  Along other lines, Sylvan made tentative steps in the foundations of recursion theory, towards a non-classical theory of computation (cf. Copeland and Sylvan 1999; Sylvan 2000a). According to work by Turing, Church, and Gödel in the 1930s, computers face logical limits on what they can compute (see the entry on the Church-Turing thesis and the entry on computability and complexity). Uncomputability proofs, though, bear a very strong resemblance to the derivations of Russell’s paradox and other diagonal paradoxes. If “dialectical” logic can be used to solve those paradoxes, though—essentially, by accepting that they have truly contradictory conclusions (see Section 2.2 above)—then could the same be done in the case of computers? Then the conclusion would be, not that there are uncomputable algorithms, but rather “there are more algorithmic functions than all algorithmic functions” (2000a, 195). Sylvan envisions “dialeth[e]ic machines”; cf. Weber (2016).