  As mentioned in the quote above, Sylvan saw that something like the “dialectical logic” DL could be used to underwrite inconsistent but non-trivial mathematical and scientific theories, which had been of interest to him since the start. Of particular note is naïve set theory, used by Cantor, Dedekind, and Frege in the foundations of mathematics (see the entry on the early development of set theory), but dealt an apparently fatal blow by Russell’s paradox circa 1900. Building from work by Brady (1971), naïve set theory as formulated with the implication connective ‘\(\rightarrow\)’ of DL (or the slightly weaker DK) takes as axioms that there is a set for every property \(A\), i.e., 