Le 28-sept.-06, à 03:32, Russell Standish a écrit :

> I assume by hypostase, you mean the word hypostasis, the plural of
> which is hypostases.

Yes. "Hyposase" is the french for "hypostasis". Sorry.

> My concise Oxford dictionary defines hypostasis as "underlying
> substance", as opposed to attributes which are unsubstantial.

Yes. But the greek means by that "fundamental". They use "substrate" 
for our physicalist notion of "substance".
Many people are confused by that.

> Are you claiming a system of logic (eg G or S4Grz1) is a "substance"?
> And if so, what do you mean by that? I have no conception.

No. G and G* are just (meta)theories about what can prove (and not 
prove) any self-referentially correct universal machine which 
introspects herself.
The "substance" would be the numbers. But it just mean that comp takes 
the notion of (natural or entire) numbers as fundamental. It is 
arithmetical realism.

> The formula p->BDp is your "little abstract Schroedinger equation" is
> it not? So you can now show that S4Grz1 proves the LASE, but also has
> the advantage of having a Kripke frame, so provides a temporal
> structure?

You are almost correct. G has Kripke frames too (the one which 
generalizes the "Papaioannou multiverse" where there are cul-de-sac 
word accessible from any "observer moment"). V and V* too (where V and 
V* are G and G* when we ask explicitly the universal machine to 
postulate comp). G* and V* have "sequence of Kripke Multiverses".
But, and that is what is interesting is that S4Grz have 
temporally-structured class of Kripke frame (Kripke multiverse). And 
the accessibility relation is antisymmetric making it a subjective time 
à-la Heraclite-Bergson-Brouwer-Prigogine manner.
Then S4Grz1 (the soul + the explicit comp assumption) leads to the same 
structure + a symmetry at the bottom. I though that the marriage of 
that symmetry + the time antisymmetry would make the logic collapse, 
but weirdly enough, this does not happen. Technically this gives the 
possibility, thanks to the existence of the "intermediate logics" 
between intuitionist logic and classical logic to figure out an 
arithmetical decoherence effect between quantum intuitionist logic and 
classical logic. But S4Grz1 does not split under the difference between 
G and G* (the soul is both divine and terrestrial apparently). It means 
the soul is too much busy to extend itself that it has not yet the 
power to recognize other souls ... and fall in the intelligible and 
sensible "material" universe.

I borrow the term "hypostasis" from the translators of Plotinus. I find 
it more neutral than "person point of view", and also I have found an 
arithmetical interpretation of Plotinus main terms which conserves all 
its main propositions. That is useful given that Plotinus' assertions, 
like all platonist if not mystical assertions, are counter-intuitive. I 
will try to sum up the arithmetical "hypostases" in informal english. 
Asap. Just now I have students coming ...



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