Hi Kea
Thanks for
http://charlotte.ucsd.edu/users/goguen/pps/nel05.pdf and other links on Peirce above. I see reading from this thread that you have also taken in Hegel.
Your theme for this thread is: The third road says "get the logic right, and you'll see how computational the universe is". And the right logic is category theory – it is a general enough theory of logics to “eat” any more particular ones that may have been suggested in the past such as Peirce’s organic/semiotic/triadic approach.
I still have no feel whatsoever for the substance of category theory despite having read a bit more about it now. Perhaps I can provoke you into some jargon-free explanation which gets at its essence.
I understand set theory is based on collections of crisp, discrete, bounded, located, persistent objects. So “atoms with properties”, a mechanical view in which all action and organisation and systemhood is emergent (thus is does not need to be represented at the most fundamental level – the object and its properties).
Category theory seems to take the correct step in saying, no, reality has both locations and motions, stasis and change, form and substance, local and global – the whole gamut of standard metaphysical dichotomies. So to define a basic something, you need both an object and its actions.
A mechanical view here would say that category theory is just accounting for an object and its properties in more distinct fashion. But a holistic or background-independent view points out that all atoms exist in a void. And the void is a thing with properties. The void has crisp spacetime structure. And even the freedoms that the void permits, such as the inertial motions of particles, are essential properties of the void.
So perhaps a more organic view of category theory is that it breaks reality into its most natural dichotomy - that which is semiotically constrained and that which is semiotically not visible, thus free to happen. An object such as a particle (or a void) is produced by a system of self-constraint acting on a ground of pure potential (Peircean vagueness, Anaximander’s apeiron). A particle gains a crisp identity as all the other things it might be become constricted to near impossibility (in simple terms, a cold and expanded Universe steadily robs an electron of its chances to be a quark or tau, etc). But within every system of constraint there are also emergent freedoms. A crisply made particle (that cannot freely transmute and which now has mass and cannot fly at light speed) can now wander about in an “empty” void with weak gravity, in fairly unconstrained inertial fashion.
Peircean logic – as outlined in that Kauffman paper – is seeking to describe a figure~ground breaking in which both figure (object, or atom) and ground (context, or void) are simultaneously developed. This is indeed a background independent approach – or rather it depends on “vagueness” as the unformed, and insubstantial, ground that then divides to make crisp atoms in a crisp void. Or in category theoretic terms(?), crisp objects and their crisply permitted contextual properties, their various possibilities for action.
Or using x and not-x terminology, we would start in a realm where x-ness and its antithesis are mere unformed possibility (like perhaps order and disorder, atom and void, chance and necessity – absolutely any dichotomy that makes metaphysical sense). Then in creating the crisply not-x, we create the x. Or with equal emphatic-ness, if we create the crisply x, it creates the crisply not-x. As in relativity, the choice of reference frame – “who moved first?” – becomes arbitrary.
I think as you get deeper into Peirce, problems start to arise. For one thing, I don’t think he considers the issue of scale and so his position on hierarchies remains fuzzily developed.
However his semiotic approach as applied to modern physics might read something like this. The Universe has a “mind” – a set of interpretative habits that we know as Newtonian/relativistic mechanics. This generalised mind (a Peircean thirdness) looks into the well of quantum potential (pure vague Peircean firstness) and interprets it into particular physical events or occasions – the classical realm of particles having interactions.
The mind of the Universe never sees a naked quantum realm, only the kinds of events and regularities it has come to expect. This is the famous irreducible triadicity of semiosis. There is the interpreter and the thing in itself. And then the joint production that is the construction of particular signs – particles whizzing about hither an thither in a disinterested void.
Peircean logic contains everything and the kitchen sink. You have the monadic principle of vagueness. You have the dyadic principle of dichotomous separations (or phase transitions or symmetry breakings we might call them). And you have the triadic principle of semiosis (or hierarchical complexity).
Again, what is category theory about at root and does it really map to the whole of Peirce’s organic framework or just perhaps to the dyadic part?
Cheers – John McCrone.
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