On 08 Jun 2015, at 20:50, Terren Suydam wrote:
On Mon, Jun 8, 2015 at 2:20 PM, Bruno Marchal <[email protected]>
wrote:
On 08 Jun 2015, at 15:58, Terren Suydam wrote:
On Thu, Jun 4, 2015 at 1:59 PM, Bruno Marchal <[email protected]>
wrote:
On 04 Jun 2015, at 18:01, Terren Suydam wrote:
OK, so given a certain interpretation, some scholars added two
hypostases to the original three.
It is very natural to do. The ennead VI.1 describes the three
"initial hypostases", and the subject of what is matter, notably the
intelligible matter and the sensible matter, is the subject of the
ennead II.4.
It is a simplification of vocabulary, more than another
interpretation.
Then, it appears that you make a third interpretation by splitting
the intellect, and the two matters.
What justifies these splits?
I am not sure I understand? Plotinus splits them too, as they are
different subject matter. The "intellect" is the nous, the worlds of
idea, and here the world of what the machine can prove (seen by her,
and by God: G and G*).
But matter is what you can predict with the FPI, and so it is a
different notion, and likewise, in Plotinus, matter is given by a
platonist rereading of Aristotle theory of indetermination. This is
done in the ennead II-4.
Why should we not split intellect and matter, which in appearance
are very different, and the problem is more in consistently relating
them. If we don't distinguish them, we cannot explain the problem of
relating them.
Sorry, my question was ambiguous. What I mean is that after adding
the two hypostases for the two "matters", you have five hypostases,
the initial three plus the two for matter.
Then, you arrive at 8 hypostases by splitting the intellect into
two, and you do the same for each of the matter hyspostases. My
question is what plain-language rationale justifies creating these
three extra hypostases? And can we really say we're still talking
about Plotinus's hypostases at this point?
We can, as nobody could pretend to have the right intepretation of
Plotinus. In fact that very question has been addressed to Plotinus's
interpretation of Plato.
Now, it would be necessary to quote large passage of Plotinus to
explain why indeed, even without comp, the "two matters" (the
intelligible et the sensible one) are arguably sort of hypostases,
even in the mind of Plotionus, but as a platonist, he is forced to
consider them degenerate and belonging to the realm where God loses
control, making matter a quasi synonym of evil (!).
The primary hypostase are the three one on the top right of this
diagram (T, for truth, G* and S4Grz)
T
G G*
S4Grz
Z Z*
X X*
Making Z, Z*, X, X* into hypostases homogenizes nicely Plotinus
presentation, and put a lot of pieces of the platonist puzzle into
place. It makes other passage of Plotinus completely natural.
Note that for getting the material aspect of the (degenerate,
secondary) hypostases, we still need to make comp explicit, by
restricting the arithmetical intepretation of the modal logics on the
sigma-& (UD-accessible) propositions (leading to the logic (below G1
and G1*) S4Grz1, Z1*, X1*, where the quantum quantization appears.
The plain language rational is that both in Plotinus, (according to
some passage----this is accepted by many scholars too) and in the
universal machine mind, UDA show that psychology, theology, even
biology, are obtained by intensional (modal) variant of the intellect
and the ONE.
By incompleteness, provability is of the type "belief". We lost
"knowledge" here, we don't have []p -> p in G.
This makes knowledge emulable, and meta-definable, in the language of
the machine, by the Theaetetus method: [1]p = []p & p.
UDA justifies for matter: []p & <>t (cf the coffee modification of the
step 3: a physical certainty remains true in all consistent
continuations ([]p), and such continuation exist (<>t). It is the
Timaeus "bastard calculus", referred to by Plotinus in his two-matters
chapter (ennead II-6).
Sensible matter is just a reapplication of the theaetetus, on
intelligible matter.
I hope this helps, ask anything.
Bruno
Terren
And can you make this justification in plain language in a way that
doesn't appear to be a "just so" interpretation that makes it
easier for AUDA to go through?
God, or the One, is played by the notion of Arithmetical Truth.
Machines and humans cannot know it, or explore it "mechanically",
and it is the roots of the web of machines dreams, but also of their
semantics, in a large part.
The Nous, is what machine can prove about themselves, and their
remation with God, etc.
The Soul, is where the machine proves true things, but not
accidentally: as it is defined by the conjunction of p and the
provability of p, for any (arithmetical) p. It is the idea of
Theaetetus, that Plotinus might use implicitly (according to
Bréhier), and which just works: it give a logic of an unameable, non-
machine, knower.
For matter; you want that the "measure one" for an event/proposition
is certain, when it is true in all consistent continuation (this
asks for []p, technically), but also, by incompleteness, this asks
fro the diamond <>t (consistency, having a model, having at least
one continuation, not belonging to a cul-de-sac world (all those
things are mathematically equivalent in our setting). So prediction
1 (like the coffee-cup in the WM-duplication + promise of coffee
made at both reconstitution place) would be []coffee & <>coffee.
There is a coffee in all my extensions, and there is at least one
extension (the act of faith made explicit).
So the logic of physical "yes" is given by []p & <>t, with p sigma_1
(to get the restriction on the universal dovetailing). That
corresponds to Plotinus theory of the intelligible matter, and that
gives a pair of "quantum logic" (by applying a result of Goldblatt).
The same with the sensible matter, where we replay the original idea
of Theatetus, on intelligible matter.
Actually, we get also a quantum logic with the first application of
the Theaetetus, which put some light perhaps why Plotinus ascribe
the roots of matter already to the soul activity. I thought at first
that arithmetic would refute that idea of Plotinus, but the math
confirms this.
I will have to go, and will be slowed down more and more, as I have
the June exams now. Feel free to ask any question though. But you
might need to be patient for the comment/answers.
Bruno
Terren
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