Making sense of 'on denoting'

The widely held assumption about what motivated "On Denoting" is irreconcilable with Russell's position shortly beforehand; but discarding it leaves one with a carefully worked out solution whose problem is missing. The real motivation is to be found in a notoriously obscure passage in OD, in which Russell exposes a decisive (though easily overlooked) flaw in his former theory of denoting; a flaw which also cripples Frege's theory of sense and reference. A comprehensive account of this passage is the chief concern of the present paper. Recognizing the critical role of this argument of Russell's leads to a more credible account of his argumentation in that essay. It also suggests that the fundamental standpoint underlying The Principles of Mathematics remains intact. In this light, the appropriation of OD to the philosophy of language may be misguided.