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

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 apoorv Posts: 53 Registered: 4/11/13
Re: some amateurish opinions on CH
Posted: Apr 11, 2013 12:12 PM

On Thursday, April 11, 2013 12:57:02 AM UTC+5:30, Dan wrote:
> On Apr 10, 6:03 pm, apoorv <skj...@gmail.com> wrote:
>

> > - show quoted text -
>
> > "If I make a program that gives for each number n as input the output 1-
>
> > (n%2) , I can be reasonably sure it's the desired sequence .
>
> > The information is finite. You've got it backwards . We can use a
>
> > finite amount of information  to generate an infinite string .
>
> > You could say we're never interested in the structure of the infinite
>
> > string per se (in the sense that we never directly observe the
>
> > infinite string in its entirety ), rather , in the structure and
>
> > morphology of the different 'shapes of information' that describe the
>
> > string .
>
> >
>
> > Anyway, there are different 'shades' of mathematics along the line
>
> > between 'finitism' and 'platonic realism'.
>
> > What I said is only not realistic for some extreme forms of finitism .
>
> > It works from 'effective computability' upwards. "
>
> >
>
> > The information is finite if we have a program that outputs the given
>
> > sequence. However, for the Universal Sentence
>
> > 'Every natural number has a successor' the information content is
>
> > clearly infinite.For we can have axiom systems where,for example
>
> > 1 has no successor or 2 has no successor or 3 has no successor etc.
>
> > It is this sentence ,along with the analogous sentences of Geometery
>
> > 'Every line segment can be subdivided'
>
> > And 'Every segment can be extended indefinitely '
>
> > That bring in the infinite into Maths and logic .
>
> > That is what needs to be reconciled with reality.
>
> > Consider the Turing Machine with the infinite tape.
>
> > The very assumption of 'infinite tape' presupposes
>
> > Infinite information, because verifying that the tape is
>
> > Infinite would need infinite number of steps.
>
> > Apoorv
>
>
>
> You have a very bleak view of what reality is .
>
> I can make a program that , for every number n I put into it, outputs
>
> (n+1), its successor. How is that any different, in essence, from my
>
> previous program?

Will your program ever output 'all' the numbers?
We can verify that on input 1 it gives 2, but maybe on input 10^(10^100)
it runs out of memory(tape); for we could never verify that the memory
was actually infinite.
So, we abstract, and say ,
On input 1 ,it gives 2 , on input 3, it gives 4 And So On .
We cannot express this in propositional logic, because that
needs an infinite conjunction, so we bring in FOL and the universal statement
'For every natural number n, there exists a successor '
and claim that this finite string conveys all the infinite information
that we are trying to grasp or convey.

>
>
> Why do you need to verify the tape?After all, when imagining the
>
> Turing machine, didn't you make the tape with your own mind?
>
> You have a faulty mind if you need to verify the tape .

A finite mind :-)
>
>
> Mathematics has always had the infinite, in some form or another . I'm
>
> sensing it won't do any good to attempt to justify the infinite
>
> directly , so , let's examine the opposite side of the infinite ,
>
> namely :
>
>
>
> The FINITE :
>
> Let's try to ban the infinite from mathematics . That means, we're
>
> going to have to pick some finite number , and ban everything that
>
> comes after that . The question is , what number do we pick?
>
>
> The problem with the finite ,
>
> is that there's always something bigger . Finitude is like a prison,
>
> and the mind needs to escape .

The questions 'Is this infinite ? ' and ' Is there something always bigger?'
both need an unending verification.Can I always put the next chalk mark?
How would I know? The quest for 'escaping the prison of finitude' can only
be unending.
>
> > That is what needs to be reconciled with reality.
>
>
>
> Who says reality isn't infinite? Go out in space and travel in any
>
> direction . You're never going to suddenly hit a wall that says :
>
> "the Universe is finite . You can go no further" .
>
> http://4.bp.blogspot.com/-5Olo8-EgrZI/TZBqclcfPqI/AAAAAAAAC5c/920EyWecwiU/s1600/background_brick_wall.jpg
>
> because the universe has no such walls.

That is Euclid :'every line segment can be extended in either direction'
Can it be ? Who can verify?
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

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