Mentalism and Calculus
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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 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 (nthompson at clarku.edu) -------------- next part -------------- An HTML attachment was scrubbed... URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20080708/e040f28c/attachment.html |
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Nicholas Thompson wrote:
> > For instance, a motive, or an intention, is not some inner thing that > directs behavior, but rather the limit of its behavioral direction. > Or it could be that the so-called `motive' or `intention' was merely a rationalization of a subconscious impulse that had already been revealed in a whole pattern of related behaviors. If so, the behaviourist would be ahead of the game using careful observation or perturbation of either the behavior of the individual, or of its brain. The easy way out of the category error, whether in regard to mentalism or calculus is to regard them as models -- separate standalone things. Marcus |
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In reply to this post by Nick Thompson
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 <nickthompson at earthlink.net> 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 (nthompson at clarku.edu) > > > > > ============================================================ > 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 > An HTML attachment was scrubbed... URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20080709/669a73df/attachment.html |
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In reply to this post by Nick Thompson
Is it possible that you have made Calculus something more than it really is?
Could it JUST be a way of seeing a way to find the instantaneous slope of an equations solution graph and the area between limits under that curve. _____ From: [hidden email] [mailto:[hidden email]] On Behalf Of Nicholas Thompson Sent: Tuesday, July 08, 2008 10:46 PM To: friam at redfish.com Cc: echarles Subject: [FRIAM] Mentalism and Calculus 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 (nthompson at clarku.edu) -------------- next part -------------- An HTML attachment was scrubbed... URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20080709/179c056e/attachment.html |
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In reply to this post by Robert Holmes
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: [hidden email] [mailto:[hidden email]] On Behalf Of Robert Holmes Sent: Wednesday, July 09, 2008 9:49 AM To: nickthompson at earthlink.net; 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 <nickthompson at earthlink.net> 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 (nthompson at clarku.edu) ============================================================ 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 -------------- next part -------------- An HTML attachment was scrubbed... URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20080709/e823f1c5/attachment.html |
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You can also look at this as being undefined for the point, but
defined for an interval on the curve which is arbitrarily close to that point. --joshua On Jul 9, 2008, at 10:37 AM, Frank Wimberly wrote: > 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: friam-bounces at redfish.com [mailto:friam-bounces at redfish.com] > On Behalf Of Robert Holmes > Sent: Wednesday, July 09, 2008 9:49 AM > To: nickthompson at earthlink.net; 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 athttp://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 <nickthompson at earthlink.net> 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 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 (nthompson at clarku.edu) > > > > > ============================================================ > 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 -------------- next part -------------- An HTML attachment was scrubbed... URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20080709/9e82f6c5/attachment.html |
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In reply to this post by Kenneth Lloyd
It may not be a category error, but a domain error... applying
definitions of objects from one domain to similarly named objects in another. This error is the basis of the classic paradox regarding immovable object's interactions with irresistible forces. The question of what happens when the former meets the latter is meaningless because an immovable object is, by definition, an object that can resist *any* force. So, a universe that contains immovable objects, cannot, by definition, contain an irresistible force. In the present case, there is the word point. And in calculus, a point has certain properties, including properties that are not attributed to points outside of calculus. If it helps, try to rename it in your mind: it's not a point, it's a plerx. ~~James |
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Well, here's the thing: If a particle were following the curve defined by
that parameterization because of forces imposed by a field, and if all forces on the particle instantaneously became zero, the particle would continue to move with the mathematically defined velocity. Frank -----Original Message----- From: [hidden email] [mailto:[hidden email]] On Behalf Of James Steiner Sent: Wednesday, July 09, 2008 1:40 PM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] Mentalism and Calculus It may not be a category error, but a domain error... applying definitions of objects from one domain to similarly named objects in another. This error is the basis of the classic paradox regarding immovable object's interactions with irresistible forces. The question of what happens when the former meets the latter is meaningless because an immovable object is, by definition, an object that can resist *any* force. So, a universe that contains immovable objects, cannot, by definition, contain an irresistible force. In the present case, there is the word point. And in calculus, a point has certain properties, including properties that are not attributed to points outside of calculus. If it helps, try to rename it in your mind: it's not a point, it's a plerx. ~~James ============================================================ 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 |
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