On 15 Jun 2015, at 15:32, Terren Suydam wrote:
On Sun, Jun 14, 2015 at 10:27 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 08 Jun 2015, at 20:50, Terren Suydam wrote:
On Mon, Jun 8, 2015 at 2:20 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 08 Jun 2015, at 15:58, Terren Suydam wrote:
On Thu, Jun 4, 2015 at 1:59 PM, Bruno Marchal <marc...@ulb.ac.be>
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
I'm not conversant in modal logic, so a lot of that went over my head.
Maybe the problem is here. Modal logic, or even just modal notation
are supposed to make things more easy.
For example, I am used to explain the difference between agnosticism
and beliefs, by using the modality []p, that you can in this context
read as "I believe p". If "~" represents the negation, the old
definition of atheism was []~g (the belief that God does not exist),
and agnosticism is ~[]g (and perhaps ~[]~g too).
The language of modal logic, is the usual language of logic (p & q, p
v q, p -> q, ~p, etc.) + the symbol [], usually read as "it is
necessary" (in the alethic context), or "it is obligatory" (in the
deontic context), or "forever" (in some temporal context), or "It is
known that" (in some epistemic context), or it is asserted by a
machine (in the computer science context), etc...
<>p abbreviates ~[] ~ (possible p = Non necessary that non p).
Thus my request for "plain language" justifications. In spite of
that language barrier I'd like to understand what I can about this
model because it is the basis for your formal argument AUDA and much
of what you've created seems to depend on it.
In AUDA, the theory is elementary arithmetic (Robinson Arithmetic). I
define in that theory the statement PA asserts F, with F an
arithmetical formula. Then RA is used only as the universal system
emulating the conversation that I have with PA.
Everything is derived from the axioms of elementary arithmetic (but I
could have used the combinators, the game of life, etc.). So I don't
create anything. I interview a machine which proves proposition about
itself, and by construction, I limit myself to consistent,
arithmetically sound (lost of the time) machine. This determined all
the hypostases.
It is many years years of work and the hard work has been done by
Gödel, Löb, Grzegorczyck, Boolos, Goldblatt, Solovay.
I still am not clear on why you invent three "new" hypostases,
granting the five from Plotinus (by creating G/G*, X/X*, and Z/Z*
instead of just G, X, and Z),
This is not a choice. G does really split in two: the provable part by
the machine, and the true part on the machine (that the machine can
prove or not). same for Z*, and X*.
But that is the chance, beacuse the notion of Plotinus are
theological, and side with the truth.
In Plato the distinction between Earth and Heaven becomes a
distinction between effective/constructive and True. The Noùs is guven
by G*. G is the "man", or the discursive reasoner, that I take too as
an hypostases, although the man is a bit despise by Plotinus (which is
normal when talking about God, by the Platonists).
except that you say "[it] homogenizes nicely Plotinus presentation,
let us say that the math shows that there are 8 hypostases (roughly
speaking, as it is more like 4 + 4 * Infinity).
Three describes well the three primary hyposates of Plotinus (divine
one!), and two describes what Plotinus called sensible matter, and
intelligible matter, and where the comp quantum logic appears, and
should apper, by the UDA.
But they did split, which is not something we can avoid or hide.
and put a lot of pieces of the platonist puzzle into place."
Symmetry isn't an explanation. What I'm looking for would be
something along the lines of "It makes sense to split the intellect
hypostases into G & G* because ...."), likewise for X, and for Z.
The splitting of G and G* comes from Gödel's theorem. It is the
splitting between what a machine can prove (notably on itself) and
what is true about the machine.
Typical example: "I am consistent", it is the same as "I don't say the
false". For the correct machine, this belongs to G* minus G. It is
true, but the machine cannot prove it.
So it is not "It makes sense to split the intellect hypostases into G
& G* because ....". It is: mathematician believed that a machine as a
provability predicate equivalent with a truth predicate until they
discover that provability and truth are different. Now it is a
mathematical theorem that provability obeys to the modal logic G (and
indeed that G is complete for it), and that the truth on provability
obeys the modal logic G*.
The same for the modal nuances, which existence are themselves
consequences of incompleteness.
All the math part, AUDA, is based on:
- Church's thesis and the discovery of the universal machine
- Gödel technics of translating meta-arithmetic (with notion as
"provable") in arithmetic,
It ought to be possible to justify the hypostases in a non-technical
way.
Read Plotinus, or any mystic remaining rational.
If not, then it strikes me as a weak spot of the argument, even if
the argument is technical.
Let me make a try. UDA is the formulation of the mind-body problem, in
"human term".
AUDA is the translation of UDA in the language of the machine.
Now, I ask the machine "will you believe this or that". What the box
[] represent is the thrid person self of the machine: it is the
explanation of the functioning of the machine, in the language of the
machine, so that I can ask her question about itself. This is a third
person self. []p means that the machine asserts p. To get the first
person I use the Theaetetus method, or variant, and this gives rise to
the horizontal layers in the diagram. The logics are different thanks
(technically) to incompleteness. Then three among the hypostases split
in two, (x and x*) again due to incompleteness.
Tell me if this helps.
In my mind, UDA *is* the layman explanation/argument of AUDA, somehow.
You might just miss a detail. []p means only the machine asserts that
p. I use the Dennett intentional stance. A machine believes p when the
machine asserts p. This is enough, as we limit ourself to ideally
correct machine.
(I guess you were not on the list when I explained a bit of the modal
logic, and its relation with incompleteness). I can explain more (but
not in June as I am busy).
Bruno
Terren
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