Ins and outs of Russell's theory of types

Enderer, Ali Bora (2018). Ins and outs of Russell's theory of types. University of Birmingham. M.A.

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Abstract

The thesis examines A.N. Whitehead and B. Russell’s Ramified Theory of Types (RTT). It consists of three parts. The first part is devoted to understanding the source of impredicativity implicit in the induction principle. The question I raise here is whether second-order explicit definitions are responsible for cases when impredicativity turns pathological. The second part considers the interplay between the vicious-circle principle and the no-class theory. The main goal is to give an explanation for the predicative restrictions entailed by the vicious-circle principle. The explanation is that set-existence is parasitic upon prior predicative specifications. The justification for this claim is given by employing the method of hierarchy of languages. Supposing the natural number structure and the language of Peano Arithmetic (PA) as given, I describe the construction of a set-theoretic language equipped with substitutionally interpreted quantifiers ranging over arithmetically definable sets. The third part considers the proposition-theoretic version of Russell’s antinomy. A solution to this paradox is offered on the basis of the ramified hierarchy propositions.

Type of Work:

Thesis (Masters by Research > M.A.)

Award Type:

Masters by Research > M.A.

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