From: [hidden email] [mailto:[hidden email]] On Behalf Of Nicholas Thompson
Sent: Monday, July 14, 2008 9:28 PM
To: Robert Holmes
Cc: [hidden email]
Subject: Re: [FRIAM] Mentalism and CalculusRobert,Some how this message got caught in my outbox and you went unchastised for a whole 48 hours.No! 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, in the same way that Lobachevski and the Rieman (??) changed the definition of "parallel". . 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 all might have for the concept of mind, because, under the influence of my New Realist ancesters, I have always thought of Consciousness as an extensionless point of view.NickNicholas S. ThompsonEmeritus Professor of Psychology and Ethology,Clark University ([hidden email])----- Original Message -----From: [hidden email]Sent: 7/12/2008 6:47:34 PMSubject: Re: [FRIAM] Mentalism and CalculusNick - 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 <[hidden email]> 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. ThompsonEmeritus Professor of Psychology and Ethology,Clark University ([hidden email])
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