On 09 Sep 2010, at 14:37, Stephen P. King wrote:

Hi Bruno,

        My thought is to look at the transformation group around which some
property is invariant to act as a generator of the properties of the, say,

Good idea. That is related with the importance of group theory and (soon) category theory in physics.

For simple numbers this would be a permutation over fields, one field
per number,

Why? We may have use combinators instead of numbers. Their role are intensional, and representational. Their intrinsic mathematical structure certainly plays some role, but I don't see why to use them directly to mirror physics. Even if that works (by chance) it would hidden the mind-body problem. Of course it might be very interesting, and the relation between physics and number theory suggest that such approach have their merits.

but this seems to not really resolve the question entirely.

I am not sure I have a clear idea of the question, here.

makes me suspicious of the entire Platonic program, for what would act as the universal generator of "twoness" as distinguished from "threeness" be in-itself? Why not some kind of nominalism that transforms asymptotically
into universalism?

You lost me.

You know how I work. I start from an assumption about some link between consciousness and Turing 'machine', and from this I derived step by step a frame which is closer to Plato and Plotinus than to Aristotle, at least on the "Matter" notion.

        BTW, I really enjoyed reading your SIENA paper. My only comment on
it is that I wish you would elaborate more on the diamond^alpha t aspect
because that is where plurality obtains.

Thanks. Actually I think, but I'm still not quite sure, that the "^alpha" feature should explain the graded aspect of the quantum logics, which should explains the origin of the tensor product, of the plurality of dimension, and eventually the (quantum) structure of space-time. The many worlds are more due to the extreme redundancy of the computational histories in arithmetic.



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