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

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From: FredJeffries on 9 Jul 2010 22:14

On Jul 9, 10:17 am, Dan Christensen <Dan_Christen...(a)sympatico.ca>
wrote:
>
> I can't imagine that you would be able to do very much using
> "finitist" methods. How do they handle such basic concepts as the
> square root of 2?
>

See for instance Jan Mycielski "Analysis Without Actual Infinity"
in The Journal of Symbolic Logic, Vol. 46, No. 3. (Sep., 1981), pp.
625-633.

From: George Greene on 9 Jul 2010 23:57

On Jul 9, 6:42 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote:
> You have a point for once. Early definitions of formal systems

idiot, please.
I have a degree in formal systems. you don't.

> were "void of semantics".

"Early definitions" are IRrelevant (except to historians of
consciousness) BECAUSE they were early: NOWadays,
WE KNOW better.

> But you missed the point of the definition,

WHAT definition?? That was rhetorical; THERE*IS*NO "the" definition.
There are plenty of DIFFERENT definitions, and it is a VERY safe bet
that whatEVER any formal "system" (the post was about formal LANGUAGE
and NOT formal "systems" IN ANY case) may be or mean, it is not
meaning it in virtue of anything YOU think.

From: George Greene on 10 Jul 2010 00:00

On Jul 7, 6:37 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Take the Heine-Borel theorem. It is not in any apparent sense "about
> words and their definitions" nor can it be with any accuracy described
> as "study of formal language and what can be said using formal
> language".

Nor is it "math" in any general sense. It is A SPECIFIC piece of
math,
and to the extent that it is in formal language, it is a confirming
example
and not a counter-example for the thesis. Besides, the kinds of
things
that the Heine-Borel theorem CAN be said to be "about" ARE THEMselves
*formal*!

> The study of formal languages and their expressiveness is a
> very marginal part of mathematics.

You are using "expressiveness" in a very technical sense which YOU
MUST
surely have known HAS LITTLE TO NOTHING to do with the sense in which
he intended it.

From: Nam Nguyen on 10 Jul 2010 00:43

K_h 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.

Sure. In your mind for example!

> To my recollection, I have never seen anybody claim
> that 2x7=14 is false or fails to be true after somebody dies.

How did you mean by that? Did you mean the dead couldn't claim
2x7=14 is false? (If so, there are many things they couldn't
possibly claim, naturally!)

> The equation
> 10+20=30 is an absolute truth and that truth does exist.

Again, in your mind perhaps. Others working in modulo arithmetic
may state 10+20=0 is absolutely true, just as you stated "10+20=30
is an absolute truth". What's the difference anyway?

> It is obvious that
> there are an infinite number of such truths so infinity, as a platonic truth,
> must exist.

"Must exist" in your mind obviously, for example.

>
>> But sadly, our ability to express the idea with language still runs into
>> the problem of potential failure to correctly communicate with some small
>> probability of error, and likewise, our ability to even think the idea
>> comes with the same error. So even if the idea is itself, when expressed
>> correctly, an absolute truth, it's not an absolute truth that our brain can
>> ever correctly express or understand the idea.
>
> Humans do have limitations but those limitations are not limitations on
> existence.

What does "limitations on existence" mean?

>
> So you have existential doubts about the truth of 4+5=9?

People have no doubt that 4+5=9 is false in some modulo arithmetic.

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

From: The Raven on 10 Jul 2010 01:22

STOP THE IRRELEVANT CROSSPOSTING!