In differential geometry a curve with a given parameterization has a velocity at a point. This is not a category error; it's a definition.
Frank From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Robert Holmes Sent: Wednesday, July 09, 2008 9:49 AM To: [EMAIL PROTECTED]; The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] Mentalism and Calculus 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=ed it> 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]) ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
