On 23 Feb 2009, at 02:21, Günther Greindl wrote:
> Hi Stathis, Bruno, List,
>>> the copy can be you in deeper and deeper senses (roughly speaking up
>>> to the unspeakable "you = ONE").
>>> I talk here on the first person "you". It is infinite and
>>> Here computer science can makes those term (like "unnameable") much
>>> more precise.
>> I don't see how the copy could be me in a deeper sense than having
>> my thoughts, memories etc. It would be like saying that if I wave my
>> magic wand over you you will become specially blessed, even though
>> nothing will actually change either subjectively or objectively.
> You must take into account Bruno's Plotinian interpretation: the One,
> the Intellect, and the Universal Soul. In this sense, you can become
> more "you" in that you penetrate false knowledge "Maya" and realize
> true nature (the Dao, if you like, roughly the ONE in Plotinus).
I would say the Universal Soul. To be the ONE? The difficulty is that
Plotinus is not always clear. Obvioulsy he did not dispose of an
arithmetical interpretation. Formidably enough he is aware that
numbers can play a big role there, like most neoplatonists.
The "universal soul" hypostase *is* a first person (or a theory about
a first person). Some would say it is just an "abstract person". That
it is just the least common part of all souls, or in the arithmetical
"toy" theology, that is the common part of all first persons
corresponding to the ideally correct machines. But (with comp) we can
make the point that such a person *is* conscious.
A sort of confirmation is given by the thought of some mystic
(Plotinus, Ibn Arabi, ...), but also from experience reports of those
who experiments with Salvia Divinorum, which makes possible to have a
total amnesia (forgetting not just who you are, but that you are, +
forgetting everything up to the idea of time and space), yet remaining
conscious, if not being even much more conscious with the feeling that
memories are making you less conscious, and that a memory-brain is a
filter on histories. Stable memories differentiate consciousness.
A problem for comp is that, well at least I have thought that comp
makes the soul (the first person, the third hypostase) conscious only
through its building or generating time. But the salvia reports and my
own experiences make me think I could be wrong there.
> What I have come to wonder: you take the Löbian Machine to be the
> of a person - say, a human. But what if the Löbian Machine is actually
> (and only) the ultimate person - the universal soul, in Plotinus'
OK. It is the ultimate person, but also the initial person.It is a
baby god. The one who has to fall from truth to be able to go back to
truth, but then the impossible marriage between just addition and
multiplication explains (assuming we are digital) why we can lost our
selves in an infinitely complex labyrinth of realities.
> This would account for the infinite (continuum!) histories (lived
> through the lives of all beings in the multiverse), the "universal
> forgetting itself in a cosmic play, sort of - but also for COMP
> immortality - immortal would be the _universal soul_, but not
> necessarily "concrete" persons (as we conceive them, which requires at
> least some continuity of memory etc)
I think you are quite correct. Except I would say "all" first persons
feel themselves always as being concrete (in all situations, OMs,
worlds, ...). Even an amnesic person can feel herself concrete, even
if she forgets the meaning of the word concrete. And see what I said
to Stathis, the point where I don't follow Parfit: we are never 100%
concrete. Concreteness is always relative to a probable history. We
are always "abstract, immaterial" types relatively embedded in
infinitely many types of histories (computations seen from inside).
So, like in Hinduism it seems comp gives the two main form of
immortality: the one when you remember you are the universal soul, and
the one which makes you live again, and again, and again, from
mornings to mornings, from lives to lives, exploring the many
realities. I think this happens when you don't remember you are the
universal soul. That remembering is somewhat paradoxical, and, to be
sure hard to extract from the interview of the universal machine.
It is really an amnesia of an amnesia. Perhaps a forgetful functor in
the category of the models of Lobian machines. I don't *know*!
The incompleteness prevents the consistent machines to ever come back
on earth with the "last" step of that remembering. It does not prevent
the machine to commit that last step, only to come back with the
memory of that step.
Hmmm ... This could look a bit mystical, so I should recall AUDA, for
the benefit of some others.
AUDA in short.
For the correct machine, the incompleteness makes obligatory to have a
"theology", in the sense that she can proves her own incompleteness
theorem and distinguish truth from provability, especially about about
what is true about her, and what is provable about her.
I associate to each (ideally correct ) machine a theology, consisting
in 8 hypostases. The simplest way is provided by the arithmetical
interpretation of Plotinus ( a beautiful sum of 1500 years of rational
mysticism). The richness comes from the machine discovering its own
incompleteness, as far as she is honest or correct about herself.
(meaning "machine says p entails p is true).
Like many Greeks (and non Greeks) there are three gods, or one god
with three aspects (whatever). Plotinus called them "primary
Hypostases". Like Günther reminds you, there are
1)The ONE (the first god)
2)The INTELLIGIBLE (or intellect, the second God)
3)The UNIVERSAL SOUL (the third God)
To call this "primary" hypostases made me called "secondary
hypostases", the two notion of MATTER that Plotinus derives from the
And this makes, when translated into arithmetic or into any universal
machine language eight hypostases. Not five. Indeed, the ONE (of the
machine M) is interpreted by the TRUTH. With comp, or with PA (as
lobian machine), we can take TRUTH as being ARITHMETICAL TRUTH, and
figure it as the set of Gödel numbers of all true arithmetical
1) ONE = TRUTH
The INTELLIGIBLE is interpreted by Gödel Beweisbar predicate. It is
the beliefs of that ideally correct machine (or PA, ZF, ...). By
incompleteness, it splits into two parts. What is true about the
provability, and what is provable (by the machine (PA, ZF, ..) about
that provability. Solovay theorems, in a nutshell, is that the
provable part of the INTELLIGIBLE obeys the modal logic G, and the
true, but not necessarily provable obeys G*. So
2) INTELLIGIBLE (by the machine on earth) = G and
2bis) INTELLIGIBLE (true, or divine, or in heaven) = G*
3) THE UNIVERSAL SOUL, I define it by the knower, and I define the
knower by the "well known and debated" Theaetetical trick: to know p
is defiend by to believe p when p is true. This has already been done
for the Lobian machine (or PA, ...), independently by many people, and
it gives an already studied logic known as S4Grz, it can be sen as
both a temporal logic of an agent building its mind in time, or
directly as a logic of subjective time. So S4Grz is the logic of the
new box [•] with [•]p defined by p & p.
A normal and sane objection could rise here. Given that the machine is
correct, is it not obviously true that p and p & p are equivalent?
Fundamental answer: if the machine is PA, or any sufficietly simple
Lobian machine, so that *you* can believe the machine is correct, then
yes p and p & p are "obviously" equivalent. But, by
incompleteness, such equivalence is not obviously true for the
machine, indeed such equivalence is true but not provable by the
machine. For each p (arithmetical proposition) it is true that "PA
proves p" is equivalent with "(PA proves p) and p", but PA cannot
prove, for any arithmetical proposition that (PA proves p) <-> ((PA
proves p) & p). Indeed if PA could prove that PA would prove (PA
proves false) being equivalent with (PA proves false) and false), that
PA would prove (not provable false), and PA would prove its own
consistency (which is impossible by Gödel's theorem). Put it
differently G* proves p <-> (p & p), but G does not prove it. This
makes the "soul", obeying a different logic from the intelligible.
Indeed the intelligible obeys G (and G*), the soul of the ideally
correct machines obeys S4Grz.
Two remarkable facts: Like truth, by a Tarski (Scott-Montague)
phenomenon; the box [•] cannot be define in the language of the
machine. Even for the machine its "first person" is already not a
machine (not a third person describable reality actually). The second
remarkable fact is that S4Grz = S4GRz*. The soul does not split into a
earth part and a heaven part.
4) INTELLIGIBLE MATTER p & <>p (or p & <>t).
5) SENSIBLE MATTER p & <>p & p (or(( p & p) & <>t).
I have to go. I will say more on the 4 and 5 tomorrow. You could try
to see why we need them to have a measure of credibility or
probability on the consistent extensions (of the ideal machine). Both
will split into an earth part and a heaven part, so we get the eight
hypostases. More in the Plotinus paper, see my url.
Of course the main contribution of Gödel was in showing how we can
translate (PA proves p) into the language of PA. That works for all
Lobian machines (quasi by definition).
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