Re: Epistemology 201: The Science of Science

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 03/04/05 

Date: Fri, 04 Mar 2005 20:50:00 GMT

On Thu, 03 Mar 2005 17:55:21 -0500, Wolf Kirchmeir
<wwolfkir@sympatico.ca> in comp.ai.philosophy wrote:

>Tony Orlow (aeo6) wrote:
>[...]
>>>IOW, your concept of the number line is peculiar, to put it mildly.
>>>You've assumed that it's a geometric line, and that it's a straight
>>>line. It is neither. One of its features is that it doesn't have to be
>>>visualised as being straight, that's just a convenience. It can be
>>>visualised as having any shape you can (or can't) imagine. It can be a
>>>knot, for example. So long as it doesn't cross itself. (A line crosses
>>>itself if in tracing the line your pass through the same point at least
>>>twice.)
>>>
>>>HTH
>>>
>>
>> Perhaps, Wolf, or maybe the geometry matters. I am of the opinion it is
>> an infinite circle, and only appears straight locally. Certainly if you
>> want to combine two or more number lines into a coordinate system, it
>> makes sense for them to be straight, and perpendicular to each other,
>> otherwise it's useless. The number line IS straight, but the rest of
>> your point is correct, in my mind, because that's irrelevant to it.
>
>Why is the number line struight?
>
>Or:
>
>If the number line were not straight, would that chnage anything else
>about it?

Yes, it would mean that transcendentals don't occur between points or
on straight lines as maintained by Bob Kolker and Richard Herring.

>Actually, the number line is a metaphor. It's when people start taking
>it literally that the silliness begins.

So what else in the magesterium of science and mathematics is a
metaphor? Or is it only those things mathematikers find themselves
embarrassed to explain in literal terms? Is transcendental
irrationality just a metaphor or just a plain contradiction? Is SR a
metaphor or just a plain contradiction? Is GR a metaphor or just a
plain contradiction? Is pi just a metaphor for pi radians? I think we
may need to make a little list of all the metaphors mathematikers
suddenly find themselves faced with using that they didn't think were
metaphors but literally exact.

Regards - Lester

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