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Re: Déjà vu

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On Tuesday, January 10, 2017 at 8:45:38 AM UTC-8, Jim Burns wrote:
> On 1/10/2017 10:44 AM, WM wrote:
> > Am Dienstag, 10. Januar 2017 15:49:08 UTC+1
> > schrieb Jim Burns:
> 
> >> Thank you for your contribution, Mr Gabriel.
> >> You have given me an excellent example of the
> >> sort of thing I was talking about to
> >> Me <franz.fritschee.ff@gmail.com>
> >>
> >> You made no attempt to clarify _what_ you were talking
> >> about, and it's a pretty good bet that whatever
> >> you mean (if anything) it is different from what
> >> WM means (if anything) by the same terms.
> >>
> >> In the face of that, whatever any actual mathematician
> >> has to say about infinity, potential or complete,
> >> seems pointless.
> >>
> >>>> I haven't been able to get a clear description of
> >>>> the distinction between complete infinity and
> >>>> potential infinity.
> >>>
> >>> That is untrue.
> >>>  WM has given you "innumerable" explanations.
> >>
> >> It's more accurate to say
> >> WM has given us innumerable "explanations".
> >
> > It is very simple: The sets |N and Q can be "proved"
> >  equinumerous only, when they are existing completely.
> 
> This notion of sets (or other mathematical objects) coming
> existence into seems to be at the heart of what you are
> potential calling infinity.
>     (I make no comparisons here with what others call
>     potential infinity.)
> 
> It seems to call for a more finely-grained notion of
> truth than the more common notion of "exactly one of
> true or false".
> 
> Let A be a set about which we know
> -- {} is in A
> -- if x is in A, then (x U {x}) is in A
> 
> Let B be the intersection of all sets C such that
> -- C is a subset of A (and may be A)
> -- {} is in C
> -- if x is in C, then (x U {x}) is in C
> 
> This is a particular set B (sometimes called the
> minimal inductive set). Also, it is infinite.
> 
> Given my indoctrination, I would say that, for a particular
> set D, exactly one of "D is in B" and "D is not in B"
> is true, and the other is false. Do you agree with that?
> 
> If you agree, then we are done here, and there doesn't
> seem to be any difference (beyond vocabulary) between
> what you call potential infinity and what I call infinity.
> 
> If you disagree, can you _clearly_ describe how that
> is supposed to work?
> 
> Is there something other than in B or not in B that might
> describe D?
> 
> Does the description of D (whatever it is) _change_
> with time or with location? If it does change, does
> it _change back_ , maybe like rewinding a tape, so
> that _everyone_ (in all of space and time) has the
> opportunity to "observe" D coming into B (or not)?
> 
> My suspicion is that the mathematicians of a certain
> era didn't want to have to bother with these questions
> (and more! Many more!). They're really just a distraction
> from what are more commonly thought of as mathematical
> questions. So, they scrapped potential infinity in
> favor of "exactly one of true or false".
> 
> Note that it is perfectly feasible (if that is your
> pleasure) to describe the gradual coming-into-B of
> potential infinity with the in-or-out of complete
> infinity. Nothing seems to me to have been lost by
> that choice. If I'm wrong about that, what, then,
> has been lost?

You may have inferred that this local retro-finitist 
troll was having a "potential infinite" that was the 
inductive set, but rather he refers to that as being 
the "doesn't exist because it is beyond the bounded".

So, you volunteered for him a correct interpretation 
of your interpretation, but without the surrounding 
context of otherwise his rejection of your (or, any) 
interpretation.


Then, there's my interpretation, about that the formation 
of your set B or "minimal inductive set" has that the 
quantification over finite elements (when they are the 
only regular elements that are already there) arrives 
at a non-well-founded (inductive) set before then what 
you accredit as the minimal inductive set.

Here this is in the context that the "infinitary" version 
of the usual pair-wise union or intersection involves the 
quantification over the elements as so satisfy the predicate, 
where that in the pair-wise there's one for the next.

Here, D "was" and "was in" B+ (the non-well-founded set that 
quantification delivers), and, it's not in B (having restricted 
the comprehension or censored what was the result of the operation 
to its "well-founded" part of its value, by some pair-wise disjoint).

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Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 12:34 -0500
  Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-09 10:08 -0800
    Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 17:18 -0500
      Re: Déjà vu genmailus@gmail.com - 2017-01-09 14:28 -0800
        Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 17:55 -0500
          Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-09 17:12 -0800
            Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 20:55 -0500
              Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-09 18:08 -0800
                Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-09 23:08 -0800
                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 10:55 -0500
          Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-10 05:13 -0800
            Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 09:49 -0500
              Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-10 07:44 -0800
                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 11:45 -0500
                Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-10 09:51 -0800
                Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 10:33 -0800
                Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 10:35 -0800
                Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 13:00 -0800
              Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-10 11:05 -0800
                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 18:08 -0500
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-10 17:25 -0800
                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 01:48 -0500
                Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 23:24 -0800
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 00:34 -0800
                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 11:26 -0500
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 08:55 -0800
                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 12:13 -0500
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 09:20 -0800
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 09:22 -0800
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 09:23 -0800
                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 13:11 -0500
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 10:26 -0800
                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 13:42 -0500
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 10:50 -0800
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 10:58 -0800
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 11:01 -0800
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 11:03 -0800
                Re: Déjà vu bursejan@gmail.com - 2017-01-11 11:11 -0800
      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-10 00:03 -0800
        Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 10:21 -0500

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