On 8/7/2012 5:37 AM, Bruno Marchal wrote:
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.
Dear Bruno,
First I must tell you that however I might get frustrated at your
seeming intransigence, I do appreciate your patience and
thoughtfulness!:-) I am learning a lot from these exchanges. Now to the
content of your reply.
(My ideas are still evolving on this and my postulate of Identity
is still not well formed.) Yes, I see a name as a "definite description"
and I see this as harmonious with my postulate that the best possible
computational simulation of an autonomous system *is* the system itself.
Thus the name of an entity (an autonomous system) is dependent on
autonomy and thus independence from any particular embedding, but this
independence is not separateness in general and this is where we
disagree on Step 8.
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?
What kind of entity might this other one be? We must show that
there exist "other" similar entities and thus at least have to show (in
our explanations and theories) how the "otherness" obtains. This is a
version of the "Other minds" problem
<http://plato.stanford.edu/entries/other-minds/> which is a corollary of
the solipsism problem. Part of my reasoning is that I see the most
necessary ability of consciousness is the ability to make distinctions.
It is with the ability to make distinctions that allows an entity to
even have beliefs. The idea of 1p indeterminacy speaks, IMHO, to this
ability and you have shown in a very clever way how to make this ability
vanish. It is for this reason that you can actually make the claim that
"I did provide a semi-axiomatic of God " in a resent post, but you must
understand that your claim is not a universal truth. It is only a finite
approximation.
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.
OK!
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.
Right! and I claim (without proof at the moment) that this
prohibits certain kinds of beliefs from possibly being true. In
particular, it prevents absolute truth valuations from being associated
with entities that cannot be named. This has profound implications! I
would even go so far as to say that it even implies that phrases like
"arithmetical truth" are meaningless iff they are not stated in
association with a named theory. I think that John Clark's contentions
about "free will" could be made coherent in this context.
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 Gödel numbers of the true arithmetical
sentences.
Yes, but only up to isomorphisms within nameable classes! Gödel
numberings in general prevent exact naming even to the point of possibly
only locating them as members of some coarse grained class (as we see in
the level of substitution idea). This has implications with regard to
the Axiom of Choice but I am not sure how to proceed further on this
question.
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.
Can COMP be extended so that we can at least define a meta-theory
of sets?
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.
I agree with you here, but this is wild speculation...
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.
If we cannot achieve a "definite description" then there is no
unambiguous name. To deal with this we could use Gödel Incompleteness
result to prove the existence of a meta-theory within which sentences
about the ambiguously named entity are true, but doing this is
equivalent to a coarse graining
<http://en.wikipedia.org/wiki/Granularity>. We are effectively defining
truth values as embedded invariants of logical theories. My question to
you is whether or not there is an algebra that captures this kind of
logical theory? I apologize that my wording is very bad, but does this
make any sense to you? It sounds a lot like your G* idea, but I am not sure.
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.
OK, but exactly how is this third person defined? Who is it? What
is their name?
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?
What is the cardinality of the infinity of computations that is
implied by a 1p?
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
<http://plato.stanford.edu/entries/nonwellfounded-set-theory/#3.1>)
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
<http://plato.stanford.edu/entries/nonwellfounded-set-theory/#2.3> -
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 <http://arxiv.org/pdf/math/0509616v1.pdf>! So my
claim is, now, that at best your step 8 is true in a forced extension.
1004.
Sorry, bad wording. I will try harder to make myself clear on this.
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,
?
I will write a separate post on this.
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.
?
I would like to point you to this blog article
http://www.scifiwright.com/2007/12/immaterialism-the-long-answer/ It
addresses many of my concerns!
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.
OK, but could you comment on the implications of this that you see?
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.
You must clearly define what 3p is in your theory! My definition of
3p is "a consensus of many distinct 1p".
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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