6 ms·
That's not how arguments from contradiction work. You've assumed H (halting problem is decidable), prove B (beauty decidable), then say "but actually !H, theref
by jacb 6y ago
That's not how arguments from contradiction work. You've assumed H (halting problem is decidable), prove B (beauty decidable), then say "but actually !H, therefore !B". All you've proven is that H => B. An actual argument from contradiction is "assume H, using H we can prove an obviously false statement, therefore not-H". And indeed, you have assumed something false (H), and shown a contradiction (various proofs for !H), so your original assumption was wrong (!H).
A concrete example: say Beauty(R,D) is trivially decidable (say it returns (popcount(R)+popcount(D))%2. Your argument "proves" this property is undecidable, but it's definitely decidable. So some step in your argument is wrong.
Another concrete example: Assume the halting problem is decidable. I would like a cookie. But the halting problem is not decidable. Therefore I would not like a cookie.
- deleted 6y ago[deleted]
- cambalache 6y agoYou are just repeating my critique. I am not the one making the mistake.
- jacb 6y agoAh, I misunderstood you! I apologize. :)
- gbjw 6y agoSo you mean your frustration is warranted then?
- cambalache 6y agoIf that is the kind of work published by academics associated with the MIT and La Pontificia Universidad de Madrid, then maybe I should not feel frustrated after all by not being an academic.
- spuz 6y agoBut you said in your first comment that you were an academic. "I confess I am a frustrated academic"
- Caylio 6y agoHe is proving his point by contradicting himself, a true mathematician.
- bryanrasmussen 6y agoif you're not being facetious, in English vernacular being a frustrated X (as in a frustrated academic, frustrated poet, etc.) means that the person is actually not that, but have in some way been prevented from being the thing (frustrated) and have perhaps rancor in regards to the frustration and towards those who actually are the thing (this second feature being sometimes implied depending on who is doing the description of the person as frustrated) on edit: formatting, clarification
- taberiand 6y agoAs an English speaker, my only interpretation was that you were an academic frustrated about academia.
- falseprofit 6y agoThat isn't even the same user.
- bryanrasmussen 6y agohttps://www.ldoceonline.com/dictionary/a-frustrated-artist-actor-poet-etc https://www.ldoceonline.com/dictionary/a-frustrated-artist-a... - came up if I search for 'meaning of frustrated poet' which is the kind of thing where the phrasing most often comes up.
- js8 6y agoThanks, I wasn't aware of the 2nd meaning. I also interpreted the "frustrated academic" as "an annoyed academic", rather than "an unsuccesfull academic".
- sgillen 6y agoI think maybe you made a typo in your OP? The authors assume beauty is decidable and use that to show that would imply that the halting problem is undecidable. It applies to anything, like you say, and to me it seems like a silly argument, but I think it’s a valid proof given the premises.
- dandanua 6y agoBut it's not an argument from the paper. The idea is that superintelligence have to understand a consequence of any program to check for harm. And this is undecidable due to the halting problem. This argument is correct, but trivial and not worth a paper, in my opinion.
- cambalache 6y agoThe harming algorithm is just used in the paper's proof as a simple wrapper around the halting algorithm.