Essay Abstract

This essay points to hidden premises in the arguments demonstrating the existence of mathematical propositions that are formally unprovable. It is argued that blindness to such premises has confused the interpretation of unprovability and uncomputability theorems. The same blindness has led many to assign improper and too prominent roles to codes and computation, roles they cannot play regardless these theorems. Similarly, there are hidden premises in the rules we use to extract predictions from quantum theory. The source of the hidden premises is the same in the mathematical and the physical cases: we have to assume outside agents who act on the system being studied - be it a formalisation of arithmetic, or an experimental setup designed to test Bell's inequalities. The relation between the agent and the system has a specific form. Everything with specific form can be used as a handle to new insights. In this case the claimed common source allows us to find common traits of formal unprovability in mathematics and physical indeterminism. To find these common traits, we need to open our eyes. We are blind to the nature of the relation between ourselves and the world since we are born with it, and thus take for granted - just like we are deaf to the harmony of the spheres since we always hear it, or so it is said.

Author Bio

The author has a PhD in mathematical physics from Lund University, Sweden. He has also engaged in cross-disciplinary research, trying to reconstruct the diffusion of innovations in Antiquity from the archaeological record. He also works outside Academia.

Download Essay PDF File

Respected Professor Per ﾃ-stborn,

Thank you for nice essay. You presented in a simple logical way with algorithmic approach. Very nice. But how to go about the sources of hidden premises?, as you said in your own words...........Similarly, there are hidden premises in the rules we use to extract predictions from quantum theory.............

I just elaborated what should be the freedom available to an author when the " real open thinking" is supported. Have a look at my essay please.

"A properly deciding, Computing and Predicting new theory's Philosophy"

=snp.gupta

12 days later

Found a great quote by Gödel that sums up a major point of my essay:

"The purpose of philosophy is not to prove everything from nothing, but to assume as given what we see as clearly as shapes and colors - which comes from sensations but cannot be derived from sensations. The positivists attempt to prove everything from nothing. This is a basic mistake shared by the prejudices of the time, so that even those who reject positivism often slip into this mistake. Philosophy is to call attention to certain immediately given but not provable facts, which are presupposed by the proofs. The more such facts we uncover, the more effective we are."

A major such mistake today is the drive to explain consciousness in terms of something else. We bang our heads into the wall, inventing phrases such as "emergence" or "the hard problem of consciuosness". Admit instead that it is an immediately given fact, explore its role in the world, and go from there.

Otherwise we will just continue to waste our time. As Gödel puts it:

"To explain everything from nothing is impossible: not realizing this fact produces inhibition."

12 days later

Dear Per,

A very interesting and important essay that directs the mind to deep thoughts on the problems of fundamental science, overcoming the crisis of understanding in the philosophical basis of knowledge. I have only one question on the ontological structure of the "beginning", the hypothesis of which is being promoted by fundamental physics today - "Big bang". Are you a supporter of this hypothesis, taking into account your philosophical thoughts and conclusions in your essay?

With kind regards, Vladimir

    Dear Vladimir,

    Thanks for your kind words. I think big bang is the inevitable end point of an extrapolation backwards in time of the observed state of the universe, given the known laws of physics. On the other hand, it is unclear what ontological status you should give to it, since there was nobody there who could observe it. What do you think yourself?

    Kind regards,

    Per

    Dear Per,

    I believe that extrapolation will not help here. One question about the nature of the "laws of Nature" and the nature of fundamental constants - immediately a philosophical stop. Moreover, the "big bang" hypothesis. Carlo Rovelli is right: Physics Needs Philosophy / Philosophy Needs Physics More specifically, we need non-ordinary ontological and dialectical ideas in understanding primarily matter and space. Today, physics is dominated by the "paradigm of the part" (atomistic, mechanistic). The physicists should come to the aid of the paradigm of the world (Universum) as a whole. Here it is necessary to reconsider the entire dialectical line, starting from Heraclitus. Particular attention should be paid to the modern interpretation of Kuzansky's idea of ​​"coincidence of opposites" and the development of Whitehead's ideas in his metaphysics and dialectics of process.

    The problem of primordial ontological structure is a purely philosophical problem. This is an attempt to unravel the "Creator's thought before the Act of Creation". Problems in physics (dark matter, dark energy and others) are pushing physicists to seek help from the "mother of all sciences" - Philosophy. This thought of thought should be an ontological and dialectical thought, the ultimate thought of the absolute forms of existence of matter (absolute states). The modern Information Revolution, a clue to the nature of the phenomenon of information, is pushing for this.

    Please look at my ontological and dialectical ideas and, if possible, give critical remarks.

    With kind regards, Vladimir

    a month later

    Dear Per,

    I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

    "The objectivity of such a world does not reside in the physical objects that are observedin three-dimensional space. Rather, it resides inthe parts of the conceptual tower and how they fit together. The tower hasits rotating cogwheels,likeamental mill, or aclock. True, this is another kind of clockwork universe than thatsuggested in the seventeenth century. Even so, it is not for us to decide how the conceptual clock tower operates in its abstract space, what the pieces look like and how they fit together. That cannot be changed by our wishes. We can still get crushed between itscogwheels. In that sense such auniverseisstill objective".

    It is fine.

    But he has keywords that can change the whole of science, how Maxwell changed science by creating his own equations, presenting his rotors in the form of simple cogwheel models.

    Gerard't Hooft says of CA:

    "We conclude that the most general model will be described as a set of simple periodic cogwheel models with varying periodicities."

    While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability".

    I hope that my modest results of work will provide you with information for thought.

    Warm Regards, `

    Vladimir

    Write a Reply...