From: lambdac-AT-globalserve.net
Date: Mon, 03 Aug 1998 13:58:37 -0500
Subject: Points and the metaphysics of geometry



>Peirce asks the question whether a line is composed of the points along
>that line, and answers that that cannot be the case, for even if you have
>an infinite number of points, there would still be gaps between the points.
>Therefore the line must be something other than the points (even infinite)
>that are arrayed along it.

Points, the way most people employ the term, is _truly_ a metaphysical
notion devoid of concept or of function.  Lines do not have to exist
because of an infinitesimally divisible nature of the line into points
that would leave gaps per force exposed as one's resolution of the line
would increase.  Nor is the line composed of an infinity of points and
gaps, or even absent points.  It is the line which must be thought of
independently of any points, since the line is the reality of the
continuous, and the mathematical point truly a metaphysical nothing. 

Further even, points do not exist as unidimensional (or worse still,
dimensionless) elements.  Points are not numbers and numbers points. 
Numbers mean nothing unless they have dimensionality.  As Reich was fond
of saying, there is no zero in natural research.  The only possible
concept of a point is as the intersection of two or more lines - such
points are called knots - and the whole problem of Euclidean Geometry
and Cartesianism stems from confusing point-knots with dimensionless
points in order to construct a line; point-knots are not elements of a
line, but the topological product of the synthesis of lines.  It is of
these point-knots that one can say that a line passes between them or in
the gaps between them, and not _through_ the points _and_ their gaps. 
Only the _concept_ of molar line subordinates the line to the point.

Question: does a striated space exist other than through and in the
mind, as representation or as plane of transcendence?

Lambda C


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