# Re: Question about PA and 1p

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 <http://scholar.google.com/scholar_url?hl=en&q=http://www.philosophy.ox.ac.uk/__data/assets/pdf_file/0005/5855/What_is_POU.pdf&sa=X&scisig=AAGBfm1jNWjOuIhOqk31VbXyGOXOBP1JiQ&oi=scholarr> 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 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 <http://books.google.com/books?id=w590r7cZ8TsC&pg=PA146&lpg=PA146&dq=haecceity+of+space-time&source=bl&ots=U6VX2mHzLF&sig=3olJFo176kK7GQxmb-iWgNu6T3I&hl=en&sa=X&ei=XmQQT7PQKcGstgeRqdmnAg&sqi=2&ved=0CCkQ6AEwAg#v=onepage&q=haecceity%20of%20space-time&f=false>. 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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