No, Robert. You have gone a bridge to far, unless you are willing to rewrite
the role of definitions in axiom systems.
In a system in which a definition is, "a point is a position in space lacking
dimension"
you cannot have a proposition that contradicts the definition.
You just cant.
You can REWRITE your definitions, add or subtract axioms, etc, but until you do
that, you are just stuck with that Euclidean definition of a point.
I assume that some mathematician is going to write me in a milllisecond and
say, "Yeah, yeah. In effect, calculus changed the definition of a point. That
is how progress is made, you rigid boob!" But then I want to continue to
wonder (for perhaps a few more days) what implications this might have for the
concept of mind. My New Realist mentors taught me to think of consciousness as
a point of view. It is a place from which the world is viewed, or at b
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([EMAIL PROTECTED])
----- Original Message -----
From: Robert Holmes
To: [EMAIL PROTECTED];FRIAM
Sent: 7/12/2008 6:47:34 PM
Subject: Re: [FRIAM] Mentalism and Calculus
Nick - the snippet below illustrates the key problem with invoking category
errors. I think giving the infinitesimal point speed and direction makes sense
and you do not. You see a category error and I do not. So how do we adjudicate?
We can't: there's no objective methodology for saying if a category error
exists. (BTW, appeals to 'common sense' have as much objectivity as Ryle's
invocation of absurdity: not much).
So if there's no remotely objective way of even saying whether we have a
category error, then it seems pointless to try and analyse calculus in terms of
its category errors. Why use a tool when all the evidence suggests that the
tool is broken?
Robert
On Wed, Jul 9, 2008 at 4:07 PM, Nicholas Thompson <[EMAIL PROTECTED]> wrote:
<snip>
If one defines a point as having no extension in space and time, one CANNOT in
common sense give it speed and direction in the next sentence
<snip>
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([EMAIL PROTECTED])
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