Mentalism and Calculus

[Nick Thompson]

Oh, I forgot to ask.

What about the flow in the opposite direction?  Can the calculus tell us anything about how we think about goal direction in human behavior?

This discussion is posted in www.sfcomplex.org/wiki/MentalismAndCalculus

Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University (nthompson at clarku.edu)




----- Original Message -----
From: Robert Holmes
To: nickthompson at earthlink.net;The Friday Morning Applied Complexity Coffee Group
Sent: 7/9/2008 9:49:11 AM
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 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)




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[Marcus G. Daniels]

Nicholas Thompson wrote:
> What about the flow in the opposite direction?  Can the calculus tell
> us anything about how we think about goal direction in human behavior?
Well, goal direction means having some way to measure achieving a goal
or getting closer.   One artificial neural net training algorithm,
backpropagation uses adjustments to signal weights based on a the
derivative of the `closeness' to the observed variables.   Neural nets
are one way to implement control systems in robots, e.g. a goal like
"pick up the rock".

http://www.learnartificialneuralnetworks.com/robotcontrol.html

[Günther Greindl]

Nick,

I think the questions you are asking won't be answered in a math book
but rather in a book like this:

Where Mathematics Comes From: How the Embodied Mind Brings Mathematics
into Being
by George Lakoff, Rafael Nu?ez

http://www.amazon.com/Where-Mathematics-Comes-Embodied-Brings/dp/0465037712/ref=sr_1_1?ie=UTF8&s=books&qid=1215709470&sr=8-1

I can recommend it warmly, it will clear up many "mysteries" of
mathematics :-)

Cheers,
G?nther

Nicholas Thompson wrote:

>
> Oh, I forgot to ask.
>  
> What about the flow in the opposite direction?  Can the calculus tell us
> anything about how we think about goal direction in human behavior?
>  
> This discussion is posted in www.sfcomplex.org/wiki/MentalismAndCalculus
> <http://www.sfcomplex.org/wiki/MentalismAndCalculus>
>  
> Nicholas S. Thompson
> Emeritus Professor of Psychology and Ethology,
> Clark University (nthompson at clarku.edu <mailto:nthompson at clarku.edu>)

--
G?nther Greindl
Department of Philosophy of Science
University of Vienna
guenther.greindl at univie.ac.at
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org/

Research Proposal:
http://www.complexitystudies.org/ph.d.-thesis.html