Category Theory as a Philosphical Tool

Posted by sol on October 03, 2003 at 04:51:57:

In Reply to: Re: Srinivasa Ramanujan posted by DickT on September 13, 2003 at 07:17:46:

Dickt,

Just wanted you to know that there has been lot of reorganzation going on in my life, so I have decided to withdraw from other forums, and superstring will be my last sort of kick at study and research, with regard to the superstring issue and some of my philosphical bend on things.

Loop Quantum in physics forum asked me this question. "how do you use category theory to see that physics is philosophicaly rendered"

For instance, Ellerman 1987 has tried to show that category theory constitutes a theory of universals which has properties radically different from set theory considered as a theory of universals. If we move from universals to concepts in general, we can see how category theory could be useful even in cognitive science. Indeed, Macnamara and Reyes have already tried to use categorical logic to provide a different logic of reference. (See, for instance, Macnamara & Reyes 1994.) McLarty, Marquis and Awodey have tried to show how it sheds an interesting light on structuralists approach to mathematical knowledge.

Thus, category theory is philosophically relevant in many ways and which will undoubtedly have to be taken into account in the years to come.

The importance of encapsulating the geoemtries seems to me to be a important aspect of describng the physics of? For instance, how do we describe something like plasma that is very dynamcal in its movement and we have to resort to the complexity issues of dynamical movement in consideration.

For me here I see, where bubble movements can also be very dynamic, and might help in the understanding of points(metric considerations) in how we would interpret quantum gravity on a scale issue?

I do not want to get to complex here but do you see the position I am taking here, and is it not most appropriate? I would in using scale(gravity field) then, in the consideration of the geometries, see how such a correlation might have taken place. Geometrodynamics would be a issue inclusive, in lets say the undertanding of Supergravity?

Higher geometries, and the roads leading too, help us to orientate a view of the movement. Shape of Space? and Pianowow asks and relates his perspective. But from the undertsnading of this post, do you see how gravity and its dynamical relationship to the fields have taken over, with considertaion to metric points considerations(Gaussian coordinates). Is this not a valid approach philosphically and important to the dynamics of our own brain functions?

How thought manifestation, reproduces dynamics, such as the issues we talk about in our momentum and position, of thinking? You are, what you think?:)

Sol

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Follow Ups: (Reload page to see most recent)

• Re: Category Theory as a Philosphical Tool -- DickT 10/03/03 (1)
  • Re: Category Theory as a Philosphical Tool -- sol 10/03/03 (0)
• Re: Category Theory as a Philosphical Tool -- sol 10/03/03 (3)
  • Is Mathematics Created or Invented? -- sol 10/03/03 (2)
    • Developing Intuitiveness in Geometry? -- sol 10/03/03 (1)
      • The Shadows of Things -- sol 10/03/03 (0)

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