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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rob Freeman" <lists@xxxxxxxxxxxxxxxxxxx>
Date: Sat, 27 Sep 2008 14:31:30 +0800
Message-id: <7616afbc0809262331m51113203t2bc2c51ff2052098@xxxxxxxxxxxxxx>
Pat and Azamat: Thanks for your comments.    (01)

Pat: What suggested to me there might be a relationship between gauge
theories in physics, Category Theory in maths, and semantics is their
common preoccupation with indeterminacy.    (02)

Rick: Thanks for those Category Theory/semantics refs. Great! I hadn't
come across Goguen's work. You haven't seen anything relating Category
Theory with geometric theories in physics have you?    (03)

Once again, of the three: probabilistic/random, geometric, and
many-body, I prefer the many-body approach. Prob./random etc,
geometric models just say things are indeterminate (and reason on that
basis?), the many-body approach presents an explanation why things are
indeterminate.    (04)

-Rob    (05)

On Sun, Sep 21, 2008 at 6:05 AM, Pat Hayes <phayes@xxxxxxx> wrote:
> On Sep 20, 2008, at 8:47 AM, Rob Freeman wrote:
>> I would welcome comments on a possible relationship between gauge
>> theories in physics, Category Theory in maths, and semantics.
> Well, you did ask. These three topics have absolutely nothing whatever
> to do with one another. Gauge theories focus on symmetries in physical
> theory: that is, ways in which theories are invariant under various
> mathematical transformations. Category theory is a branch of pure
> mathematics, a kind of ultimate abstraction of algebra, which focusses
> on systems ('categories') defined by mappings . Semantics is concerned
> with the relationship between representations and what it is that they
> represent. One might as well ask for comments on a possible
> relationship between botany, music and gardening.
> Let me ask in return, what was it that  suggested to you that these
> three topics might have any relationship?
> Pat    (06)

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