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Topic: Matheology § 288
Replies: 160   Last Post: Jun 21, 2013 8:42 AM

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 fom Posts: 1,968 Registered: 12/4/12
Re: Matheology § 288
Posted: Jun 17, 2013 11:19 PM

On 6/17/2013 7:53 PM, Virgil wrote:
> In article <kpnvo3\$3ue\$1@dont-email.me>, Sam Sung <no@mail.invalid>
> wrote:
>

>> Virgil schrieb:
>>

>>> In article
>>> apoorv <skjshr@gmail.com> wrote:
>>>

>>>> On Jun 17, 9:47 am, Virgil <vir...@ligriv.com> wrote:
>>>>> In article
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> apoorv <skj...@gmail.com> wrote:

>>>>>> On Jun 17, 3:48 am, Virgil <vir...@ligriv.com> wrote:
>>>>>>> In article

>>>>>
>>>>>>> apoorv <skj...@gmail.com> wrote:
>>>>>>>> On Jun 17, 1:28 am, Virgil <vir...@ligriv.com> wrote:
>>>>>>>>> In article

>>>>>>>>>> ,
>>>>>
>>>>>>>>> apoorv <skj...@gmail.com> wrote:
>>>>>>>>>> On Jun 16, 1:44 am, Virgil <vir...@ligriv.com> wrote:
>>>>>>>>>>> In article

>>>>>
>>>>>>>>>>> mueck...@rz.fh-augsburg.de wrote:
>>>>>>>>>>>> On Friday, 14 June 2013 21:11:16 UTC+2, Zeit Geist wrote:
>>>>>>>>>>>>> The symmetry does prevIail. The three Unions in the
>>>>>>>>>>>>> "completed"
>>>>>>>>>>>>> list all
>>>>>>>>>>>>> have same number of elements.

>>>>>
>>>>>>>>>>>> 1
>>>>>>>>>>>> 11
>>>>>>>>>>>> 111
>>>>>>>>>>>> ...

>>>>>
>>>>>>>>>>>> The hight and diagonal have aleph_0 elements. Is there a
>>>>>>>>>>>> line
>>>>>>>>>>>> with
>>>>>>>>>>>> aleph_0
>>>>>>>>>>>> elements?

>>>>>
>>>>>>>>>>> If there isn't then WM's claimed "triangle" does not have
>>>>>>>>>>> three
>>>>>>>>>>> sides.
>>>>>>>>>>> --

>>>>>
>>>>>>>>>> This is an interesting thought.
>>>>>>>>>> Suppose we draw up triangles
>>>>>>>>>> ...............................l..
>>>>>>>>>> ...........................1....1
>>>>>>>>>> ........................1....1....1
>>>>>>>>>> .....................1....1....1....1
>>>>>>>>>> ....................................................
>>>>>>>>>> ...........................................................
>>>>>>>>>> 1....1....1....1....1....1....1....1....1....1....1....1
>>>>>>>>>> Each of the diagonal is of the order type {1,2,3....w}
>>>>>>>>>> The question is what is the order type of the bottom horizontal
>>>>>>>>>> line?
>>>>>>>>>> -apoorv

>>>>>
>>>>>>>>> If your triangle has diagonal edges of a given finite order type,
>>>>>>>>> it
>>>>>>>>> has
>>>>>>>>> a base edge of the same type.
>>>>>>>>> A problem arises only when the edges are allowed to have the
>>>>>>>>> order
>>>>>>>>> type
>>>>>>>>> of |N.
>>>>>>>>> --

>>>>>>>> Do you mean such a triangle does not exist?
>>>>>
>>>>>>> When two sides having a common vertex no longer have two endpoints
>>>>>>> each,
>>>>>>> but only one common endpoint at that vertex, the resulting diagram is
>>>>>>> called simply an angle, not a triangle, at least everywhere outside
>>>>>>> the
>>>>>>> wild weird world of WMytheology.

>>>>>> The two sides are of the order type {1,2,3...w} I.e like
>>>>>> xxxxx.....x.

>>>>>
>>>>> In my world, the limit of the increasing sequence of elements of order
>>>>> type {1,2,3,...,n} is of order type {1 2 3,...}, with no last member.
>>>>> --

>>>> The sequence 1,1/2,1/4,1/8.....0 is of the order type {1,2,3...w}.
>>>> Apoorv

>>>
>>> How about of order type {1,2,3,...,w} ?
>>>
>>> The difference being that your "sequence" is not a sequence in the usual
>>> sense of being indexed by a subset of the naturals.

>>
>> ...which does ("is") like even a proper subset.

>
> Finite subsets of N can be index sets for finite sequences,
> infinite subsets of N can be index sets for infinite sequences,
> but being a sequence at all requires that the members of such a sequence
> be indexable by SOME subset of |N.
>

So, Poincare criticized Hilbert's foundational investigations
as always assuming induction.

Leibniz stated that he chose not to include existential
statements in his logical studies, largely because he
believed them to implicitly invoke infinities.

And, of course, so many have problems with the axiom of
infinity, but Russell found it to be a necessary evil.

As your correct statement so eloquently expresses, the
very assumption of an inductive set seems impredicative
(in the sense of Leibniz' concerns) and circular (in the
sense of Poincare's criticisms).

Date Subject Author
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Virgil
6/16/13 apoorv
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/16/13 apoorv
6/16/13 Virgil
6/16/13 apoorv
6/17/13 Virgil
6/17/13 apoorv
6/17/13 Virgil
6/17/13 Tanu R.
6/17/13 Virgil
6/17/13 fom
6/16/13 FredJeffries@gmail.com
6/16/13 apoorv
6/16/13 apoorv
6/17/13 FredJeffries@gmail.com
6/17/13 Virgil
6/17/13 FredJeffries@gmail.com
6/18/13 LudovicoVan
6/18/13 mueckenh@rz.fh-augsburg.de
6/18/13 Virgil
6/18/13 LudovicoVan
6/18/13 Tucsondrew@me.com
6/18/13 LudovicoVan
6/18/13 Tucsondrew@me.com
6/18/13 mueckenh@rz.fh-augsburg.de
6/18/13 Tucsondrew@me.com
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Tucsondrew@me.com
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Tucsondrew@me.com
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 Virgil
6/20/13 Virgil
6/20/13 Virgil
6/20/13 Virgil
6/20/13 Virgil
6/19/13 Virgil
6/19/13 Virgil
6/18/13 Virgil
6/18/13 fom
6/18/13 fom
6/18/13 LudovicoVan
6/18/13 fom
6/19/13 LudovicoVan
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Virgil
6/19/13 LudovicoVan
6/19/13 fom
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 Virgil
6/20/13 Virgil
6/20/13 FredJeffries@gmail.com
6/20/13 LudovicoVan
6/21/13 LudovicoVan
6/21/13 LudovicoVan
6/20/13 FredJeffries@gmail.com
6/20/13 Virgil
6/20/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/14/13 Virgil
6/14/13 Virgil
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Tucsondrew@me.com
6/15/13 Virgil
6/15/13 Tanu R.
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Tanu R.
6/14/13 Virgil
6/14/13 Virgil
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Bergholt Stuttley Johnson
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Tanu R.
6/15/13 Bergholt Stuttley Johnson
6/14/13 Virgil
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 fom
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 fom
6/16/13 Virgil
6/17/13 mueckenh@rz.fh-augsburg.de
6/17/13 Virgil
6/17/13 fom
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 fom
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/16/13 fom
6/16/13 Virgil
6/16/13 fom
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/17/13 mueckenh@rz.fh-augsburg.de
6/17/13 Virgil
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/15/13 Tanu R.