My reference is to that eminent logician, nthompson, who wrote.that in logic,Once you have said in your definitions,"A point has neither extension nor direction"you cannot start talking about a point's direction or movement with out going back to your definitions and starting over.consider the following syllogism(1) All swans are white(2) Well, except the odd black one.(3) This bird is black.(4) This bird is a swan."Absurd" in this case means what it means in a reductio argument. Violates the must fundament precepts of logic.QEDNickNicholas S. ThompsonEmeritus Professor of Psychology and Ethology,Clark University ([hidden email])Sent: 7/15/2008 9:40:34 AMSubject: Re: [FRIAM] Mentalism and CalculusHey Nick,
I'm not talking about points. I don't care about points. All I'm doing is using the existence of a disagreement about points (you think one thing, I think another) and our inability to resolve it to illustrate my claim that one cannot objectively identify category errors. So identifying supposed category errors in calculus (or anything else for that matter) is probably a fruitless endeavour.Here's what you need to do to show I'm wrong:
- find someone who has a well-accepted methodology for identifying category errors
- apply it to our point argument to show that there is/is not a category error.
I confidently predict that you'll not get past item #1. Ryle tried it, but his argument reduces to the one you are making: saying "It's absurd!" in ever louder tones. IMHO, that just doesn't cut it.So send me a link to the author and his/her methodology for identifying category errors
Robert
On Mon, Jul 14, 2008 at 9:35 PM, Nicholas Thompson <[hidden email]> wrote:
> 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 ([hidden email])
>
>
>
>
>
> ----- Original Message -----
> From: Robert Holmes
> To: [hidden email];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> a djudicate? 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. Thompson
>> Emeritus Professor of Psychology and Ethology,
>> Clark University ([hidden email])
>>
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