Re: Epistemology 201: The Science of Science
From: Wolf Kirchmeir (wwolfkir_at_sympatico.ca)
Date: 03/07/05
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Date: Mon, 07 Mar 2005 18:00:15 -0500
Lester Zick wrote:
> On Mon, 07 Mar 2005 13:38:18 -0500, Wolf Kirchmeir
> <wwolfkir@sympatico.ca> in comp.ai.philosophy wrote:
>
>
>>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?
>
>
> Mainly. The rationals and irrationals lie between points and can be
> pointed out on a straight line using right angles for that reason.
> Transcendentals require commensuration between curves and straight
> lines to be pointed out on curves. By the phrase "accommodated on a
> straight line" I basically mean a number must lie between points in
> space because points in space define straight line segments.
>
> Transcendentals don't lie between points in space. They lie on curves
> and not between points.
Does this mean that you think curves don't have endpoints? That's odd,
since I'm sure someone taught you that between any two points you draw
as many lines as you want, but only one them is a so-called "straight
line" - the one whose measure of the distance between those points is
smallest.
Or do you believe that curves aren't lines? What are they, then?
>>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.
>
>
> I would expect reduction of the latter to the former. We don't need to
> walk around with a straight edge and compass to count and calculate
> but we do need to understand the reduction of numeric concepts and
> their implications as matters of science in general.
>
> Regards - Lester
Reduction to what? Geometry? I wish you'd be more explicit.
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