Well, no. The correct thing to do is conclude that H is impossible; that there are things which cannot be computed.
8 hours ago — Banno
Well, no. The correct thing to do is conclude that H is impossible; that there are things which cannot be computed. — Banno
↪PL Olcott Repetition and appeal to (supposed) authority. — Banno
↪PL Olcott I wouldn't be here apart from trying to help articulate the point.
That's why I've asked you to show as explicitly as you can where Carol's question occurs.
In the other thread I suggested that the analogue would be "Will Program Z loop forever if fed itself as input?"
— Banno — Banno
Assume to reach a contradiction that there exists a program Halt(P, I) that solves the halting problem, — Prof Kirk Pruhs
↪PL Olcott
Assume to reach a contradiction that there exists a program Halt(P, I) that solves the halting problem,
— Prof Kirk Pruhs — Banno
↪PL Olcott What you have done is to display the contradiction that we all agree on. It's what you conclude from that which is problematic. — Banno
These words may be a little too technical for you. — PL Olcott
You started this with Carol's question, went on to claim that Gödel's theorem was wrong, backtracked to Turing and now obfuscate. — Banno
If you would prove Turing wrong, you will need more than mere assertion. — Banno
If one's assumptions lead to contradiction, then at least one is in error. Assuming we can produce H leads to contradiction. Hence we cannot produce H. — Banno
Yep. Quite agree. If your conclusion is a logical impossibility, there is something amiss with your assumptions. — Banno
↪PL Olcott Yeah, OK. No progress to be made here. Publish your article and then invite me to the ceremony when you win the Turing Award so you can say "I told you so". — Banno
↪PL Olcott Yeah, OK. No progress to be made here. Publish your article and then invite me to the ceremony when you win the Turing Award so you can say "I told you so". — Banno
↪PL Olcott It's an inveterate issue in Psychoceramics. — Banno
PL Olcott "logically impossible" is not recognized in philosophy. It's either "illogical" or "impossible". The two are used in different contexts. — L'éléphant
"logically impossible" is not recognized in philosophy. — L'éléphant
This entry is about worlds that are not possible, with “possible” understood in an unrestricted sense. Start with the intuitive idea of the totality of possible worlds, which capture all and only the genuine possibilities. The worlds we are interested in are not in there. These worlds are often called logically impossible worlds, as logical laws such as the Law of Non-Contradiction or the Law of Excluded Middle are assumed to be the most general and topic-neutral: they are supposed to hold at all possible worlds. From now on, we are talking of impossible worlds simpliciter, meaning worlds that are not possible with respect to an unrestricted notion of possibility, however this is further characterized. — Impossible Worlds (Stanford Encyclopaedia, my bolding)
Tell that to an electron in a double-slit experiment.i.e. it's impossible to be in two places at the same exact time. — L'éléphant
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