Path: ...!local-2.nntp.ord.giganews.com!Xl.tags.giganews.com!local-4.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Sun, 17 Nov 2024 18:41:27 +0000 Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-standard) Newsgroups: sci.math References: <84d9831f-d23a-4937-8333-4029c6c1f4a9@att.net> <263d223c-c255-4158-aa08-84ed11a48f20@att.net> <488cfa55-d881-4097-9825-d7630d7221eb@att.net> <5281d9d5-b6e8-4952-8cb3-8308957a497f@att.net> <7da62e1a-4e04-444a-9a3e-b9f6312d14d0@att.net> <6xidnYmzCoBVD6T6nZ2dnZfqnPWdnZ2d@giganews.com> <2dddcc3e-6622-4dea-9895-2e10d9f94428@att.net> From: Ross Finlayson Date: Sun, 17 Nov 2024 10:41:58 -0800 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.6.0 MIME-Version: 1.0 In-Reply-To: <2dddcc3e-6622-4dea-9895-2e10d9f94428@att.net> Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Message-ID: Lines: 133 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-XoIdrSAWT0WGtdNTo9uFy5fKdoTB0cyffRsJZxEKKMk+iYwYKyrAx6/kl+VOe4LnItS7BGtVTebVu4K!M+ShiruS/qMtdI2vLSZ0RYIsKLAlLlMcGqrU8Y7YzRJjXsFKFD13lmJ38EjRgOUFG2LFJoeYwg== 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 Bytes: 6516 On 11/17/2024 10:35 AM, Jim Burns wrote: > >> > > On 11/16/2024 02:22 AM, Jim Burns wrote: >> > >> On 11/15/2024 9:52 PM, Ross Finlayson wrote: >> > >>> On 11/15/2024 02:37 PM, Jim Burns wrote: >> > >>>> On 11/15/2024 4:32 PM, Ross Finlayson wrote: >> > >> > >>>>> Ah, yet according to Mirimanoff, >> > >>>>> there do not exist standard models of integers, >> > >>>> >> > >>>> If it is true that >> > >>>> our domain of discourse is a model of ST+PQ >> > >>>> then it is true that >> > >>>> our domain of discourse holds a standard integer.model. >> > >>>> What is Mirimanoff's argument that >> > >>>> it doesn't exist? >> > >>> >> > >>> Mirimanoff's? Russell's Paradox. >> > >> >> > >> ST+PQ does not suffer from claiming >> > >> that the set of all non.self.membered sets >> > >> is self.membered or claiming it isn't. >> > >> >> > >> While I am at it, >> > >> ZFC does not suffer from claiming >> > >> that the set of all non.self.membered sets >> > >> is self.membered or claiming it isn't, >> > >> and >> > >> ordinal.theory=Well.Order >> > >> does not suffer from claiming >> > >> that the set of all non.self.membered sets >> > >> is self.membered or claiming it isn't. > >> > On 11/16/2024 12:07 PM, Ross Finlayson wrote: >> >> >> you have ignored Russell his paradox and so on > > On 11/17/2024 1:52 AM, Ross Finlayson wrote: >> On 11/16/2024 10:11 PM, Ross Finlayson wrote: >>> On 11/16/2024 09:59 PM, Ross Finlayson wrote: >>>> On 11/16/2024 09:56 PM, Jim Burns wrote: > >>>>> ⎛ The modern study of set theory was initiated by >>>>> ⎜ Georg Cantor and Richard Dedekind in the 1870s. >>>>> ⎜ However, >>>>> ⎜ the discovery of paradoxes in naive set theory, >>>>> ⎜ such as Russell's paradox, >>>>> ⎜ led to the desire for >>>>> ⎜ a more rigorous form of set theory >>>>> ⎝ that was free of these paradoxes. >>>>> >>>>> https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory > >>>> How about Finsler and Boffa? > > Meaning: > how about non.well.founded set theories? > > ⎛ I learned a new word recently: 'sanewashing'. > ⎜ > ⎜ For example, > ⎜ it is sanewashing > ⎜ when I snip context in which > ⎜ you call me a liar for stating facts > ⎜ accessible to Wikipedia.level research. > ⎜ > ⎜ I don't wish to dwell on my sanewashing. > ⎜ I doubt that anyone beyond you (RF) or me > ⎜ would find it the least bit interesting if I did. > ⎜ I only note it in passing for the benefit of > ⎝ the future, when the cockroaches evolve archeologists. > > On a lighter note, > how about Finsler or Boffa or Mirimanoff or > non.well.founded set theories? > Do they show that ST+PQ or ZFC or ordinals > suffer from Russell's {S:S∉S}? > > No. They do not show that. > > The less.interesting reason that they don't > is that > they are different domains of discourse. > ⎛ 0 < 1/2 < 1 does not show that > ⎜ there is an integer between 0 and 1 > ⎝ because 1/2 isn't an integer. > > That less.interesting reason seems to > lie close to the heart of your objection. > You (RF) seem to not.believe that > things can be not.referred to. > > In that respect, > I don't see what I can do for you. > I will continue to not.refer to > what I choose to not.refer to. > > The more.interesting reason is that > ST+PQ and ZFC and well.ordering > do not suffer from Russell's {S:S∉S} > _by design_ > > Without looking up what Mirimanoff or > Finsler or Boffa have to say about > non.well.founded set.theories, > I am confident that their theories > do not suffer from Russell's {S:S∉S} > _by design_ > > Because they know that, otherwise, > they would be talking gibberish. > > You (RF) seem to argue that > ☠⎛ they cannot not.refer to Russell's {S:S∉S} > ☠⎜ and therefore they ARE talking gibberish > ☠⎝ and a standard model of the integers not.exists. > > ☠( and anyone who disagrees with that is a liar. > > It is so that that is what I argue, for, yes. Mirimanoff says so, too. Then there's also the "not.first.false is not necessarily not.ultimately.untrue" bit, and the demonstration of the "yin-yang ad-infinitum" bit, then also as with regards to doubling-spaces and halving spaces and the continuum in mathematics.