[FOM] Question on the number line
Steven Ericsson Zenith
steven at semeiosis.com
Tue Nov 15 21:25:50 EST 2005
Dean Buckner wrote:
> Forgive me if this is a naïve question. It occurs in the chapter in
> Suarez (the 16C philosopher & mathematician) that I mentioned in a
> previous posting. Suppose one takes a line segment of length 1 and
> break it in half (assuming we can break it "in half"). Intuitively, you
> would imagine you get two identical segments of length 0.5. But if you
> "identify" that line segment with the reals from 0.0 to 1.0, you have to
> ask what happens to the point at 0.5 -- which "half" does it belong to?
In the first case you specify the reals are a function of the points on
the line - and points have no magnitude so the divided segments at the
respective end points each have 0.5 as a map since they are the same
point with respect to the original length.
The second case you specify is a contradiction to the first and
describes a different mapping. In that case the line you describe is a
function of the reals - and therein lies the problem, the number line is
not a geometric line in the world. The number line has epistemology,
but no ontology - it can be known, but it does not exist.
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