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Topic: Matheology § 074
Replies: 114   Last Post: Jul 22, 2012 4:15 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 074
Posted: Jul 15, 2012 3:35 PM

In article <jtul9o\$tei\$1@speranza.aioe.org>,
"LudovicoVan" <julio@diegidio.name> wrote:

> "WM" <mueckenh@rz.fh-augsburg.de> wrote in message

> > On 15 Jul., 02:03, "LudovicoVan" <ju...@diegidio.name> wrote:
> >

> >> That remains invalid reasoning, a paralogism that simply does not model
> >> the
> >> problem: a sensible statement would be that for every digit that goes to
> >> the
> >> right 2 more are added on the left, so that never all digits are on the
> >> right.

> >
> > Infinity is tow-sided.
> > A) We can reach every number n when counting from 1 to n.
> > B) There remains always a number m outside of what we have counted,
> > how big ever n may be.

>
> That is essentially the principle of recursion which we justify inductively.
> You put it in the form of a paralogism, but there are no two sides:
> *potential infinity* is all we are dealing with, with its many applications.
> Then, of course, that informal principle can be implemented in slightly
> different ways, and some of them could turn out to be incorrect: but I am
> only speaking very generally here.
>

> > That makes infinity impossible to deal with in a consistent
> > mathematics.

>
> So, I disagree: there is only one kind of mathematical infinity (and a
> transfinite ordinal structure is a structure *within* it). One can "get it
> wrong" but that has never been a problem in itself. -- What would be the
> consequences of a collapse of the cardinal hierarchy?
>

> > Matheologians simply suppress B and rely on A only.
>
> I finally think I agree with the literal statement: there are no infinite
> sets. There are infinite classes, though. In fact, there is bad
> mathematics, there are no bad numbers (or, equivalently, sets).
>

> > Therefore
> > matheology yields inconsistent reults, as becomes obvious when
> > considering B, as you did it here.

>
> I should agree. It is to me more and more obvious that we are just dealing
> with a seriously corrupted state of affairs. But then let's not forget that
> this is the general state of affairs: I do not believe there is a
> "mathematical conspiracy" as such.
>

> >> Then, I have checked the definitions of limit inferior and superior: I
> >> can
> >> see a problem when said limits are defined in terms of unions of
> >> intersections and vice versa (entirely due to my limited understanding),
> >> although it is apparent that the two limits must diverge, period.

> >
> > If the definitions of set theory are applied, then they are both
> > empty. (For instance, there is no natural number that is always in the
> > set M_n.)

>
> I have checked those definitions again. There are surely details still
> above my head, yet everything seems to sum up quite well: the two limits
> just diverge. -- Note that some models *require* an extended domain.
>
> -LV
>

I never though to see someone arguing with WM from a position of greater
ignorance of standard mathematics, but LV does so.
--

Date Subject Author
7/13/12 mueckenh@rz.fh-augsburg.de
7/13/12 MoeBlee
7/13/12 Virgil
7/14/12 dilettante
7/14/12 LudovicoVan
7/14/12 dilettante
7/14/12 mueckenh@rz.fh-augsburg.de
7/14/12 LudovicoVan
7/14/12 Virgil
7/14/12 dilettante
7/14/12 mueckenh@rz.fh-augsburg.de
7/14/12 dilettante
7/14/12 LudovicoVan
7/14/12 Virgil
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 LudovicoVan
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 LudovicoVan
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 Virgil
7/15/12 LudovicoVan
7/15/12 Virgil
7/15/12 Virgil
7/15/12 Virgil
7/15/12 Virgil
7/15/12 Virgil
7/14/12 Virgil
7/14/12 dilettante
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 dilettante
7/15/12 Frederick Williams
7/15/12 dilettante
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 Virgil
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7/15/12 dilettante
7/16/12 mueckenh@rz.fh-augsburg.de
7/16/12 LudovicoVan
7/16/12 mueckenh@rz.fh-augsburg.de
7/16/12 LudovicoVan
7/17/12 mueckenh@rz.fh-augsburg.de
7/17/12 Virgil
7/16/12 Virgil
7/16/12 Virgil
7/16/12 mueckenh@rz.fh-augsburg.de
7/16/12 Virgil
7/16/12 LudovicoVan
7/16/12 Virgil
7/16/12 LudovicoVan
7/16/12 LudovicoVan
7/16/12 Virgil
7/16/12 Virgil
7/17/12 William Hughes
7/18/12 mueckenh@rz.fh-augsburg.de
7/18/12 LudovicoVan
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7/18/12 mueckenh@rz.fh-augsburg.de
7/18/12 LudovicoVan
7/18/12 Virgil
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7/18/12 Virgil
7/19/12 mueckenh@rz.fh-augsburg.de
7/19/12 Virgil
7/19/12 mueckenh@rz.fh-augsburg.de
7/19/12 Virgil
7/19/12 mueckenh@rz.fh-augsburg.de
7/19/12 YBM
7/19/12 mueckenh@rz.fh-augsburg.de
7/19/12 Virgil
7/19/12 FredJeffries@gmail.com
7/19/12 MoeBlee
7/19/12 Virgil
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7/20/12 mueckenh@rz.fh-augsburg.de
7/20/12 Virgil
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7/20/12 Virgil
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7/20/12 Virgil
7/21/12 mueckenh@rz.fh-augsburg.de
7/21/12 Virgil
7/22/12 mueckenh@rz.fh-augsburg.de
7/22/12 Virgil
7/20/12 Marshall
7/20/12 mueckenh@rz.fh-augsburg.de
7/20/12 YBM
7/20/12 Virgil
7/21/12 mueckenh@rz.fh-augsburg.de
7/15/12 Virgil
7/15/12 Virgil
7/15/12 Virgil
7/14/12 mueckenh@rz.fh-augsburg.de
7/14/12 dilettante
7/14/12 LudovicoVan
7/14/12 Virgil
7/14/12 Virgil