Well Beyond Uncertainty, Uncomputability, and Unpredictability by Daniel Sudarsky

Dear Daniel,

I enjoyed your excursion through various discoveries that show we should embrace epistemic modesty, as well as your personal remarks and proposals on the topic.

You wrote

> Heisenbergs "uncertainty principle", ought not to be taken (at least not without some modification of the theory, such as that embodied in the de-Broglie-Bohn proposal) as characterizing an epistemic limitation. It is a surprising fact that a large number of physicists and practitioners of related disciplines (such as cosmology) continue to do so. The word "indefiniteness" comes to mind as a good alternative to the word "uncertainty" in this regard.

Indeed, this thing still happens, maybe sometimes because of some lack of understanding, sometimes because of lazy language.

> The possibility I would like to briefly contemplate here, one that seems particularly appropriate if one adopts the Humean approach, is that no such things exists. No absolute, exception free, everlasting laws. [...] My proposal: untheoretizability. That is, such position would contemplate the ultimate untheoretizability of nature.

This possibility is something worth being remembered constantly. I think we can take this suggestion, and at the same time keep going with the next paragraph you wrote:

> looking for that ultimate law with a seemingly undaunted determination. That theory of everything that would, among other accomplishments, unify in a smooth manner some version of quantum mechanics free of its already mentioned problems, i.e. a version of the theory without a measurement problem and a completely clear ontology, with our currently most successful theory of gravitation, General Relativity.

I mean in the sense that we can accept the possibility of untheoretizability, and at the same time try at least the more modest goal of finding compressed descriptions of the world, in terms of Chaitin-Kolmogorov complexity or Occam's razor etc, as a middle way. After all, we have to make choices on a daily basis in the absence of enough information, we start new projects and have expectations based on very little reliable data, even if at some point we will die etc. Do you think this middle way of being aware of the possible untheoretizability and at the same time keep searching even a "final theory" is merely a compromise, or indeed is a way to keep going with an open mind?

To what extent do you think that Wheeler's "Law without law" and Unger & Smolin's ideas that the laws of nature evolve, come close to your own views on untheoretizability?

Thanks again for a great reading!

Cheers,

Cristi

Hi Daniel,

Thank you for your reply, and for the references to two of your articles, which I bookmarked for reading. I had the feeling that your view is more radical than Wheeler's and Unger & Smolin's, it seems it is indeed.

Some skeptics declare themselves Bayesian, but even this has a major blind spot in the prior probabilities Miklós, Rédei and Gyenis, Zalán (2019) Having a look at the Bayes Blind Spot. No wonder then that Bayes's theorem was used to justify opposite points of view, an example being its original application by Bayes himself, to prove the existence of God, as well as an application to justify Pascal's wager, and another one to refute God :)

But anyway, if we want to avoid assumptions as much as possible, Bayesianism seems a good instrument. And I'd claim that it is embedded by Nature in the very structure of our neural networks, our brains. I think this explains why so many people can work very well based on naive intuitions, which we know to be biased at least when taken outside of the range of the training of their neural networks, often being able to make faster and better decisions than people who try to be rational, and either overanalyse, or try to rely on some presumed absolute principles.

Speaking of bayesianism, the most systematic approach in physics of this method of avoiding making assumptions is, I think, QBism, which seems to me from some point of view a "radical orthodox" systematic development of Wheeler's "law without law". I think QBism comes into two major flavors, one that denies "reality", and one that doesn't. The first flavor seems to follow for example from some statements by Fuchs and Schack, who say things like "the problem evaporates", and claim that QM is local because Bob has to go to Alice or vice-versa, or at least to send the result through some reliable local means, to compare the outcomes. This kind of subjectivism and skepticism goes, perhaps too much for the taste of ontologists, very much in the direction of solipsism. This may explain why your coauthor Tim Maudlin and others think it's nonsense. The other way, in my opinion, is to interpret QBism not as denying ontology and laws, but as considering them possible underlying explanations of the probabilities, in a somewhat neutral, and I would say, apophatic manner. This understanding of QBism seems to be supported by this FAQBism, in which both the idea that QBism is solipsistic and that it denies reality are rejected. And some of Fuchs's statements are consistent with this. It is very hard to try to avoid making assumptions, and at the same time say things that are not easily misinterpretable.

While not a QBist myself, I think the latter form of QBism is useful to isolate models of quantum reality that may work from those that don't, in a way consistent to the data accumulated up to a moment of time. After all, Bell's theorem and other no-go theorems work like a via negativa too, by allowing the rejection of classes of models that don't fit the data. Perhaps this is the best what science can do. On the other hand, any no-go theorem is as true as its assumptions+proof. In my work, I try to be guided by both, that is, to rely on no-go results, but at the same time to take care not to declare as impossible things that are actually allowed by the hypotheses of the theorems. I mean I think both "no-go" and "still-go" results are important, and I consider this consistent with open skepticism.

Cheers,

Cristi

Dear Daniel,

I read your essay with great interest. You give very important and deep thoughts on the problem of finding a way out of the crisis of understanding in the philosophical (metaphysical) basis of fundamental science.

I will give your main, as I believe, very important thoughts for discussion:

On the other hand, there was the realm of knowledge that seemed to be independent of the contingent details of our world: the laws of nature themselves, among which those of physics seemed to enjoy a particularly dominant position, as well the laws governing mathematics and logic.

I would put in first place the "laws governing mathematics and logic." Here, I believe, one must proceed not only from the fact that "mathematics is the language of Nature" and not only from the opinions of some mathematicians, such as the mathematician Ludwig Faddeev, who expressed this idea in an interview for "Expert" magazine entitled "The equation of the evil spirit"

芦Academician Ludwig Faddeev believes that today mathematical rigor is more important than physical intuition and it is thanks to mathematics that a "unified theory of everything" will be built. .. Faddeev is convinced that just as physics solved all the theoretical problems of chemistry, thereby "closing" chemistry, so mathematics will create a "unified theory of everything" and "close" physics.

But how can mathematics "close physics" if the problem of substantiating mathematics ("foundations of mathematics") has been going on for more than a century. This was perfectly shown by Morris Kline in "Mathematics: The Loss of Certainty禄. And the problem of "foundations" is swept under the carpet by mathematicians themselves. Just look at the "Millennium Challenges." "The tasks of the millennium" are being solved, and the main task, problem No. 1 for all cognition, remains unsolved. What "language of Nature" can we talk about then? What is its ontological structure? Physics, mathematics, logic - here the question is not even a priority, but in the nature of the "laws of Nature" themselves, in the problem of the source of the laws of mathematics and logic. This is the problem of a single ontological basis of knowledge. I call it the problem of the ontological basis of mathematics (knowledge).

Doctor of Physical and Mathematical Sciences Alexander Zenkin in "Scientific Counter-Revolution in Mathematics" notes:But how can mathematics "close physics" if the problem of substantiating mathematics ("foundations of mathematics") has been going on for more than a century. And the problem of "foundations" is swept under the carpet by mathematicians themselves. Just look at the "Millennium Challenges." "The tasks of the millennium" are being solved, and the main task, problem No. 1 for all cognition, remains unsolved. What "language of Nature" can we talk about then? What is its ontological structure? Physics, mathematics, logic - here the question is not even a priority, but in the nature of the "laws of Nature" themselves, in the problem of the source of the laws of mathematics and logic. This is the problem of a single ontological basis of knowledge. I call it the problem of the ontological basis of mathematics (knowledge).

Doctor of Physical and Mathematical Sciences Alexander Zenkin in "Scientific Counter-Revolution in Mathematics" notes:

"About thirty years ago, for the sake of" sports interest "I began to collect various" logics "used in modern logical-mathematical treatises. When their amount exceeded the second hundred, it has become clear: if the logic can be selected "on a taste" (or even can be constructed "on a need"), such notion as "science" becomes here simply inappropriate. Perhaps, the situation somewhat reminds the famous "Babylon" epic: the sounds - symbols of abstract speeches are almost the same, but the sense, if that is present, of everyone is peculiar. What was the end of the First Babylon is described in The Holy Bible ... " A. Zenkin concludes: "the truth should be drawn ... " I agree with A.Zenkin. Draw in silence, without words, only one "Symbol of symbols".

芦We, nevertheless, held on to the conviction, that even in such dire circumstances, where we were unable to establish what the correct answer is, each meaningful statement was either true or false: The Principle of the Excluded Middle. The situations where this did not seem to occur were, in turn, regarded, as places which we should consider simply as bifurcation points in the development of our ideas: we could add a new axiom or its negation, and have now two branches or lines of research: Euclidean and NonEuclidean geometry.禄

Here it's good to rethink the whole line of development of dialectical thinking, especially the principle of "coincidence of opposites" by Nikolai Kuzansky, the history of "The Principle of the Excluded Middle". It is also especially careful to comprehend the ideas of Edmund Husserl in "The Beginning of Geometry." Here is the problem of understanding "space". I believe that Pavel Florensky is right: "We repeat: world-understanding is space-understanding."

芦This represents a much deeper limitation, in comparison to the previously discussed ones, as it does not refer to our state of knowledge regarding the system, but somehow about the properties of the system itself. I.e., it is not an epistemic limitation but an ontological barrier.禄

An excellent concept is the "ontological barrier". Here, to break through or "grasp" the barrier, deeper dialectic-ontological ideas are needed, first of all, a conscious transition to the paradigm of the world (the Universe) as a holistic process, to a deeper ontological understanding of matter in the spirit of Plato (taking into account all modern problems of understanding it - "dark matter "): Matter is what all forms are born of. Here the main ideas are the ideas of "generation" and "form." What are the "forms"? Absolute (unconditional) forms of the existence of matter (absolute, ultimate state). Moreover, when "grasping" primordially the structure of integrity, it is necessary that the "Occam's razor" be extremely sharp.

芦The fact is that even after having had to digested all of the above limitations, we seem to remain fully committed to the existence of fundamental laws of physics. We might view them metaphysically either as governing laws, or, in the Humean sense, as the maximal synthetization of acquired knowledge about nature. However in any event, these are laws: Unshakable, everlasting, fundamental, truths about the physical world. We do not know them all " but there they are".禄

I fully agree with this conclusion. But the main thing is to "dig" further into the ontology in order to "grasp" (understand) the nature of the "laws of Nature". Or rather, attempts to "grab" the First Law (meta law), which governs the Universe and thinking, the manifestations of which are numerous "laws of Nature", the laws of logic. Here is the question of the primary structure (ontological structure) of the Universe.

芦The possibility I would like to briefly contemplate here, one that seems particularly appropriate if one adopts the Humean approach, is that no such things exists. No absolute, exception free, everlasting laws.禄

Here I do not agree.

芦That theory of everything that would, among other accomplishments, unify in a smooth manner some version of quantum mechanics free of its already mentioned problems, i.e. a version of the theory without a measurement problem and a completely clear ontology, with our currently most successful theory of gravitation, General Relativity.禄

Quantum theory and General relativity are phenomenological (parametric, operationalist) theories without an ontological basis. These theories are not compatible. Let everyone work on their own "field". Any "theory of everything" should begin with the deepest (ultimate) ontology.

芦What, besides inductive arguments, leads us to be so convinced that such a theory ought to exist? What would be wrong in adopting the view that, yes there are indeed regularities in the world, in fact surprisingly large number of regularities, but there is simply no way to encode them all into a single unified coherent picture, because a picture, made out of postulates and formulas is after all, what our theories about the world are. There is a world out there, I am convinced, but why should it be susceptible to such characterization?禄

And again, physics, do not be afraid of metaphysics, ontology, dialectics! I completely agree with Carlo Rovelli: "Physics needs Philosophy." Notice, Carlo Rovelli put in conclusion the first among the questions. Discussed in the scientific community, the question: "What is space?" And only by sweat the question "What is time?". The picture of the world of physicists, mathematicians, biologists, poets and composers should be unified.

芦My proposal: untheoretizability. That is, such position would contemplate the ultimate untheoretizability of nature.禄

I strongly disagree with this conclusion. A breakthrough requires a new ontology and dialectics in the spirit of N. Kuzansky "coincidence of opposites", taking into account all the problems in understanding matter, a dialectic of the material and the ideal.

芦At this point I do not have much to add, but I think it would be worthwhile if the issue was studied, and some arguments against it or in its favor were brought up by people in the community.禄

I propose "assembling" all the crazy "ontological ideas" and conducting a Big Global Brainstorm.

So, there we have it, beyond Uncertainty, Uncomputability, and Unpredictability, there is Indefiniteness, and well beyond that there might be Untheoretizability.

I suggest starting with the attack on Uncertainty, recalling Morris Klein's work Mathematics: The Loss of Certainty and the articles by Calo Rovelli Physics Needs Philosophy / Philosophy Needs Physics and SCIENCE IS NOT ABOUT CERTAINTY: A PHILOSOPHY OF PHYSICS:

"I seem to be saying two things that contradict each other. On the one hand, we trust the knowledge, and on the other hand, we are always ready to modify in-depth part of our conceptual structure about the world. There is no contradiction between the two, because the idea of the contradiction comes from what I see as the deepest misunderstanding about science, which is the idea that science is about certainty.聽

Science is not about certainty. Science is about finding the most reliable way of thinking, at the present level of knowledge. Science is extremely reliable; it's not certain. In fact, not only it's not certain, but it's the lack of certainty that grounds it. Scientific ideas are credible not because they are sure, but because they are the ones that have survived all the possible past critiques, and they are the most credible because they were put on the table for everybody's criticism.禄

I believe that the motto for Brainstorming should be the philosophical covenant of John Archibald Wheeler: "Philosophy is too important to be left to the philosophers."

Excuse me, please, for English. I am doing a translation using a google translator.

Please also see my ontological ideas . and give, if possible. your critical questions and comments.

Sincerely,

Vladimir

A.Zenkin SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS

Dear Prof Daniel Sudarsky,

I must congratulate you as you got a very good sharp thinking. I can see the same from your wonderful essay and some of your postings. It is actually i saw some of your posts in other essays and came here......

Though I do not fully accept your words...............That theory of everything that would, among other accomplishments, unify in a smooth manner some version of quantum mechanics free of its already mentioned problems, i.e. a version of the theory without a measurement problem and a completely clear ontology, with our currently most successful theory of gravitation, General Relativity..............

Bur Your thinking is wonderful in saying that ..........It is, nonetheless, a logical alternative that we might want to at least contemplate: if there is no way to win, the only rational option is to be a defeatist. In order to contemplate the possibility, we should start by giving it a name: My proposal: untheoretizability. That is, such position would contemplate the ultimate untheoretizability of nature.......... I FULLY accept this idea.

Why dont you spare some time on my proposal: another untheoretizability of nature..... " https://fqxi.org/community/forum/topic/3416 "

Best Regards

=snp

Greetings Professor Sudarsky,

I wandered over, after seeing your well-informed comments to Andrew Beckwith. My framework produces a transition similar to DGP gravity via Pourhasan, Afshordi, and Mann except with torsion on the brane in the precursor or parent universe. That this scenario is linked to a massive graviton has forced me to examine those complications.

My current essay does not deal much with the astroparticle Physics, but I think graviton condensation as in Dvali and Gomez' work points to a settling or laying flat of the ground state gravitons at the horizon (quantum critical surface). I think this idea has promise as a way to unite the String theory and loop quantum gravity picture. So the Misiurewicz point I discuss in my essay may be of interest.

I will comment on it; once I have read your essay.

All the Best,

Jonathan

A delightful short essay Professor Sudarsky...

I agree with your assessment that you are examining a rather dire possibility or a grim reality. And I downloaded the papers you recommended to Cristi, to get a better handle on why you feel as you do. As it turns out; I met one of your coauthors, Yuri Bonder, at GR21 in NYC. But, in any case, I like that you emphasize that the uncertainty problem may be worse than we realize. I give you kudos and high marks.

It is brilliant to point out that indefiniteness is part of the problem, apart from the limited aspect of that in quantum indeterminacy. People are loath to think about the possibility that something can have an inherently indefinite value, in addition to our lacking knowledge about what the value might be. Nor is it proper to stop with 'it is only indefinite until we measure it' because it could still be floating or actually fuzzy then - before and after measurement.

I have rather the opposite problem, in terms of grappling with theorizability. My fate is like what Haldane describes, where a fortuitous discovery is made almost by accident, and then the implications are understood only after years of study and research. Some of the necessary Maths were not sufficiently developed to make a reasonable determination 32 years ago, so I had to go slow. But my challenge was to figure out "Why does this appear to describe all of Cosmology and Physics?" and to determine "Is this real?"

My essay gives you enough information to make a fair determination.

Regards,

Jonathan

Dear Daniel,

Thank you very much for your answer and good question.

Of course, I also doubt, as Rene Descartes bequeathed to all seekers of truth, that such a program will be successful. But my analysis of the development of philosophy, physics and mathematics allows me to conclude that the current crisis of understanding, crisis of interpretation and representation in the PHILOSOPHICAL BASIS of fundamental science is caused by the fact that physicists and mathematicians did not "dig" deeply into ontology and metaphysics. More than four centuries was ruled by the motto: "Physics, beware of metaphysics!"... The development of physics in the four centuries since the scientific revolution of Modern times is a period of Phenomenological physics (parametric, orperationalistic). I do not agree that some philosophers of science refer to periods as "classical", "non-classical", "post-nonclassical". This leads away from the essence, from the truth.

In metaphysics (ontology), physicists (as well as mathematics, as Morris Kline well showed in "Mathematics: The Loss of Certainty") tried not to "dig deep". Enough for the experience ("torture of Nature") was the study of phenomena. In physics, the "part paradigm" (atomistic, mechanistic) prevailed and continues to prevail. The paradigm of the world as a whole (the holistic paradigm) should come to the rescue. We need to look at the world (Universe) not as a system, but as a whole (an holistic process). "Understand" means "grasp the structure" (G. Gutner "Ontology of mathematical discourse"). In other words, it is necessary to "grasp» the ontological structure of the world (Universe) as an holistic process of generation of structures and meanings / senses (!!!). Moreover, meaning / senses should be put in the first place.

I would call this program "the program of Ontological basification of (fundamental) knowledge". First of all, we need a new view of matter in the spirit of Plato, taking into account the problems of understanding its fundamental (ontological) structure ("dark matter", "anti-matter", "dark energy») and the modern Information revolution: matter is what all FORMS are born from. This understanding of matter, where the key words "form" and "born" makes it possible to conduct a total unification of matter across all levels of existence of the Universe as an holistic generating process. The problem in understanding matter and, consequently, space (Absolute space) was laid down by the cognitive attitudes of the scientific revolution of the New time: the absolute rest of matter was excluded from the scientific picture of the world.

So first of all it is necessary to overcome the crisis of understanding: A)Universe as an holistic process of generation of meanings and structures; B) New understanding ("grasping») matter in the spirit of Plato: the absolute forms of existence (absolute, ultimate states); C) New understanding ("grasping») space (absolute, ontological).

Here, in just a few sentences, are the first steps in the program of Ontological basification of knowledge, the transition from Phenomenological physics to Ontological physics. I believe that any theory that claims to be called "fundamental" must not only have an empirical basification, but it must also be ontologically based (Ontological basification of the theory). In my essay, I gave a more detailed analysis and steps for gaining ontological certainty in the philosophical basis of knowledge, constructing the ontological basis of knowledge: ontological framework, ontological carcass, ontological foundation.

Best regards ,

Vladimir

Hi Daniel,

I loved your short essay. I totally agree on your replacement of uncertainty by indefiniteness. It indicates, that there is something wrong of attributing properties to object independent of its relation to something around it (in order not to fix too much what that shall be.) Then the problem of course is how we can achieve objectivity in the description of the world.

And more so I liked, that there might be an untheoretizability. As a nihilist (depending on who is asking), I stopped to believe at an underlying mechanism that controls the laws an phenomena. Then we can ask the interesting question of why we can so successfully theorize and find pretty unifying laws describing the universe.

In my essay I try to describe the possibility of laws and objects being emergent and dependent of the environment, which is contingent. So in free space or near a black hole different laws and objects might emerge. And the change from one law to the other might be beyond theoretizability.

Luca