*On The Limits of Deducibility* by Stefan Weckbach

Respected Professor Stefan Weckbach,

Wonderfully argued essay please. I just quoted some of your words............Let us now assume that we have a complete list of all things at hand that are impossible to exist. Let us further assume that this list is not infinite and that we have enough time to completely go through it...............

Now the question arises whether is possible form a complete list of all the things impossible to exist? How to do it?

Of-course I made a list of impossible things! in my essay ("A properly deciding, Computing and Predicting new theory's Philosophy")!!! Hope you will look make your comments please.....

Best Regards

=snp

Dear Stefan,

A very important essay, topic and deep ideas that you give to comprehend, especially in the direction of the deepest metaphysics. I believe that the crisis of understanding in the philosophical basis of fundamental science, its metology, is caused precisely by the crisis of metaphysics and ontology. Gödel sought metaphysics in tune with Leibniz's philosophy. He described his views as "rationalistic, idealistic, optimistic and theological. [Wang Hao. A Logical Journey: From Gödel to Philosophy. Cambridge, 1996.].

Gödel believed that in metaphysics there existed such fundamental primitive concepts, the discovery of which would be a genuine breakthrough in philosophy. Godel argues that philosophy has not yet been developed sufficiently to assert something with the necessary certainty. He even speaks more harshly about "the underdevelopment of philosophy at the present stage". [Gödel 1995 - Gödel K. Collected Works. V. III. Unpublished Essays and Lectures. Ed. S. Feferman. NY, Oxford, 1995.]

I believe that a breakthrough in search of a stronger ontological basis of science, knowledge in general, its boundaries, carcass and foundation will help the dialectic, which for some unknown reason is ignored by modern philosophy of science.

Respectfully, Vladimir

Hello Mr Weckbach,

I like how you see the generality of our universe. Thanks for developing and sharing your thoughts. I know that the sciences Community is divided about God.

Personally I consider an infinite eternal consciousness beyond this physicality , a Little bit like Einstein, a God of Spinoza with determinism respecting our rational laws. In studying the philosphy of our best thinkers, I have remarked that all they considered a creator , Planck, Einstein, Newton, Tesla, Galilei, Poincare, Godel, Cantor, Maxwell, Lorentz, Fermi, Lie and so more. I beleive strongly even that it is essential to well understand the transformations matters energy and the informations but I respect also the thinkers thinking the opposite witha kind of mathematical causes and Hazard if I can say.

In my model of spherisation, an optimisation evolution of the universal sphere or future sphere with 3D coded quantum spheres, I consider a central main cosmological sphere and it is there that this infinite eternal consciousness codes and tranforms the energy in particles. So I have considered this generality.

Imagine this with humility, take 3 main systems, series finite of quantum 3d spheres where this space disappears due to a specific serie having the same finite number than our cosmological 3D spheres. so one for the vacuum space , they are coded, one for the photonic fuel, they are coded differently and one for the other fuel a cold dark matter and so when they fuse they create our geometries, topologies, matters ann properties because they are coded simply ,now consider this at this planck scale and utilise these series and superimpose 3 E8 for the geometrisations, utilise the Ricci flow, the poicare conjecture, the Topological and euclidian spaces, an assymetric Ricci flow for the unique things, and the lie derivatives.....all will be easier to explain all our unknowns than just a E8 and geonetrodynamics. E8xE8xE8 in fact with finite series of 3D spheres instead of points or strings. the main codes are in this space , the two others are fuel permitting the gravitation and the electromagnetism simply, see the combinations possible , we can create all Shapes, geometries, topologies and the unique things ....

Best Regards

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