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