The aim of Russell's early logicism: : a reinterpretation

• Autores: Anders Kraal
• Localización: Synthese, ISSN-e 1573-0964, Vol. 191, Nº. 7, 2014, págs. 1493-1510
• Idioma: inglés
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• Resumen

  • I argue that three main interpretations of the aim of Russell's early logicism in The Principles of Mathematics (1903) are mistaken, and propose a new interpretation. According to this new interpretation, the aim of Russell's logicism is to show, in opposition to Kant, that mathematical propositions have a certain sort of complete generality which entails that their truth is independent of space and time. I argue that on this interpretation two often-heard objections to Russell's logicism, deriving from Gödel's incompleteness theorem and from the non-logical character of some of the axioms of Principia Mathematica respectively, can be seen to be inconclusive. I then proceed to identify two challenges that Russell's logicism, as presently construed, faces, but argue that these challenges do not appear unanswerable