Re: Epistemology 201: The Science of Science

From: aeo6 (aeo6_at_cornell.edu)
Date: 03/15/05 

Date: Tue, 15 Mar 2005 11:34:27 -0500

Daryl McCullough said:
> aeo6 says...
>
> >If they're meaningless symbols, don't call them numbers,
> >and you can order them any way you like. If you claim
> >they are numbers, then don't violate their basic meanings to prove
> >"counterintuitive" conclusions, or I will see that as a result of that
> >violation.
>
> So your objection is that people are using numbers in
> an unapproved way? Perhaps there should be regulations
> about proper and improper use of numbers? Perhaps
> people should submit an environmental impact statement
> before doing unnatural acts with natural numbers?
If this had anything to do with approval, would I be taking the position I am
taking? LOL. Yes, we need a movement to save the endangered transcendentals.
No.
What I object to is the use of numbers in orderings that are not consistent,
using a technique that is not proven, to derive results that contradict more
basic notions of set theory
>
> >> No. It's just that there is no reason to restrict ourselves to the
> >> usual ordering on the naturals. Betweenness is defined for any ordering.
> >
> >And using an artifical ordering gets you artificial results, like
> >there are an infinite number of naturals between any two naturals.
>
> I already told you, the result is not "there are an infinite number
> of naturals between any two naturals", the result is that for the
> particular ordering that I defined, there are infinitely many
> naturals between any two naturals.
Right, but do you believe the conclusion based on that ordering? Is it true
that there are infinitely many naturals between any two naturals, given the
normal meaning of "between" for natural numbers? If you believe this, then
please list just one natural number between 2 and 3 (exclusive). If not, then
you should examine the train of thought that led to that conclusion, because
you either have a faulty premise, or a flawed method of calculation. This is
yet another example of how artificial orderings that violate the natural order
of real numbers can lead to erroneous results.
>
> >Doesn't a result like that give you any kind of twinge?
>
> The fact that you left out the qualifying phrase "for that particular
> ordering" certainly does.
That is my point. The ordering is the problem. The conclusion is wrong, by any
normal sense, unless you violate the number system by divorcing order from
quantity. It's the same as demonstrating a difference between absolute
foreknowledge and predetermination based on a violation of the nature of time.
Garbage in garbage out - you start with faulty assertions, you get faulty
conclusions.
>
> >If "order type" represents what I am saying then maybe that's what
> >I *really* mean. Why must I go through weeks of being accused of
> >not understanding cardinality, or of being confused and stupid, to
> >get anywhere with this?
>
> Because you say things like
>
> anyone who argues there are as many rationals as integers is nuts,
> in my mind
>
> Why should anyone show you respect when you don't show any respect?
I have already made my case regarding the integers and rationals. If, for EVERY
unit on the real number line there is exactly ONE integer and INFINITE
rationals, in EVERY unit, then it is a no-brainer to conclude that overall,
there are an infinity of rationals for every integer, not one. To draw a
conclusion so drastically different from the blatantly obvious, using a
technique that is assumed to work because it looks neat, but is not supported
by any empirical evidence or application to reality, and to accept that
conclusion over what makes sense, to me, makes no sense. I believe I am
entitled to that opinion.

And, if you think I have been treated with a lot of respect through this, where
almost everyone seems to think I just don't understand cardinality and repeats
the same thing over and over without listening, and tries to shoot me down
because they didn't learn it in a book, think again. The only folks who have
been open to the idea are not mathematicians, which may lead you to believe
they are being taken for a ride, but it's my opinion that mathematicians, like
everyone else, are so steeped in their discipline they can't see the forest for
the trees any more.

Do you really believe there are an infinite number of naturals for every
natural, or that the method is flawed?
>
> --
> Daryl McCullough
> Ithaca, NY
>
> 

-- 
Smiles,
Tony

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... > such that between any two naturals x and y, ... >>I have already made my case regarding the integers and rationals. ... that between any two naturals there are an infinite number of distinct ... More bijection genuflection. ...
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  • Re: Epistemology 201: The Science of Science
    ... > such that between any two naturals x and y, ... >>I have already made my case regarding the integers and rationals. ... that between any two naturals there are an infinite number of distinct ... More bijection genuflection. ...
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  • Re: Epistemology 201: The Science of Science
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    (sci.physics)
  • Re: Cantor and the binary tree
    ... > Virgil wrote: Since the rest of WM's daydream is based on the ... > It is based on the existence of infinitely many rationals and on the ... > As it has not an infinite member, ... > naturals, then there are only elements, which count their initial sets. ...
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  • Re: Epistemology 201: The Science of Science
    ... >>integer and an INFINITE number of rationals. ... > This ordering has the same order type as the naturals. ...
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