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Reprinted in On the Foundations of Geometry and Formal Theories of Arithmetic Über die Grundlagen der Geometrie. (Schluß.) III. Jahresbericht der Deutschen Mathematiker-Vereinigung, XV (1906) 423-430. Neudruck in Kleine Schriften (1967). Reprinted in On the Foundations of Geometry and Formal Theories of Arithmetic
He is considered to be one of the founders of modern logic and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on the philosophy of language and mathematics.
Abstract. This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work.
This page is a summary of: On the Foundations of Geometry and Formal Theories of Arithmetic., Philosophy and Phenomenological Research, December 1973, JSTOR, DOI: 10.2307/2106700. You can read the full text:
[Show full abstract] characterized by: i) an abstract or formal axiomatic view; ii) an empiricist stance regarding the origins of geometry and its place among the different mathematical theories.
10Foundations of mathematics. 11Theories of judgement. 12The logical analysis of language. 4Philosophy and the new physics. 5The idea of social science. 6Ethics, politics, and legal theory. 7Philosophy of religion and art. Interlude. II1914–1945.
Volume 2 focuses on notes for lectures on the foundations of the mathematical sciences held by Hilbert in the period 1894-1917. They document Hilbert’s first engagement with ‘impossibility’ proofs; his early attempts to formulate and address the problem of consistency, first dealt with in his work on geometry in the 1890s; his engagement with foundational problems raised by the work of ...
