Path: ...!local-3.nntp.ord.giganews.com!Xl.tags.giganews.com!local-2.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Fri, 03 Jan 2025 19:22:43 +0000 Subject: Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Newsgroups: sci.logic,sci.math References: <881fc1a1-2e55-4f13-8beb-94d1f941b5af@att.net> <85194aeb-1b24-4486-8bcc-4dcd43b4fd2f@att.net> <2e188e21-4128-4c76-ba5d-473528262931@att.net> <3df3c8f4-05b1-477b-8812-f49bd46fa764@att.net> <672c2c2a-2f01-4cc6-9e2d-52c0f4bb2996@att.net> From: Ross Finlayson Date: Fri, 3 Jan 2025 11:22:24 -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: Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Message-ID: <0PudnSrAfJGepOX6nZ2dnZfqn_adnZ2d@giganews.com> Lines: 108 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-f8HrAvX9GOnfo19KVX2azQbRumIScDD8CGV47axW8YuiRnMes7nzKisl9mquR8mKPYd0s2MtKZWHOHG!bx8PwWmZrsHOEAJPfyJlxockoF2HaZhIQE1BEGDMgPsGthhNLeHqDcMEotvFPw4gdlH+ZW/WZB2i 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: 5546 On 01/02/2025 11:14 AM, Ross Finlayson wrote: > On 01/02/2025 11:07 AM, Ross Finlayson wrote: >> On 01/02/2025 09:35 AM, Jim Burns wrote: >>> On 1/1/2025 6:50 PM, Ross Finlayson wrote: >>>> On 01/01/2025 01:14 PM, Jim Burns wrote: >>>>>> On 07/29/2024 12:46 PM, Ross Finlayson wrote: >>> >>>>>>> Or, you know, "infinity plus one". >>>>> >>>>> Consider the definition of a finite.cardinal as >>>>> the cardinal #A of a set A >>>>> smaller.by.one than sets fuller.by.one >>>>> #A ∈ ⟦0,ℵ₀⦆ :⇔ (#A < #(A∪{a}) ⇐ A ≠ A∪{a}) >>>>> >>>>> If, >>>>> as might be expected, >>>>> infinity.plus.one is different from simple.infinity, >>>>> then, >>>>> under that definition, >>>>> infinity is finite. >>>> >>>> It's "well-ordering the universe". >>> >>> Please complete this sentence: >>> ⎛ In "It's 'well-ordering the universe'", >>> ⎜ "it" refers to >>> ⎝ >>> >>>> Yeah, I know, >>>> you don't have a universe in your theory, >>>> as you say that >>>> there's no meta-theory your theory, >>>> yet, what's that then, all one theory? >>> >>> I think that a universeᴿꟳ and a universeⁿᵒᵗᐧᴿꟳ >>> are different. >>> >>> ⎛ In the formal sciences, the domain of discourse, >>> ⎜ also called the universe of discourse, universal set, >>> ⎜ or simply universe, >>> ⎜ is the set of entities over which >>> ⎜ certain variables of interest in some formal treatment >>> ⎝ may range. >>> https://en.wikipedia.org/wiki/Domain_of_discourse >>> >>> I have universesⁿᵒᵗᐧᴿꟳ for my theories, as I must >>> wherever there are variables, and >>> there are lots and lots of variables in 'my' theories. >>> >>> I take your universeᴿꟳ to be >>> a unique, all.inclusive universeⁿᵒᵗᐧᴿꟳ.and.domain. >>> >>> The logic (FOL) of variables and universesⁿᵒᵗᐧᴿꟳ >>> does not require an all.inclusive universeᴿꟳ >>> We only need to be able to talk about >>> what we are talking about, the current universeⁿᵒᵗᐧᴿꟳ, >>> whichever that is. >>> >>> >>> There are pragmatic motivations for talking about >>> an all.inclusive universeᴿꟳ. >>> >>> There are also pragmatic motivations for talking about >>> only what we are talking about, the current universesⁿᵒᵗᐧᴿꟳ. >>> >>> For example, if someone denies the existence of infinities, >>> a good place to start might be the universeⁿᵒᵗᐧᴿꟳ of finites, >>> which is itself not finite, and >>> which can disobey rules designed for finites. >>> >>>> there's no meta-theory your theory, >>>> yet, what's that then, all one theory? >>> >>> In these discussions, my bottom.floor logic is typically FOL, >>> the logic of variables and their universesⁿᵒᵗᐧᴿꟳ. >>> >>> My meta.theory of FOL is the theory of >>> finite sequences of claims, each claim of which is >>> true.or.not.first.false. >>> I think that I've mentioned that. >>> >>> >> >> So, is it, "not.ultimately.untrue"? >> >> See, here there's a meta-theory of all that, >> yet it's all in the theory, a heno-theory, >> otherwise being both formalist and platonic >> all the time. >> >> "The Logic", ? >> >> >> Is it, "not.ultimately.untrue"? You don't say, .... >> >> > > https://www.youtube.com/watch?v=zwX9Y2oEtHs&list=PLb7rLSBiE7F4_E-POURNmVLwp-dyzjYr-&index=35 > > > "Logos 2000: paradox-free reason", Ross Finlayson > > https://www.youtube.com/watch?v=tODnCZvVtLg&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=5 "Moment and Motion: points and space inversion"