The Substitutional Paradox in Russell's 1907 Letter to Hawtrey

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  • This note presents a transcription of Russell's letter to Hawtrey of 22 January 1907 accompanied by some proposed emendations. In that letter Russell describes the paradox that he says \"pilled\" the \"substitutional theory\" developed just before he turned to the theory of types. A close paraphrase of the derivation of the paradox in a contemporary Lemmon-style natural deduction system shows which axioms the theory must assume to govern its characteristic notion of substituting individuals and propositions for each other in other propositions. Other discussions of this paradox in the literature are mentioned. I conclude with remarks about the significance of the paradox for Russell.

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    © 2002 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. (2002). The Substitutional Paradox in Russell's 1907 Letter to Hawtrey. Russell: The Journal of Bertrand Russell Studies, 22(2), 151-160.
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