Re: Distinct linear orderings on Z

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 03/29/05 

Date: Tue, 29 Mar 2005 15:36:22 GMT

On Mon, 28 Mar 2005 20:06:42 -0600, Albert Wagner
<albertwagner@cox.net> in comp.ai.philosophy wrote:

>Lester Zick wrote:
><snip>
>> Well the difference is that you don't need rotation. All you need is
>> bisection and static construction techniques to define circles by
>> approximation. In other words my definition of a circle doesn't rely
>> on circular rotation. That's something that has always bothered me in
>> common geometric definitions.
>
>Why?

Mainly because rotation presumes circular rotation which assumes the
thing we're trying to define. It also presumes an action or process as
the basis of definition where the thing we're trying to define is not
an action.

>> My definition only relies on successively smaller subdivisions. We
>> start off with a straight line segment and straight angle and through
>> bisection of the segment determine radius and successively bisect the
>> angle at a distance of the radius and take a circle to represent the
>> curved limit of that approximation process.
>
>In that a point is the bisection of lines, haven't you then just
>introduced a way of constructing points? And thereby only
>entered the back door to a set definition of a circle?

Well I consider a point the intersection of lines but not necessarily
straight lines and not necessarily a bisection. But yes construction
does delimit points on the perimeter of a circle. However the circle
itself is the limit of a series of line segments between those points
rather than the points themselves.

And as far as sets themselves go I don't really mind them very much.
There are in fact a great many things we can do under the set rubric
without going to far astray. The problem is what the mathematikers do
with sets that make them impossible to use consistently. Even infinity
makes sense in terms of sets of infinitessimals between cardinal
limits. Sets in general have ordinality and certain subsets have
cardinality and a variety of other properties.

Epistemologically the problem isn't with sets so much as regression of
dimensional properties to dimensionless points. Mathematikers want to
believe they can regress things terminologically without performing
any kind of scientific reduction. They just adopt a new vocabulary to
talk about cardinality, ordinality, well order, denseness, sparseness,
etc. as if they were contributing something useful to the history of
knowledge when all they're really doing is talking about everything
pretty much already known in different terms. It's the same trick the
materialists and behaviorists use in calling everything behavior as if
they were contributing some kind of radical scientific insight without
reducing behavior to any kind of mechanical insight worth discussing.

Regards - Lester

Relevant Pages

  • Re: Distinct linear orderings on Z
    ... > Well the difference is that you don't need rotation. ... > bisection and static construction techniques to define circles by ... In other words my definition of a circle doesn't rely ... > bisection of the segment determine radius and successively bisect the ...
    (sci.math)
  • Re: Rotating a Plane
    ... original circle to corresponding points on the rotated circle. ... onto x-y plane and then rotate points around this vector. ... As to the direction of rotation, you can adopt the convention that the ... This last equation gives us the equations that define the transformation ...
    (comp.soft-sys.matlab)
  • Re: Rotating a Plane
    ... rotating the circle about a line in the ... onto x-y plane and then rotate points around this ... As to the direction of rotation, ... terms of x, y, z, a, b, and c to derive the transformation ...
    (comp.soft-sys.matlab)
  • Re: geometry - construction
    ... I did mean that the circle is a unit circle, ... Any construction of points with compass and straightedge is ...
    (sci.math)
  • Re: Rotating a Plane
    ... I want transformation equations for rotating points on the ... original circle to corresponding points on the rotated circle. ... to "map" each point on the original circle to the rotated circle. ... rotation you describe? ...
    (comp.soft-sys.matlab)