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Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: joes <noreply@example.org> Newsgroups: comp.theory Subject: Re: The philosophy of logic reformulates existing ideas on a new basis --- Date: Sat, 9 Nov 2024 11:01:50 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: <2a5107f331836f388ad259bf310311a393c00602@i2pn2.org> References: <vfli1h$fj8s$1@dont-email.me> <vg4uem$3o3ca$1@dont-email.me> <vg7f7l$a1jf$1@dont-email.me> <vg8ulh$9stc$1@dont-email.me> <vgakbd$vlda$1@dont-email.me> <vgbm5r$sgg9$1@dont-email.me> <vgg6fh$2s61$1@news.muc.de> <vgg7tk$26klj$1@dont-email.me> <vggjtb$1f3u$1@news.muc.de> <vggund$2am72$1@dont-email.me> <vgkudf$1lrm$1@news.muc.de> <vgl78d$37h38$2@dont-email.me> <vgl9cm$6e3$1@news.muc.de> <vgl9uh$37h38$9@dont-email.me> <vglcnh$agb$1@news.muc.de> <vgldr3$38uph$1@dont-email.me> <vglfui$agb$2@news.muc.de> <vglhij$39mg2$1@dont-email.me> <8c2cbbe343934d211ad8c820c963702e70351a27@i2pn2.org> <vglk31$3a6hn$1@dont-email.me> <19d0838dd000cc4f67c8c64ac6005d5405cf2bd6@i2pn2.org> <vglv58$3bn2s$3@dont-email.me> <cd6cbe7d70fcc282da94aea2107e48ad4b3f44b5@i2pn2.org> <vgm79v$3d9gu$1@dont-email.me> <4b24331953934da921cb7547b6ee2058ac9e7254@i2pn2.org> <vgmb06$3e37h$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Sat, 9 Nov 2024 11:01:50 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1641167"; mail-complaints-to="usenet@i2pn2.org"; posting-account="nS1KMHaUuWOnF/ukOJzx6Ssd8y16q9UPs1GZ+I3D0CM"; User-Agent: Pan/0.145 (Duplicitous mercenary valetism; d7e168a git.gnome.org/pan2) X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 4417 Lines: 50 Am Fri, 08 Nov 2024 18:39:34 -0600 schrieb olcott: > On 11/8/2024 6:33 PM, Richard Damon wrote: >> On 11/8/24 6:36 PM, olcott wrote: >>> On 11/8/2024 3:59 PM, Richard Damon wrote: >>>> On 11/8/24 4:17 PM, olcott wrote: >>>>> On 11/8/2024 12:31 PM, Richard Damon wrote: >>>>>> On 11/8/24 1:08 PM, olcott wrote: >>>>>>> On 11/8/2024 12:02 PM, Richard Damon wrote: >>>>>>>> On 11/8/24 12:25 PM, olcott wrote: >>>>>>>> >>>>>>>>> That formal systems that only apply truth preserving operations >>>>>>>>> to expressions of their formal language that have been >>>>>>>>> stipulated to be true cannot possibly be undecidable is proven >>>>>>>>> to be over-your-head on the basis that you have no actual >>>>>>>>> reasoning as a rebuttal. Gödel showed otherwise. >>>>>>>> No, all you have done is shown that you don't undertstand what >>>>>>>> you are talking about. >>>>>>>> Godel PROVED that the FORMAL SYSTEM that his proof started in, is >>>>>>>> unable to PROVE that the statement G, being "that no Natural >>>>>>>> Number g, that satifies a particularly designed Primitive >>>>>>>> Recursive Relationship" is true, but also shows (using the Meta- >>>>>>>> Mathematics that derived the PRR for the original Formal System) >>>>>>>> that no such number can exist. >>>>>>> The equivocation of switching formal systems from PA to meta-math. There’s no such thing happening. They are very clearly separated. >>>>>> No, it just shows you don't understand how meta-systems work. >>>>> IT SHOWS THAT I KNOW IT IS STUPID TO CONSTRUE TRUE IN META-MATH AS >>>>> TRUE IN PA. MM doesn’t even contain the same sentences as PA. >>>> But, as I pointed out, the way Meta-Math is derived from PA, >>> Meta-math <IS NOT> PA. >>> True in meta-math <IS NOT> True in PA. Yes it is. If MM proves that a sentence is true in PA, that sentence is true in PA. >>> This sentence is not true: "This sentence is not true" >>> is only true because the inner sentence is bullshit gibberish. It’s a perfectly wellformed sentence. >> But MM has exactly the same axioms and rules as PA, so anything >> established by that set of axioms and rules in MM is established in PA >> too. >> There are additional axioms in MM, but the rules are built specifically > One single level of indirect reference CHANGES EVERYTHING. > PA speaks PA. Meta-math speaks ABOUT PA. > The liar paradox is nonsense gibberish except when applied to itself, > then it becomes true. What is "the liar paradox applied to itself"? -- Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math: It is not guaranteed that n+1 exists for every n.