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.
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.
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 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.
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.
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.
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/
Or perhaps it
well help when I learn logic at the university, though I guess it
will be
not so much in depth.
It depends on many things.
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.
It is hard for me to explain the sense of Plotinus, which itself is
discussed by many scholars, and in different terms according to their
own inclinations. But I did provide an arithmetical translation, and
there I can be more precise. Eventually in that translation all is
reduced to number relations. Of the theological statement will
correspond to non recursive (and highly so) arithmetical statements,
or complex structured set of arithmetical statements.
Why is matter evil?
Platonist doesn' like matter. It is an illusion which can hurt you.
Because it is not perfect as platonia is?
Platonia was inspired by the idea that mathematics described indeed
perfect object, and that imperfection is part of the rudeness of
Earth. Today we know that Platonia itself is not perfect, but the
neoplatonist comes to intuit this too.
As it provides
a field were truth can manifest itself, it seems like this is a good
thing
for the soul to learn to know itself, even if some aspect of matter
are bad.
I don't take seriously the Platonist demonization of matter, but I can
relate a bit to it too.
The tension between the divine intellect and the soul is the gap
between
truth and believability, right?
More precisely between Bp and Bp & p, that is between belief and
knowledge.
The gap between truth and believability is the gap between me and
'god', and is mainly incompleteness.
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.
God cannot create itself, in most conception of Gods. Again, with "big
things" you can quickly be led to contradiction or triviality. The UD
and UD* are big things which remains non trivial. That is rare in math.
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.
Do you mean it literally that the soul leaves matter at some point?
Matter does not exist, so soul never leaves matter. Souls build matter
when they fall (in Plotinus) by a curious form of contemplation. It is
already of form of extrapolation on the purely indeterminate. Both God
and Matter are defined by negation from intelligible existing things,
like numbers and circles, ...
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. Matter is unavoidable when
souls get free. This provides theological opening on free-will, which
will be taken seriously by Christians, but made a bit contradictory by
God's omnipotence. The free-will problem is really a problem for the
Christians, and probably even more for catholic, with that respect.
But like Grim, I think that 'omnipotence' is a contradictory concept.
Bruno
http://iridia.ulb.ac.be/~marchal/
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