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RECENT POSTS IN THIS TOPIC

Vladimir Fedorov: on 5/17/20 at 6:20am UTC, wrote Dear Paul I greatly appreciated your work. I am very glad that you are not...

George Gantz: on 5/15/20 at 20:47pm UTC, wrote Paul - I like your essay. Simple and straightforward. An elegant way to...

Marcel-Marie LeBel: on 4/26/20 at 15:11pm UTC, wrote *** I am not sure I understand what you mean by all theories start with...

Paul McKarris: on 4/25/20 at 21:30pm UTC, wrote Hello, Thank you for your comment. I am not sure I understand what you...

Marcel-Marie LeBel: on 4/25/20 at 14:34pm UTC, wrote If one arrives at a conclusion by making choices, the result is an opinion,...

David Brown: on 4/24/20 at 12:03pm UTC, wrote "The way we argue the truth of a statement in a model is not precise...

Satyavarapu Gupta: on 4/23/20 at 19:23pm UTC, wrote Dear Paul McKarris, Godel's law as.........Godel proved that any...

Paul McKarris: on 4/23/20 at 17:35pm UTC, wrote Essay Abstract The Godel incompleteness metatheorem seems to bring...


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FQXi FORUM
September 17, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: A Redefinition of the Notion of Truth by Paul McKarris [refresh]
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Author Paul McKarris wrote on Apr. 23, 2020 @ 17:35 GMT
Essay Abstract

The Godel incompleteness metatheorem seems to bring a sense of discomfort. This discomfort appears to stem from the notion of truth that originates from model theory. This notion of truth is in some sense not precise. By accepting a simple statement, one can conclude that the notion of truth has to change. In this new view of truth, we will explore how physics could be done.

Author Bio

Paul McKarris is an undergraduate student in Mathematical Physics at the University of Waterloo, Ontario, Canada.

Download Essay PDF File

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 23, 2020 @ 19:23 GMT
Dear Paul McKarris,

Godel's law as.........Godel proved that any consistent mathematical theory (formalized as an axiomatic deductive system in which proofs could in principle be carried out mechanically by a computer) that contains enough arithmetic is incomplete (in that arithmetic sentences ' exist for which neither ' nor its negation can be proved)...................

I have few questions about it. This law is applicable to Quantum Mechanics, but will this law be applicable to COSMOLOGY.......?????.........

I never encountered any such a problem in Dynamic Universe Model in the Last 40 years, all the the other conditions mentioned in that statement are applicable ok

I hope you will have CRITICAL examination of my essay... "A properly deciding, Computing and Predicting new theory’s Philosophy".....

Best Regards

=snp

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David Brown wrote on Apr. 24, 2020 @ 12:03 GMT
"The way we argue the truth of a statement in a model is not precise enough. ... we should have the capacity write to everything down explicitly." Does a mathematical formula potentially exist if and only if there is some empirical possibility that the formula can somehow be represented in a material medium? Define googol as 10 raised to the power 100. Define googolplex as 10 raised to the power googol. Is there a time interval with a duration in seconds equal to the reciprocal of googol? Is there a time interval with a duration in seconds equal to the reciprocal of googolplex?

According to Frreman J. Dyson’s translation of an 1896 speech by Emil Wiechert, “… The universe is infinite in all directions, not only above us in the large but also below us in the small. …”

p. 36 of 2004 edition of “Infinite in All Directions” by Freeman J. Dyson, 1985 Gifford Lectures

Which theory is more likely: string theory with the infinite nature hypothesis, or string theory with the finite nature hypothesis?

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Marcel-Marie LeBel wrote on Apr. 25, 2020 @ 14:34 GMT
If one arrives at a conclusion by making choices, the result is an opinion, since someone else could make choices different from him and rightly come to a different conclusion/opinion.

If one follows the rules of a mathematical equation, his result will be a truth because everyone else will have no choice but to come to the same conclusion.

A truth is an absence of choice for everyone. The strongest truth of all is an impossibility, because the truth value of something possible is just that, possible. But the truth value of an impossibility is certain!

This is why our best theories all start by an impossibility; … to go faster than light (SR), …. to distinguish between gravity and inertia (GR) … to measure momentum and position …

But the price for such certain true start is that it can never be proven. “impossibility” is timeless i.e. it means it was, is, and always will be that way; that we can’t prove. So, those initial strong “impossibility” truths can only be POSTULATED, never proven right, be definitely be proven wrong.

The start of any truth system is such impossibility. In fact, the topmost truth of everything is the law of non-contradiction; it tops the creation and operation of the universe as well as all our truth making activities, maths, logic, etc.

IF absolutely anything was possible … this universe would a big mess … if it existed at all. But we see regularities, laws of physics etc. Therefore, there must be at least ONE thing that is not possible; one impossibility that makes everything else possible; the law of non-contradiction.

A truth is an absence of choice for everyone. This is an operational definition of truth i.e. answering the question: What can I do about it? Nothing!

Q: Can you put this in modal logic?

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Author Paul McKarris replied on Apr. 25, 2020 @ 21:30 GMT
Hello,

Thank you for your comment.

I am not sure I understand what you mean by all theories start with impossibilities.

Postulates are all associations between a physical notion and a mathematical object.

For example, a quantum system would be a separable complex Hilbert space. I also gave the example of Spacetime in my essay.

In SR it is not postulated that faster than light is impossible.

In my essay, I do not discuss how to verify a physical theory, I just give a framework for which theories have to at least satisfy to be considered physical theories.

Whatever is said in my essay is very general about any language, so it would work for modal logic as long as you are clear about your deductive system.

Best,

Paul

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Marcel-Marie LeBel wrote on Apr. 26, 2020 @ 15:11 GMT
*** I am not sure I understand what you mean by all theories start with impossibilities.

A specific impossibility is what defines a theory and all the inferences that come from it; a truth system. To “define” is to make “finite”, to limit and form a boundary. Prigogine noticed it;

“Let us observe that curiously, the two great revolutions in physics over the century have been precisely connected with the inclusion of impossibilities in the frame of physics. In relativity a fundamental role is played by the velocity of light which limits the speed at which we may transmit signals. Similarly Planck's constant h limits the possibilities of measuring simultaneously position and momentum.”

Ilya Prigogine, 1983

The “inclusion of impossibilities” is not an accident; this is how it works. In SR, did we say it was possible that light speed is a limit? No, we said it is impossible to go faster. But, as said above, an impossibility can’t be proven. Since different impossibilities define different truth systems, it is normal that GR and QM can’t be logically reconciled, …. without bending the rules.

***Postulates are all associations between a physical notion and a mathematical object.

Postulates are “let’s assume x is true” statements. I believe that in order to have a “defining” “constraining” “boundary” power it should read as: “let’s assume that it is impossible that x is not true”.

To “assume” is just a way to admit our ignorance about the possibility that the statement is either true or false. It is therefore clearer to include this fact in the postulate and to make it “definite” as an impossibility. Bottom line; we can’t prove a "possible" assumption true all the time but we need to prove an impossibility assumption wrong, only once.

Thanks,

Marcel

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George Gantz wrote on May. 15, 2020 @ 20:47 GMT
Paul - I like your essay. Simple and straightforward. An elegant way to side-step the difficulties of Godel's incompleteness theorem. But I think it's a limited side-step that gives a practical answer but fails to address the deeper metaphysical ones. I'd be interested in your reaction to my essay. I take the limits of Godel and Turing (and QP and complexity) as evidence of limits to "knowing" and then examine what these limits suggest. My thoughts are speculative, and unprovable, but I think they are at least coherent and consistent.

Cheers - George Gantz: The Door That Has No Key: https://fqxi.org/community/forum/topic/3494

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Vladimir Nikolaevich Fedorov wrote on May. 17, 2020 @ 06:20 GMT
Dear Paul

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

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

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