ION: (x)(x s {yiP} P[x/y]) (where P is any formula of classical quantification theory constructed using &, v, -, and universal and existential quantifiers, which does not contain x free, and P[x/y] is the result of replacing every free occurrence of y by an occurrence of x). EXTENSIONALITY: A = B (x)(x s A _ x s B), where 'A' and 'B' are set abstracts as characterized above. The question of the consistency of this kind of set theory with the indeterminacy of identity can be settled by showing that these axioms may hold even when identity is sometimes indeterminate; and that can be established in turn by showing that whenever there is a model for indeterminate identity of the sortdescribed in the first part of this paper, then the model may be extended by the addition This content downloaded from 207.46.13.123 on Tue, 28 Jun 2016 06:50:29 UTC All use subject to http://about.jstor.org/terms 12 / Terence Parsons of sets, in such a manner that:
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Terence Parsons (1987) studied this question.
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