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Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon <richard@damon-family.org> Newsgroups: sci.logic Subject: Re: Mathematical incompleteness has always been a misconception --- Tarski Date: Sun, 9 Feb 2025 08:10:37 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <7e532aaf77653daac5ca2b70bf26d0a3bc515abf@i2pn2.org> References: <vnh0sq$35mcm$1@dont-email.me> <vni4ta$3ek8m$1@dont-email.me> <vnikre$3hb19$1@dont-email.me> <vnkov9$1971$1@dont-email.me> <vnl9vj$4f8i$1@dont-email.me> <vnndqs$kef3$1@dont-email.me> <vnpd96$vl84$1@dont-email.me> <vnqm3p$1apip$1@dont-email.me> <vnqsbh$1c5sq$1@dont-email.me> <vnsm90$1pr86$1@dont-email.me> <vnte6s$1tra8$1@dont-email.me> <vnv4tf$2a43e$1@dont-email.me> <vo0249$2eqdl$1@dont-email.me> <vo1qae$2s4cr$1@dont-email.me> <vo2i10$302f0$1@dont-email.me> <vo4nj4$3f6so$1@dont-email.me> <vo5btf$3ipo2$1@dont-email.me> <vo7ckh$q2p$1@dont-email.me> <vo7tdg$36ra$6@dont-email.me> <voa09t$idij$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sun, 9 Feb 2025 13:10:37 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="3424083"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: <voa09t$idij$1@dont-email.me> X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US On 2/9/25 5:33 AM, Mikko wrote: > Of course, completness can be achieved if language is sufficiently > restricted so that sufficiently many arithemtic truths become > inexpressible. > > It is far from clear that a theory of that kind can express all arithmetic > truths that Peano arithmetic can and avoid its incompletness. WHich, it seems, are the only type of logic system that Peter can understand. He can only think in primitive logic systems that can't reach the complexity needed for the proofs he talks about, but can't see the problem, as he just doesn't understand the needed concepts.