Re: Infinity can not exist

From: Corey Kat (coreykat_at_hotmail.com)
Date: 07/09/04 

Date: 8 Jul 2004 18:39:53 -0700

Ann <aon2@hotmail.com> wrote in message news:<Pine.LNX.4.44.0407081319270.21684-100000@cicero.local>...
> 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?

Hi Ann,

Very interesting question...I guess one could say that infinity exists
at infinity, however, the unit interval on the real line is an example
where we can look at a set with infinite number of elements (i.e.,
infinite amount of information). However, the concept of infinity
exists only as a thought that might or might not occur to us. You can
ask the same question of, what does it mean to add the number "one" to
itself and yield the number "two"? After all, where do numbers exist?
 Numbers certainly are not physical objects. I hate to use this word,
but again, numbers, just like infinity, are abstractions. We are only
able to grasp them because we develop symbols for them and manipulate
these symbols, or drawings, stick figures, etc. Numbers only make
sense if we assign symbols to them, otherwise, how do we know 1+1=2??

CK

> > 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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