Nick, Have you read Penrose's "Emperor's New Mind", "Shadows of the Mind", and "Road to Reality". These all explore the relationship between physics, mathematics and how they relate to / represent the mind. Ken
_____ From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Nicholas Thompson Sent: Monday, July 14, 2008 9:28 PM To: Robert Holmes Cc: FRIAM@redfish.com Subject: Re: [FRIAM] Mentalism and Calculus Robert, 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. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([EMAIL PROTECTED]) ----- Original Message ----- From: Robert Holmes <mailto:[EMAIL PROTECTED]> To: [EMAIL PROTECTED];FRIAM <mailto:Friam@redfish.com> 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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