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Philosophia Mathematica Advance Access published online on April 3, 2008
Philosophia Mathematica, doi:10.1093/philmat/nkn010
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© The Author [2008]. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Book Review

STEFANO DONATI. I Fondamenti della Matematica nel Logicismo di Bertrand Russell [The Foundations of Mathematics in the Logicism of Bertrand Russell]

Gianluigi Oliveri*

* Dipartimento di Filosofia Storia e Critica dei Saperi, Università di Palermo, 90128 Palermo, Italy. gianluigi.oliveri@unipa.it

Florence: Firenze Atheneum, 2003. ISBN 88-7255-204-4. Pp. 988

The first 150 words of the full text of this article appear below.

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 (PM); 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 . . . [Full Text of this Article]


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