Russell's Logical Atomism
Contents
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1 Types and classes 1 Types and classes
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2 The substitutional theory 2 The substitutional theory
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3 Basic ideas of the simple theory of types 3 Basic ideas of the simple theory of types
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4 The elimination of classes 4 The elimination of classes
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5 A formal presentation 5 A formal presentation
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6 What is missing: Validity and extensionality 6 What is missing: Validity and extensionality
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7 Concluding remarks 7 Concluding remarks
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4 The Contradiction (ii): A Simple Solution
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Published:19 April 2012
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Abstract
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.
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