Re: Infinity can not exist

From: Ann (aon2_at_hotmail.com)
Date: 07/08/04 

Date: Thu, 8 Jul 2004 13:27:52 +0200

Hi Chris,

> On Thu, 8 Jul 2004, Chris Parker wrote:

> I didn't mean to call you silly.

I know, I quoted you jokingly, it might have sounded a bit rude but was
in fact meant to be funny. And of course "I guessed that you take the
concept of infinity for granted", it was clear from the start. Actually
accepting the word 'infinity' is like with any other abstract
construction: it starts as a game, at first it even seems rather
convenient bearing in mind all the other infinitesimals, fluxions,
infinite and universal sets that logically followed suit; and the next
moment, however, we've already forgotten it were a game and took them
for real, the question I posed was: Real where?

Infinity exists where?

> I guess that I take for granted the concept of infinity.

> You do sound like a bit like a Constructivist, which is not a bad thing.
> I know that they have gotten a bit of bad press, but Brouwer's
> ideas are interesting.

> I did not say that infinity exists, but that it is a concept (and a very
> convenient one when dealing with things such as the set of natural
> numbers, pi, e, etc).

Totally agree with you (noticing the careful precision of your
language:), though if you think about it, we cannot even COUNT
'things', or if we do that would be some 'imaginary' numbers (instead
of the "real", "rational", "natural" ones, but clever names they have,
who would dare question the reality of the "real number":) or money
(again numbers:) or other hypothetical elements of "the set" or just
'straight' lines in the sand. That is why little children have problems
with the concept of counting, for we could rarely find in nature two or
more absolutely identical things to be added, subtracted or otherwise
manipulated algebraically (they might have problems imagining the
result too:).

Instead, we usually imagine the objects were uniformly the same, that
this talking 'animal' here (Chris) and that one (Ann) are two
immaculate elements/members of the flock of sheep ('people') to then
add them to produce the result of... the sum total of two... :). Maybe
you've heard of the Greek Eleatics from 2500 years ago, like Zeno who
almost proved that all measures, numbers and sets (including the
sublime one of the "natural numbers":) are unreal ("numbers of the
Beast":), do not exist independently (of our gorgeous brain:) in the
external world. "Zeno was concerned to show that our understandings of
time, motion, change, position, magnitude, unity, singleness, and
plurality are incoherent; or that they result in contradictions."
(http://www.gmu.edu/courses/phil/ancient/pzm3.htm)

          Many different mathematical universes are possible. When we
          accept or reject the Axiom of Choice, we are specifying which
          universe we shall work in. Both possibilities are feasible --
          i.e., neither accepting nor rejecting AC yields a contradiction;

:) The "existence" of f -- or of any mathematical object, even the
          number "3" -- is purely formal. It does not have the same kind
          of solidity as your table and your chair; it merely exists in
==> the mental universe of mathematics.

                 http://www.math.vanderbilt.edu/~schectex/ccc/choice.html

To paraphrase you, "I did not say that infinity [does not] exist, but that
it is a concept" that "merely exists in the mental universe of
mathematics". And so do the numbers and all other mathematical objects,
they need the support of the human mind, they badly 'need' us, go figure
(you see, who would have thought; I mean, until very recently I was
convinced that it was only us who badly needed them:).

Best,
Ann

PS: Random quote generator:

            "Two things are infinite: the universe and human stupidity;
            and I'm not sure about the universe."
                                                        Albert Einstein

> On Thu, 8 Jul 2004, Chris Parker wrote:
>> On Wed, 07 Jul 2004 Ann wrote:

>> Hi Chris,

>> "silly me" but it "seems to me" (the skeptic realist I am, not "the
>> Constructivist":) that before we could "believe" or disbelieve the real
>> "existence" of "infinity" you need to tell us "something" about your
>> definition of existence and its whereabouts: in reality outside or
>> within. Until then we may choose some point in the middle between "it
>> does" and "it does not exist"--sitting and waiting ('indefinitely':)
>> for the arrival of the overwhelming evidence that will finally force us
>> to make up our gullible mind (i.e. fix it to the absolute 'truth', and
>> stick to it to the bitter end:).

>>> On Wed, 7 Jul 2004, Chris Parker wrote:

>>> Or look at the Constructivists - L.E.J. Brouwer. They believe that if
>>> something can not be constructed in a finite number of steps that it
>>> does not exist.

>>> This argument seems silly to me.
>>> Infinity is not a measurable unit.
>>> Infinity is an abstract concept.

>> ... therefore, its reality is... outside or within? Come on, it must be
>> easy, is 'infinity' a sublime product of the supreme mind (like all the
>> words--"abstract" creations of Lord Logos), or is it something else
>> entirely, or is it more, and how much more than a regular word. Or
>> perhaps you could "construct" it for us, and it doesn't matter in how
>> many "finite (or more:) number of steps" you do it, important is the
>> experiment to last less than 'indefinitely'.

>> I mean, people are impatient these days, few would like to be told to
>> repeat some imaginary process 'forever'. We are just 'unprepared' to
>> wait until the end of 'eternity' in order to witness the miracle (the
>> actual "construction" or coming into existence of the 'infinitesimal'
>> converging rapidly to the infinite loop, approaching but never actually
>> reaching it:), you know why? Because...:), to experience anything it
>> has to cross our path during our 'lifetimes' -- which happen to be...
>> finite or infinite? (or more than 'finite' but less than 'infinite':)
>> Best,
>> Ann

> I didn't mean to call you silly. I guess that I take for granted
> the concept of infinity.
>
> You do sound like a bit like a Constructivist, which is not a bad thing.
> I know that they have gotten a bit of bad press, but Brouwer's
> ideas are interesting.
>
> I did not say that infinity exists, but that it is a concept (and a very
> convenient one when dealing with things such as the set of natural
> numbers, pi, e, etc).
>
> Chris

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