Path: csiph.com!xmission!news.snarked.org!border2.nntp.dca1.giganews.com!nntp.giganews.com!buffer2.nntp.dca1.giganews.com!buffer1.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Fri, 10 Jul 2020 16:25:29 -0500 Subject: =?UTF-8?Q?Re=3a_Simply_defining_G=c3=b6del_Incompleteness_and_Tarsk?= =?UTF-8?Q?i_Undefinability_away_V24_=28Are_we_there_yet=3f=29?= Newsgroups: comp.theory,comp.ai.philosophy,comp.ai.nat-lang,sci.lang.semantics References: <87k0zc8ps5.fsf@nosuchdomain.example.com> <87v9iv6t9z.fsf@nosuchdomain.example.com> From: olcott Date: Fri, 10 Jul 2020 16:25:29 -0500 User-Agent: Mozilla/5.0 (Windows NT 10.0; WOW64; rv:68.0) Gecko/20100101 Thunderbird/68.10.0 MIME-Version: 1.0 In-Reply-To: <87v9iv6t9z.fsf@nosuchdomain.example.com> Content-Type: text/plain; charset=utf-8; format=flowed Content-Language: en-US Content-Transfer-Encoding: 8bit Message-ID: Lines: 76 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-O774REVkfpXaiCh4M61j83WVzmydhd4wqv9+QFidqn/ybQ6yJVqbJVzcbTYMjok9fA4WLhnhZByNm8o!XxObt7yR7eIBhyB2LtnBjpxp2bwHw+sNjP026pMsVP4mShpX7/AITeTRnNDLp3huv+4UbPxUF49p X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 X-Original-Bytes: 5417 Xref: csiph.com comp.theory:21566 comp.ai.philosophy:21884 comp.ai.nat-lang:2318 On 7/10/2020 2:53 PM, Keith Thompson wrote: > olcott writes: >> On 7/9/2020 2:14 PM, Keith Thompson wrote: >>> olcott writes: >>>> On 7/9/2020 8:40 AM, André G. Isaak wrote: >>> [...] >>>>> I've asked you repeatedly about Robinson's arithmetic, in which x + >>>>> y = y + x is not provable. Neither is ¬(x + y = y + x) provable. The >>>>> law of the excluded middle demands that one of those be true, so >>>>> there exists a true statement in Q which is not provable in Q. >>>>> >>>>> And one can prove that x + y = y + x is true in Q. You just can't >>>>> prove it from within Q. >>>> >>>> That is the exactly same key mistake that you, Tarski and presumably >>>> Gödel made. How do we know that it is true IN Q when it is not >>>> provable IN Q (We look outside of Q). THEN IT IS NOT TRUE IN Q, IT IS >>>> ONLY TRUE OUTSIDE OF Q. >>> >>> If it is not true in Q, then there are values x and y in Q such that >>> x + y = y + x is false in Q. >>> >>> In fact there are no such values. (You could refute that if you could >>> provide such values.) >>> >>> I'm assuming that "x + y = y + x is true in Q" and "x + y = y + x is >>> false in Q" are the only possibilities (law of the excluded middle). >>> Do you accept that assumption? No I do not accept that assumption. Q does not know about the commutative property of addition so it is neither true nor false in Q. >> >> This is my current best guess of the correct use of the term >> satisfiable if the term satisfiable can even be applied to a single >> theory: >> >> ∃φ (Q ⊢ "x + y = y + x") would seem to be unsatisfiable in Q. >> ∃φ ¬(Q ⊢ "x + y = y + x") would also seem to be unsatisfiable in Q. >> >> This would seem to indicate that Q is incomplete relative to commutativity. >> >> I am certain that the ideas are correct. I am uncertain if my use of >> the term unsatisfiable corresponds to its conventional use. >> >> I am certain that my use of the term incomplete correctly augments the >> conventional use of the term such that my use is more correct than the >> conventional use. > > And this is an example of why trying to have a conversation with you is > so frustrating. > > I asked what I thought was a straightforward yes or no question, I answered with all of the reasoning behind the correct answer. It is like you asked me are their any five million pound giant humans? I answer that there is no animal that weighs more than 330,000 lbs. Then you said I did not answer your question. > "Do you > accept that assumption?". Your response did not include the word "yes" > or "no", nor did it attempt to demonstrate that neither "yes" nor "no" > would be a meaningful answer. Instead you wrote several paragraphs > about the meaning of "satisfiable". > > By all means, write all you like about the meaning of "satisifiable", > but please don't do so in a context that makes it look like you're > trying to answer my question. Perhaps what you wrote has some relevance > to what I asked, but I don't see it. > > You have not answered my question. "Yes" or "No" would be an answer. > -- Copyright 2020 Pete Olcott