Dear Stephen,

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> We can go on and on about relations between states, numbers, UDs, or
> whatever, but unless we have a consistent way to deal with the source
> of
> individuation and thus distinguishability, we are going nowhere...
The source of individuation could be personal memory I think. Like a
sequence of W and M appears in the diary of someone subjected to an
iterated WM-self-multiplication experiment. Memory is rather easy to
define once we assume comp. The main difficulty here is to get an idea
of what "personal" means, and for this we need a theory of
self-reference, ... and that is what the diagonalization posts are all
about.
***
Concerning Pratt's dualism, it seems to me it is a purely mathematical
dualism a priori coherent with number platonism, although further
studies could refute this. Open problem. I don't see Pratt reifying
either primary matter or primary time, it seems to me.
I think a similar dualism appears in Plotinus cosmogony where
(simplifying a lot!) *from outside* the Good transforms itself
degenerating eventually into Evil (also called Matter by the
(neo)platonist!) and by doing so makes the soul falling inexorably in
that matter) and *from inside* all souls extract themselves from that
matter and are inexorably attracted by the Good and converge toward it.
Arrows are reversed. And with comp it can be argued that the choice of
the Categories of sets and its dual (which funnily enough gives the
category of boolean algebras) is a genuine one, although some
quasi-constructive alpha-categories could fit in a still more better
way (I think). But I have neither the time nor the competence to really
develop such approaches. Also, finding good notion of coherence here
seems to me to be a little bit ad hoc so that I refer to you the the
comp derivation path of those coherence conditions.
Bruno
http://iridia.ulb.ac.be/~marchal/
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