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Leon Chwistek on the no-classes theory in Principia Mathematica

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Leon Chwistek's 1924 paper 'The Theory of Constructive Types' is cited in the list of recent 'contributions to mathematical logic' in the second edition of Principia Mathematica, yet its prefatory criticisms of the no-classes theory have been seldom noticed. This paper presents a transcription of the relevant section of Chwistek's paper, comments on the significance of his arguments, and traces the reception of the paper. It is suggested that while Russell was aware of Chwistek's points, they were not important in leading him to the adoption of extensionality that marks the second edition of PM. Rudolf Carnap seems to have independently rediscovered Chwistek's issue about the scope of class expressions in identity contexts in his Meaning and Necessity in 1947.

Document Type: Research Article


Publication date: February 1, 2004

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