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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