On Sunday, August 20, 2017 at 11:00:22 AM UTC+5:30, Paul Rubin wrote: > Rustom Mody writes: > > Specifically the term 'comprehension' used today as a programming construct > > traces somewhat tenuously to an axiom that Zermelo/Fraenkel formulated > > in the 1920s > > I thought went back to Frege. Also, it appears in Zermelo set theory Z. > ZF is Z with the Axiom of Replacement added, but Z was somewhat earlier > than ZF.
Do you mean Frege or Cantor? No I am not an historian, not even amateur, so my data may be quite screwed up What I know [open to correction!] - Cantor invented naive¹ Set Theory — late 19th century - He was the first to discover paradoxes — Cantor's paradox — which were not taken too seriously - Russel discovered his paradox — generally regarded as a bigger problem - Frege — inventor of predicate calculus — was, like Russel, interested in a sound and complete foundation of math - Russell's paradox dashed Frege's hope and put him into depression - This is about what (I know of) the relation between Frege and set theory - From beginning 20th century upto 1930 uncovering paradoxes became a cottage industry - While at the same time people like Hilbert were rebelling against the attempts 'to expel us from the paradise created by Cantor' - Zermelo-Fraenkel and Gödel-Bernays-Neumann were two of the principa lattempts at formalizing systems (called axiomatization then) so as to avoid the contradictions. At the risk of over-simplification, the Gödel-Bernays system is haskell-like (typed) and the Zermelo-Fraenkel system is python-like (untyped) - All this cottage-industry got decimated by Gödel's (2nd)² theorem showing that a single unitary axiomatization is impossible Today maybe we should say systematization? Or programming language ? 😇 Many people seem to think that all this is not related to computer science… Amusing! [For Turing a 'computer' was a (dumb) mathematician doing a computation] ¹ If such anachronism is permissible. But then much of this thread is anachronistic! ² http://mathworld.wolfram.com/GoedelsSecondIncompletenessTheorem.html -- https://mail.python.org/mailman/listinfo/python-list
