*On The Limits of Deducibility* by Stefan Weckbach

Stefan Thanks for your essay. I agree with he the conclusions of your essay even though our methods to attain those conclusions are very different. In my essay " Clarification Of Physics: A Derivation Of A Complete, Computable, Predictive Mode Of "Our" Multiverse", I present the Creation of your ..metaphysical realm" and the reasons for it to work. Successful Self Creation is the processing that becomes the metaphysical result and the reasons for it to work is that it has to overcome entropy in order to emerge from chaos and exist. Also the SSC processing produces and "uses" its own mathematics which "maps" to its processing and results. Hopefully, the mathematical model and its narrative can be of some help in your thinking. Also, I would appreciate your comments on my essay. JohnCrowell

Hi Mr Weckbach, see this for the quantum gravitation,

take a serie of quantum BHs farer than the nuclear forces,, take their mass , now consider particles of DM cold encoded in nuclei and encircling this standard model and particles, now consider the distances between a relative sphere of quantum BHs and the electrons encircled by this DM and now apply the equation of newton about the force of this gravitation between mass.....see the result .....quantum gravitation reached because the standard model is just emergent and we must take into account others distances and mass .

All this is due to fact that the main codes are farer than our actual standard model, now consider for the formalisation 3 E8 , and consider the finite series of 3D coded spheres, one for the space, vacuum, one for the photons, a fuel and one for the DM, an other fuel cold. Now consider the space and these finite series like the main codes and so see the finite series of quantum BHs......do you see what it appears in making the fusion of these 3 E8 and their 3D spheres instead of points or strings ?

Regards

Dear Stefan Weckbach,

Your essays are always fundamental and always enjoyable. Your first statement that grabbed me was concerning systems or machines and the "profound limit of their own abilities to deduce something to be ontologically true or false."

Guthry's essay; "no amount of computation will lead you to discovery of a pattern that wasn't in the data in the first place."

This seems to relate to your: "neither machine nor humans can reliably deduce that certain things exist or do not exist."

I fully support your conclusion that "the naked act of deduction is really only a deterministic, mechanical process."

You and I treat ontology from quite different directions. I hope you will enjoy my take on a specific problem of ontology: Deciding on the nature of time and space

My best regards to you,

Edwin Eugene Klingman

Dear Stefan,

Thanks for this stimulating essay, which, like every good essay, raises more questions than it answers. The link between deductibility and finite information has also been raised by Nicolas Gisin, and is the topic of the essay by his collaborator Flavio Del Santo in this very competition, perhaps you can read each other's essays and comment. My overall view on this, shared by Gisin and Del Santo, is that intuitionistic mathematics should be incorporated into physics to really deal with these issues. Concerning your own essay I would also make this point: to make your claims rigorous (apart from the ones that are already well argued) you would also need some of the ideas of L.E.J. Brouwer, especially about choice sequences. Otherwise, I agree with everything you write, and you write it very well!

Best wishes, Klaas

Dear Stefan,

For some reason, Lawrence Crowell cannot post on the FQXi and has not been able to do so for several days. FQXi is fixing the problem. In the meantime, Lawrence asked me to post here his comments on your Essay. I past them below. I profit by this email to inform you that I will also read comment and score your Essay soon.

Good luck in the Contest and best wishes,

Ch.

From Lawrence Crowell

This is a bit late, for some reason I can't post to FQXi. I meant to post this several days ago.

I just read your informal essay and there are points I agree with. Thanks for the kind words with respect to my essay. I finally just now got to reading yours, as this illness came roaring back yesterday and I am still feeling not too well. I am coming up on a month with this thing. I have not been horribly ill, but it is rather debilitating and leads to deep levels of fatigue.

You are making issues with what I see as the continuum. The continuum hypothesis Чђ_0 < C < 2^{Чђ_0} is something that haunts all of this. I am not an expert on this, though I have Cohen's book on the proof he worked on that it is consistent with ZF set theory, but not provable. From a physics perspective it seems almost absurd to worry about this. Though with Robinson's numbers and related matters this does impact the ideas behind calculus. With large N entanglements of states a continuum though should exist. The Raamsdonk idea that spacetime is an epiphenomenology of quantum entanglement should imply that a smooth continuum will emerge from a finite, or with N в†'П‰,using ordinal notation instead of в€ћ, discrete system of states. This can never be observed completely with physics, but it would give a theoretical reason to think there are no granular disruptions to spacetime, at least for IR (E в†' 0) measurements such as across cosmological distances. The NASA and ESA Fermi and Integral measurements bear this out. At UV measurements spacetime should I think appear very bubbly or granular with discreteness, where what are measured are just discrete states and not even what we could call space or spacetime.

You wrote, "Hence, our axiom that the world is an informationally closed (void) system must be erroneous, since the fact that Gödel-incompleteness is factually constructible contradicts this axiom." This is a part of what I advocate on several fronts. A black hole with mass m = GM/c^2 has a temperature T = 1/8πm in natural units. If this black hole were placed in a spacetime region with a background temperature equal to its Bekenstein temperature the black hole will emit and absorb photons in a stochastic way. This will mean the temperature and mass of the black hole will drift away from this condition of equality in a Langevin manner. The result is there is no equilibrium. This then points to an open world perspective instead of a closed world.

The halting issue also impact spacetime. Suppose there is a binary state on a Turing machine that we read out. We set this machine to make its first step in 1 second, the next in ½ of a second, the next in ¼ of a second, it is not hard to see that after 2 seconds we should have an answer. If this machine halts it will finish before 2 seconds. If not something odd happens, for the energy required to fun this machine diverges in an asymptote and even it if is "unbreakable" the energy involved will generate a black hole. If this machine does not halt, we have a black hole, and even if it halts but takes a huge amount of time it could be in a black hole. Thus, if we generate a black hole, we have no information about the halting state of the machine. We must go into the black hole to find out. A Kerr black hole has an inner event horizon, and we could instead have the Turing machine send a regular interval of binary pulses into the black hole. An observer who goes into the black hole could then in principle read off this binary stream and determine completely if a black hole halts or does not halt. This is because the inner horizon is continuous with I^∞ and the infalling observer would reach this in a finite time in an eternal black hole. However, the Planck unit of distance muddles this up, and further Hawking radiation breaks the connection between r_- and I^∞. In fact, as the observer reaches r_- it is a singularity at the end point in the black hole explosion into Hawking radiation. So, either spacetime physics or quantum mechanics enforces a condition whereby the Gödel-Turing result can't be overruled by physical means.

These are interesting matters to ponder and think about. Your essay does provide food for thought along these lines.

Cheers LC

Dear Stefan

Congrats for you essay which is well argued and illuminating, you gave some details on Godel and Turing theorems that are quite interesting for me. In my essay I argue that science is about truth, in yours you seem to imply that truth is an illusion. In my view, as science progresses we are reaching a metastable truth. The understanding of electromagnetic phenomena, light, gravity, biology, condensed matter and nuclear energy are some of the clear examples where we can see some truth.

Good luck in the contest!

Israel

I am finally back in action. For some reason I was locked out.

In college I read Hofstadter's Gödel, Escher, Bach and I remember I had a sort of reaction "So maybe there is a God." I can't say I lean much that way these days. However, Gödel was somewhat mystical and thought his theorem demonstrated a Platonic nature of mathematics and its relationship with the physical world.

Cheers, LC

Sounds great; I agree with your view, it seems that it is quite in parallel to the one I express in my essay. I hope you find some spare time to read it, any criticism will be more than welcomed.

Good luck in the contest!

Since you have read my essay then you already know that we are in agreement, at least for the most part. Therefore, I will skip any minor criticisms as well as any agreements and disagreements so that I can directly address your Conclusions.

You wrote, "But human intelligence can transcend its antivalent logics by inferring that there must be some irreducible reasons for those abstractions to work and these reasons must be rooted in a real metaphysical realm. Consequently, compared to this metaphysical realm, our whole physical universe must in many respects also be considered as a kind of abstraction, being possible due to the existence of this metaphysical realm."

This statement is too close to a Platonic conception of reality for me to completely agree. However, the obvious reality of this "metaphysical realm" is the important point.

In the religions of the East some of their extreme sects will assert that the "physical world" is nothing but a dream. In the West this can only be looked upon as solipsistic lunacy because Westerners are taught, from the time they are little, that the only thing that we are absolutely certain about is the "physical world." In modern philosophical parlance this is called Scientism.

The irony is that the West is, today, simply going to the opposite extreme. This becomes obvious when scientists assert that "consciousness" is nothing but a fantasy, an epiphenomenon of the material brain, or something similar. (Note that I am obviously relating "consciousness" to your "metaphysical realm" even though they might not be (legitimately) related. Hence, this relation may be considered to be illustrative only.)

People of the future will most certainly look back on the the people of the 20th century and say, "Those idiots almost convinced themselves that they weren't real!" (Note that I am contrasting reality and existence similar to how you contrasted what is theoretical and practical.)

It appears that our papers may be complementary opposites. Whereas I tried to adhere strictly to what has been (formally) proven and to say as little as possible about the (meaningful) philosophical ideas underlying the proofs, you choose to focus on philosophical analysis.

Your essay makes me think of the book, What Computers Still Can't Do by Hubert Dreyfus. The book has a phenomenological perspective similar to where you seem to be coming from. Your ontological truth is similar to the phenomenological idea of being. The book is about the (potential) "intelligence" of computers and thus on what can be known by a "mechanical, algorithmic process" as you called it.

Dear Stefan,

I agree with the opinion of your essay. I really enjoyed reading this. This seems to be ironical sense of the data-driven science. What do you think about this scientific style to open the new theory?

While I am studying quantum random number generation, in the context of the hacking of the random numbers, as discussed in my essay, how to show the limitation of the deduction?

Best wishes,

Yutaka

Dear Stefan,

Please forgive me if my comments show the ignorance of what you have discussed. I tried repeatedly to give some ground to what I read, but I do not believe that I succeeded. Also, by the time, I got to the end, I felt, several deductions were on the lines that I thought correct, yet, I decide to log the discussion below.

1. You write, "Because for knowing the existence of certain things one had at first to know whether or not the existence of these things should necessarily be considered a possibility, a necessity or even an impossibility."

How does it fair against the existence of consciousness? Must we necessarily know the possibility or necessity of existence of consciousness, before we can have consciousness?

2. You state, "Despite our problems to decide between the above mentioned modalities, we nonetheless obviously can know a truth that mathematical systems or machines presumably never can know. We know that machines and thus, their algorithms, lack the needed ontological awareness of the terms 'possible', 'necessary' and 'impossible..."

With such comfort 'we' use the term 'we' in statements like 'we know', without asking a question what exactly are terms such as 'I' and 'we' refer to? Many questions, and discussions become ill-posed because of a lack of understanding of entities referred to by 'I' and 'we'. Keeping in the same tradition of usage of such terms, let me assert first the following before offering any clarity, "If 'we' know things, then in the same sense, computers can be made to know the same things." Simply stating, if there is an objectivity to the creation of entities such as 'I' and 'we', then the same objective function can also create a device to express 'I' and 'we'.

Consider for a moment, what if neuronal system in modular hierarchy represents meaningful information that expresses relations among objects, where one of the represented objects refers to certain characteristics of self either as an individual, 'I', or as a group, 'we'. Every object is referable by the constancy of its relation with other objects, and constancy of structural relation among component objects. The same is true for the object that refers to characteristic composition that we refer to as 'I', which entails characteristics of an embodiment of physical body, an observer, an actor, a controller, and so on. A reference to the self is an attribution in a represented semantics (meaning) of information. For instance, when we refer to pain in our hand, the represented semantic value includes reference to the hand as a component of unified system, the specifics of pain, the specifics of location, etc.

Now, the point is that, for this to be represented, hand need not exist, as is established from phantom limb experiments. That is, pain is an attribution to the represented extension of the body, as the attribution of consciousness to the represented unified self. The semantics of being an observer, of bearer of knowledge (the knower) not only of the objects, but also of their inter relations and their causal dependence are all representable by physical states as neural states represent these semantics. The attribution of all this characteristics to an unified system as unitary referable system composes the self; it is that self that gets referred to in expressions like, 'I know', 'we know', etc. Just because, physics has not touched upon the reality of semantic values (meanings) of information, we face such a void in our understanding. But first step in establishing the same has already been done in 'Fundamentals of Natural Representation', https://doi.org/10.3390/info9070168.

Now, let us revisit the same statement -- we nonetheless obviously can know a truth that mathematical systems or machines presumably never can know. A caveat must be added -- machines need not be mathematically consistent, as is a requirement in Godel's theorems. We now know why processing in the brain, and for that reason in any physical system, is not mathematically consistent, the same can be implemented even in the computers. After all, human brain is a biological (physical) device that processes information. Godel's theorems do not apply to processing in physical systems, therefore, they do not apply anywhere except in pure mathematics. Pure mathematics does not bound the limits of existence.

3. You seem to take a position in terms of possibles and impossibles. One must keep in mind that with the aid of a language, created by a non deterministic device (brain), arbitrary semantics can be constructed, which may not have anything to do with realizability of the expressed semantics to have causal powers. Since a statement can be constructed in terms of possibles with no reference to causal basis, does not mean that such an expression can be given any objective basis or legitimacy to infer the limits of existentiality, particularly in the domain of limited indeterminism. If existentialism does not have a deterministic basis, then an arbitrary class of logical possibles cannot be used to deduce conclusions about the existentiality of objects. For instance, a statement about objects can be constructed that are self contradictory, such as 'I do not exist'. But it must not allow a conclusion to be drawn that a universe allowing such relations among objects to be expressed cannot exist because such a relation among objects can never have an existential reality; i.e, a universe is forbidden if it leads to impossible contexts. But, there is an objective difference between impossible contexts and expression of impossible contexts. One may express the list of impossibles, but one may not causally have one. Hence, a logical conclusion based on having such a list is not operational.

Rajiv

Dear Stefan,

Thanks for responding.

From your agreement, "machines may become conscious", one may infer that you accept the objectivity of physical function that gives rise to consciousness. And if a process is objective, then it is repeatable, it is same for all, and it applies the same way in all applicable contexts, then its description must be constructible. The process of emergence is algorithmically expressible. But then, you also add, "but in that case my assumption is that the "algorithmic" activity for that to happen will be such complex that ... no one will be able to point to those parts of the algorithmic activity that initialize a state of conscious awareness within these machines". By this addition, you seem to be taking away the same objectivity that you granted a moment ago. Somehow, you tend to maintain that consciousness is fundamentally inexplicable, and that an entity is either conscious or non-conscious as given as in a corporal sense. My effort in the following paragraphs was to show that 'association of consciousness to an entity' is a representation of semantics (meaning) that attributes consciousness to a body as a person.

Consider for a moment, the neuronal system in modular hierarchy represents meaningful information that expresses relations among objects, where one of the represented objects refers to the self in the same way as another represented object refers to 'a book', and yet another object refers to the 'act or reading'. The three combined together in conjunction refers to, "I am reading a book". Every object is referable by the constancy of its relation with other objects, and constancy of structural relation among component objects. Try constructing a description by any other relations, and you will know that these are the only two ways to construct a description of any object. Hence, the mechanism of representation of semantic value (meaning) is knowable for all objects including the self.

For instance, when we refer to pain in our hand, the represented semantic value includes a reference to the hand as a component of the represented unified system, the specifics of pain, the specifics of location, etc. Now, the point is that, for this to be represented, hand need not exist, as is established from phantom limb experiments and dream events. That is, the sense of pain is a semantic attribution to the represented extension of the body, as the attribution of consciousness to the represented unified self. The attribution of all this characteristics to an unified system as unitary referable system composes the self with the semantics of knower, actor, and controller; it is that represented self that gets referred to in an expression like, 'I know', 'we know', etc. As I referred to a publication, where the physics or mechanics of representing and processing of semantic values (meanings) of information has been worked out.

If it makes good sense to you, then reconsider the statement, "We know X", and determine how it is constructed. So, if we know the mechanism of how to build structured and abstract semantics via organized phyiscal interaction, then we can lay down the algorithm, and we also know what processing constructs the self with the associated properties of consciousness.

Rajiv