arXiv subjects
Publications and source records attributed to Evgeny Chutchev.
The paper offers a mathematical formalization of the Turing test. This formalization makes it possible to establish the conditions under which some Turing machine will pass the Turing test and the conditions under which every Turing machine (or every Turing machine of the special class) will fail the Turing test.
A certain mathematician M, considering some hypothesis H, conclusion C and text P, can arrive at one of the following judgments: (1) P does not convince M of the fact that since H, it follows that C; (2) P is the proof that since H, it follows that C (judgment of the type "Proved"). Is it possible to replace such a mathematician with an arbitrary Turing machine? The paper provides a proof that the answer to the question is negative under the two following conditions: (1) M is faultless, namely his judgment "Proved" always implies that since H, it actually follows that C; (2) M recognizes a certain P' as the correct proof of the fact that for certain H' and C', if H', then C' (where P', H', and C' are stated in the paper).