Gödel ja Turing

”A decade after Wittgenstein pointed out the limits of spoken language, Gödel proved a parallel result for mathematics : there are truths that can be seen to be true in a system but that cannot be deduced within that system. To describe the structure of natural language, Wittgenstein showed that one must step outside it”.

(Lynn Gamwell: mathematics + art a cultural history , 2016 by Princeton University Press, s. 328 )


” ..Turing was able to show that Hilbert’s Entscheidungsproblem – a decision
procedure for all mathematical statements – is impossible. Adopting methods from Gödel’s 1931 incompleteness proof, Turing used a mapping of machines to numbers the way Gödel had mapped statements to numbers”.

(Sama teos, Lynn Gamwell, kuin yllä – s. 357)

Alan Turing

Ehdin jo ihmetellä, olenko tulkintani kanssa aivan harhateillä, kunnes törmäsin ! Lynn Gamwellin teokseen. Onneksi, näin on aiheellista sanoa, argumenttini, toisin kuin hänen perustuvat suoraan Wittgensteinin ”pyrkimykseen” (Tractatuksen esipuhe / (4.112 , 4.114) ) ja ”tosiseikkojen logiikkaan” (4.0312) .
I was already wondering , if I am astray with my Interpretation until I hit ! Lynn Gamwell’s book. Fortunately, my argument’s rest on directly ”the aim of the book” (Preface of Tractatus Logico-Philosophicus / (4.112 , 4.114) ) and ”the logic of the facts” (4.0312) .

(Update, 8. 2022 : It is uncertain, if Turing was influenced by Gödel’s result in 1931  –  at all. https://link.springer.com/article/10.1007/s00283-022-10177-y)