SUO: Re: Arete, Episteme, Techne
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Jack,
Second take, under less hurried circumstances,
of your initial tug on this thread:
Jon Awbrey wrote:
>
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>
> Jack,
>
> Brief response now, fuller one later,
> since I am in the middle of another
> bit of postage in the same spirit
> as the current chain of letters.
>
> Jack Park wrote:
> >
> > Jon,
> >
> > Below, you state "The mathematical and computational tools needed
> > to implement such a perspective goes beyond the understanding of
> > systems and their spaces that I currently have in my command,"
> > to which this reply is directed.
>
> I wrote that in the Fall of 1992, a Happy Fall, in Word, in Deed,
> But I am much smarter now, if sadder for the ex-change of colors,
> And though I am tempted to lament the flagrant lack of agreement
> Between that plurality of "tools" and that singularity of "goes",
> I will stick instead to the bit I have learned in the Mean Times.
>
> > The keywords 'manifold' and 'fiber bundle' attracted my attention here.
> > You have moved the discussion into a topological space and I am reminded
> > that the Mathematical Biologist Robert Rosen has written two books (and
> > a third published post mortem) in the field of Relational Biology. In
> > his _Anticipatory Systems_, he discusses fiber space. In _Life Itself_,
> > he discusses Aristotle's causality, and rounds the discussion with an
> > exposition of Category Theory (CT) as a candidate mathematics for
> > knowledge modeling of complex systems.
I have read a little of bit of Rosen, Casti, and the Abrisko Bunch.
Aristotle's way of looking at causality returned to this scene when
Wiener tried to rehabilitate the notion of teleology in cybernetics.
Arbib made category theory a standard part of AI at its very outset.
> > CT, a topological algebra, is far beyond my reach,
>
> I doubt that. You are probably aware that the "theory of categories" (TOC),
> a name that was confessedly "purloined" from Kant and Carnap, is just the
> most koiney of the "lingua fracta" that are shared throughout mathematics
> at the present time, but it is mostly just a glorified apotheosis of what
> every schoolchild knows about sets and functions, and most of these folks
> only speak the native (read "naive") subset of it, which is all with what
> this e-mediate writer would ever have anything to do, or to be able to do.
>
> Several references that I mentioned a while back may be useful here:
>
> Locus Classicus:
>
> Saunders Mac Lane, 'Categories for the Working Mathematician',
> Graduate Texts in Mathematics 5, Springer-Verlag, 1971.
>
> More recent texts, with an eye to applications:
>
> J. Lambek & P.J. Scott, 'Introduction to Higher Order Categorical Logic',
> Cambridge Studies in Advanced Mathematics 7, Cambridge University Press, 1986.
>
> Michael Barr & Charles Wells, 'Category Theory for Computing Science',
> Prentice Hall International Series in Computer Science, Prentice Hall, 1990.
>
> Several folks have contributed bits of TOC to the SUO Persutra from time to time --
> here are a few odds and ends of thread that I have tangled up in my suo-wing basket:
>
> http://ltsc.ieee.org/logs/suo/msg00405.html
>
> http://ltsc.ieee.org/logs/suo/msg00918.html
> http://ltsc.ieee.org/logs/suo/msg00922.html
> http://ltsc.ieee.org/logs/suo/msg00932.html
>
> http://ltsc.ieee.org/logs/suo/msg01328.html
>
> http://ltsc.ieee.org/logs/suo/msg02362.html
> http://ltsc.ieee.org/logs/suo/msg02388.html
> http://ltsc.ieee.org/logs/suo/msg02421.html
> http://ltsc.ieee.org/logs/suo/msg02427.html
> http://ltsc.ieee.org/logs/suo/msg02429.html
>
> > and I am not capable of extending Rosen's arguments in favor of looking at CT,
> > but there certainly are others who have seen the relationship between CT and
> > knowledge modeling. Indeed, Barwise and others brought it into their work.
> > My friend Howard Liu
>
> The one in Chambana?
>
> > and I have been discussing ways to map Peirce's thinking into a CT framework,
> > perhaps through extensions to John Sowa's work. Our primary link to Peirce
> > has been through discussions with Mary Keeler, coupled with your writing.
> >
> > Extending that field of thinking may not be appropriate to the SUO list.
> > Perhaps it warrants a separate venue?
>
> When it comes to changing the venue:
> If you build it, this one will come,
> Till then this looks like the place!
I will go where the Wild Michi-Gander goes, of course,
but I believe that these topological topics are very
critical to the success of our efforts in these fora,
and so I will try a while longer to demonstrate how.
Mathematicians are as lacking in historical consciousness
as most folks can be, but those brave souls who do manage
to master their own recursèd horrors of drowning in their
own "horror of history" (HOH) will most likely be able to
inform you that the concepts of "category" and "manifold",
as used in their current and continuing argosies of argot,
come straight -- well, moderately straight! -- out of the
precursory and prolegomenal problematics of Aristotle and
Kant, and there are specific reasons for their provenance
that we would do well to recognize in these fora, even as
we strive to recreate ourselves here in re-creating a lot
of what was developed in 19th Century mathematics, if but
slightly transmuted with epistemological and ontological
nuances. But that yarn will have to be the carding and
the spinning and the weaving of yet another looming day.
Many Regards,
Jon Awbrey
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