Dear Gabriele,

I'm really glad that you enjoyed the opening four pages. Originally, the philosophy and history part was going to be longer but then I remembered that the contest rules asked for 'rigorous argument' so I thought I should put in some mathematics to show that I know what a rigorous argument in mathematics looks like!

I too also wanted a compact way of understanding Goedels incompleteness theorems as I struggled to understand the details of his work - it's not like I wanted to work as model theorist or logician - so it was a real discovery that proveability theory made the whole thing more focused. In fact, I thought this is the way that they should teach it as what he was trying to say comes out much more clearly.

I'm basically saying that quantum physics is telling us something about the nature of time. A lot of quantum interpretations work hard to remove it - for example Everetts Many Worlds; but I've never been someone who thought twice about the collapse postulate. To me it appeared to be quite natural and it showed that time, on a deep level, is irreversible and this is of course what we happen to know is as one of the key attributes of time. Of course, Newtons laws is time symmetric which should have been one of the first clues it wasn't the full story.

"are future statement an example of yet unknown things? Or you are arguing that they are special? I can state many things in the present that are unknown to me, and I can state other things about tomorrow that I know will be true."

Good question. It probably means that we would need to make the basic apparatus of modal logic a little more sophisticated so that we can handle the difference between future statements that are neccessary and those that are contingent.

Thank you for taking the trouble to read the essay.

Warm Wishes

Mozibur Ullah

Dear Edwin,

Thank you for taking the trouble to read my essay. Much appreciated. I'll make sure to read your essay properly when I get a chance. I just had a quick look through now and left a comment.

Warm wishes

Mozibur Ullah

I'd like to expand upon the point that I've made in my reply to Gabrielle:

In the Order of Time by Rovelli, he writes that:

"The difference between past and future is deeply linked to this

blurring. . . So if I could take into account all the details of the exact, microscopic state of the world, would the characteristic aspects of the flowing of time disappear? Yes. If I observe the microscopic

state of things, then the difference between past and future vanishes."

I'm saying that the collapse postulate shows that it doesn't - that is it establishes a direction of time; moreover, I think some aspect of thermodynamics must hold here too since - although we might model just one particle quantum mechanically - we know that there are many, many more; that's one of the main outcomes of incorporating special relativity into quantum mechanics.

Moreover, I actually think that the symmetry of time we find in Newtons Laws is something of a chimera. This is because by postulating time symmetry we can come up with Newtons theory. Usually, that time is a symmetry of Newtons theory is shown as something that we can deduce. I'm saying here, its actually an input into the theory.

    Dear Mozibur,

    >I remembered that the contest rules asked for 'rigorous argument'

    >so I thought I should put in some mathematics to show that I know

    >what a rigorous argument in mathematics looks like!

    I debated the same thing, and then decided not to include it. I essentially took this as an exercise to introduce the ideas we are working on in a light way... I usually have way too much math!

    >A lot of quantum interpretations work hard to remove it

    From what I have seen, most people who works on quantum field theory essentially remove the projection and assume evolution is always unitary. They do this because the projection is inherently non-local. Once the evolution is unitary, time does not matter: you work in the Heisenberg picture. So, yes, time is essentially removed. On the other side, people who work on quantum information/measurement that are closer to the experimental side, would be more aligned to your stance. I have met some that even dislike quantum field theory because it does not have the projection.

    This actually matter to the question I posed: any statement that has to do with spatial aggregates (i.e. total mass in a region, average charge in a region) cannot be defined at equal time for all observers.

    I am interested on the logic side because I have been working on a small framework to essentially handle the idea of "possible assignments" of statements. I never quite understood whether it was equivalent to modal logic or not, but the whole point is that a scientific theory establishes what can or cannot be found experimentally. So it's a series of logical relationship on what can happen.

    The structure I developed is done so that it maps very well to other mathematical structures used in math and physics (i.e. topologies, sigma-algebras, ...) and one way to do that was to make the structures algebraic instead of propositional. For quantum mechanics, the algebra of statements is the sigma-algebra that one has on the Hilbert space, which is therefore a standard sigma-complete Boolean algebra

    Therefore I did not need to break LEM or LNC. So I never really resolved whether breaking them is a good or bad thing... So I am always interested to see how exactly arguments for that work. I still do not understand exactly which new "theories" are brought in. So, any insight is appreciated!

    Gabriele

    Dear Mozibur,

    I just read your Essay with great pleasure. I will give a comment shortly. Meanwhile could you qualify, what you mean by "I actually think that the symmetry of time we find in Newtons Laws is something of a chimera. ..."? And that time symmetry is just an input into the theory. What does follow from that?

    Thanks

    Luca

    Dear Mozibur,

    I enjoyed your essay very much. The story I heard was the story of the struggle to find the right language to understand and describe quantum phenomena and maybe also a handle on the incompleteness theorems. The language can be found in the paraconsistent logic which can be grounded in the phenomenology of time: factual past and open future.

    You seem to take the asymmetry of time as fundamental, maybe grounded in our apriori intuition. It is more usual in physics to take the time symmetry laws as prior and then search an explanation for the asymmetry. Shouldn't you conversely explain the symmetry of the laws despite the apriori asymmetry. Where do you see the origin of the symmetry?

    You also seem to take the Born rule first, where most of the physicist feel the need to derive it from the deterministic unitary evolution. Also here, where do you see the origin of the unitary evolution?

    Recently I saw again the derivation of the group of addition on the whole numbers from the semigroup of the natural numbers. Identifying the semigroup with irreversible processes and group operations with reversible processes, I asked myself how that was possible at all. Was reversibility really derived from the former or was it already contained in the former?

    I though, that creation of natural numbers by the irreversible process of counting is only possible, if I can remember, from where I started to count and hence the process is reversible. If droplets would fall in water, the two droplets would not be distinguishable and so the natural numbers.

    Brouwers intuitionism is very interesting, because it puts the conceptual foundation of numbers on counting in time. This means on physical processes.

    Similar tried Dingler and later Lorenzen derive Euclidean geometry on the operations of rubbing three stones. They showed that you can get an Euclidean plane. The idea was to be able to build measurements apparatuses, that are law independent and can be used as conceptual foundation for physics.

    Von Weizsäcker argued, that the process of rubbing might fail if gravitational forces are to strong. Similarly one could ask under which physical conditions counting might fail or succeed. There cannot be a conceptual foundation of numbers without considering the laws of physics and maybe not even logic.

    The question now is, what is the physical condition for the possibility of having the asymmetry of time as foundation of logic and mathematics?

    In my essay I try to imagine physical laws as emergent from contingent physical conditions. The laws are described as semantically closed theories and I speculate that the phenomenology of time might come from a succession of such theories (laws), where the newer contains the older theory.

    I also wonder if you know Karl Von Weizsäcker?

    Sorry for the lengthy reply. I hope you found it interesting and hope you would comment and rate my essay.

    Thanks

    Luca

      Dear Mozibur,

      Thanks for a stimulating essay.

      In your conclusion you state: "In calculus we have infinitesimals. Newton called them fluxions, the infinitesimal element of change. It is something close to zero but not quite zero."

      It would seem that Newton's fluxions solve the dichotomy paradox of Zeno of Elea and its extensions, where infinitely many points can be reached in a finite time. The early Greek school of atomism, founded by Democritus and Leucippus, claimed that matter is not infinitely divisible, and by a similar argument, distance in space. Successive division of matter eventually terminates in atoms, that is, in discrete particles incapable of being further divided. Modern reductionism has now been formalised and currently stops at quarks and leptons, but my preon theory reduces both of these further to gimlis, at which stage we reach the bottom of the stack of turtles regarding matter. The only smaller particles are the ginn (aether) which form inseparable force relationships with gimlis (matter). Thus Newton's fluxions are the best way of mathematically describing my form of objective reality.

      You conclude: Thus dropping LEM, far from ushering us into a no-mans land of paradoxical, hostile and recalritant functions, has instead found us, if not a Cantorian paradise, then a Brouwerian paradise of an endlessly open and real future. To this I would respond, borrowing from Wittgenstein "I would say, 'I wouldn't dream of trying to drive anyone out of this (Cantorian) paradise.' I would try to do something quite different: I would try to show you it is not a paradise - so that you'll leave of your own accord. I would say, 'You're welcome to this; just look about you.'" Ha ha. The Brouwerian paradise is my "universe" of ginn and gimlis, that exists only in the now, but promises an endlessly open and real future!

      Cheers

      Lockie Cresswell

        Dear Mozibur,

        You presented a very interesting essay in the spirit of a deep Cartesian doubt, with historical analytics of the development of science and philosophy, important ideas and conclusions to overcome the crisis of understanding in the philosophical basis of fundamental science.

        Morris Kline in "Mathematics: The Loss of Certainty" showed well the entire hundred-year-old epic to overcome the crisis in the foundations of mathematics. M. Kline quotes the words of Hermann Weil, said in 1946 (16 years after Godel's discoveries): "We are now less than ever confident in primary fundamentals of mathematics and logic. We are going through our own "crisis" just like all and everything goes through it in the modern world."

        Doctor of Physical and Mathematical Sciences Alexander Zenkin (1936-2006) in SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS noted:

        "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 ... "

        The problem with the justification of mathematics and logic ontological basification) is problem No. 1 for fundamental science and for cognition as a whole. One hundred years of trying to solve the problem did not lead to success. Some philosophers of mathematics consider this problem "eternal". But the whole saga of solving the problem of "foundations of mathematics" says that the methods and approaches were inadequate.

        As Grigory Gutner notes in "Ontology of Mathematical Discourse», understanding is "grasping the structure". To «grasp» the primordial generating structure, common to Nature and thinking, dialectic ontologics is necessary. But the philosophy of science "sweeps the rug" of dialectics. There are also problems in philosophical ontology. Need breakthrough new ideas. To solve the problem of the foundations of knowledge, a dialectic-ontological basification of mathematics and logic is necessary. Mathematics is the "language of Nature", therefore, a deeper observation of Nature and its absolute forms of existence is necessary. At the same time, it's good to recall the philosophical testament of the philosopher and theologian Pavel Florensky: "We repeat: worldunderstanding is spaceunderstanding / Повторяем: миропонимание-пространствопонимание."

        If you have time, look also at my dialectic-ontological ideas .

        Yours faithfully,

        Vladimir

          Dear Luca,

          Thanks very much for your comment. I read it with interest and I'll make sure to read your essay. I've just had a look at it and thought it interesting and well-written but I want go through it a bit more carefully before responding to it.

          First, I want to say that the 'story' you heard is on the right lines and you summarised it very well. I liked your term - 'factual past and open future'.

          I suggested that time symmetry is 'chimeric' since it's possible to derive Newtons laws from this plus Galilean relativity and Aristotles law of motion, which is more or less Newtons first law of motion. Aristotle phrased it more generally, in that he was concerned about change in general, and not motion in particular.

          We know that Newton was aware of Democritean/Epicurean atoms. Take two such atoms that we suppose are exactly the same and throw them at each other with uniform velocity. They collide and bounce of each other. By Galilean relativity we can move to a frame where they are both approaching each other with exactly the same speed. What should we expect afterwards - that is what is the relationship of the final speeds compared to the initial?

          Given that the situation is symmetric the simplest thing to *postulate* is that it is symmetric, that is symmetric in time (around the point of collision). From this we can work out the change in momentum and so the second law. And obviously by the symmetry of the situation we *expect* the third law: the first atom hits the second, and by spatial symmetry, we must also think of the second hitting the first. Then we take the giant step of induction - we suppose this little test situation holds for all bodies given the Democritean stance that all things are made of atoms ...

          This is why I think time symmetry in Newton is a chimera. Don't get me wrong, it is there but I don't think it holds universally - and especially for atoms in the philosophical sense.

          I find Brouwers intuitionism interesting as it's quite concrete. For example, there are such things as Heyting algebras that play the same role there as Boolean algebras play in Classical logic/mathematics - have you heard of them? It's what got me first interested - plus I wanted to see how the LEM can be denied, especially in a mathematics context.

          I tried looking up Dingler and Lorenzen as I was curious as to how they 'derive Euclidean geometry from rubbing stone', as I was thinking it all began with measuring the earth (geo-metry!). Unfortunately all I found was an article on naturalistic epistemology, and that was behind a paywall. I think by your description I can guess: three stones are required for the vertices of a triangle - it was the 'rubbing' that fooled me!

          I only very recently heard about von Weisacker in connection with quantum logic, but I don't know very much about him. What did he have to say? Personally speaking, I'm doubtful about whether one can really take gravity into account here in the way Weisacker is saying. A similar charge was laid against Kant when he said that we 'intuit' Euclidean geometry 'apodicatally' (that is without even questioning it), that is he was criticised for not acknowledging the possibility of non-Euclidean geometry. But could we, or any biological creature, live in such extreme gravity fields that the curvature of space is appreciably different - I would suggest not.

          Thanks very much for taking the trouble to read my essay and for your own careful comments.

          Warm Regards

          Mozibur Ullah

          Dear Lachlan,

          Thanks for taking the trouble to read my essay.

          'I wouldn't dream of trying to drive anyone out of this (Cantorian) paradise.' I would try to do something quite different: I would try to show you it is not a paradise - so that you'll leave of your own accord. I would say, 'You're welcome to this; just look about you.'"

          Actually, I think von Neumann had pretty much the same idea. The day that Goedel announced his theorem he wrote to Carnap saying that Hilbert programme was dead in the water and the only game in town was intuitionism, but he didn't like it on 'aesthetic grounds' which for him was the 'key factor'.

          I think those were early days, remember classical logic has had a very long innings. Intuitionism by that kind of timescale is barely a child - still, from what I've seen of it, it's looking at quite a rosy future.

          I'll make sure to leave a reply on your entry.

          Best

          Mozibur Ullah

          Dear Vladimir,

          Thanks for taking the trouble to read my essay. Your comments are very much appreciated.

          What Zenkin has to say about our current zoo of logics is very appropriate (there is an even bigger zoo in algebra and please don't mention geometry) ... Still, one musn't mistake the many variations of a theme for the theme itself and this, in my reading was the rebirth of logic, in the early 20C.

          It was ripe for a rebirth as Hegel himself didn't think much of logic. He said, philosophy is always leaping ahead and logic is always limping far behind ...

          I can't say that I'm keen on what is now known as the philosophy of science. It feels rather narrow and constraining. I much prefer the ancients, they had a much broader view. Aristotle not only wrote on physics and logic, but also on poetry, politics and how to lead the good life.

          It's advice we could all do with following to find the flourishing life (and a flourishing planet).

          Warm Regards

          Mozibur Ullah

          Hi Mozibur,

          In fact it is difficult to find stuff about Paul Lorenzen and Dingler in the net. I recall that Lorenzen, for the prove to construct an Euclidean measurement apparatus, used symmetry arguments. That is why I think Weizsäcker's argument is a good one and central to the view in my essay. In the presence of strong gravitational fields the rotational symmetry is broken. This will exercise forces on the stones and deform them while the are rubbed against each other. The constructions will fail. It is not possible to realize concepts independent of the laws that they ought to describe. It is this unity of law and definition of concepts that makes intuitionistic mathematics interesting for physics in my opinion. But then if mathematical operations are equivalent to physical ones, then the laws the conditions under which these laws can be realized, become relevant also for the mathematical structures. Although we would like to think them independently of the physical world.

          Hope this makes sense.

          Weizsäcker for me is the best physicist who knows philosophy and vice versa. If you want you can look him up a little in one of my essays called Knowledge and time.

          And again: Great essay you wrote.

          Luca

          You present a very good argument that appears to be very similar to my own essay. Hence, I will proceed by contrasting our approaches.

          Since you referred to the sacred texts I will begin by pointing out that both (the psychologist) Carl Gustav Jung and (the Egyptologist) R. A. Schwaller de Lubicz made the case that the story of Genesis refers to the awakening of consciousness. However, I would make the case that they are referring to the rational, reasoning aspect of consciousness. Or at least that aspect of our minds (abstraction?) that is responsible for our ability to construct and use language. After all, only ten chapters later was the creation of "the first human language" that all the world was united under (or at least all of their world).

          The defining feature of natural language is its ability to give expression to absolutely anything. However, there is simply no way to determine whether what is expressed is accurate or true. Thus arises the need for our modern scientific language; the defining feature of which is its ability to adjudicate, at least to some potentially limited extent, the Accuracy or Truth of what is expressed in it.

          This is reflected in my essay when I juxtaposed the feature of "formal systems that accurately reflect reality... [and] formal systems that can accurately predict reality." This is my primary complaint with "Graham Priest and his paraconsistent ilk", which is that Priest's entire argument relies on asserting that contradictions exist and thus must be admitted into the language. However, in my opinion, a scientific language must be able to make use of the elements in its language. They are added for a reason, not just because they exist. We already have a language that strives to give expression to everything that exists.

          Therefore, I do not think that any progress on the issues with the LEM and LNC can occur by simply making the argument that they do not accurately reflect reality. I think that progress will occur when someone creates a (scientific) language that transcends the simplistic, superficial, bivalent language that exists today and, more importantly, one that "works" in the sense that the language can be employed to actually solve problems that could not previously be resolved. Of course, that assumes that some such language is even possible.

          I enjoyed reading your essay and wish you well in the contest. I will close by simply pointing out that every (sufficiently educated) person throughout the entire world can read and understand the sentence:

          "1 1 = 2"

          I would like to say that I have made progress on creating such a language and that my essay reflects this. However, unfortunately, I avoided the issue in my essay for the most part because all my attempts thus far to create such a language appear to be hopelessly contrived and, more importantly, do not resolve any of the issues that I have attempted to apply it to.

            Hi Mozibur!

            I really enjoyed reading your essay! I want to ask you one of my favorite questions: Do you think the only entity in the universe with access to complete information about the universe is the universe itself? I wonder this myself, since it seems like a trivial result, but then the subset of universe minus a single atom would probably have access to complete information too (since the universe could use probably deduce the movement of the lone atoms based off the interactions it has with other, known atoms).

            Just curious to know what your thoughts are!

            Cheers!

            Alyssa

            Mozibur,

            Vastly underrated so far. An intelligent, definitive and entertaining discussion of the ambiguities and the certainties of our difficult subject. Your adventure into being a bat is not only humorous and clever, but instructive.I go for the endlessly open and real future too: https://fqxi.org/community/forum/topic/3396. My rating is your 8th.

            Jim Hoover

            Dear Mozibur,

            My spirits raised on reading your excellent essay, pointed, out by another who saw our theses matched. You do a far more comprehensive job than me in demolishing the indivisible atom and Law of the Excluded Middle (LEM), but I focused on explore the important consequences of a replacement 'Law of the reducing middle', a Gaussian or sine curve, which I proposed 3 essays ago.

            I also suggest more than just 'time' falsifies the Law of non contradiction (LNC). If Aristotles 'sea battle' had involved just 3 boats against 3, or 1 vs 1, or a 3/5ths each fleet, would it have been that 'battle'.

            I'd also proposed the very concept of the = sign is flawed, and the root of the problem, by pointing out that everything observable in the universe is different!, a proposition nobody[/] has yet falsified! The consequences, when tested in physics, have proved to have a massive resolving power across all physics, shown in my last few essays & papers and reviewed this year. The last paper (see refs) effectively used Newtons 'fluxion' as the Wilczec 'Higgs Condensate' particle, now well rationalised in Wolfram et al's seminal new paper here; (maybe best read from p360 on). arxiv.org/abs/2004.08210

            I think and hope you'll appreciate my essay as much as I appreciate yours. I note our scores are close, and doubtless yours had received some 1 scores as mine has (or if not it probably will!) so I suggest a pact and mutually high scores. But please do read mine and give your views and comments.

            Very best.

            Peter

            Dear Mozibur Rahman Ullah!

            Your essay made us very happy.)) We agree with many of your theses. We evaluate it by the maximum possible rating of 10 points. We also believe that understanding time depends on logical principles. Therefore, we propose introducing some new principles for understanding time, which will allow us to understand in a new way both classical logic and set theory.The following definitions are given: 1) there is a set that we call "Time"; 2) this set consists of an infinite number of individual elements, which we call "Moments"; 3) all elements of a given set have a peculiarity: if one element is REAL, all other elements of the set are UNREAL; 4) we will call sets of this type - "AREAL SETS". It was found that the elementary areal relation is a logical law of contradiction: statements A and NOT-A together form an areal set of two elements. Formulating the law of contradiction, Aristotle and all the logicians after him constantly emphasized: there cannot be A and NOT-A in the same respect at the same TIME. We propose to rearrange the emphasis: in our formulation, AREALITY is a special logical relation that can simulate natural Time. The new model defines the time order in the form of definite characters' sequence. The proposed ontology is related to the definition and introduction of the digital physics paradigm.

            We hope that our approach will be useful to you.

            Truly yours,

            Pavel Poluian and Dmitry Lichargin,

            Siberian Federal University.

            8 days later

            Dear Jason,

            First of all, thank you for your kind words about my essay. They were appreciated.

            I haven't read anything by Jung, although I did mean to once. I found his notion of archetypes intriguing. Indeed, I think I read once, somewhere, that the myth of Prometheus, was also a story about the awakening consciousness of man. However, perhaps because I am older (but not necessarily wiser), I'm more apt to return to my own religious roots and read the sacred texts, as they were originally intended, as a gateway into a more numinous realm; although, admittedly, with my scientific training, and the kind of secular world we live in now, that is not always easy.

            I also appreciate your honesty in your assessment of the progress you have made on creating the kind of language you are hoping for. I think this is often true for any task that is worth the trouble of doing well. Often it is one step forward, two steps back, and then a third step sideways.

            I think this is the same task that Liebniz embarked on. So you have illustrious predeccessors. My own take on this, is that modern scientific language is the language in which to express such objective propositions about the world. Nevertheless, because we are human, because we are many, and thinking is diverse and plural, such a language is likely never to be uniform. My own experience of mathematical language, which many people take to be uniform, I find is often shot through with many discontinuities, and I so often wished that people would stick to a uniform notation!

            Warm wishes,

            Mozibur Ullah

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