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date: 05 March 2021

Abstract and Keywords

This article examines the logical and mathematical background to “analytic philosophy.” “Analytic philosophy” as here understood, regards mathematics, and especially mathematical logic as a central contributor to philosophical progress and an indispensable component of philosophical reasoning. On the philosophical side, this article counts as “analytic philosophy” the work in the stream tracing back to and back from the Vienna Circle and subsequently “logical positivism,” or to Bertrand Russell. It first looks at the logic of geometry and space, focusing on projective geometry, non-Euclidean geometry, logic and freedom from intuition, rigor, and theories of types. It then focuses on the views of several philosophers such as Georg Friedrich Bernhard Riemann, Hermann Günther Grassmann, Moritz Pasch, David Hilbert, Richard Dedekind, Friedrich Ludwig Gottlob Frege, Giuseppe Peano, and Russell.

Keywords: Friedrich Ludwig Gottlob Frege, analytic philosophy, mathematics, mathematical logic, space, geometry, theories of types, Moritz Pasch, David Hilbert, Richard Dedekind

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