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
Videos
Logicism: For the Establishment of a Unified Universal Philosophy
- Amazon Kindle Edition
- Kitt, H. Michael (Author)
- English (Publication Language)
- 78 Pages - 04/24/2013 (Publication Date)
Logicism and its Philosophical Legacy
- Demopoulos, William (Author)
- English (Publication Language)
- 286 Pages - 03/05/2015 (Publication Date) - Cambridge University Press (Publisher)
Logicism, Intuitionism, and Formalism: What Has Become of Them? (Synthese Library Book 341)
- Amazon Kindle Edition
- English (Publication Language)
- 512 Pages - 11/25/2008 (Publication Date) - Springer (Publisher)
Love and Logicisms: Wise Words About Kids
- Used Book in Good Condition
- Fay, Jim (Author)
- English (Publication Language)
- 130 Pages - 01/14/2001 (Publication Date) - Love and Logic Press (Publisher)
Logicism Renewed: Logical Foundations for Mathematics and Computer Science, Lecture Notes in Logic 23
- Amazon Kindle Edition
- Gilmore, Paul C. (Author)
- English (Publication Language)
- 250 Pages - 11/18/2005 (Publication Date) - A K Peters/CRC Press (Publisher)
Does Logicism overcome the problems presented by Russell’s Paradox?
- Amazon Kindle Edition
- Whitehead, Elliott (Author)
- English (Publication Language)
- 25 Pages - 11/21/2013 (Publication Date) - LostWords (Publisher)
The Logicist Tribulation of Sophia: Book Two: Recuperation of the Theological Ethics of Happiness versus Logicism and Phil-Ideology
- Amazon Kindle Edition
- Bueno, A. J. (Author)
- English (Publication Language)
- 404 Pages - 02/06/2017 (Publication Date) - Strategic Book Publishing & Rights Co. (Publisher)
Last update 2020-06-17. Price and product availability may change.