Theory, due to Gottlob Frege (1848-1925) and Bertrand Russell (1872-1970), that the concepts and theories of mathematics (in particular of arithmetic) can be derived from those of logic.
This, if feasible, would support logical positivism and reductionism in general.
Arithmetic was in fact reduced to set theory – developed by Georg Cantor (1845-1918) – as a first step, but set theory itself has never successfully been derived from pure logic, and the enterprise was frustrated by K Gödel’s (1906-1978) proof in 1931 that for any system rich enough to formalize arithmetic there will always be truths that can be stated in the system (and so form part of it) but cannot be proved within it.
Source:
S Korner, Philosophy of Mathematics (1960), chs 2, 3
Table of Contents
- 1 Videos
- 2 Related Products
- 2.1 Love and Logicisms: Wise Words About Kids
- 2.2 Logicism: For the Establishment of a Unified Universal Philosophy
- 2.3 Logicism
- 2.4 Logicism and its Philosophical Legacy
- 2.5 Does Logicism overcome the problems presented by Russell’s Paradox?
- 2.6 Logicism (Original Mix)
- 2.7 Logicism, Intuitionism, and Formalism: What Has Become of Them? (Synthese Library)
- 2.8 Logicism
- 2.9 Logic as Universal Science: Russell's Early Logicism and its Philosophical Context (History of Analytic Philosophy)
- 2.10 Logicism Renewed: Logical Foundations for Mathematics and Computer Science, Lecture Notes in Logic 23
Videos
Love and Logicisms: Wise Words About Kids
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Logicism: For the Establishment of a Unified Universal Philosophy
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Logicism and its Philosophical Legacy
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- 288 Pages - 01/03/2013 (Publication Date) - Cambridge University Press (Publisher)
Does Logicism overcome the problems presented by Russell’s Paradox?
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- Whitehead, Elliott (Author)
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Logicism, Intuitionism, and Formalism: What Has Become of Them? (Synthese Library)
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Logic as Universal Science: Russell's Early Logicism and its Philosophical Context (History of Analytic Philosophy)
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- 289 Pages - 02/05/2013 (Publication Date) - Palgrave Macmillan (Publisher)
Logicism Renewed: Logical Foundations for Mathematics and Computer Science, Lecture Notes in Logic 23
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- Gilmore, Paul C. (Author)
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- 250 Pages - 11/18/2005 (Publication Date) - A K Peters/CRC Press (Publisher)
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