. His student Wittgenstein, in turn, introduced a linguistic philosophy that limited the world to the scope of the application of an ideal symbolic languages, or calculus. As a result, the sole task of philosophy was, according to Wittgenstein, the critique of language in the form of an activity of clarification, without yielding a distinctive philosophical body of knowledge or set of propositions.