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

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From: George Greene on 11 Jul 2010 12:15

On Jul 10, 12:31 pm, Wolf K <weki...(a)sympatico.ca> wrote:
> The dictionary records what the dictionary maker figures people mean
> when they use words.

True.

> The dictionary doesn't stipulate anything,

False.

> even though many people (still dazed by the nonsense passed off as "grammar
> in grade 6) believe that the dictionary tells you what words "really" mean.

We are not going to fight the prescriptive/descriptive battle all over
again here in this thread.
That battle long predates us and it really is a philosophical battle.
OF COURSE the dictionary prescribes. It cannot ENFORCEABLY prescribe,
but
neither can anybody else. There is a sense in which it doesn't even
matter if stipulations are enforceable.

You may choose to believe if you like that words don't really mean
things.
Good luck "THINKING" that, and thinking is in scare-quotes for a
reason.
The obvious problem with your skepticism about whether "words really
mean" things is that
it doesn't cope too well with fuzziness about the meaning of "really"
or of "mean".

From: George Greene on 11 Jul 2010 12:16

On Jul 10, 12:31 pm, Wolf K <weki...(a)sympatico.ca> wrote:
> (still dazed by the nonsense passed off as "grammar
> in grade 6)

No farting in church. This is sci.logic.
Even if grammar isn't all that coherent for NATURAL languages, it is
still very much
necessary&relevant for computer programming languages, formal
languages, and logic.
Around HERE, what you call "nonsense" was a noble attempt to get
people to think straight
and write clearly -- even if it got a little Procrustean at times.

From: George Greene on 11 Jul 2010 12:36

On Jul 10, 12:28 pm, Wolf K <weki...(a)sympatico.ca> wrote:
> Infinity is not a limit.

At this point I could say something about "that nonsense that passes
for
Algebra II in 11th grade", but I'm trying not to.

You need a clearer understanding about WHERE we are, formal-system-
wise.
A lot of the time, around HERE, we are in first-order ZFC, where ONE
OF THE AXIOMS
basically asserts the existence of something called a LIMIT Ordinal,
namely, an
ordinal that is closed under successor. That IS a limit. The
smallest infinity is in fact
THE ARCHETYPAL limit-ordinal. That's not quite the same thing as "a
limit"
but it's CERTAINLY an ADEQUATE defense against your curt dismissal
here.

From: K_h on 12 Jul 2010 01:22

"Curt Welch" <curt(a)kcwc.com> wrote in message
news:20100711120058.644$rX(a)newsreader.com...
> "K_h" <KHolmes(a)SX729.com> wrote:
>> In regular arithmetic 4+5=9 is true but Curt was claiming
>> that there is some tiny chance it could be wrong in regular arithmetic.
>> Curt is obviously wrong there.
>
> If you limit the scope of the measure of "truth" to "in regular arithmetic"
> then you are correct, it's an absolute truth. I was not talking about "in
> regular arithmetic". I was talking about "in life". I was talking about
> reality vs the fairy tale stories we make up called "in regular
> arithmetic". In the stories we make up, we pretend that absolute truth can

The truth embodied in 4+5=9 is an absolute truth in life. It is not a "fairy
tale". This is all obvious.

> and does exist, and all of math takes place in that fairy tale land. It's
> highly useful and important to do math under that belief. But what's
> invalid, is to assume the lies we use to do math, actually happen (or
> exist) in the real world.

Mathematical truth exists in the real world and those truths are not lies.
Again, this is obvious.

> I can produce language that describes a reality where pink flying elephants
> with no mass exist. But no one is going to get confused about whether the
> reality I am talking about actually exists in our universe or not. It's
> just a story I made up by taking things that do exist in our universe, and
> combining them in a way that has never been seen, and which is highly
> unlikely to ever be seen in our universe. That's how the idea of absolute
> truth was created as well.

No, there are absolute truths of the universe, for example conservation of
electric charge.

> But yet, somehow, many people get so engrossed in the stores we make up as
> we talk the language of mathematics, they start to believe the world of
> mathematics is not just a story, but that it actually exists. That it not
> only exists, but that it "lives on" even after all the story tellers die
> off. It is as if they believe the pink elephants exist and live on
> forever, even after everyone that's heard the story has died off.

No, because mathematical truth is discovered not invented. An alien on another
planet must also discover the same prime numbers that humans have. I was going
to reply to another post of yours but decided to paste it here instead. You
claim:

> So what physical thing are you making reference to when you say truth
> embodied in the statement 2x7=14 lives on?
>
> My point is that the physical universe is the only existence here. And if
> we are suggesting something actually exists, and "lives on" we _must_ be
> making reference to some physical attribute of the universe. So what
> physical attribute of the universe do you think is the truth embodied in
> that particular lagniappe statement?

What is your definition of physical? Why do you think that "lives on" must be a
"physical" attribute and what do you mean by "lives"? Your claim that the
universe is the "only existence here" is not a testable hypothesis and so it is
an unscientific hypothesis.

> some internal representation of separate "objects". Once you have one of
> these machines, we get closer to the truth embodied in 2x7=14,. But
> without that machine, that "truth" really doesn't exist at all.

Nonsense. You just claim the truth embodied in 2x7=14 doesn't actually exist and
that is plainly untrue. Marshall, thanks for the heads-up on Nam; it looks like
Curt is another Nam.

_

From: K_h on 12 Jul 2010 01:37

"Transfer Principle" <lwalke3(a)lausd.net> wrote in message
news:ea13e664-c127-4d99-98cd-c9855fe61d16(a)w12g2000yqj.googlegroups.com...
On Jul 9, 6:22 am, Wolf K <weki...(a)sympatico.ca> wrote:
>
> that set theorists reject axioms that violate their notions of reality
> all the time. For example, they reject V=L because it's too
> restrictive and say that it's not "really true." If set theorist can

I doubt if they are saying it is untrue although some have doubts about it. V=L
is a plausible axiom.

> reject "V=L," then Herc can reject the Axiom of Infinity.

He is free to reject it if he likes. But we need to make a distinction here
between somebody simply stating their beliefs as opposed to somebody trying to
convince others to believe something. Justification is required for the latter
but not the former. So if Herc wants other to reject the axiom of infinity then
the explanatory obligation falls on him. To me, it is self-evident that the
axiom of infinity is true. Simple examples for it are the non-repeating numerals
of, for example, the square root of 2. Algorithms for root 2 allow one to
exactly define the nth numeral in its decimal expansion.

_