PROOF INFINITY DOES NOT EXIST! Not even ONE type [Logic]

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From: K_h on 9 Jul 2010 15:45

"Curt Welch" <curt(a)kcwc.com> wrote in message
news:20100708174523.499$Zc(a)newsreader.com...
> "K_h" <KHolmes(a)SX729.com> wrote:
>> "Curt Welch" <curt(a)kcwc.com> wrote in message
>> news:20100708093928.442$LY(a)newsreader.com...
>> > "|-|ercules" <radgray123(a)yahoo.com> wrote:
>> >> "Curt Welch" <curt(a)kcwc.com> wrote...
>> >
>> >> I realize the difficulty in confirming a rock exists. But all you
>> >> have to do is confirm *something* exists. Even if you're in error the
>> >> conclusion is still true. E x
>> >>
>> >> Herc
>> >
>> > That's an interesting point. I don't see any argument against the idea
>> > that something exists is an absolute truth. I think therefore I am.
>> > That might be the one and only absolute truth.
>>
>> Mathematical truth exists. To my recollection, I have never seen anybody
>> claim that 2x7=14 is false or fails to be true after somebody dies.
>
> That's generally true. The question is not normally thought about. Humans
> tend to think and talk as if there are always humans around.
>
> But what happens if _everyone_ that understands the language died? What
> does it mean to suggest the "truth of the statement lives on" at that
> point? All that is left is ink marks in books at that point. Since when

The truth embodied in the statement lives on. Of course, the symbols 2x7=14 are
conventions.

>> The
>> equation 10+20=30 is an absolute truth and that truth does exist.
>
> But what do you think you are making reference to when you say it exists?
> Where exactly does it exist? What form does it exist in? How do truths
> (absolute or otherwise) even exist at all?

This question doesn't need to be answered in order to know that these truths
always exist. How does anything exist? How does the galaxy exist? People don't
need to have those answers to know that they exist.

>> > We currently have no way of knowing if our understanding of E x might
>> > suffer such a condition. As such, we have no way of proving that E x
>> > is an absolute truth for any given understanding of "existence" or
>> > "absolute". We can only define it to be an absolute truth we we limit
>> > our scope to within the framework of the language itself (which is
>> > saying we are limiting it to the times where the langauge processing
>> > hardware (our brains) are functioning correctly.
>>
>> So you have existential doubts about the truth of 4+5=9?
>
> No, I have no doubt. I simply understand that truth is never absolute. We
> just pretend it is. To have doubt about the truth is to fail to pretend
> that truth is absolute. I don't fail to do the same pretending we all do

You have no doubt that 4+5=9 because it is an absolute truth. There is no
pretending involved in it.

> on these issues. I accept (and well know) that humans make mistakes for
> example. I've looked at what you wrote above and checked the math about 5
> times now to make sure you didn't try to trick me by listing a non-truth
> (or didn't accidentally make a typo in creating your example). Even with
> all that extra checking, my belief that you created a true statement in the
> language could still be in error with some small probability. But this

Not at all, there is no error in the equation 4+5=9.

> This all gets down to the fact that you can't separate the intent of the
> language (or the intent of the ideas), from the actual physical
> implementation of it. We can for example try to say "it is possible to

No, they are easily separated.

> As long as that computer works correctly, then the "truth" of that
> statement exists. But it's impossible to build a computer that will follow
> the intent of that code example above with 100% accuracy. Given enough
> time, you can guarantee the machine will fail to act correct. And because
> it fail at some point, there is no "absolute truth" in the statement, or in
> the hardware implementation that defines the "meaning" of the language.

Not at all. Limitations of computers are not limitations on existence.

> But there is no God machine, and there is no absolute truth. Just truths

Sorry, but 4+5=9 is an absolute truth.

_

From: George Greene on 9 Jul 2010 16:44

On Jul 7, 2:36 pm, c...(a)kcwc.com (Curt Welch) wrote:
> You have to be careful in such debates to understand what "exists" means
> and how you are using it.

You MEANT to say that ONE has to be careful.
*I* certainly do not have to be any more careful than usual.
I am already aware of the point you are trying to make here.
You are in no position to lecture me personally.
You have to be careful in these debates to understand what "you"
means,
and how you are going to be perceived as using it.

From: George Greene on 9 Jul 2010 16:46

On Jul 7, 2:31 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> c...(a)kcwc.com (Curt Welch) writes:
> > But math isn't about simple physical existence. It's about words and
> > their definitions. It's a study of formal langauge and what can be
> > _said_ using a formal language.
>
> No it's not.

I wouldn't've been that simplistic about it, but I'll take your side
on this,
even though I usually defend that math is formal. NOTHING CAN be said
with a formal language. That's THE WHOLE POINT; it's FORMAL.
It doesn't MEAN ANYthing. It doesn't even NEED to mean anything.
To the extent that math DOES mean something, there is more going on
than "formal language".
ANYthing "can" be said using a formal language, once you admit the
possibility that formal languages
can say things. You can just stipulate (don't ask ME how -- the SAME
way the DICTIONARY does it;
THAT'S how) -- that this or that formal gibberish MEANS whatever.

From: |-|ercules on 9 Jul 2010 18:38

Perhaps you don't understand the proof, it only contradicts a well used axiom, not a well established fact.

A REVISED PROOF OF THE NON-EXISTENCE OF INFINITY

C10 = 0.12345678910111213141516...

x = the number of digits in the expansion of C10
y = the number of consecutive digits of PI in C10

As x->oo, y->oo
x = oo

Assume the limit exists.
y=oo
Contradiction (for each finite starting digit of PI in C10 there is a finite ending digit)
Limit doesn't exist.

y cannot reach infinity
therefore x cannot reach infinity

x = the number of digits in the expansion of C10
x =/= oo

INFERENCE there is no oo

Herc

From: |-|ercules on 9 Jul 2010 18:42

"George Greene" <greeneg(a)email.unc.edu> wrote
> On Jul 7, 2:31 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
>> c...(a)kcwc.com (Curt Welch) writes:
>> > But math isn't about simple physical existence. It's about words and
>> > their definitions. It's a study of formal langauge and what can be
>> > _said_ using a formal language.
>>
>> No it's not.
>
> I wouldn't've been that simplistic about it, but I'll take your side
> on this,
> even though I usually defend that math is formal. NOTHING CAN be said
> with a formal language. That's THE WHOLE POINT; it's FORMAL.
> It doesn't MEAN ANYthing. It doesn't even NEED to mean anything.
> To the extent that math DOES mean something, there is more going on
> than "formal language".
> ANYthing "can" be said using a formal language, once you admit the
> possibility that formal languages
> can say things. You can just stipulate (don't ask ME how -- the SAME
> way the DICTIONARY does it;
> THAT'S how) -- that this or that formal gibberish MEANS whatever.
>

You have a point for once. Early definitions of formal systems were "void of semantics".

But you missed the point of the definition, "about words and meaning" of what formal
systems can say.

Herc