On 10 Aug 2012, at 18:45, Brian Tenneson wrote:
Yeah but you can't define what a set is either, so...
The difference, but is there really one?, is that we the notion of set
we can agree on axioms and rules, so that we can discuss independently
on the metaphysical baggage, as you pointed out once. This can be done
both formally, in which case what we really do is an interview of a
machine that we trust, or informally, betting on the human willingness
to reason.
For example, with sets, we can agree on the fact that they are
identified by their elements: the extensionality axiom:
For all x, y, z, if (x belongs to y <-> x belongs to z) then y = z.
We might prefer to work in an intensional set theory, where a set is
defined by their means of construct, and which is more relevant for
the study of machines and processes. But then we do lambda calculus or
elementary topoi, or we work in a variety of combinatory algebra.
But it will not be a disagreement, as we know there can be different
notion of set, and so different tools.
Likewise with consciousness. We might not been able to define it, but
we can agree on principle on it, notably that, assuming comp, it is
invariant for a set of computable transformations, like the lower
level substitutions, and reason from that. We can agree that if X is
conscious, then X cannot justify that through words.
Likewise with God. An informal definition could be that God is
Reality, not necessarily as we observe or experience it but as it is.
We can only hope or bet for such a thing. It might be a physical
universe, or it might be a mathematical universe, or an arithmetical
universe, but with comp it is a "theological universe" in the sense
that comp separates clearly the communicable and the non communicable
part of that reality, if it exists. Life and creativity develop on
that frontier, as it develops also in between equilibrium and non
equilibrium, between computable and non computable, between
controllable and non controllable, etc.
And we can agree on axioms on "GOD", that is "REALITY" or "TRUTH". For
example that it is unique, that we can search on it, that it is not
definable, so that such words are really only meta pointer to it, etc.
The advantage of the definition of GOD by REALITY, or GOD = TRUTH, is
that no honest believers, in any confessions, should have a problem
with it, and for the atheists or the materialist GOD becomes a
material physical universe a bit like 0, 1, and 2 became number when
'number' meant first 'numerous'.
Mathematicians always does that trick, to extend the definition of a
concept so that we simplify the key general statements.
Is GOD a person? That might be an open problem for some, and an open
problem for others. Truth might be subtile: in NeoPlatonism GOD (the
ONE) is not a person, nor a creator, but from it emanates two other
GODS (in the ancient greek sense, Plotinus call them hypostases) the
third one being a person (the universal soul).
For all matter, we need only to agree on semi-axiomatic definition,
the rest is (a bit boring imo) vocabulary discussions. It hides the
real conceptual differences in the attempt to apprehend what is, or
could be.
Bruno
On Fri, Aug 10, 2012 at 2:22 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
Hi Roger,
On 07 Aug 2012, at 11:53, Roger wrote:
Hi Bruno Marchal
OUR FATHER, WHICH ART IN HEAVBEN,
HALLOWED BE THY NAME.
Luther said that to meditate of the sacredness of God
according to this phrase is the oldest prayer.
In old testament times, God's name was considered too sacred to speak
by the Jews. The King James Bible uses YHWH, the Jews never say
"God" as far as I
know, they sometimes write it as G*d.
We have relaxed these constrictions in the protestant tradition,
use Jehovah and all sorts of other sacfed names.
It is the problem with the notions of God, Whole, Truth,
consciousness, etc. we can't define them.
You can sum up Damascius by "one sentence on the ineffable is
already one sentence too much, it can only miss the point". (But
Damascius wrote thousand of pages on this!).
Like Lao Tseu said that the genuine wise man is mute, also. John
Clark said it recently too!
This is actually well explained (which does not mean that the
explanation is correct) by computer science: a universal machine can
look inward and prove things about itself, including that there are
true proposition that she cannot prove as far as she is consistent,
that machine-truth is not expressible, etc. My last paper (in
french) is entitled "la machine mystique" (the mystical machine) and
concerns all the things that a machine might know without being able
to justify it rationally and which might be counter-intuitive from
her own point of view.
The word "god" is not problematical ... as long as we don't take the
word too much seriously. You can say "I search God", but you can't
say "I found God", and still less things like "God told me to tell
you to send me money or you will go to hell".
God is more a project or a hope for an explanation. It cannot be an
explanation itself. For a scientist: it is more a problem than a
solution, like consciousness, for example.
Bruno
Roger , rclo...@verizon.net
8/7/2012 Is life a cause/effect activity ?
If so, what is the cause agent ?
----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-08-07, 05:37:56
Subject: Re: God has no name
Hi Stephen,
On 8/6/2012 8:29 AM, Bruno Marchal wrote:
[SPK] Which is the definition I use. Any one that actually
thinks that God is a person, could be a person, or is the
complement (anti) of such, has truly not thought through the
implications of such.
[BM
For me, and comp, it is an open problem.
[SPK]
? Why? It's not complicated! A person must be, at least,
nameable. A person has always has a name.
[BM]
Why?
Because names are necessary for persistent distinguishability.
OK. You are using "name" in the logician sense of "definite
description". With comp we always have a 3-name, but the first
person have no name.
Let us try an informal proof by contradiction. Consider the case
where it is *not* necessary for a person to have a name. What
means would then exist for one entity to be distinguished from
another?
By the entity itself: no problem (and so this is not a problem for
the personal evaluation of the measure). By some other entity?
We might consider the location of an entity as a proxy for the
purposes of identification, but this will not work because
entities can change location and a list of all of the past
locations of an entity would constitute a name and such is not
allowed in our consideration here.
Sure.
What about the 1p content of an entity, i.e. the private name that
an entity has for itself with in its self-referential beliefs?
It has no such name. "Bp & p", for example, cannot be described in
arithmetic, despite being defined in arithmetical terms. It is like
arithmetical truth, we can't define it in arithmetic language.
Since it is not communicable - as this would make the 1p aspect a
non-first person concern and thus make it vanish - it cannot be a
name. Names are 3p, they are public invariants that form from a
consensus of many entities coming to an agreement, and thus cannot
be determined strictly by 1p content. You might also note that the
anti-foundation axiom is "every graph has a unique decoration".
The decoration is the name! It is the name that allow for non-
ambiguous identification.
A number's name is its meaning invariant symbol representation
class... Consider what would happen to COMP if entities had no
names! Do I need to go any further for you to see the absurdity of
persons (or semi-autonomous entities) not having names?
Say that it is X. There is something that is not that person and
that something must therefore have a different name: not-X. What
is God's name? ... It cannot be named because there is nothing
that it is not! Therefore God cannot be a person. Transcendence
eliminates nameability. The Abrahamist think that Satan is the
anti-God, but that would be a denial of God's transcendence.
There are reasons why Abrahamists do not tolerate logic, this is
one of them.
With comp if God exists it has no name, but I don't see why it
would make it a non person. God is unique, it does not need a name.
God is unique because there is no complement nor alternative to
it. Ambiguously stated: God is the totality of what is necessarily
possible.
That is not bad in a first approximation. With comp, you can make
it precise through the set of Gé°€el numbers of the true
arithmetical sentences. Obviously this is not a computable set, and
it is not nameable by the machine (with comp), making set theory
somehow too rich for comp. Of course, arithmetic contains or
emulates a lot of entities believing in set theory, but we should
not reify those beliefs in the ontology. It is better to keep them
only in the machine epistemology.
On 8/6/2012 10:37 AM, Bruno Marchal wrote:
Is the translation or encoding a unique mapping? How many
possible ways are available to encode B?
There is an infinity of way to encode "B". Some can be just
intensionally equivalent (different codes but same logic), or
extensionally equivalent but not intensionally equivalent, like
Bp and Bp & Dt. They prove the same arithmetical proposition, but
obeys different logic.
OK, do you not see that the infinity of ways that "B" can be
encoded makes the name of "B" ambiguous?
I don't see that at all.
The name of "B" is at most 1p; a private name and thus subject to
Wittgenstein's criticism.
All the names of "B" are third person notion, even if "B" itself
cannot recognize its body or code. It is only "self-ambiguous",
which is partially relevant for the measure problem. This is why I
use modal logic to handle that situation, besides the fact that
incompleteness leaves no real choice in the matter.
The experiences are strictly 1p even if they are the
intersection of an infinity of computations, but this is what
makes then have a zero measure!
Ah?
A finite and semi-closed consensus of 1p's allows for the
construction of diaries and thus for the meaningfulness of
"shared" experiences. But this is exactly what a non-primitive
material world is in my thinking and nothing more. A material
world is merely a synchronized collection of interfaces (aka
synchronized or 'aligned' bisimulations) between the experiences
of the computations. I use the concept of simulations (as
discussed by David Deutsch in his book "The Fabric of Reality") to
quantify the experiences of computations. You use the modal
logical equivalent. I think that we are only having a semantical
disagreement here.
?
The problem that I see in COMP is that if we make numbers (or any
other named yet irreducible entity) as an ontological primitive
makes the measure problem unsolvable because it is not possible to
uniquely name relational schemata of numbers. The anti-foundation
axiom of Azcel - every graph has a unique decoration - is not
possible in your scheme because of the ambiguity of naming that
Godel numbering causes. One always has to jump to a meta-theory to
uniquely name the entities within a given theory (defined as in
Godel's scheme) such that there is a bivalent truth value for the
names. Interestingly, this action looks almost exactly like what
happens in a forcing! So my claim is, now, that at best your step
8 is true in a forced extension.
1004.
On 8/6/2012 10:37 AM, Bruno Marchal wrote:
[SPK] At what level (relative) is the material hypostases?
[BM]
This is ambiguous. The material hypostases (Bp & Dt) defines the
(high) level where machines (the person incarnated by the
machine) can make the observations.
But it is preferable to extracts all those answer by yourself,
for all what I say here needs to be extracted to get the UDA step
by step.
Dear Bruno,
OK, we seem to be in agreement on this. At the "high level"
there is a meaningful notion of observations (and naming as I have
discussed in previous posts) but never at the primitive level.
OK.
My point is that this meaningfulness vanished anywhere outside of
this high level.
I agree.
We cannot pull back the meaning of a term when and if we pull back
the term to the primitive level, because doing so, as you discuss
in step 8,
?
severs the connection that carries the relations that define the
unique name that occurs at the high level. This is the problem of
epiphenomena of immaterialism.
?
On 8/6/2012 10:37 AM, Bruno Marchal wrote:
We cannot use the Godel numbering because they are not unique,
?
If the names (description) were unique, there would be no first
person indeterminacy. A enumerable infinity , non mechanically
enumerable though, of explicit description of Stephen King exists
in arithmetic, if comp is true.
Dear Bruno,
But it does not exist uniquely as a singleton in arithmetic
OK.
and that is the problem.
The interesting problem, yes. That is the point.
It does exist as the equivalence relation on a infinite class of
computations, but these equivalence classes do not have a power-
set of which they are a uniquely defined.
?
Names are only meaningful when and if they are 3p.
Sure.
Bruno
http://iridia.ulb.ac.be/~marchal/
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