Stefano Donati. I fondamenti Della matematica Nel logicismo di Bertrand Russell [the foundations of mathematics in the logicism of Bertrand Russell]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 17 (1):109-113 (2009)
Bertrand Russell's contributions to last century's philosophy and, in particular, to the philosophy of mathematics cannot be overestimated.Russell, besides being, with Frege and G.E. Moore, one of the founding fathers of analytical philosophy, played a major rôle in the development of logicism, one of the oldest and most resilient1 programmes in the foundations of mathematics.Among his many achievements, we need to mention the discovery of the paradox that bears his name and the identification of its logical nature; the generalization to the whole of mathematics of Frege's idea that it is not possible to draw a demarcation line between logic and arithmetic; the programme, carried out with Whitehead, of derivation of mathematics from the logical system of Principia Mathematica ; and the ramified theory of types, devised by Russell to protect the system of PM from the known paradoxes.Although there is an ample literature on these topics, it is quite important to reconsider Russell's contributions to the foundations of mathematics at a time when, as a consequence of the crisis of the classical programmes in the foundations of mathematics, new trends are beginning to develop within the philosophy of mathematics. These are trends which move in a very different direction from that of logicism, intuitionism, and Hilbert's programme.To see this we need to consider that, in spite of profound disagreements on the nature of mathematical activity, on the relationship existing between logic and mathematics, on the causes of and therapies for the paradoxes, etc., logicism, intuitionism, and Hilbert's programme share an important metaphor: the idea that mathematics is an edifice built on unshakable foundations,2 an edifice which makes possible only a cumulative growth of mathematical knowledge.Such a metaphor—which, together with more specific theses belonging to these schools of thought, remained unsupported …
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Ray Monk (1999). Cambridge Philosophers IX: Bertrand Russell. Philosophy 74 (1):105-117.
I. Grattan-Guinness (1985). Bertrand Russell's Logical Manuscripts: An Apprehensive Brief. History and Philosophy of Logic 6 (1):53-74.
Paul Arthur Schilpp (1952). The Philosophy of Bertrand Russell. New York, Tudor Pub. Co..
Bertrand Russell (ed.) (1973). Bertrand Russell, the Social Scientist. Bertrand Russell Supranational Society.
Added to index2009-02-07
Total downloads41 ( #80,927 of 1,725,865 )
Recent downloads (6 months)1 ( #348,716 of 1,725,865 )
How can I increase my downloads?