2013 | 61 | 2, Special No: Studie k filosofii Bertranda Rusella | 167-187
Axiom redukovatelnosti: za zrcadlem paradoxu a co tam Russell našel
Axiom of Reducibility: Through the Looking Glass of Paradox and What Russell Found There
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Russell’s ramified type theory did not allow generalising in mathematical practice, which is why Russell introduced the axiom of reducibility that postulated the existence of a predicative function of the lowest order formally equivalent to any propositional function of a higher order. This historiographical paper deals with the nature of the axiom of reducibility – that Russell expected to eliminate the paradoxes undermining the project of logicism – in the context of theory of types. The axiom has been intensively criticized as an illogical principle that actually had a destructive effect on the ramified hierarchy of types. Instead of the well-known criticisms by famous thinkers (Ramsey, Chwistek, Wittgenstein, Quine), this paper focuses on Waismann’s analysis of the axiom that originated in the period of his collaboration with Wittgenstein and showed that the axiom is not a logical principle because it does not correspond with the concept of tautology as proposed in the Tractatus. Although Waismann’s contribution went almost unnoticed, overshadowed by Wittgenstein’s own work, it is an illustrative example of the reception of Russell’s thinking within the Vienna Circle.
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