The Resolution of Hume's Problem, and New Russellian Antinomies of Induction, Determinism, Relativism, and Skepticism
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philosophy Research Archives 12:471-517 (1986)
A necessary refinement of the concept of circular reasoning is applied to the self-and-universally-referential inductive justification of induction. It is noted that the assumption necessary for the circular proof of a principle of induction is that one inference is valid, not that the entire principle or rule of induction governing that inference is true. The circularity in an ideal case is demonstrated to have a value of lin where n represents the number of inferences asserted valid by the conclusion of the justifying argument, and the ‘I’ represents the inference necessarily assumed valid.An induction antinomy modeled after Russell’s antinomy of the set of all and only non-self-containing sets is derived. Isomorphic antinomies are noted to be derivable for other arguments of philosophical interest, including those purported to undermine theories of determinism, relativism, and skepticism, and including the one that Descartes reduced and converted to ‘Cogito, ergo sum’
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