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:
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
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
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
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
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
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
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
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
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
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
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 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 <http://plato.stanford.edu/entries/universals-medieval/>.
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
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
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
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