Path: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory,sci.logic Subject: Re: H(D,D) cannot even be asked about the behavior of D(D) --- Truth Itself is not Broken. (Just misunderstood) Date: Sat, 15 Jun 2024 11:24:43 -0400 Organization: i2pn2 (i2pn.org) Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 15 Jun 2024 15:24:44 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="67625"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: Content-Language: en-US X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 4392 Lines: 58 On 6/15/24 11:17 AM, olcott wrote: > On 6/15/2024 8:52 AM, Richard Damon wrote: >> On 6/15/24 8:26 AM, olcott wrote: >>> On 6/15/2024 6:48 AM, joes wrote: >>>> Am Fri, 14 Jun 2024 21:39:50 -0500 schrieb olcott: >>>> >>>>> The key aspect of all of this is that if the halting problem is >>>>> correct >>>>> then truth itself is fundamentally broken. Since truth itself cannot >>>>> possibly be fundamentally broken it must be fallible human >>>>> understanding >>>>> of truth that is actually broken. >>>> I've got bad news for you, and you're a century late. Gödel proved that >>>> not all true statements are provable. It sure would have been nice. >>>> >>> >>> He didn't even prove this. >>> He proved that a statement that can be expressed in PA >>> cannot be proving in PA that is not true in PA yet can be >>> proved in matamath thus is true in metamath. >> >> No, you are just showing you don't know what you are talking about. >> >> You have admitted that you don't even understand the actual statement >> he was using, but can only understand it as the simplication through >> implication in the meta-thoery. >> >> G, the statement about the non-existance of a Natural Number 'g' that >> satisfied the specified relationship. >> >> It can be shown (in the meta-theory) that no such number can exist, so >> G must be true. Either the number 'g' exists or it doesn't so their >> can be no middle ground, and it if is shown (in the meta theory) that >> if such a number 'g' existed, then we could build a proof (as encoded >> in the finite number 'g') in PA that PROVES CONCLUSIVELY no such >> number exist. > >> There can not be a number that proves that itself doesn't exist, so >> there must not be such a number. >> > > Isomorphically there can be no proof that proves itself doesn't exist, > so there must not be such a proof. > So? In the meta-math there IS a proof that there is no number 'g' that satisfies that relationship, but that isn't doing a proof about ITSELF. The key is that if we find a number 'g' in PA that satisfies the relationship, then via the operations in the meta-math, we can CONSTRUCT an actual proof in PA that such a number can not exist. This becomes the proof, in the meta-math, that no number 'g' can exist. In PA alone, we can still establish that fact, but only with infinite work, so we can't form a proof of that fact.