This is based on nothing more than reading the entry on categories at
http://plato.stanford.edu/entries/categories/ so please take with a pinch of
salt...
It seems that the tools necessary to construct category systems are severely
broken. Specifically, there is no generally accepted method for
distinguishing between categories. For example, the Ryle/Husserl method
boils down to a highly subjective notion of whether a statement is absurd or
not. That means it's perfectly possible for Nick to see a category error
("it's crazy to say that a point can have position and velocity") and me not
to see one ("nothing wrong with a point having position and velocity") and *we
can both be right*.
IMHO, this means that category theory really can't tell us very much about
calculus.
Robert
On 7/8/08, Nicholas Thompson <[EMAIL PROTECTED]> wrote:
>
> All who have patience,
>
> Once of the classic critiques of mentalism .... the belief that behavior is
> caused by events in some "inner" space called the mind ... is that it
> involves a category error. The term "category error" arises from ordinary
> language philosophy (I think). You made a category error when you start
> talking about some thing as if it were a different sort of thing altogether.
> In other words, our language is full of conventions concerning the way we
> talk about things, and when we violate those conventions, we start to talk
> silly. To an anti-mentalist a "feeling" is something that arises when one
> palpates the world and to talk about our "inner feelings", say, is to doom
> ourselves to silliness. Feelings are inherently "of" other things and to
> talk of "feeling our own feelings" is, well, in a word, nutty.
>
> As many of you know, I have been engaged in a geriatric attempt to recover
> what slipped by me in my youth, the chance to understand the Calculus. As I
> read more and more, it became clear to me that the differential calculus was
> based on a huge "category error." To speak of a point as having velocity and
> direction one had to speak of it at if it were something that it essentially
> wasn't. And yet, of course, the Calculus flourishes.
>
> Now the reason I am writing is that I am not sure where to go with this
> "discovery." One way is to renounce my behaviorism on the ground that
> category errors ... any category errors ... are just fine. Another way is to
> start to think of the mind/behavior distinction in some way analogous to the
> derivative/function distinction. That mind is just the derivative of
> behavior. For instance, a motive, or an intention, is not some inner thing
> that directs behavior, but rather the limit of its behavioral direction. A
> third way, is to wonder about how the inventors of calculus thought about
> these issues. They, presumably, were steeped in mentalism and it cannot have
> escaped their notice that they were attributing to points qualities that
> points just cannot have. Many of the texts have been reading have alluded to
> the idea that some contemporaries ... perhaps Newton himself ... attributed
> to the Calculus some sort of mystic properties. I really would like to know
> more about that. Any intellectual historians out there????
>
> So, I am hoping somebody will help me go in any, or all, of these
> directions.
>
> --Nthompson<http://www.sfcomplex.org/mediawiki/index.php?title=User:Nthompson&action=edit>04:14,
> 9 July 2008 (GMT)
> This noodle, and perhaps some subsequent revisions and commentary, may be
> found at http://www.sfcomplex.org/wiki/MentalismAndCalculus
>
> Nicholas S. Thompson
> Emeritus Professor of Psychology and Ethology,
> Clark University ([EMAIL PROTECTED])
>
>
>
>
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