Chapter

The Contradiction (ii): A Simple Solution

David Bostock

in Russell's Logical Atomism

Published in print April 2012 | ISBN: 9780199651443
Published online September 2012 | e-ISBN: 9780191741197 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199651443.003.0004
The Contradiction (ii): A Simple Solution

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Seeking for a solution to his ‘contradiction’, Russell came to think that he could set aside classes in favour of propositional functions. In fact his first attempt in this direction, i.e. the ‘substitutional’ theory, also set aside propositional functions, in favour of quantification over propositions. But he then discovered that unrestricted quantification over propositions itself leads to contradictions, and so went back to treating propositional functions as independent entities, but now subjected to distinctions of type. This chapter treats only of simple types, which is all that the earlier substitutional theory requires. It gives a formal presentation of this theory, and notes that Russell’s own principles prevent us from providing it with a useful definition of validity.

Keywords: classes; propositional functions; propositions; substitutional theory; simple type theory; validity

Chapter.  14213 words. 

Subjects: History of Western Philosophy

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