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Topic: some amateurish opinions on CH
Replies: 57   Last Post: Apr 16, 2013 8:12 PM

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 fom Posts: 1,968 Registered: 12/4/12
Re: some amateurish opinions on CH
Posted: Apr 11, 2013 4:43 PM

On 4/11/2013 1:48 PM, apoorv wrote:
> "> That is Euclid :'every line segment can be extended in either direction'
>> Can it be ? Who can verify?
>
> I don't need to "verify" . Just apply the principle of sufficient
> reason to show how various properties fit together (including
> infinitude) .
>
> There's an interesting correspondence between the points of the plane
> (unbounded/infinite) and the points of the surface of the sphere
> (bounded/finite)
> It's absurd to reject one and accept the other . "
> Can we subdivide a segment ad infinitum?
> A line segment of zero length-
> Should that be a null segment, or a point?
>
>
> "> Is there always a next cell on the tape? Is the tape infinite?

>> Can these questions ever be answered?
>>
>>
>>

>>> Within infinity is harmony.
>>
>> But can something finite really represent the infinite?
>>
>> apoorv

>
> Why should we even be able to talk about the infinite if it's
> something completely beyond our gasp?Is it some cruel joke form Nature? "
> We talk about so many things ,some forming the present reality and some
> being possibilities for the future.
> Apoorv
>

You hit the nail on the head with your statement.

Perception of the future as a collection of possible
futures introduces modal thinking and language. Tense
logic is represented similarly to modal operators.

Once one begins to deal with possibility, what one
can and cannot talk about becomes harder.

Leibniz framed existents in terms of their potential
existence (possible worlds) because practical knowledge
of the world was insufficient to specify an individuated
being. Mathematically, this is later found in Hilbert
who reportedly stated something like "that which is not

A different tradition follows from Newton and his
followers because Newton "let the mathematics speak
for itself". Ultimately, this led to the foundational
crises and interpretation of universal quantifiers as
a course of values rather than an arbitrary application.

It is curious that the quantifiers over constructive
objects in Markov have the classical feature of being
applied to any arbitrarily given constructive object.
The practicality that had led to Leibniz' expansive view
of existents is the same practicality that leads to a
rejection of the course-of-values interpretation for
universal quantifiers in the Russian constructive school.

Date Subject Author
4/7/13 fom
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Bergholt Stuttley Johnson
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Virgil
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 Virgil
4/8/13 Virgil
4/9/13 apoorv
4/8/13 Virgil
4/7/13 Virgil
4/9/13 Guest
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 Guest
4/10/13 dan.ms.chaos@gmail.com
4/10/13 fom
4/10/13 JT
4/11/13 apoorv
4/11/13 dan.ms.chaos@gmail.com
4/11/13 apoorv
4/11/13 fom
4/15/13 apoorv
4/15/13 fom
4/16/13 Shmuel (Seymour J.) Metz
4/16/13 fom
4/7/13 Virgil
4/7/13 William Elliot
4/7/13 fom
4/7/13 fom
4/8/13 William Elliot
4/8/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/9/13 fom