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  "body": "\n## Statement\n\nIn 1902 Russell sent a letter to Frege pointing out that Frege's 1879 *Begriffsschrift* allowed a function to be an argument of itself: \"On the other hand, it may also be that the argument is determinate and the function indeterminate . . ..\" From this unconstrained situation Russell was able to form a paradox:\n\n\"You state ... that a function, too, can act as the indeterminate element. This I formerly believed, but now this view seems doubtful to me because of the following contradiction. Let *w* be the predicate: to be a predicate that cannot be predicated of itself. Can *w* be predicated of itself?\"\n\nFrege responded promptly that \"Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic\".\n\nFrom this point forward development of the foundations of mathematics became an exercise in how to dodge \"Russell's paradox\", framed as it was in \"the bare \\[set-theoretic\\] notions of set and element\".\n",
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