1. turing-intro.ppt version:20101123

2. Turing 1936: “On Computable Numbers” William J. Rapaport Department of Computer Science & Engineering, Department of Philosophy, Department of Linguistics, and Center for Cognitive Science rapaport@buffalo.edu http://www.cse.buffalo.edu/~rapaport

3. Hilbert’s “Entscheidungsproblem” “Decision Problem”: –  proposition of math,  ? finite procedure (algorithm) that “decides” its truth-value? or that proves/disproves it? –Possibly:  such proposition,  such a proof/disproof but no algorithmic way to find it –Gödel:  true proposition G of arithmetic such that ¬  proof of G

5. Turing 1936 age ≈ 24 (!) analysis of idealized human computer intuitive conception of “mechanical calculation” –Euclid  Leibniz  Babbage  Hilbert formal mathematical theory (TM) –convinced Gödel, because of intuitive simplicity showed: –intuitive conception  formal theory  -calculus –showed Decision Problem unsolvable Halting Problem not computable –existence of Universal TM (= programmable computer)