On 21 Feb 2011, at 13:26, benjayk wrote:
Bruno Marchal wrote:
On 20 Feb 2011, at 00:39, benjayk wrote:
Bruno Marchal wrote:
Isn't it enough to say everything that we *could* describe
in mathematics exists "in platonia"?
The problem is that we can describe much more things than the one
we
are able to show consistent, so if you allow what we could describe
you take too much. If you define Platonia by all consistent things,
you get something inconsistent due to paradox similar to Russell
paradox or St-Thomas paradox with omniscience and omnipotence.
Why can inconsistent descriptions not refer to an existing object?
The easy way is to assume inconsistent descriptions are merely an
arbitrary
combination of symbols that fail to describe something in particular
and
thus have only the "content" that every utterance has by virtue of
being
uttered: There exists ... (something).
So they don't add anything to platonia because they merely assert
the
existence of existence, which leaves platonia as described by
consistent
theories.
I think the paradox is a linguistic paradox and it poses really no
problem.
Ultimately all descriptions refer to an existing object, but some
are too
broad or "explosive" or vague to be of any (formal) use.
I may describe a system that is equal to standard arithmetics but
also has
1=2 as an axiom. This makes it useless practically (or so I
guess...) but it
may still be interpreted in a way that it makes sense. 1=2 may mean
that
there is 1 object that is 2 two objects, so it simply asserts the
existence
of the one number "two".
But what is two if 2 = 1. I can no more have clue of what you mean.
Two is the successor of one. You obviously now what that means.
So keep this meaning and reconcile it with 2=1.
You might get the meaning "two is the one (number) that is the
succesor of
one". Or "one (number) is the successor of two". In essence it
expresses
2*...=1*... or 2*X=1*Y.
And it might mean "the succesor of one number is the succesor of the
succesor of one number". or 2+...=1+... or 2+X=1+Y.
The reason that it is not a good idea to define 2=1 is because it
doesn't
express something that can't be expressed in standard arithmetic,
but it
makes everything much more confusing and redundant. In mathematics
we want
to be precise as possible so it's good rule to always have to
specifiy which
quantity we talk about, so that we avoid talking about something -
that is
one thing - that is something - that is two things - but rather talk
about
one thing and two things directly; because it is already clear that
two
things are a thing.
OK.
Bruno Marchal wrote:
Now, just recall that "Platonia" is based on classical logic where
the
falsity f, or 0 = 1, entails all proposition. So if you insist to say
that 0 = 1, I will soon prove that you owe to me A billions of
dollars, and that you should prepare the check.
You could prove that, but what is really meant by that is another
question.
It may simply mean "I want to play a joke on you".
All statements are open to interpretation, I don't think we can
avoid that
entirely. We are ususally more interested in the statements that are
less
vague, but vague or crazy statements are still valid on some level
(even
though often on an very boring, because trivial, level; like saying
"S afs
fdsLfs", which is just expressing that something exists).
We formalize things, or make them as formal as possible, when we
search where we disagree, or when we want to find a mistake. The idea
of making things formal, like in first order logic, is to be able to
follow a derivation or an argument in a way which does not depend on
any interpretation, other than the procedural inference rule.
Bruno Marchal wrote:
3=7 may mean that there are 3 objects that are 7
objects which might be interpreted as aserting the existence of (for
example) 7*1, 7*2 and 7*3.
Logicians and mathematicians are more simple minded than that, and it
does not always help to be understood.
If you allow circles with edges, and triangles with four sides in
Platonia, we will loose any hope of understanding each other.
I don't think we have "disallow" circles with edges, and triangles
with four
sides; it is enough if we keep in mind that it is useful to use
words in a
sense that is commonly understood.
That is why I limit myself for the TOE to natural numbers and their
addition and multiplication.
The reason is that it is enough, by comp, and nobody (except perhaps
some philosophers) have any problem with that.
I think it is a bit authoritarian to disallow some statements as
truth.
I feel it is better to think of truth as everything describable or
experiencable; and then we differ between truth as non-falsehood and
the
trivial truth of falsehoods.
It avoids that we have to fight wars between truth and falsehood.
Truth
swallows everything up. If somebody says something ridiculous like
"All non
christian people go to hell.", we acknowledge that expresses some
truth
about what he feels and believes, instead of only seeing that what
he says
is false.
This is a diplomatic error. Doing that will end up with everyone doing
war to you. It is far too much "politically correct'.
Of course, when someone genuinely says that all "non christian people
go to hell", there are many possible "truth" behind the statement,
like "F..ck the atheists", "F..ck the agnostics", "I hate you", "you
have to obey to what I say", "You don't belong to my club", etc.
On the contrary, when you want to make a point, especially a new one,
it is far better to respect the truth of your opponents, but then you
have to distill what you and your opponent agree on. In science this
works very well in theory (in practice we have often the obligation to
wait that the opponent dies).
I believe the only way we can learn to understand each other is if we
acknowledge the truth in every utterance.
That is extreme relativism, and makes truth so trivial that it lost
its meaning. On the contrary I think that once we truly love or
respect someone, we are able to tell him "no", or "I disagree", or
"you are wrong".
There is absolutely no shame in being wrong. The shame is when someone
knows that he/she is wrong, but for reason of proud or notoriety, is
unable to admit it.
Bruno Marchal wrote:
I don't think the omnipotence paradox is problematic, also. It
simply shows
that omnipotence is nothing that can be properly conceived of using
classical logic. We may assume omnipotence and non-omnipotence are
compatible; omnipotence encompasses non-omnipotence and is on some
level
equivalent to it.
For example: The omnipotent God can make a stone that is too heavy
for him
to lift, because God can manifest as a person (that's still God, but
an
non-omnipotent omnipotent one) that cannot lift the stone.
That makes the term "omnipotent" trivial. You can quickly be lead to
give any meaning to any sentence.
Well I think this makes sense on some level. Language is symbols
that are
interpreted. There is no absolute rule how to interpret them, so we
*can*
interpret everything in it (but we don't have to!).
We can do poetry. But if you allow this practice in science (including
theology) you will just prevent progresses.
Language are interpreted plausibly by universal machine (brains,
bodies). The interpretation have to follow constraints to be sensical.
In most cases it is most useful to interpret some quite specific
meaning
into a sentence (if you don't want to act madly), but as we use more
broad
and vague terms there are more and more ways to interpret what is
said.
I think that humans suffering is in great part due to a feeling that
in religion and in human affair we have to let people believe in what
they want to believe. We just tolerate superstition.
So in this case omnipotency is trivial. It might just be open for
too many
interpretations to say anything really useful.
Yes.
Bruno Marchal wrote:
Did you confess that you killed your wife? yes, sure, but by "I
killed
my wife" I was meaning that "I love eggs on a plate".
This will not help when discussing fundamental issues.
Right, but I am not saying we *should* talk in a way that is
impossible for
others to understand.
OK. Now, in complex matter, like "is there something after life", even
when people agree on many things, the subject is so much difficult and
so much emotional, that it is part of the problem to be understood, or
even just heard.
We should talk as clearly as possible.
That is the point.
For this reason
saying 1=2 or "I killed my wife" while meaning that "I love eggs on
a plate"
is mostly not a good idea.
OK.
But that it is impractical to speak in a in an incomprehensible way
can be
reconciled with that it still makes sense on some level.
Of course. But that is the reason that we should avoid going to that
level. If you approach that level, you can please everyone for a time,
but soon enough, everyone will disagree and feel betrayed.
Bruno Marchal wrote:
Bruno Marchal wrote:
Bruno Marchal wrote:
Like in Plotinus, the ultimate being (arithmetical platonia) is
not a
being
itself (nor is matter!).
Could you explain what you mean with that?
Platonia, the platonia of Plato, is the Noûs, [...]
Many thanks for your effort to explain this to me. :)
Honestly your non-technical explanation is a bit vague for me and
your
technical explanation is simply way to technical for me. Some things
seem to
make sense, but overall it's still quite mysterious to me.
Frankly I am a bit afraid to ask questions concerning your technical
explanation, because I'm not sure if you can answer them succintly
or
whether I understand your explanations and I don't want you to waste
your
time explaining it to me in great detail and then still be not much
more
smarter.
There are good book on self)-reference, but they need some
familiarity
in mathematical logic. An excellent book on Logic is the book by
Elliot Mendelson, another one is by Boolos, Jeffrey and Burgess.
Thanks. :) I will consider buying one of them.
I think that the last edition of Mendelson book might be the best. It
does ask for a lot of work.
In logic beginners take a lot of time to understand the beginning. The
reason is that in logic you have to understand that you have to NOT
understand what you talk about. And at the beginning things are so
easy that you do understand them, but then it is too almost to late
for understanding how to not understand them. That difficulty is made
easy with computer science, where your "non-understanding" is replaced
by the "obvious" lack of understanding of the machine.
Bruno Marchal wrote:
Maybe I will try searching some terms that I don't understand (or
that I
don't understand the context of) on the list or in the web.
You will find the best and the worst. Podnieks' page is not too bad.
http://www.ltn.lv/~podnieks/
It looks interesting, though a bit disorganized.
Yes, and for logic this might be a problem.
Bruno Marchal wrote:
A have a few questions regarding the non-technical part of
explanation,
though:
What does it mean that the soul falls, falls from what?
From Heaven. From Platonia. From the harmonic static state of the
universal consciousness to the state with death and taxes.
How come that we don't have memories of falling from heaven?
Plotinus begins his treatise by that very question (at least in the
Porphyry's assemblage).
It is a very good question. The 'official' answer is that we ate the
fruit of knowledge and God was pissed of.
Some people do, or at least pretend they do have memories of heaven,
or sometimes hell. They usually get such memories either 'naturally',
or after an extreme conditions (like with Near Death Experience), or
after ingesting some mind altering substance.
The case of salvia divinorum is particularly interesting with respect
to your question. Many experiencers get a distinct feeling that they
got information that they are not supposed to know, or to memorize,
and still less to make public.
Sometimes they got the understanding of the reason why it makes no
sense to 'come back' on earth, with such information, or worse to
propagate it. It is apparent in the following video which shows
(plausibly) a breakthrough, during which the person remains able to
speak, somehow:
http://www.youtube.com/watch?v=YsRML9wa9yc
Note at 3:30 ("I can't tell")
Then she remembers that she "was doing drug", and tries again to tell,
but eventually (the 'hallucination' is too strong) and says only
"nothing" with a smile, at 3:38. Then "I can't tell you about it" at
3:49. But she can talk about the other side. Coming back, in the
intermediate state, she dares to say a bit more.
This is very common with the salvia experience. You get the feeling of
retrieving a secret information that you are not, in this life,
supposed to know, still less to communicate.
You are not supposed to remember "heaven", because ..., well, because
if comp is correct, that kind of information belongs to G* minus G. It
is true but unbelievable, incommunicable. So, to make them public,
makes no sense. Those who knows, already knows, and those who does not
know, will not understand. If they are "sane", they will burn you
alive or send you to an asylum, and if they are mad or wounded, they
will call you a god, and repeat what you say, without any
understanding, during centuries, and eventually lead people even more
far away of what they could have been trying to say.
It is the paradox of enlightenment: it has no direct use here at all.
It might have an indirect role, because it might make you more happy,
especially in dramatic circumstances, and you might become cooler with
the others. It is a state which can have some evolutionary purpose,
also, making someone able to fight back in hard circumstances, like
wars, conflicts, ...
The 'falling from heaven' can also be related to the discovery, made
by the initially happy children, of the 'real life', when they have to
find a job, and get the first taxes, and death (of friends). Like in
the Buddha legend/story.
For some people, heaven is just a reminiscence of the state you were
in, when in the womb of your mother. Any idea of heaven can be a
mourning of that state. Many psycho-analytical 'explanation' can be
found. A frequent error here consists in believing that such type of
explanations are all incompatible with each other (the mystical, the
psycho-analytical, the mathematical, the physical, the biblical), but
that relies on reductionist interpretations of them.
Many dismiss the mystical experience as 'just' a brain neuronal firing.
Of course, such a dismiss would also be a brain neuronal firing, and
to reduce knowledge to such firing makes no sense at all.It is a self-
defeating idea. It is as absurd as saying that the theory of
relativity is only but ink on paper.
Bruno Marchal wrote:
How can the One / matter be outside of existence? I have no clue
what this
could mean. Is the "outside" of existence not existence as well?
It is a bit like in most set theories, the set of all sets is not a
set. For example usually the set of all subsets of a set is bigger
than the set itself, and if the collection of all sets is a set, then
the set of the subsets of the set of all sets is bigger than the set
of all sets.
This makes sense, since there might be something outside of sets.
But existence seems to be all-encompassing. What would the One be,
if not
existent? It isn't non-existent, surely?
You can say that. The idea is that the ONE is all encompassing, and
that there might be difficulties to consider it as an object inside
itself. It is more easily conceived, as a sort of recipient of all
beings. But some will say that this is an image to give a glimpse of
what we just cannot conceive at all.
Bruno Marchal wrote:
God cannot create itself, in most conception of Gods.
Because he already is himself, right?
Yes. Same idea as above.
Bruno Marchal wrote:
Is the one conscious? What you write seems to imply it is (eg "the
ONE and
the Divine Intellect are overwhelmed by the Universal Soul,"), but I
thought
only the universal soul can experience?
I thought that too, but my mind evolves on this. Plotinus is himself
full of doubts on that question. I really don't know. I would still
say that the ONE is not a person, but I am less sure. Technically,
any
set of sentences defined a canonical believer/person, which is the
one
believing exactly those sentences. And what is sure is that it is not
a Löbian person, so what is is? There is a need of a 'truth theory"
or
meta-truth-theory, but none in the literature, a part of Tarski
theory, satisfies me, in the comp setting.
Okay, I probably imagined that there is clearer picture of the ONE
or the
universal soul is.
With the comp hyp. I do show that there is a reasonably clear picture
(assuming you read a bit of book on logic, to be sure). Of course,
being clear makes it debatable, but that's the goal.
The ONE, there, is arithmetical truth (the set of all true
arithmetical sentences), and the soul is the conjunction of
(machine's) provability and truth. That defines a first person knower,
in a manner which uses the concept of truth without giving it a name.
And this shows that by accepting comp, we can already listen to the
machine. It illustrates that the singularity point is in the past. We
are just too much sleepy, and too much feeling superior to realize it.
The soul of the machine is already falling!
Bruno Marchal wrote:
Why does
the one let matter eminate at all then?
Matter is defined by what God cannot control. It is the border of
God.
God is not so much powerful in Neoplatonism. The idea that God is
omnipotent has been added by the Christians, I think. God is good,
sure (in Plato, Plotinus), but, well, he does its possible but he is
limited, notably by logic and mathematics.
Does god ever had control?
Yes, and no. Terms like "god" and "control" are very large. The god of
plato is just truth. The truth we search, not the one we might found.
You can give sense to the idea that such a "truth" controls
everything, or ... nothing.
Control seems only possible if we can make sense
of the future or of consequences, but since God is the source of
both future
and consequences, he's more like bomb.
Yes, even with a static explosion/implosion, or emanation/conversion.
That's common among the monist, time is part of the 'illusion'.
God is limited by logic and mathematics? This seems strange since
the ONE is
that which everything emanates of, which seems to mean God is the
source of
all limitations - and how could this be if God is already limited?
God is beyond the intelligible existence (being), but as far as we
dare to mention "It", it is both the source of everything which exist,
and the source of its own limitation. Humans did give all power to
God, as a manner to give all power to the religious authorities. Give
me money or you will go to hell (easy!).
But there is a difficulty about the ONE, which admits a solution in
the comp frame. No machine can give a name to the ONE, or God, etc.
So no machine can be aware in any sense that "God is limited". Now, a
machine M1 can study the complete theology (with the ONE becoming the
truth about the machine) of a much simpler machine M2 than itself, and
THEN, such a machine M1 can lift that M1's theology, or its logical
structure, for herself, but can do so only in the interrogative way,
and by hoping or praying or betting on her own "correctness". This is
necessarily a risky enterprise, especially in moving and changing
worlds. This is also a reason for being as clear as possible, with the
drawback that it will look provocative, because Truth (God) is
provocative itself.
The study of 'machine's theology' is close to a Near Inconsistency
Adventure.
Bruno
http://iridia.ulb.ac.be/~marchal/
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