Re: Epistemology 201: The Science of Science

From: Wolf Kirchmeir (wwolfkir_at_sympatico.ca)
Date: 03/07/05 

Date: Mon, 07 Mar 2005 13:38:18 -0500

Lester Zick wrote:
> On Mon, 07 Mar 2005 11:30:04 -0500, "robert j. kolker"
> <nowhere@nowhere.net> in comp.ai.philosophy wrote:
>
>
>>>Whether either or both definitions can be accommodated on straight
>>>lines between points.
>>
>>Real numbers can be developed completely without geometric content. For
>>some applications it is useful (but not necessary) to associatate real
>>numbers with points on a curve (or straight line). If the world were
>>blind but could count real number theory could be developed.
>
>
> Do you admit there is no real number line? Certainly transcendentals
> cannot be accommodated between points on straight lines or on any one
> curve. So why haven't counting animals developed real number theory?

AHA!

I think I finally undeestood what you mean: for a number to be
"accommodated on line", there must a geometric construction of a line of
that length.

Is that what you mean?

It's not clear whether the construction is limited to straight edge and
compass, or whether you permit the abstract construction possible in
Cartesian co-ordinate space and the associated arithmetic.

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