Was the Axiom of Reducibility a Principle of Logic?

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  • THE TITLE OF this paper is in the past tense to indicate that the question it will address is whether the Axiom of Reducibility is a principle of logic according to the view of logic that Russell had when writing the first edition of Principia Mathematica.' It is often said that Logicism was a failure because when it avoided the Scylla of contradiction in Frege's system it fell into the Charybdis ofrequiring'obviously non-logical principles at Russell's hands. The axiom reducibility is cited along with the Axiom ofInfinity as a non-logical principle which Russell had to add to his system in order to be able to develop mathematics. I want to consider this criticism of the axiom from several points of view. Why is it thought that the axiom of reducibility is not a principle of logic? What reasons does Russell actually give for doubting its logical status? Are they good reasons?

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    © 1990 Bernard Linsky et al. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.
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    • Linsky, B. (1990). Was the Axiom of Reducibility a Principle of Logic? Russell: The Journal of the Bertrand Russell Archives, 10(2), 125-140.
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