Sign Relational Manifolds • Discussi on

• http://inquiryintoinquiry.com/2012/10/22/sign-relational-manifolds-1/
• http://inquiryintoinquiry.com/2012/10/22/sign-relational-manifolds-2/

JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/8850
JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/8854
JC: http://permalink.gmane.org/gmane.science.philosophy.peirce/8861

JC: Why restrict yourself to Differential Geometry?

JC: Category theory is more appropriate for computation
     as a general syntax for engineering and for variety,
     isn't it?

JC: Why restrict your thinking to geometry when a more general
     semantics is absolutely essential to engineering pragmatically?

JC: I seek to find coherence among your various and very extensive writings.
     Thus far, I failed.

Jerry,

There is no restriction implied.  Category theory is one of those resources,
supports, or tools that is used throughout mathematics today, and so it has
its application here, not only in the development of differential geometry,
but in my efforts to develop the analogous subject of differential logic.
Indeed, one of the first major subgoals that came up in my work on that
was to find the fitting logical analogue of a “tangent functor”, the
category-theoretic generalization of the “differential” in geometry.

I will say more about how this connects to Peirce, inquiry, semiotics,
and triadic relations as we go, but I still have a bunch of old notes
to excavate from the web before I can do that.

Meanwhile, here is one of my slightly more coherent expositions
in this general area:

http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0

Regards,

Jon

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