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Re: Erroneous conclusions from applying material conditionals?

Newsgroups	sci.logic
Date	2023-05-28 22:14 -0700
References	(11 earlier) <720529bb-1699-46a3-a426-e75700c2d5e0n@googlegroups.com> <584e51a2-1d27-4541-b0f8-213c737363f0n@googlegroups.com> <9734c98a-f56c-4204-aa5a-429bdc9ea405n@googlegroups.com> <de84c45c-a783-4b35-b0d5-33310c5ebfcfn@googlegroups.com> <2af7ef68-75be-4dc3-a242-1ecba7791666n@googlegroups.com>
Message-ID	<bfb85e35-4e7d-43f1-8750-dec105230967n@googlegroups.com> (permalink)
Subject	Re: Erroneous conclusions from applying material conditionals?
From	Ross Finlayson <ross.a.finlayson@gmail.com>

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On Sunday, May 28, 2023 at 9:51:51 PM UTC-7, Ross Finlayson wrote:
> On Sunday, May 28, 2023 at 6:46:07 PM UTC-7, Dan Christensen wrote: 
> > On Sunday, May 28, 2023 at 9:23:14 PM UTC-4, Mild Shock (aka Mr. Collapse) wrote: 
> > [snip childish abuse] 
> > > I already wrote were it goes wrong. See the last section here, 
> > > I refering to a post by Carl Mummert: 
> > > > Material implication is critizised for obeying two laws, 
> > > > because it is seen as (A => B) == (~A v B): 
> > > > 
> > > > Law of noncontradiction (LNC) 
> > > > Formally this is expressed as the tautology ¬(p ∧ ¬p). 
> > > > https://en.wikipedia.org/wiki/Law_of_noncontradiction 
> > > > 
> > > > Law of excluded middle (LEM) 
> > > > precise statement of the law of excluded middle, P ∨ ~P 
> > > > https://en.wikipedia.org/wiki/Law_of_excluded_middle 
> > > > 
> > Pay attention, Mr. Collapse! Again, these laws are legitimate methods of proof that are widely accepted by the vast majority of mathematicians. It is rejected only by a fringe element, the self-styled "constructionists." If you want your work to be widely accepted, this is probably the worst possible approach. 
> > > > Banach–Tarski paradox 
> > > > https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox 
> > > > 
> > > > In this case, the issue is that the entire concept of partitions 
> > > > and equivalence classes, which underlies the usual proof of 
> > > > the Banach-Tarski paradox, behaves very differently in constructive systems. 
> > [snip] 
> > 
> > You mean "constructive" (aka fringe) systems??? 
> > Dan 
> > 
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com 
> > Visit my Math Blog at http://www.dcproof.wordpress.com
> Hey, you just learned there "exists" constructivism, it's not "fringe", it's a central effort 
> in _rigorous formalism for mathematics_. 
> 
> I.e., some constructivists have the "non-constructive" is not even _sound_, and is at 
> best incomplete and not self-contradictory. 
> 
> Then, about Banach-Tarski, what the Burse-bot there is doing is what's called 
> "talking out the ass", because it's just something you don't know, and whether 
> "the devil made you do it" is a sufficient "arbitrary consequent" or "arbitrary antecedent" 
> would suffice, something "you don't know". 
> 
> About Banach-Tarski, there are two at-odds approaches, one's plainly geometric and 
> is for Vitali-Hausdorff. Another is plainly geometric and for, say, Micielski-Marczewski. 
> 
> Here's a thread about "Banach-Tarski". Of course, I think what I write is most informative, 
> and I understand that's subjective. 
> 
> https://groups.google.com/g/sci.logic/c/UFQub2CKXQo/m/eksBibcTAQAJ 
> 
> One hopes that someday you might understand 
> that "ALGEBRAIC geometry" is not "algebraic GEOMETRY". 
> 
> 
> 
> "So, you can see that "re-Vitali-ization" is ongoing in 
> mathematics writ large, and quite more accessibly these 
> days then that as the dust arises of the construction, 
> it all has to settle to the foundations again. Then, 
> looking to "re-Vitali-ize" measure as from some quite 
> fundamental notions as the spiral-space-filling curve 
> and unique properties of the equivalency function (in 
> continuity, analysis, differential analysis, singularity 
> theory, and probability theory) makes a neat course for 
> then laying out what are building up as these quite 
> immense structures in categorical algebra in descriptive 
> set theory, as somewhat neatly primitive (and accordingly 
> fundamental)." 
> 
> "Too wordy?" 
> 
> 
> 
> "It's a "spherical group". 
> 
> One's geometry's, the other algebra's. 
> 
> This is in "dynamical topology" in "descriptive set theory". " 
> 
> 
> 
> "Now, why this relates to Marczewski-Dougherty-Foreman's 
> Banach-Tarski's is because the "group paradoxical action" 
> that was set under "decomposition paradoxical action" 
> (so they didn't look "stupid" or plain "wrong" or otherwise 
> have to defend another "paradox") is these days being disambiguated 
> from where they were framed together in the corresponding 
> systems together. 
> 
> This arrives full-circle at Zeno. " 
> 
> 
> 
> Of course you can always read Burse instead: 
> "Lol, banach-tarski-fication of herpes boy" - Burse. 
> 
> 
> 
> Ross: 
> 
> "This then is for such notions about 
> Szpilrajn that these days are framed 
> in notions of "transfer principle" 
> and "antitransfer principle", but 
> re-using the development without 
> re-seating the terms leaves a bit 
> of an inconsistency in the middle 
> that naive inference could work out 
> either way. 
> 
> Informed inference though is rather 
> setting such notions in the first-class 
> where they belong and able to redress 
> such hand-waving abandonment of topology's 
> usual difference between results in union 
> and results in intersection about the 
> special or limit cases for the transfer 
> principle where such infinitary results 
> would be disambiguated to hold or not. 
> 
> 
> classical geometry -> "paradoxical" decompositions 
> algebraic geometry -> "paradoxical" group actions 
> 
> "... as long as we have two copies here, 
> might as well just stop at the first 
> and call it the action, though we'll 
> frame it in the results of the second." 
> 
> But, really it's that both meet in the middle 
> (and either way, under some ambiguous assumptions). 
> 
> So, one might neatly consider a theory of 
> Banach-Tarski as independent of some usual 
> assumptions, here basically under topology 
> and of course as here about that being under 
> all these usual assumptions of measure, and 
> whether for example it's "area", as least 
> under the quadratic , or, "volume", as 
> under the sphere. " 
> 
> 
> 
> "An anagram of Banach-Tarski's Paradox 
> is Marczewski-Swierczkowski's Banach-Tarski's Paradox". 
> 
> "Here then Banach and Tarski's development 
> is Banach and Tarski's, vis-a-vis, variously, 
> Groot, Steinhaus, Swierczkowski, and 
> algebraic interpretations. " 
> 
> 
> "That appears to be among Hausdorff's theorems, there (and see above)."



The original development of Banach and Tarski
is more "geometric" than "algebraic", more
about "congruences" than "generators", and
constructively. 



Here, I wrote this:


Looking to Banach's and Tarski's paper:

http://matwbn.icm.edu.pl/ksiazki/fm/fm6/fm6127.pdf

With for example "Grace a une remarque due a M.Lindenbaum,
on peut enoncer un theoreme analogue au lemme precedent
pour les ensembles lineaires, in remplacant le term "segment"
par "point"."

Then it seems that Banach Tarski are using:
Vitali "we have non-measurable sets"
Lindenbaum "hi these are Veronese's"
Hausdorff "I spun Vitali's around for a 2-D analogue"
that Banach Tarski are coming across then
as "there's certainly enough here to find
some non-measurable ones then what
Hausdorff said holds and it doesn't matter
that our actual constructions don't add up
because they're non-measurable because
they're non-measurable there are uncountably
many to get them all and Vitali points out how
they double up".

So, the development on the Banach-Tarski wiki
is not Banach and Tarski's.

"Comme l' indique M.Hausdorff (en utilisant
une idee M.Vitali) on peut decompose tout
segment en une infinite nombrable de sous-
ensembles disjoints equivalents par decomposition
finite deux a deux. Soient: ..."

-- http://matwbn.icm.edu.pl/ksiazki/fm/fm6/fm6127.pdf

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Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-27 12:04 -0700
  Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-27 13:25 -0700
    Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-27 19:42 -0700
  Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 08:39 -0700
    Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 11:50 -0700
    Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 12:01 -0700
      Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 13:47 -0700
        Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 13:57 -0700
          Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 14:02 -0700
          Re: Erroneous conclusions from applying material conditionals? olcott <polcott2@gmail.com> - 2023-05-28 16:12 -0500
          Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 15:39 -0700
            Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 15:56 -0700
              Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 16:04 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 16:14 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 16:24 -0700
              Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 16:49 -0700
              Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 16:52 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 02:25 +0200
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 02:31 +0200
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 02:45 +0200
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 17:59 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 17:46 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 17:51 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:01 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:07 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 18:12 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:15 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 18:17 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:23 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:28 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 18:46 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-28 21:51 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-28 22:14 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 22:33 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 22:36 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-29 09:01 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 09:27 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 09:32 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 09:35 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 10:03 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 19:45 +0200
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-30 05:52 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-30 15:16 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-29 11:14 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-29 22:53 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-30 17:45 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 08:23 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:22 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:31 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:38 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:51 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 19:56 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 21:35 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:44 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 18:54 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 19:55 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 21:13 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:19 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:23 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 21:30 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 22:02 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 22:28 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 22:31 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 22:34 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 22:39 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 23:29 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:14 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:23 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 23:26 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-02 09:42 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 20:41 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 20:58 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 21:24 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:28 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:31 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:34 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 22:49 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-03 04:49 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-03 04:51 -0700
        Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 15:33 -0700
    Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 02:52 -0700
      Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 02:58 -0700
        Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 03:03 -0700
          Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 07:35 -0700
            Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 08:23 -0700
              Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 08:30 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 08:33 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 09:56 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 19:56 +0200
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 11:40 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 11:43 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 13:32 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 13:38 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 13:59 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 15:19 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 15:21 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 17:37 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 19:00 -0700
  Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-06-02 09:41 +0200
    Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-02 09:42 -0700
      Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-02 11:00 -0700
        Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-02 11:14 -0700

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