Hi Bruno,
You seem to not understand the role that the physical plays at
all! This
reminds me of an inversion of how most people cannot understand the
way that
math is "abstract" and have to work very hard to understand notions
like "in
principle a coffee cup is the same as a doughnut".
On 1/14/2012 6:58 AM, Bruno Marchal wrote:
On 13 Jan 2012, at 18:24, Stephen P. King wrote:
Hi Bruno,
On 1/13/2012 4:38 AM, Bruno Marchal wrote:
Hi Stephen,
On 13 Jan 2012, at 00:58, Stephen P. King wrote:
Hi Bruno,
On 1/12/2012 1:01 PM, Bruno Marchal wrote:
On 11 Jan 2012, at 19:35, acw wrote:
On 1/11/2012 19:22, Stephen P. King wrote:
Hi,
I have a question. Does not the Tennenbaum Theorem prevent the
concept
of first person plural from having a coherent meaning, since it
seems to
makes PA unique and singular? In other words, how can multiple
copies of
PA generate a plurality of first person since they would be an
equivalence class. It seems to me that the concept of plurality of 1p
requires a 3p to be coherent, but how does a 3p exist unless it is
a 1p
in the PA sense?
Onward!
Stephen
My understanding of 1p plural is merely many 1p's sharing an
apparent 3p
world. That 3p world may or may not be globally coherent (it is most
certainly locally coherent), and may or may not be computable,
typically I
imagine it as being locally computed by an infinity of TMs, from
the 1p. At
least one coherent 3p foundation exists as the UD, but that's
something very
different from the universe a structural realist would believe in
(for
example, 'this universe', or the MWI multiverse). So a coherent 3p
foundation always exists, possibly an infinity of them. The parts
(or even
the whole) of the 3p foundation should be found within the UD.
As for PA's consciousness, I don't know, maybe Bruno can say a lot
more
about this. My understanding of consciousness in Bruno's theory is
that an
OM(Observer Moment) corresponds to a Sigma-1 sentence.
You can ascribe a sort of local consciousness to the person living,
relatively to you, that Sigma_1 truth, but the person itself is
really
related to all the proofs (in Platonia) of that sentences (roughly
speaking).
OK, but that requires that I have a justification for a belief in
Platonia.
The closest that I can get to Platonia is something like the class
of all
verified proofs (which supervenes on some form of physical process.)
You need just to believe that in the standard model of PA a
sentence is true
or false. I have not yet seen any book in math mentioning anything
physical
to define what that means.
*All* math papers you cited assume no less.
I cannot understand how such an obvious concept is not
understood, even
the notion of universality assumes it. The point is that mathematical
statements require some form of physicality to be known and
communicated,
OK. But they does not need phyicality to be just true. That's the
point.
Surely, but the truthfulness of a mathematical statement is
meaningless
without the possibility of physical implementation. One cannot even
know of
it absent the possibility of the physical.
it just is the case that the sentence, model, recursive algorithm,
whatever
concept, etc. is independent of any particular form of physical
implementation but is not independent of all physical
representations.
Of course it is. When you reason in PA you don't use any axiom
referring to
physics. To say that you need a physical brain begs the question
*and* is a
level-of-reasoning error.
PA does need to have any axioms that refer to physics. The fact
that PA
is inferred from patterns of chalk on a chalk board or patterns of
ink on a
whiteboard or patterns of pixels on a computer monitor or patterns of
scratches in the dust or ... is sufficient to establish the truth
of what I
am saying. If you remove the possibility of physical implementation
you also
remove the possibility of meaningfulness.
We cannot completely abstract away the role played by the physical
world.
That's what we do in math.
Yes, but all the while the physical world is the substrate for
our
patterns without which there is meaninglessness.
I simply cannot see how Sigma_1 sentences can interface with each
other such
that one can "know" anything about another absent some form of
physicality.
The "interfaces" and the relative implementations are defined using
addition
and multiplication only, like in Gödel's original paper. Then UDA
shows why
physicality is an emergent pattern in the mind of number, and why
it has to
be like that if comp is true. AUDA shows how to make the derivation.
No, you have only proven that the idea that the physicalist
idea that
"mind is an epiphenomena" is false,
No. I show that the physical reality is not an ontological reality,
once we
assume we are (even material) machine.
And I agree, the physical is not a primitive in the existential
sense,
but neither is the information. Idealism would have us believe that
differences can somehow obtain without a means to make the
distinction.
i.e. that material monism is false.
I insist everywhere that this is not what I showed. I show that all
form of
weak materialism is incompatible with mechanism. All. The monist
one, the
dualist one, etc.
How weak does materialism get when its primary quality is
removed? This
is a case of "vanishing in the limit", something similar to the
heap that
vanishes when we remove the last grain.
A proof that I understand and agree with.
Clearly you did not. You even miss the enunciation of the result.
Mechanism
is incompatible with WEAK materialism, that is the idea that
primitive
matter exist, or the idea that physics is the fundamental science.
Can you not understand these words? How is materialism any
weaker than
the case of no material at all? My argument is that the possibility
of
physical implementation cannot be removed without removing the
possibility
of meaningfulness. It is not an argument for a primitive
ontological status
for matter. You even seem to follow this reasoning when I ask you
where does
the computation occur then there is not paper tape for the TM and
you say
"on the walls of Platonia".
Your arguments and discussions in support of ideal monism and,
I prove that ideal monism is the only option, once you believe that
consciousness is invariant for digital functional substitution done
at some
level.
No, you did not. Your result cannot do such a thing because you
cannot
have your cake (a meaningful set of expressions) and eat it too.
Digital
functional substitution is the substitution of one physical
implementation
for another, it shows that the fact of universality does not depend
on any
particular physical implementation but DOES NOT eliminate the need
for at
least one form of physical implementation. Digital substitutability
is an
invariance over the class of physical implementations, but what
happens then
you remove all members of a class? It vanishes!
like Berkeley's, still fail because while the physical is not
primitive, it
is not merely the epiphenomena of the mind either.
It has to be by the UDA.
And the UDA (like the UD) must have some implementation, even
though the
particulars of that implementation are irrelevant.
You are perhaps confused by the fact that unlike the physical,
ideas can
represent themselves.
I believe that comp makes the "physical" into an aspect of number's
self-reference.
There we agree but I would say that a number's self-reference
is its
connection to some physical representation. My point is that there
cannot be
a self-reference without an implementation even if the particulars
of the
implementation do not matter.
If I take away all forms of physical means of communicating ideas, no
chalkboards, paper, computer screens, etc., how can ideas be possibly
communicated?
Because arithmetical truth contains all machine 'dreams", including
dreams
of chalkboards, papers, screens, etc. UDA has shown that a "real
paper", or
& "real screen" is an emergent stable pattern supervening on
infinities of
computation, through a competition between all universal numbers
occurring
below our substitution level. You might try to tell me where in the
proof
you lost the arguement.
When these "infinities of computations" are taken to have
specific
properties merely because of their existence. You are conflating
existence
with property definiteness. Most people have this problem.
This does not make sense. I assume not just O, s(0), etc. I assume
also
addition and multiplication. That's enough to get the properties.
There is an "I" in that statement! What is this "I"? What is its
function? What class is it an invariant upon? Exactly how is it
that you
know of these properties? Absent the possibility of some form of
implementation in the physical, there is no distinction between you
and
anything. Meaning requires distinction. Some even say that meaning
*is*
distinction. What other than the persistence of pattern that the
physical
offers acts to allow for the ability to know differences?
Mere existence does not specify properties.
That's not correct. We can explain the property "being prime" from
the mere
existence of 0, s(0), s(s(0)), ... and the recursive laws of
addition and
multiplication.
No, existence does not specify anything, much less that "0, s(0),
s(s(0)), ..." is distinct from any other string, nor does it
specify the
laws of addition or multiplication. Existence is not a property
that an
object has.
Exactly. that's the point. You seem to contradict it.
But existence is thus independent of properties and thus
distinctions.
So your claim that " "being prime" from the mere existence of 0,
s(0),
s(s(0)), ... and the recursive laws of addition and multiplication"
requires
a substrate that allows form representative patterns to obtain.
Universality
allows us to substitute one form of substrate for another so long
as the
function is the same. But universality and existence alone are
insufficient
for your claim that "I prove that ideal monism is the only option".
You also
have to show how the properties are both definite and invariant. This
requires implementation in a form that is invariant (to some
degree) with
respect to time. There is not time in Platonia therefore there in no
invariance with respect to time for the patterns of difference to
occur for
implementation to be said to obtain.
You need to study the "problem of universals" in philosophy, it is
well
known and has been debated for even thousands of years. For example
see 1 or
2.
This is a red herring.
In a way, surely, but the essence of the problem is not. The
paper that
is reference 1 explains this well.
I go so far as considering that the wavefunction and its unitary
evolution
exists and it is a sufficiently universal "physical" process to
implement
the UD, but the UD as just the equivalent to Integers, nay, that I
cannot
believe in. “One cannot speak about whatever one cannot talk.” ~
Maturana
(1978, p. 49)
I think Maturana was alluding to Wittgenstein, and that sentence is
almost
as ridiculous as Damascius saying "one sentence about the ineffable
is one
sentence too much". But it is a deep meta-truth playing some role in
number's theology.
OK, I deeply appreciate your erudition, you are much more
educated than
I am, but nevertheless, I submit to you that you cannot just ignore
the
universals vs. nominal problem and posit by fiat that just because
one can
proof the truth of some statement that that statement's existence
determines
its properties. Our ability to communicate ideas follows from their
universality, that they do not require *some particular* physical
implementation, but that is not the same as requiring *no* physical
implementation. You argue that *no* physical implementation is
necessary; I
disagree.
It is the result of the proof. It is up to you to show the flaw, or
to
abandon comp.
The problem is that mathematics cannot represent matter other
than by
invariance with respect to time, etc. absent an interpreter. What
you seem
to think is that mathematics can prove things to itself in a manner
consistent with how I might be able to write out a set of symbols
on your
chalkboard that represent a proof of some theorem. You reject David
Deutsch's discussion of how this is wrongheaded out of hand, that is
unfortunate since it would greatly strengthen your case if you
could show
exactly where Deutsch is going wrong, if he is...
But I think that you cannot define the universal wave without
postulating
arithmetical realism. In fact real number+trigonometrical function
is a
stronger form of realism than arithmetical realism. Adding
"physical" in
front of it adds nothing but a magical notion of primary substance.
Epistemologically it is a form of treachery, by UDA, it singles out a
universal number and postulate it is real, when comp explains
precisely that
such a move cannot work.
I am allowing for realism, it is a belief that may be true, but
it is
not a unique singleton in the universe of models. I am arguing
against the
idea that the physical is primitive, against substantivalism
especially as
it is occurring in physics, for example see:
www.dur.ac.uk/nick.zangwill/Haeccieties.doc or 4.
In physics there is a huge debate over the haecceity of space-
time and
your result is important in this, but your attempt to argue from
the other
side is as treacherous because it ignores the necessity of the
physical.
Comp makes necessary that there is no *primitive* physicalness. But
as David
points in his reply, you cannot say that I ignore the physical. The
whole
work is an explanation of why we believe in the physical, why and
how such
belief emerges and are persistent, etc. Physics is entirely given
by the
material hypostases, which are defined by number's self-reference,
as UDA
shows it to be the case necessarily so.
This is insufficient. Merely postulating a property does not
make it so.
You continued intransigence on the non-existence of the physical
world with
statements that is shown to not be primitive is an avoidance of the
problem
by ignoring it, not a solution to it. The fact that is removing all
possibility of physical implementation by a theory of Everything
makes it
worse than mute, it eliminates itself as a meaningful theory simply
because,
to be consistent, it cannot be communicated.
Onward!
Stephen
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