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

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From: Curt Welch on 10 Jul 2010 20:35

George Greene <greeneg(a)email.unc.edu> wrote:
> On Jul 7, 2:31=A0pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> > c...(a)kcwc.com (Curt Welch) writes:
> > > But math isn't about simple physical existence. =A0It's about words
> > > and their definitions. =A0It'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.

Well, that's a good point. The axioms of meaning on which the language is
built has to come from the real world. Without it, the language can have
no meaning at all. But even though they originate from reality, they are
often twisted to a point that doesn't exist in reality, such as this point
about absolute truth, instead of "nearly absolute" truth.

--
Curt Welch http://CurtWelch.Com/
curt(a)kcwc.com http://NewsReader.Com/

From: Curt Welch on 10 Jul 2010 21:27

"K_h" <KHolmes(a)SX729.com> wrote:
> "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.

Then if you believe that, tell me how it lives on without doing what you
have done so far, which is simply by you saying, "because I said so".

What exactly do you mean by "it lives on"? In what form does it exist
which allows it to "live on"? Explain to me what you believe is "living
on" here.

The problem here is that it's very easy for us to think just like you seem
to be thinking and talk as if "truth" can "live on". Especially a very
fundamental truth of logic and language and space, such as what is
represented in the language "2x7=14". Even if the Earth and the human race
was exterminated, it's a "truth" that could be rediscovered by some other
alien life form a million years from now. In that sense, we can say it's a
truth that exists "out there" an not "in us".

But what exactly is the truth that "lives on" here which we are talking
about?

Let me show another "truth". When I push the key that has a label of "e"
on my keyboard, the symbol "e" shows up on my screen. This is a
fundamental "truth" of the universe. The "truth" embodied in the language
of this paragraph "lives on" even after I die, and even after all copies of
this paragraph have been destroyed. But does it "live on" after the Earth
and everything on it, and everything we have produced, and every creature
that might have some memory of our language and our computers is gone from
the universe? No, it doesn't. The truth expressed in the language would
be gone from the universe at that point.

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?

When we talk about ideas living on, we are making reference to some aspect
of human brains (their behavior maybe), or maybe the language we write in
books, but we are always making reference to one or more physical things in
the end.

Because of the abstract nature of mathematical language, it can be a bit
hard to nail down what we are making reference to when we use the language.
I'm open to arguments about what it might be that we are making reference
to - it's valid to argue a few different stances there I suspect. But no
matter what the position, it MUST be a reference to some physical aspect of
the Universe, or we have to express some valid argument about why it
doesn't have to be.

I suggest it's a reference to a fundamental aspect of how brains (and
machines like brains - such as our computers) work. Before we can have
simple math, we need the ability to delineate objects or concepts. We need
to know that the big rock, is _separate_ _from_ the small rock. This
ability to slice up our sensory environment into "thinks" is so fundamental
to how or brain works, that it becomes a fundamental nature of how we
understand the universe. We see the universe not as some large continuum
of energy, but instead, as a world full of separate "things". This ability
to see A as different from B, is needed, before the axioms of mathematical
language can be written.

And it's an important part of the "fundamental truths" that lives on the
language "2x7=14". But it's not a fundamental truth of the universe, as
much as it's a fundamental truth of MACHINES that produce a sensory
representation of the universe and divide that sensory representations into
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.

If the universe goes back to being a large cloud of plasma, where does the
truth in the math of 2x7=14 live on?

> > 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.

That's just not true at all. What people in fact don't need, is to know
the truth. They say things, simply because they have been conditioned to
say them, whether they understand the meaning of what they so or not. They
say "God exists" and they believe with all their heart that this is true,
but yet, they don't have a clue what "God" actually is, or what "exists"
actually means. They don't need to. The reasons they say it go far beyond
"truth". It in fact has nothing to do with truth. And they don't for a
second need to understand the reasons they say it.

Likewise, you don't need to understand why you say "The truth embodied in
the statement lives on". You also don't need to know what it means. All
you need to know, is that it is the "right thing to say". That is, you
have been conditioned to talk, and think that way, by the society you live
in.

But, as you might guess, I find it interesting to try and understand the
real meaning of these sorts of things. I find it interesting to try and
understand why we throw around a word like "exist" so haphazardly. It all
grows from my interest in AI and building machines that act like humans -
including talking in the fun and interesting way humans talk about these
things (and everything else). Where does our view of reality come form
that allows us to talk in these ways? Why do we so easily talk as if
something is "living on" about these marks we scratch on paper when the
"something" is not something obvious that lives on, like our sun lives on
after we die?

None of these questions and issues are the least bit important for doing
mathematics. We can do math just fine by assuming the fundamental "truths"
of math and logic always "lives on" without or without a universe full of
mathematicians. But to fully understand the universe, and humans, so that
we can do things like build AI machines, these little philosophical points
become interesting (and somewhat important) debating points.

--
Curt Welch http://CurtWelch.Com/
curt(a)kcwc.com http://NewsReader.Com/

From: |-|ercules on 10 Jul 2010 21:42

"George Greene" <greeneg(a)email.unc.edu> wrote ...
> On Jul 9, 6:38 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote:
>> Perhaps you don't understand the proof, it only contradicts a well used axiom, not a well established fact.
>
> AND WHICH axiom is that??
> If you can answer that one question (which if course you can't),
> we MIGHT get somewhere.

Axiom Of Infinity.
EI ( {} e I ^ Ax e I ( ( x U {x} ) e I ) )

Herc's Axiom Of No Infinity
If the Qth element of a sequence is the natural number Q,
then the size of the sequence equals some element of the sequence.

Herc's Axiom Of Pseudo Infinity (based on above equation AOF)
There is a set, I, that includes all the natural numbers that could physically be computed
(before the end of the computer sustainable Universe)

Herc

From: Marshall on 10 Jul 2010 22:36

On Jul 10, 5:01 pm, "Vesa Monisto" <vesa.moni...(a)elisanetPOISTA.fi>
wrote:
> "Marshall" <marshall.spi...(a)gmail.com> wrote:
>
> >> On Jul 10, 2:22 pm, Don Stockbauer <don.stockba...(a)gmail.com> wrote:
> >> You can save yourself a lot of bother if you just go with the
> >> cybernetic interpretation of infinity:
>
> >>http://pespmc1.vub.ac.be/INFINITY.html
>
> > I felt myself getting stupider with each sentence of that
> > article that I read, so I stopped early. I expect a complete
> > recovery.
>
> "To find his stupidity is the first step to get rid of it". ;)
> The link Don gave is worth to read!

No it wasn't. It was worthless tripe.

> Curt gave the idea of infinity in the form "10 goto 10".
> I gave the idea in Basic; here even in more conventional notation:

Bleah. The crappy reference, and the stuff you're talking about,
all bring irrelevant concepts of procedure into simple questions
of cardinality.

Marshall

From: Nam Nguyen on 11 Jul 2010 01:38

K_h wrote:
> "Nam Nguyen" <namducnguyen(a)shaw.ca> wrote in message
> news:MTSZn.2663$Bh2.125(a)newsfe04.iad...
>> K_h wrote:

>>> Mathematical truth exists.
>> Sure. In your mind for example!
>
> And also outside of the human mind.

Did you mean _physically outside of human mind_ ? That's very bizarre to say
of mathematical abstractions that human thinks of. No?

>
>>> 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?
>
> If you don't believe that 10+20=30 is true in regular arithmetic then there's not
> much point in arguing it. Obviously I was not referring to modulo arithmetic.

I didn't say I don't believe such in regular arithmetic. But if you have to
refer to regular arithmetic then that isn't "an absolute truth" as you had
incorrectly claimed! An absolute mathematical truth is a statement which is
just true _independent of any context_ that you're referring to. And there
isn't such an absolute truth.

>
>>> 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.
>
> So we agree that there are absolute truths in both regular and modulo arithmetic.

No, I didn't agree to that. A truth that requires a context for it to be true
isn't an absolute truth. And in any rate it's not "outside of the human mind"
as you incorrectly stated above.

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

NYOGEN SENZAKI
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