 Russell’s antinomy and related ones establish that Dedekind’s original conception of set is untenable. Yet they do not invalidate his other contributions to set theory. His analysis of continuity, the use of Dedekind cuts in the introduction of the real numbers, the definition of being Dedekind-infinite, the formulation of the Dedekind-Peano axioms, the proof of their categoricity, the analysis of the natural numbers as finite ordinal numbers, the justification of mathematical induction and recursion, and most basically, the insistence on extensional, general notions of set and function, as well as the acceptance of the actual infinite—all of these contributions can be isolated from the set-theoretic antinomies. As such, they have been built into the very core of axiomatic set theory, model theory, recursion theory, and other parts of current logic.