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**Stefan Weckbach**: *on* 3/14/18 at 7:08am UTC, wrote Stephen Hawking died in the early morning hours. RIP Stephen Hawking.

**Stefan Weckbach**: *on* 2/25/18 at 4:51am UTC, wrote O.K., here is the attachment:

**Stefan Weckbach**: *on* 2/25/18 at 4:50am UTC, wrote I attach an addendum to my essay that can be read on page 9 of the...

**Vladimir Fedorov**: *on* 2/22/18 at 6:13am UTC, wrote Dear Stefan, I highly appreciate your beautifully written essay. It is...

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**Stefan Weckbach**: *on* 2/19/18 at 14:16pm UTC, wrote Hi Steve, happy that you read and liked it! Thanks for your good wishes...

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FQXi FORUM

April 14, 2021

CATEGORY:
FQXi Essay Contest - Spring, 2017
[back]

TOPIC: "No rule without an exception, except this rule." by Stefan Weckbach [refresh]

TOPIC: "No rule without an exception, except this rule." by Stefan Weckbach [refresh]

ABSTRACT: In this paper we show that the term ‘fundamental’, as used in physics, can generally be defined from two different points of view. Firstly by looking at this term from the frog’s perspective within our limited world and secondly by looking at it from a bird’s perspective above and beyond our limited world. One of our main results is that what seems to be fundamental from a viewpoint within a certain system can be fundamentally meaningless from a viewpoint outside this system and vice versa. We further demonstrate that unequivocally answering the question “what is ‘fundamental’?” is an instant of the so called ‘Boolean satisfiability problem’ (SAT-problem). We solve this SAT-problem by a modus operandi which transcends these extrinsic and intrinsic viewpoints by introducing a fundamental concept that is capable of being universally valid inside as well as outside our limited world. Our approach is able to explain the origins of mathematics as well as those of antivalent logic. It further shows that the problem to assign any truth value ‘true’ to the ‘possibility’ that absolutely nothing instead of something could have existed in the past is an unsatisfiable SAT-problem. By the very reason that our framework spans the bridge between the extrinsic and the intrinsic, it finally establishes a bird’s view on certain aspects of ultimate reality.

The author's main scientific interests are mathematical undecidability, algorithmic information theory, questions concerning consciousness, human free will and logics. Additionally he is interested in various interpretational questions about quantum mechanics.

Hi Stefan - I enjoyed reading your paper - You sound very philosophical in this presentation. I gather from your conclusions that it is not possible to start with nothing. You must start with "F" and accept it as a fundamental truth from which everything else can be logically (and mathematically) derived. That leaves us with one important question... (which in essence is the same question I posed to another similar philosophical essay)... Who gets to figure out "F"?

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Scott, thank you for the comment. My opinion on this is that one cannot completely ‘figure out’ F, in our limited world this is impossible. Every F can simply be doubted. If you mean by ‘figure out’ a kind of formal proof, one cannot prove by means of a formalized procedure that ultimate reality is *not* entirely only a formal system. Only a formal system can prove itself to be formal, what gives us no new information. ‘F’, in my opinion, is not fully formalizable and therefore not provable, similar to every nuance of our emotions. Surely, one may believe that consciousness and emotions can one day be formalized completely as kinds of special mathematical patterns (in the brain). I doubt this. This led me to conclude that – due to my conviction that one has to start with ‘F’ – one either ends with ‘F’, or with the deduction that ‘F’ must exist – but cannot be fully formalized. The latter not due to practical impossibilities, but due to a *fundamental* principle. This ‘principle’ says, in my opinion, that ultimate reality is not exclusively only composed of formal systems but necessarily must be more than that. Because since mathematics as the prime formal system cannot prove its own consistency and completeness, the assumption that formal systems are fundamentally capable of encompassing the real ‘F’ seems to be absurd to me. Especially if this ‘F’ should be mathematics itself.

I agree - "F" cannot be provable - but "F" can be physical with a mathematical description. If the initial conditions involving "F" sets off an inevitable chain of events that also follows a mathematically derivative course, and in doing so leads to every known law of physics and property of particles... then we may have something!

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Yes, then we have at least a logically consistent scheme. But it would not automatically be a scheme that necessarily must be realized by nature. I think – due to Moore’s theorem mentioned in my essay – that what you describe is indifferent to the status quo of fundamental physics today. Cause there are a multitude of different interpretations of quantum mechanics, all matching the ‘known’ laws of physics, means the observational output these laws generate. In all these interpretations, ‘initial conditions’ are interpreted differently.

I love your essay. This is my turf.

A truth is an absence of choice, a fact.

A truth is only valid in the truth system that created it.

Nothingness is the necessary logical opposite to existence.

Existence-being is not possible from nothingness.

But existence as "happening" is possible. Happening is not being...

We must understand the universe as such a logical system, born from nothingness via a loophole in the primitive rule of non-contradiction...

My essay is coming up. You might like it.

Marcel,

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A truth is an absence of choice, a fact.

A truth is only valid in the truth system that created it.

Nothingness is the necessary logical opposite to existence.

Existence-being is not possible from nothingness.

But existence as "happening" is possible. Happening is not being...

We must understand the universe as such a logical system, born from nothingness via a loophole in the primitive rule of non-contradiction...

My essay is coming up. You might like it.

Marcel,

report post as inappropriate

Marcel, thanks for your comment. Happy that you like what i exemplified in my essay. I am looking forward to your essay contribution to be published!

Hi Stefan, In your last response to my statement (Scott S Gordon) :

"If the initial conditions involving "F" sets off an inevitable chain of events that also follows a mathematically derivative course"

You stated,

"Yes, then we have at least a logically consistent scheme. But it would not automatically be a scheme that necessarily must be realized by nature.

Actually if the initial condition is so basic with only one ingredient (and the energy associated with it), and it derives every law of physics, the manner in which each particle exists and came to exist, every force, every energy field.. - It would have to be the ONLY scheme possible - And afterall, are we not looking for the solution to the theory of everything? Do you think there are multiple solutions?

Once the laws of physics are known and the manner in which they came into existence is known - there should only be ONE solution. So again the question becomes - Who finds the initial ingredient (and its associated energy) and their mathematical representations?

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"If the initial conditions involving "F" sets off an inevitable chain of events that also follows a mathematically derivative course"

You stated,

"Yes, then we have at least a logically consistent scheme. But it would not automatically be a scheme that necessarily must be realized by nature.

Actually if the initial condition is so basic with only one ingredient (and the energy associated with it), and it derives every law of physics, the manner in which each particle exists and came to exist, every force, every energy field.. - It would have to be the ONLY scheme possible - And afterall, are we not looking for the solution to the theory of everything? Do you think there are multiple solutions?

Once the laws of physics are known and the manner in which they came into existence is known - there should only be ONE solution. So again the question becomes - Who finds the initial ingredient (and its associated energy) and their mathematical representations?

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Scott, you make some very strong claims.

I have a question: how can you know that

“…it would have to be the only scheme possible”?

As I outlined in my essay, the criterion for every TOE must be Truth, not simplicity. This somewhat simple statement may hit you, but even your own approach has to obey a simple scientific rule for being able to claim to be the one and only TOE: it must make a testable prediction that could be falsified. Even for the case that such a ‘TOE’ incorporates ‘all the known laws of physics’ (what I seriously doubt in case of your approach) – it must be able to derive from within itself a prediction of a phenomenon that has not yet been observed. Or do you think that mankind has already observed ALL natural phenomena that are observable according to our hitherto known physical laws? Do you really think that physics is theoretically and practically a finished job? Wouldn’t claiming such things have at least a little bit of hybris within it and for the more serious case even the inability to discriminate between what has factually been achieved by physics (or by the own approach) and what one wishes to have achieved by one's own approach?

For the case you want to talk me into your approach to be indeed THE TOE…, I would recommend you to go again to the drawing board and find a testable prediction your approach is able to make from within itself.

I have a question: how can you know that

“…it would have to be the only scheme possible”?

As I outlined in my essay, the criterion for every TOE must be Truth, not simplicity. This somewhat simple statement may hit you, but even your own approach has to obey a simple scientific rule for being able to claim to be the one and only TOE: it must make a testable prediction that could be falsified. Even for the case that such a ‘TOE’ incorporates ‘all the known laws of physics’ (what I seriously doubt in case of your approach) – it must be able to derive from within itself a prediction of a phenomenon that has not yet been observed. Or do you think that mankind has already observed ALL natural phenomena that are observable according to our hitherto known physical laws? Do you really think that physics is theoretically and practically a finished job? Wouldn’t claiming such things have at least a little bit of hybris within it and for the more serious case even the inability to discriminate between what has factually been achieved by physics (or by the own approach) and what one wishes to have achieved by one's own approach?

For the case you want to talk me into your approach to be indeed THE TOE…, I would recommend you to go again to the drawing board and find a testable prediction your approach is able to make from within itself.

Yes - I AM making a huge claim - and of course people will question it... like when you say you serious doubt that my theory explains everything. You asked what my theory predicts... My theory predicts that the experiment planned for neutrino/anti-neutrino annihilation that there will be no annihilation despite the "fact" that neutrinos were "proven" to have mass.

By definition the math of the theory of everything must begin very simple since it starts with one ingredient. It has to be more simple than any equation we have because it starts before ANY particles were created to exist in spacetime (and all we know is the physics and math of particle that exist in spacetime). The math of the theory of everything has to built to the math that derives the postulates used to create GR and QM. If the postulates used to derive these two theory can be derived by one model, then they will automatically be united under one theory.

Physicists do not seem to understand that it is not possible to unite these theories using the math of the theories because you will never be able to derive why their initial postulates are true and why they should exist in the first place.

I suggest you learn exactly what the ruby slipper conundrum and the concept of infinite scales are and how my model increases in complexity through the hierarchy of energy before you automatically dismiss it. AND YES - If a theory that starts with one building block ingredient (and energy) does explain everything and also explains what is not possible, then it is the one and only scheme possible for the theory of everything.

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By definition the math of the theory of everything must begin very simple since it starts with one ingredient. It has to be more simple than any equation we have because it starts before ANY particles were created to exist in spacetime (and all we know is the physics and math of particle that exist in spacetime). The math of the theory of everything has to built to the math that derives the postulates used to create GR and QM. If the postulates used to derive these two theory can be derived by one model, then they will automatically be united under one theory.

Physicists do not seem to understand that it is not possible to unite these theories using the math of the theories because you will never be able to derive why their initial postulates are true and why they should exist in the first place.

I suggest you learn exactly what the ruby slipper conundrum and the concept of infinite scales are and how my model increases in complexity through the hierarchy of energy before you automatically dismiss it. AND YES - If a theory that starts with one building block ingredient (and energy) does explain everything and also explains what is not possible, then it is the one and only scheme possible for the theory of everything.

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Scott, i read your essay. Even in the papers you cited on your essay page, you mention your ‘ruby slipper conundrum’ only for the purpose that for understanding it one has to buy and read your 300 page book available on amazon.

In your essay, this presupposed important concept is not exemplified, not referred to a single time. You have to understand that for your strong claims, you can’t simply refer to a 300 page book (one has to buy for 40-90 Dollars) in an essay contest like this. You missed the chance to give the reader an access to the ‘ruby slipper conundrum’ (if it at all exists) by outlining it in your essay. Everyone of us has the problem of limited space and characters for accurately writing down one’s own ideas. Compressing these ideas into a 9 page, 25000 character body is difficult, but a challenge.

Your essay is in large parts a copy of your papers published on academia.ru. Why you didn’t use the 9 pages to explain the ‘ruby slipper conundrum’ a bit closer is a hint for me that this conundrum doesn’t play the important role you claim. Anyways, you can’t expect that the reader buys your book (350 pages for 89 Dollar hardcover), when you can’t convince him with what is the sole purpose of this essay contest – namely with a well composed essay on the essay’s theme.

What is a conundrum for me, is that you are in my opinion one of many people who think they found THE TOE, people who want the appropriate merits and credit for what they think to be THE TOE, but different from most of this people, you deny the access to the claimed understanding of your TOE by trying to SELL it, instead of publishing it for free. Therefore I recommend you to give away your book’s content for free, so that everybody can prove for himself whether or not your claims are justified.

“Yes - I AM making a huge claim - and of course people will question it... like when you say you serious doubt that my theory explains everything.”

Remember that the one who makes huge claims has to justify them. I will not buy your book to refute your claims, simply make it available for free and we can further discuss it.

In your essay, this presupposed important concept is not exemplified, not referred to a single time. You have to understand that for your strong claims, you can’t simply refer to a 300 page book (one has to buy for 40-90 Dollars) in an essay contest like this. You missed the chance to give the reader an access to the ‘ruby slipper conundrum’ (if it at all exists) by outlining it in your essay. Everyone of us has the problem of limited space and characters for accurately writing down one’s own ideas. Compressing these ideas into a 9 page, 25000 character body is difficult, but a challenge.

Your essay is in large parts a copy of your papers published on academia.ru. Why you didn’t use the 9 pages to explain the ‘ruby slipper conundrum’ a bit closer is a hint for me that this conundrum doesn’t play the important role you claim. Anyways, you can’t expect that the reader buys your book (350 pages for 89 Dollar hardcover), when you can’t convince him with what is the sole purpose of this essay contest – namely with a well composed essay on the essay’s theme.

What is a conundrum for me, is that you are in my opinion one of many people who think they found THE TOE, people who want the appropriate merits and credit for what they think to be THE TOE, but different from most of this people, you deny the access to the claimed understanding of your TOE by trying to SELL it, instead of publishing it for free. Therefore I recommend you to give away your book’s content for free, so that everybody can prove for himself whether or not your claims are justified.

“Yes - I AM making a huge claim - and of course people will question it... like when you say you serious doubt that my theory explains everything.”

Remember that the one who makes huge claims has to justify them. I will not buy your book to refute your claims, simply make it available for free and we can further discuss it.

See godels incompleteness hypothesis

https://en.wikipedia.org/wiki/G%C3%B6del%27s_incom

pleteness_theorems

says the main point with far more rigor

Andrew

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https://en.wikipedia.org/wiki/G%C3%B6del%27s_incom

pleteness_theorems

says the main point with far more rigor

Andrew

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Andrew, what is the main point you refer to? Let’s have real discussions here at the Essay contest, with arguments from yourself instead of citing chapters from wikipedia. I cannot conclude from your citings what your main point is and if there is any point at all you want to make.

stepan

your point was far better made by Godel, and you still do not get it. I am not castigating you, but until you read the Godel incompleteness proof and understand it, then there is not a lot more I can bring up

To whit, what you wrote is a tautology and until you actually read the PROOF of what Godel wrote, and understand it, I have little to discuss with you.

https://plato.stanford.edu/entries/goedel-incompleteness

/

Just read it, please, and if you do not, I will abstain from any further comments.

Good luck

report post as inappropriate

your point was far better made by Godel, and you still do not get it. I am not castigating you, but until you read the Godel incompleteness proof and understand it, then there is not a lot more I can bring up

To whit, what you wrote is a tautology and until you actually read the PROOF of what Godel wrote, and understand it, I have little to discuss with you.

https://plato.stanford.edu/entries/goedel-incompleteness

/

Just read it, please, and if you do not, I will abstain from any further comments.

Good luck

report post as inappropriate

bluntly put, Godel did a far better job than you did, and all I am asking you to do , is to read the source of the idea.

If you cannot bother doing that, I have nothing further to say.

Your demands for a "real discussion" do not get to the point.

The point is, that your essay is a loose paraphrase of what Godel was bringing up, and until you accept that, and actually get some mathematical rigour to your exposition, there is little to discuss.

I.e. Godel nailed it.

Paraphrasing Godel as you have done, is not exactly a strategy to break new ground.

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If you cannot bother doing that, I have nothing further to say.

Your demands for a "real discussion" do not get to the point.

The point is, that your essay is a loose paraphrase of what Godel was bringing up, and until you accept that, and actually get some mathematical rigour to your exposition, there is little to discuss.

I.e. Godel nailed it.

Paraphrasing Godel as you have done, is not exactly a strategy to break new ground.

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https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_

theorems

quote

Completeness[edit]

A set of axioms is (syntactically, or negation-) complete if, for any statement in the axioms' language, that statement or its negation is provable from the axioms (Smith 2007, p. 24). This is the notion relevant for Gödel's first Incompleteness theorem. It is not to be confused...

view entire post

theorems

quote

Completeness[edit]

A set of axioms is (syntactically, or negation-) complete if, for any statement in the axioms' language, that statement or its negation is provable from the axioms (Smith 2007, p. 24). This is the notion relevant for Gödel's first Incompleteness theorem. It is not to be confused...

view entire post

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Exelent essay

In my opinion, Newton's theory of gravity holds:

- 1. The theory is not wrong, but at the same time also not necessarily a complete description of what is going on.

Do you think so?

Regars,

Brfanko Zivlak

meteorologist

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In my opinion, Newton's theory of gravity holds:

- 1. The theory is not wrong, but at the same time also not necessarily a complete description of what is going on.

Do you think so?

Regars,

Brfanko Zivlak

meteorologist

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Branko, thanks for your comment, your question and that you cherish what you read.

As to your question, you cited a case where a prediction of a theory has been confirmed. Let’s say this is the precession of Mercury’s perihelion, what comes about in GR to be approximately the value of observation. Since GR was not designed to a posteriori fit these observational data (as far as I can know!:), I would say that GR predicted it.

I cannot exclude that there are different theories possible which also can predict this phenomenon, theories that rest on different postulates than GR does.

For the case of Newton’s theory of gravity, I cannot see how it can hold to explain the precission of Mercury’s perihelion. But that I cannot see it does not mean that you necessarily must be wrong. Tell me more about your view on Newton’s theory of gravity if you like.

As to your question, you cited a case where a prediction of a theory has been confirmed. Let’s say this is the precession of Mercury’s perihelion, what comes about in GR to be approximately the value of observation. Since GR was not designed to a posteriori fit these observational data (as far as I can know!:), I would say that GR predicted it.

I cannot exclude that there are different theories possible which also can predict this phenomenon, theories that rest on different postulates than GR does.

For the case of Newton’s theory of gravity, I cannot see how it can hold to explain the precission of Mercury’s perihelion. But that I cannot see it does not mean that you necessarily must be wrong. Tell me more about your view on Newton’s theory of gravity if you like.

No doubt Anstein's contribution to the understanding of nature is huge.

But I do not believe that the explanation of Merkur's problem with the GR is essential.

According to Ruđer Bošković, 2 in the square of the distance of Newton's gravitational formula is not exact 2.

I believe, the essential is the surface, not the distance in Newton formula.

I do not know how to prove it.

Regards,

Branko

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But I do not believe that the explanation of Merkur's problem with the GR is essential.

According to Ruđer Bošković, 2 in the square of the distance of Newton's gravitational formula is not exact 2.

I believe, the essential is the surface, not the distance in Newton formula.

I do not know how to prove it.

Regards,

Branko

report post as inappropriate

stepan

your point was far better made by Godel, and you still do not get it. I am not castigating you, but until you read the Godel incompleteness proof and understand it, then there is not a lot more I can bring up

To whit, what you wrote is a tautology and until you actually read the PROOF of what Godel wrote, and understand it, I have little to discuss with you.

https://plato.stanford.edu/entries/goedel-incompleteness

/

Just read it, please, and if you do not, I will abstain from any further comments.

Good luck

report post as inappropriate

your point was far better made by Godel, and you still do not get it. I am not castigating you, but until you read the Godel incompleteness proof and understand it, then there is not a lot more I can bring up

To whit, what you wrote is a tautology and until you actually read the PROOF of what Godel wrote, and understand it, I have little to discuss with you.

https://plato.stanford.edu/entries/goedel-incompleteness

/

Just read it, please, and if you do not, I will abstain from any further comments.

Good luck

report post as inappropriate

Andrew, you claim very much with your comment… You claim e.g. that

1. I have not read Gödel’s work

2. I do not understand it

3. My essay is a loose paraphrase of what Gödel was bringing up

All three points you made are false.

Even for the case that Gödel’s work would turn out to be – for whatever hitherto unknown reasons – false, my essay does not in any way depend on the correctness of Gödel’s work. The latter just reassures my conclusions, it is not in opposition to my conclusions. I think you misunderstood what I intended to say with the realm of fundamental truth. This is not merely a realm of logical / mathematical tautologies, but an existential realm that incorporates consciousness as a fundamental ingredient. Not all tautologies are fundamental truths, but according to my essay, all fundamental truths are perceived (and are) as self-evident tautologies in the realm of fundamental truth. Self-evidently, this realm must be located beyond space and time, since space and time could turn out to be just temporary appearances. They are, in my opinion, for the reasons I layed out in my essay, not fundamental truths, since in my opinion, a fundamental truth should be timeless.

I have not found any hints in Gödel’s official mathematical work that states that truth must be in union with consciousness, what my essay says is independent from what Gödel brought up with his work. Therefore the points you made are twice devoid of any meaning for the conclusions in my essay. Gödel’s work is important, but for me, Gödel is not the one and only authority when it comes to the question “what is fundamental”.

Good luck also for you!

1. I have not read Gödel’s work

2. I do not understand it

3. My essay is a loose paraphrase of what Gödel was bringing up

All three points you made are false.

Even for the case that Gödel’s work would turn out to be – for whatever hitherto unknown reasons – false, my essay does not in any way depend on the correctness of Gödel’s work. The latter just reassures my conclusions, it is not in opposition to my conclusions. I think you misunderstood what I intended to say with the realm of fundamental truth. This is not merely a realm of logical / mathematical tautologies, but an existential realm that incorporates consciousness as a fundamental ingredient. Not all tautologies are fundamental truths, but according to my essay, all fundamental truths are perceived (and are) as self-evident tautologies in the realm of fundamental truth. Self-evidently, this realm must be located beyond space and time, since space and time could turn out to be just temporary appearances. They are, in my opinion, for the reasons I layed out in my essay, not fundamental truths, since in my opinion, a fundamental truth should be timeless.

I have not found any hints in Gödel’s official mathematical work that states that truth must be in union with consciousness, what my essay says is independent from what Gödel brought up with his work. Therefore the points you made are twice devoid of any meaning for the conclusions in my essay. Gödel’s work is important, but for me, Gödel is not the one and only authority when it comes to the question “what is fundamental”.

Good luck also for you!

Hi Stefan, I enjoyed your essay. I like the idea of the frog and birds eye views. Both in Max Tegmark's paper 'shut up and calculate" and when you use the same different viewpoints idea. Though I am now thinking that (excuse the diversion) it would be good to have a frogs eye view and the view of the hive mind of a swarm of intelligent flies. The flies can then have multiple viewpoints of the same arrangement and relations within it rather than a singular viewpoint. All of the flies, though having different individual opinions on variable values, orientations and so on will all be correct.(This ties in with relativity.) In that way the picture constructed comes closer to the truth than the impoverished single viewpoint, singular value and states that are the product of singular observers 'saying what is there'. The flies rather than frog is many worlds of possible measurements that become just one value or state for a single frog. The many worlds, other than its own view, for the frog, are not other universes but different views of the universe not made. Which ties in with quantum mechanics, in particular. Though it is also relevant to your discussion of a realm of truth. I agree with you that there is such a foundational reality. I did like your pointing out that true falsehood is a kind of truth itself. I think the truth can be arrived at by finding all of the falsehoods and putting them out of the way. Which is how the scientific method at its best works.'Certainly not like that' is closer to the truth than 'it might be like this or it might not' of a not dis-proven hypothesis. Its like drawing, which can be done by outlining the positive filled spaces or by drawing the outline of the negative empty spaces. The techniques arrive at the same outcome if done accurately. Using both can help with accuracy of the drawing. Well done, kind regards Georgina

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By 'realm of truth', I mean the existent the universe as it fully is and is happening, rather than as seen and experienced, and measured; with singular viewpoints or apparatus and protocol giving a single outcome.

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Hi Georgina, thanks for reading and of course for commenting! Your effort of commenting is appreachiated by me.

I indeed took the terms frog’s view and bird’s view from Max’ paper. They encode a huge problem not yet solved, the dichotomy between the subject (consciousness) and the object (matter), between relative, subjective truths (in reference to what is fundamental) and the necessity for the existence of such fundamental truths, means the fact that there is an external world independent of relative, subjective truths (objective truths) and whether or not these objective truths come out of literally nothing in the sense I defined it in the essay.

Many accounts on these problems assume the realm of what is most fundamental to be infinite. I am not quite sure if Max does also, but I take both possibilities into account. If mathematics is infinite, then one cannot speak meaningfully of an ‘outside’ for the black box I described as gedankenexperiment, hence there cannot be a bird’s view, since then, the mathematical landscape is infinitely infinite, so to speak. Otherwise, if what is most fundamental would be finitely describable (albeit in a coarse-grained manner), one could refer to an ‘outside’ meaningfully in the sense whether or not there are further objective reasons for this most fundamental thing (in the case of Max’s paper it would again be mathematics) to be fundamental at all.

If maths is finite, I think this would be a surprise for everybody. But I conclude just this in my essay: mathematics is a finitely, physical construct, as physical as one assumes matter, enery, wave functions and laws of physics to be physical. I consider ‘infinity’ from a logical point of view as merely an alternative term to express that something is fundamentally undefined – and undefinable (at least in our limited world).

You raise the question of many worlds. Many worlds fall naturally out of a global wave function, the latter seen as fundamental. The question is whether or not such a global wave function does exist ontologically. I cannot exclude this, but I doubt it, due to the arguments I gave in my essay against the exclusiveness of the complete formalizability of all that exists.

I like your painting analogy. This is what we normally do by inferencing due to antivalent thinking. The point I wanted to make in my essay is that you never can picture such a painting objectively with only antivalent thinking at hand. The best example for this impossibility seems to me the very essay contest here, where different assumptions are hold about what is true and what is false.

My own approach stems from the considerations of what properties a realm must have that does not suffer from the dichotomy of true and false propositions. My conclusion is that falseness as an option should evaporate into ‘thin air’ for at all being able to meaningfully speak about a ‘most fundamental’ as the basis for objective reality. Just consider what an angel in a spiritual realm (‘heaven’) would experience: she wouldn’t experience the possibility that her realm could be just a fake, a kind of computer animation (since then it wouldn’t be heaven anymore but just like earth…). She wouldn’t experience this possibility, but not due to an error in her perception, but due to the fact (the truth) that this realm refers not anymore to ‘time’, but to eternity. Eternity in this sense means eternal truth without falseness in it. So the reason why you can’t objectively paint this realm is that there is only ‘white’ in it, but no black.

You state that “I think the truth can be arrived at by finding all of the falsehoods and putting them out of the way. Which is how the scientific method at its best works.” Albeit there is some truth in this statement, personally I wouldn’t fully agree, since obviously there are situations where you aren’t able to unequivocally identify some falsehood in the sense of a decisive proof for a counterexample, or a decisive proof for a certain assumption to be true at all. The problem is not that we can’t observe in many cases *how* nature behaves, the problem is to unequivocally prove for at least some cases *why* it does so.

Thanks again for your thoughtful comment and good luck in the constest!

Kind regards, Stefan

I indeed took the terms frog’s view and bird’s view from Max’ paper. They encode a huge problem not yet solved, the dichotomy between the subject (consciousness) and the object (matter), between relative, subjective truths (in reference to what is fundamental) and the necessity for the existence of such fundamental truths, means the fact that there is an external world independent of relative, subjective truths (objective truths) and whether or not these objective truths come out of literally nothing in the sense I defined it in the essay.

Many accounts on these problems assume the realm of what is most fundamental to be infinite. I am not quite sure if Max does also, but I take both possibilities into account. If mathematics is infinite, then one cannot speak meaningfully of an ‘outside’ for the black box I described as gedankenexperiment, hence there cannot be a bird’s view, since then, the mathematical landscape is infinitely infinite, so to speak. Otherwise, if what is most fundamental would be finitely describable (albeit in a coarse-grained manner), one could refer to an ‘outside’ meaningfully in the sense whether or not there are further objective reasons for this most fundamental thing (in the case of Max’s paper it would again be mathematics) to be fundamental at all.

If maths is finite, I think this would be a surprise for everybody. But I conclude just this in my essay: mathematics is a finitely, physical construct, as physical as one assumes matter, enery, wave functions and laws of physics to be physical. I consider ‘infinity’ from a logical point of view as merely an alternative term to express that something is fundamentally undefined – and undefinable (at least in our limited world).

You raise the question of many worlds. Many worlds fall naturally out of a global wave function, the latter seen as fundamental. The question is whether or not such a global wave function does exist ontologically. I cannot exclude this, but I doubt it, due to the arguments I gave in my essay against the exclusiveness of the complete formalizability of all that exists.

I like your painting analogy. This is what we normally do by inferencing due to antivalent thinking. The point I wanted to make in my essay is that you never can picture such a painting objectively with only antivalent thinking at hand. The best example for this impossibility seems to me the very essay contest here, where different assumptions are hold about what is true and what is false.

My own approach stems from the considerations of what properties a realm must have that does not suffer from the dichotomy of true and false propositions. My conclusion is that falseness as an option should evaporate into ‘thin air’ for at all being able to meaningfully speak about a ‘most fundamental’ as the basis for objective reality. Just consider what an angel in a spiritual realm (‘heaven’) would experience: she wouldn’t experience the possibility that her realm could be just a fake, a kind of computer animation (since then it wouldn’t be heaven anymore but just like earth…). She wouldn’t experience this possibility, but not due to an error in her perception, but due to the fact (the truth) that this realm refers not anymore to ‘time’, but to eternity. Eternity in this sense means eternal truth without falseness in it. So the reason why you can’t objectively paint this realm is that there is only ‘white’ in it, but no black.

You state that “I think the truth can be arrived at by finding all of the falsehoods and putting them out of the way. Which is how the scientific method at its best works.” Albeit there is some truth in this statement, personally I wouldn’t fully agree, since obviously there are situations where you aren’t able to unequivocally identify some falsehood in the sense of a decisive proof for a counterexample, or a decisive proof for a certain assumption to be true at all. The problem is not that we can’t observe in many cases *how* nature behaves, the problem is to unequivocally prove for at least some cases *why* it does so.

Thanks again for your thoughtful comment and good luck in the constest!

Kind regards, Stefan

Stefan, thanks for your reply giving further information about the thoughts that have gone into your essay.Much appreciated.

I agree that practically it isn't possible to uncover all falsehoods to reveal the complete truth. Nevertheless it is a good method. It will only work well where there is a clear division between true and false. There is also a grey area of it depends. Which can be a matter of whether or not the conditions can be carefully controlled to minimize unwanted influences. Something that springs to mind as not definitely true or false is the health benefit of beta carotene, unless you are a smoker. More problematic for things like health studies and social science of populations investigations than physics.

I should mention I have put a short 2 page article in the Ultimate reality forum under Alternative models of reality that cites your essay paper.

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I agree that practically it isn't possible to uncover all falsehoods to reveal the complete truth. Nevertheless it is a good method. It will only work well where there is a clear division between true and false. There is also a grey area of it depends. Which can be a matter of whether or not the conditions can be carefully controlled to minimize unwanted influences. Something that springs to mind as not definitely true or false is the health benefit of beta carotene, unless you are a smoker. More problematic for things like health studies and social science of populations investigations than physics.

I should mention I have put a short 2 page article in the Ultimate reality forum under Alternative models of reality that cites your essay paper.

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Your rule F is similar to Russell's set that does not include itself, or the barber who shaves everyone who does not shave themselves. Who then shaves the barber? This is a sort of paradox.

Gödel's theorem is in a way an approximation to a paradox of this sort. It concerns theorems that state their own unprovability. These can be shown to exist by taking all predicates of a system, form their Gödel numbers and use them as the subject or variable in these predicates. The possible set of such self-referential propositions is larger than any enumerable listing of them by this process. This means there exist theorems T that are unprovable. Also since T → ¬Prov(T), and so by modus tolens Prov(T) → ¬T, so if T is provable then T is false which means it is provable. That is a contradiction. Therefore T must be true and provable, which is a contradiction.

Nagel and Newman argued that the fifth axiom of geometry. In some qualitative sense that may be so, for we can work with geometries where the parallel axiom works, such as flat space Euclidean geometry, or we can work in geometries where it is false such as curved spaces. Bernays and Cohen showed the Continuum hypothesis is a form of Gödel theorem, and so it is unprovable and one can work with models where it is true or false. This has lead to the whole abstract business of forcing.

Gödel theorem might have some role with quantum measurement. Of course some people are horrified by this suggestion, and at this time I consider this as just a possibility. The superposition of states in a system shifts to entanglements with states in an apparatus, which evolve through many states. We can think of the superposition of photons passing through a double slit, where if we place spin states at one slit we convert that superposition into the entanglement with spins. If we then have a general needle state this entanglement is spread into more states which is associated with the einselected state of a classical outcome. This evolution is a sort of diffusion that because of its complexity is extremely difficult to track. As a result we have decoherent sets that are in effect coarse grained sets of states.

Even if an observer could observe all possible states of the apparatus or the general needle state, this leads to the difficulty that the observer herself is also a complex of quantum states. This means that a fine grained description may be simply impossible. This leads to a situation where a set of quantum states are encoding quantum states, which can't be completely described in a closed system. Measurements tend to involve a classical system that in some ways is an open system, not closed. There is a sort of Universal Turing Machine or Godel numbering involved with attempting to describe this in a completely axiomatic manner.

Cheers LC

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Gödel's theorem is in a way an approximation to a paradox of this sort. It concerns theorems that state their own unprovability. These can be shown to exist by taking all predicates of a system, form their Gödel numbers and use them as the subject or variable in these predicates. The possible set of such self-referential propositions is larger than any enumerable listing of them by this process. This means there exist theorems T that are unprovable. Also since T → ¬Prov(T), and so by modus tolens Prov(T) → ¬T, so if T is provable then T is false which means it is provable. That is a contradiction. Therefore T must be true and provable, which is a contradiction.

Nagel and Newman argued that the fifth axiom of geometry. In some qualitative sense that may be so, for we can work with geometries where the parallel axiom works, such as flat space Euclidean geometry, or we can work in geometries where it is false such as curved spaces. Bernays and Cohen showed the Continuum hypothesis is a form of Gödel theorem, and so it is unprovable and one can work with models where it is true or false. This has lead to the whole abstract business of forcing.

Gödel theorem might have some role with quantum measurement. Of course some people are horrified by this suggestion, and at this time I consider this as just a possibility. The superposition of states in a system shifts to entanglements with states in an apparatus, which evolve through many states. We can think of the superposition of photons passing through a double slit, where if we place spin states at one slit we convert that superposition into the entanglement with spins. If we then have a general needle state this entanglement is spread into more states which is associated with the einselected state of a classical outcome. This evolution is a sort of diffusion that because of its complexity is extremely difficult to track. As a result we have decoherent sets that are in effect coarse grained sets of states.

Even if an observer could observe all possible states of the apparatus or the general needle state, this leads to the difficulty that the observer herself is also a complex of quantum states. This means that a fine grained description may be simply impossible. This leads to a situation where a set of quantum states are encoding quantum states, which can't be completely described in a closed system. Measurements tend to involve a classical system that in some ways is an open system, not closed. There is a sort of Universal Turing Machine or Godel numbering involved with attempting to describe this in a completely axiomatic manner.

Cheers LC

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Hi Lawrence, thanks for your excellent comments and your thoughts envoled in them. I will give my answers subsequently in this reply according to the points you made.

According to Russell’s barber, this paradox necessarily presupposes that *none* of the other men (wich means the group of men in the village *except* the barber) are allowed to shave those other men of the village. Otherwise the barber wouldn’t be a barber - *according to Russell’s definition*. So, Russell’s whole definition of a barber is *ill-defined*, since this is not what a barber must be defined, even for the case that there is only one barber in the village. The point is, that Russell’s definition of the barber as “no men in the village are allowed to shave other men – except the barber” (this is the real fixed-point that can be extracted from the context in which Russell’s definition seems to be true) does *not imply* that people are *not* allowed to shave themselves. Therefore the barber can shave himself.

What you say about Gödel’s theorem and provability is interesting. It all crucially relies on whether or not logics is able to capture some fundamental truths. If logic and with it the mathematical systems which produced Gödel’s results in the first place are inconsistent, then of course everything is provable with the help of these systems. So, the presupposition that logics is consistent demands that there are some true statements within those systems which are not provable with the help of these systems.

Otherwise one potentially could prove a system to be inconsistent and incomplete, but could also prove that a system is *not* inconsistent and incomplete. So would the latter proof be a stronger one, in the sense that the system under consideration should be considered as consistent, but incomplete? This is a senseless question, since we observed from the very start that the system generated a contradiction, leading to *everything* at the end of the day. If you can’t make anymore a reliable distinction with a certain system, it is then senseless to further use this system.

Gödel’s results are only *fundamentally* true under the following two presuppositions:

1. logics is consistent

2. Mathematics is eternal and infinite

If one of these two presuppositions is false, Gödel’s results have no fundamental impact whatsoever. In my essay I argue that the second point may be false in the sense that our traditional view of mathematics as an eternal platonic realm is difficult to reconsile with Gödel’s results, since every extension of a mathematical system critically hinges on what one considers to be a necessary additional axiom – for making such an extension not only *consistent*, but *eternally true*.

The problem is, if there exists an infinite, non-denumerable number of truths within this mathematical landscape, then also Moore’s theorem should hold and every physically or mathematically defined final theory of everything would be a final theory of nothing – when refered to the question why our universe is what it is – and why mathematics is what it is. The suggested advantage of an eternal landscape of mathematics is that it seems to justify that there exists something at all, rather than nothing. What brings me back to the very beginning, since even the quest for the existence of God is in some form an instance of unprovability – in the same sense the eternal mathematical landscape is. In this sense, people knew all along, long before Gödel’s results, that there may be things which cannot be logically proven nor disproven, but nonetheless could be true. Surely, the mathematical universe hypothesis, for example, does rest on empirically gathered data, means, on the truth that nature indeed incorporates a certain amount of mathematics. But it is also true that it incorporates a certain amount of consciousness. Max’s (the latter I appreciate in very many respects) claim of the MUH rests (beneath others) on the assumption that even consciousness is fully formalizable by mathematics. I doubt this by saying that mathematics can at the maximum merely establish correlations between some brain actions and some mathematical patterns.

The question of how to properly interpret such correlations is a fundamental one. I am currently working on this, but cannot present yet any robust results. Trying to describe a strictly deterministic system in terms of axioms seems to be impossible to me other than taking it at face value and therefore as a true axiom that all that exists is indeed ‘merely’ a strictly deterministically acting system. It could turn out that a superposition of states yields *less* information about the system then the parts of the system themselves. Therefore it is crucial for me to look how one can incorporate an observer into quantum mechanics, the latter being independent of a strict determinism, but nonetheless being able to have some limited free-will at hand to decide between two mutually exclusive options. And you are right about closed systems. As I described in my essay, it may turn out that defining ultimate reality solely in terms of formal systems may itself be just a closed system. I am working on stepping out of such a system in a logically and meaningful manner in terms of how to properly interpret a global wave function. If I succeed, I surely will publish what I found.

According to Russell’s barber, this paradox necessarily presupposes that *none* of the other men (wich means the group of men in the village *except* the barber) are allowed to shave those other men of the village. Otherwise the barber wouldn’t be a barber - *according to Russell’s definition*. So, Russell’s whole definition of a barber is *ill-defined*, since this is not what a barber must be defined, even for the case that there is only one barber in the village. The point is, that Russell’s definition of the barber as “no men in the village are allowed to shave other men – except the barber” (this is the real fixed-point that can be extracted from the context in which Russell’s definition seems to be true) does *not imply* that people are *not* allowed to shave themselves. Therefore the barber can shave himself.

What you say about Gödel’s theorem and provability is interesting. It all crucially relies on whether or not logics is able to capture some fundamental truths. If logic and with it the mathematical systems which produced Gödel’s results in the first place are inconsistent, then of course everything is provable with the help of these systems. So, the presupposition that logics is consistent demands that there are some true statements within those systems which are not provable with the help of these systems.

Otherwise one potentially could prove a system to be inconsistent and incomplete, but could also prove that a system is *not* inconsistent and incomplete. So would the latter proof be a stronger one, in the sense that the system under consideration should be considered as consistent, but incomplete? This is a senseless question, since we observed from the very start that the system generated a contradiction, leading to *everything* at the end of the day. If you can’t make anymore a reliable distinction with a certain system, it is then senseless to further use this system.

Gödel’s results are only *fundamentally* true under the following two presuppositions:

1. logics is consistent

2. Mathematics is eternal and infinite

If one of these two presuppositions is false, Gödel’s results have no fundamental impact whatsoever. In my essay I argue that the second point may be false in the sense that our traditional view of mathematics as an eternal platonic realm is difficult to reconsile with Gödel’s results, since every extension of a mathematical system critically hinges on what one considers to be a necessary additional axiom – for making such an extension not only *consistent*, but *eternally true*.

The problem is, if there exists an infinite, non-denumerable number of truths within this mathematical landscape, then also Moore’s theorem should hold and every physically or mathematically defined final theory of everything would be a final theory of nothing – when refered to the question why our universe is what it is – and why mathematics is what it is. The suggested advantage of an eternal landscape of mathematics is that it seems to justify that there exists something at all, rather than nothing. What brings me back to the very beginning, since even the quest for the existence of God is in some form an instance of unprovability – in the same sense the eternal mathematical landscape is. In this sense, people knew all along, long before Gödel’s results, that there may be things which cannot be logically proven nor disproven, but nonetheless could be true. Surely, the mathematical universe hypothesis, for example, does rest on empirically gathered data, means, on the truth that nature indeed incorporates a certain amount of mathematics. But it is also true that it incorporates a certain amount of consciousness. Max’s (the latter I appreciate in very many respects) claim of the MUH rests (beneath others) on the assumption that even consciousness is fully formalizable by mathematics. I doubt this by saying that mathematics can at the maximum merely establish correlations between some brain actions and some mathematical patterns.

The question of how to properly interpret such correlations is a fundamental one. I am currently working on this, but cannot present yet any robust results. Trying to describe a strictly deterministic system in terms of axioms seems to be impossible to me other than taking it at face value and therefore as a true axiom that all that exists is indeed ‘merely’ a strictly deterministically acting system. It could turn out that a superposition of states yields *less* information about the system then the parts of the system themselves. Therefore it is crucial for me to look how one can incorporate an observer into quantum mechanics, the latter being independent of a strict determinism, but nonetheless being able to have some limited free-will at hand to decide between two mutually exclusive options. And you are right about closed systems. As I described in my essay, it may turn out that defining ultimate reality solely in terms of formal systems may itself be just a closed system. I am working on stepping out of such a system in a logically and meaningful manner in terms of how to properly interpret a global wave function. If I succeed, I surely will publish what I found.

Oh, of course it should be

“Otherwise one potentially could prove a system to be inconsistent and incomplete, but could also prove that *this* system is *not* inconsistent and incomplete.”

Instead of

“Otherwise one potentially could prove a system to be inconsistent and incomplete, but could also prove that a system is *not* inconsistent and incomplete.”

“If you can’t make anymore a reliable distinction with a certain system, it is then senseless to further use this system.”

The latter statement is, for avoiding misunderstandings, of course in reference to what the system can and has to say about ‘more or less fundamental’ things. For example non-euclidean geometry us indeed useful for examining the consequences of GR, but it doesn’t (and cannot) say anything about whether or not gravity is merely a statistical description of something else (as annotated in the Contest Guidelines).

I hope to have clarified some rather uncouthed formulations in my previous post. If not – just ask.

“Otherwise one potentially could prove a system to be inconsistent and incomplete, but could also prove that *this* system is *not* inconsistent and incomplete.”

Instead of

“Otherwise one potentially could prove a system to be inconsistent and incomplete, but could also prove that a system is *not* inconsistent and incomplete.”

“If you can’t make anymore a reliable distinction with a certain system, it is then senseless to further use this system.”

The latter statement is, for avoiding misunderstandings, of course in reference to what the system can and has to say about ‘more or less fundamental’ things. For example non-euclidean geometry us indeed useful for examining the consequences of GR, but it doesn’t (and cannot) say anything about whether or not gravity is merely a statistical description of something else (as annotated in the Contest Guidelines).

I hope to have clarified some rather uncouthed formulations in my previous post. If not – just ask.

Hi Lawrence… and of course I have once more forgotten to answer an important part of your comment, because there are so many issues involved in your comment. So here is my answer to your remarks concerning rule F:

This rule is perfectly consistent and not paradoxical. Try to imagine it like this:

There are 1000 doors. Behind every door, there is a certain rule. Behind the first 999 doors, there are arbitrary rules, with each an exception. Behind door number 1000, there is a rule that captures a regularity common to all the other rules behind the 999 doors, namely that each of these rules have an exception.

The paradoxical character of Rule F only comes about due to the semantical issue of the usage of the word “exception” in the second part of rule F. If you imagine door number 1000 (behind where rule F resides) and compare it to the other rules, it has no exception, since all rule F is about is a compressed commonality all the 999 other rules have. For rule F to have an exception itself would depend on at least one of the 999 other rules having *no exception*, right? Then rule F could indeed no more considered as truly describing a commonality all the 999 other rules have.

In this sense, the fact that *no* rule of those 999 rules has *no* exception (caution, double negation!), necessitates that rule number 1000 (rule F) *has* indeed *no* exception. Remember, Rule F is exclusively only about the 999 other rules’ exceptions. In the form I wrote it down in my essay, it may seem that it is also about some exceptions for Rule F itself, because Rule F is as well as all the other 999 rules a rule. Despite the undeniable fact that rule F is indeed a rule, it is clear that it refers the whole lot only to the 999 other rules’ exceptions, not to an exception that it has itself - albeit rule F indeed does refer to itself in the form I wrote it down in my essay. But this self-reference is harmless and non-paradoxical.

Replace one of the 999 rules with a rule that has *no exception* - and rule F is forced *to have an exception*. Globally seen, in this system, when just one of the 999 rules are replaced in the manner described, there will always be one rule without an exception. Surely it is not guaranteed that such a replacement results again in the original rule F. This depends on what one does insert as a new rule behind the one of those 999 doors.

This rule is perfectly consistent and not paradoxical. Try to imagine it like this:

There are 1000 doors. Behind every door, there is a certain rule. Behind the first 999 doors, there are arbitrary rules, with each an exception. Behind door number 1000, there is a rule that captures a regularity common to all the other rules behind the 999 doors, namely that each of these rules have an exception.

The paradoxical character of Rule F only comes about due to the semantical issue of the usage of the word “exception” in the second part of rule F. If you imagine door number 1000 (behind where rule F resides) and compare it to the other rules, it has no exception, since all rule F is about is a compressed commonality all the 999 other rules have. For rule F to have an exception itself would depend on at least one of the 999 other rules having *no exception*, right? Then rule F could indeed no more considered as truly describing a commonality all the 999 other rules have.

In this sense, the fact that *no* rule of those 999 rules has *no* exception (caution, double negation!), necessitates that rule number 1000 (rule F) *has* indeed *no* exception. Remember, Rule F is exclusively only about the 999 other rules’ exceptions. In the form I wrote it down in my essay, it may seem that it is also about some exceptions for Rule F itself, because Rule F is as well as all the other 999 rules a rule. Despite the undeniable fact that rule F is indeed a rule, it is clear that it refers the whole lot only to the 999 other rules’ exceptions, not to an exception that it has itself - albeit rule F indeed does refer to itself in the form I wrote it down in my essay. But this self-reference is harmless and non-paradoxical.

Replace one of the 999 rules with a rule that has *no exception* - and rule F is forced *to have an exception*. Globally seen, in this system, when just one of the 999 rules are replaced in the manner described, there will always be one rule without an exception. Surely it is not guaranteed that such a replacement results again in the original rule F. This depends on what one does insert as a new rule behind the one of those 999 doors.

Hi Stefan,

first of all, I would like to congratulate you on the fact that your essay is one of comparatively few that actually*tackle* the contest question head-on, rather than merely *tacking* it on to otherwise nearly unrelated ruminations. You lay out the groundwork in a thorough manner, noting the inherent confusions in talking about 'nothing' and 'everything'---in particular, your nothing is a real nothing, not some vacuum state, or Riemannian manifold, or other excessively something-y idea of nothing some physicists make a habit of slipping into their discussions of 'creation from nothing'.

Unfortunately, I seem to get lost a fair bit in your prose---maybe it's just that I haven't quite had my head on straight for most of the day, and I need to think about things more deeply, but at times you seem to tangle yourself up into a semantic knot I can't seem to untie.

In some parts, I feel a certain closeness to my own ideas---and after all, we already seem to share many similar interests. For instance, you seem to share a similar thesis of human limitations when it comes to deciding purported 'truths' about the world. After all, it seems like 'this machine halts' should be either true, or false, but there's as we all know no general effective way of getting at that truth or falsity.

I'm not sure I understand your characterization of the empirical content of physical theories, however. The classical account (following Popper) would be that if an experiment confirms a theory's prediction, it may yet be either right or wrong (some other experiment might disagree with it), while falsification rules a theory out (in, uh, theory at least). You seem to view both much more symmetrically. Do you think that the Popperian account is insufficient?

(I should note that I think the falsificationist credo has its shortcomings, but it's so often portrayed as essentially the 'received wisdom' that your apparent dissent sticks out.)

However, I think you're selling logic short. Not all logic is deterministic---there are probabilistic logics, fuzzy logic, etc. Some systems of logic (paraconsistent logics) are even capable of dealing with inconsistencies---although they're a little out there for my taste. I'd want to keep the principle of explosion. And your leap from the examples you give to stipulating that 'every rule has an exception' seems a little quick, and far, to me.

I agree, however, that while your rule F seems like it should be paradoxical at first blush, it isn't---it could be rephrased as 'F: For any x such that x is a rule and x is not F, x has an exception'.

It's not quite clear to me, however, that F is actually right. It seems that there are lots of rules that permit no exception, since they are logically tautologous---such as, 'for any x and y such that x=z and y=z, x=y'. But I'll have to think more about this!

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first of all, I would like to congratulate you on the fact that your essay is one of comparatively few that actually

Unfortunately, I seem to get lost a fair bit in your prose---maybe it's just that I haven't quite had my head on straight for most of the day, and I need to think about things more deeply, but at times you seem to tangle yourself up into a semantic knot I can't seem to untie.

In some parts, I feel a certain closeness to my own ideas---and after all, we already seem to share many similar interests. For instance, you seem to share a similar thesis of human limitations when it comes to deciding purported 'truths' about the world. After all, it seems like 'this machine halts' should be either true, or false, but there's as we all know no general effective way of getting at that truth or falsity.

I'm not sure I understand your characterization of the empirical content of physical theories, however. The classical account (following Popper) would be that if an experiment confirms a theory's prediction, it may yet be either right or wrong (some other experiment might disagree with it), while falsification rules a theory out (in, uh, theory at least). You seem to view both much more symmetrically. Do you think that the Popperian account is insufficient?

(I should note that I think the falsificationist credo has its shortcomings, but it's so often portrayed as essentially the 'received wisdom' that your apparent dissent sticks out.)

However, I think you're selling logic short. Not all logic is deterministic---there are probabilistic logics, fuzzy logic, etc. Some systems of logic (paraconsistent logics) are even capable of dealing with inconsistencies---although they're a little out there for my taste. I'd want to keep the principle of explosion. And your leap from the examples you give to stipulating that 'every rule has an exception' seems a little quick, and far, to me.

I agree, however, that while your rule F seems like it should be paradoxical at first blush, it isn't---it could be rephrased as 'F: For any x such that x is a rule and x is not F, x has an exception'.

It's not quite clear to me, however, that F is actually right. It seems that there are lots of rules that permit no exception, since they are logically tautologous---such as, 'for any x and y such that x=z and y=z, x=y'. But I'll have to think more about this!

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Hi Jochen, thank you for your comment and all the very important questions and remarks therein.

Firstly I want to mention that I do not believe in mathematical infinities as ontologically real facts – be it physically or as a platonic fact. This concept of infinities is suspect to me, I view the notion of ‘infinite’ as an alternative term for ‘undefined’.

Although I did not explicitely write about the issue of infinity in my essay, an aspect of it seems to me the problem of infinite recursive reasoning, especially about what is fundamentally true in physics and nature.

To remove any misunderstandings, I certainly believe two things: firstly that there is a true ontology behind all phenomena and hence I consider it as true that “this machine halts” should be either true or false – as long as if follows the valid definitions of turings halting problem and all the subsequent consequences derived from it. Even for the case of Chaitin’s results I would say that a machine defined according to his framework must either halt or not – to whatever objective reasons.

So truth is not exclusively a subjective, relative concept, in my opinion. The question is rather whether or not our contemporary picture of reality as exclusively only following the first three causes of Aristotle (as mention in my essay and in footenote 2) is complete or not. And surely, I think that also this question has a definite answer, independent of whether I can know it or not.

I think that for coming closer to truth for whether or not the ontological reality merely encompasses the first three Aristotelian causes, one has to consider the possibility that the first three causes of Aristotle are merely limiting cases of the fourth cause Aristotle gives.

As you surely are aware of, the question about the truth or falsity of any theory that purports to having captured all ‘necessary’ ingredients to be a complete theory for at least all physical phenomena (and therefore for the contemporarily purported ontological framework of exclusively *non-subjective* causes) must necessarily be causally closed. With ‘causally closed’ I do not only mean that it encompasses all three Aristotelian causes, it even may incorporate true irreducible randomness – the latter in the sense of some timeless or time-dependent quantum fluctuations.

According to the picture of such a causally closed system, one cannot label other reasons for the modal ontology for whole existence (ultimate reality) than merely refer to either randomness – which must then be governed by some eternal mathematics (probabilities etc.) or to a strict determinism, or eventually to both.

Nevertheless, as you rightfully wrote in your own essay, understanding something is (at least in parts) equivalent to give a step-by-step description. By such a step-by-step analysis I come to the conclusion that for the cases that such a causally closed explanation for the ontological status of ultimate reality should be fundamentally true, it implies the following truths:

1. If someone claims that ultimate reality is strictly deterministic, this implies that she or he had to come to this conclusion just the way she / he did, and no jota other. It further implies that consciousness is an inevitably ontological phenomenon. It also implies that I had no other chance then to write exactly these lines of reasoning to you.

2. If someone claims that ultimate reality is irreducibly random at its core (‘quantum fluctuations and the like), this either necessitates an eternal realm where at least the probabilistic framework of mathematics resides, or – vaguely in the spirit of the MUH – it implies that ‘quantum fluctuations and the like’ *are* in some sense the mathematics with which we assumed to merely *describe* those fluctuations. In fact, this mathematics then couldn’t be anymore the traditionally fixed mathematics, but must have a random element. Hence, this kind of ‘platonic realm’ would be kind of dynamical in which mathematical truths are randomly generated by the mysterious power of mathematics to generate truly random values. Alternatively one could understand randomness in mathematics as an infinite sea of prefixed mathematical relations of any conceivable combination. So, if someone claims that ultimate reality is irreducibly random, what she / he means is either irreducible randomness in the absence of any platonic mathematical realm (ex nihilo truths), or that there has to exist an eternal platonic mathematical realm consisting of infinitely many prefixed mathematical relations of any conceivable combinations.

3. If someone claims that ultimate reality is a mixture of determinism and irreducible randomness, this necessitates that either this mixture came about ex nihilo, or that determinism and ‘irreducible’ randomness can be reduced to an eternally existing platonic mathematical realm consisting of infinitely many prefixed mathematical relations of any conceivable combinations. Alternatively one could interpret the mentioned claim as being a mixture of eternally prefixed mathematical relations and some ex nihilo created new mathematical relationships. This would necessitate that the eternal prefixed part of mathematics cannot be complete, since otherwise every ‘new ex nihilo created’ mathematical relationship would already be contained within the eternal prefixed part of the platonic mathematical realm. It is obvious that the latter possibility is completely indistinguishable from an infinite, prefixed platonic realm of mathematics. Any purported claim that it should nonetheless be distinguishable due to the very fact that there is indeed a dynamical external world out there that ‘proves’ that the platonic mathematical realm has to be understood as a *dynamical* realm – is anthropical reasoning, based on the fact that mathematics is indeed able to give a *coarse-grained* step-by-step description of some physical dynamics.

Let me resume point 3 a bit more detailed.

If it is true that the real meaning of mathematics has to be understood as a dynamical realm of mathematical relationships, this necessitates ex nihilo creations of mathematical relationships which are genuinly irreducibly random. The latter in the sense that every such creation at point t in time could have reasonably been also another relationship, other than that which has been created ex nihilo. So, if it is indeed true – and for the sake of my following arguments I will adopt the truth of the claim – that the real meaning of mathematics is that the latter is of a dynamical ontology which executes ex nihilo creations, then the big question is how this dynamics and especially its ex nihilo creative part is able to facilitate at all observers which can capture this truth. Surely and obviously, this must be impossible, since all we are talking about here is conditionally restricted by merely assuming that the claim in question is indeed true. We are not talking about that we unequivocally have found that this claim *must* be true. It does not help to push the lack of objectifiability for this claim a level up the chain of step-by-step descriptions. Even if we *assume* that there is a multiverse out there and in some multiverses observers indeed unequivocally can capture the truth of the claim in question – this would again not only be merely an assumption, but due to the very axioms of the claim in question, in every ‘branch’ of such a multiverse, observers could merely conclude what we conclude in our branch.

To make my long story short here: For explaining what generated some dynamics for a physical world to exist at all, one is left with some mysterious power of mathematics to do that and / or with some creation ex nihilo.

If we allow ex nihilo creations, we either allow the existence of a God in the traditional sense, or we allow what I called in my essay ‘nothing’ as an ontological fact. So the only way to escape both possibilities is to adopt that there necessarily has to exist something eternally from which the existence of our physical world can be derived. This could be the mysterious power of a platonic realm of mathematics – or simply the eternal existence of physical stuff, for example some steady-state universe.

Surely one can also assume that an eternally existing, finite landscape of platonical mathematical relationships, together with some ex nihilo creation, should be the ontologically real deal. But in my opinion, this would merely increase the mysterium of existence – especially the mysterium why there should be eternal existence of something and at the same time there should be the fact of ex nihilo creations.

In a very deep sense, the combination of eternal mathematics with ex nihilo creations merely resembles what human beings have figured out millennia ago, namely the possibility that there could exist an eternal thing – God – that is able to bring about some ex nihilo creation. Albeit the eternal realm of mathematics together with some ex nihilo creation of randomness seems to be able to explain some coarse-grained regularities of nature, I think it completely fails to explain the existence of consciousness and its ability to indeed capture some coarse-grained truths about ontological reality. Take for example the truth that every object falls down to earth or all the other physical facts that enable us to build all sorts of machines that follow in their behaviour at least a coarse-grained model we have about the behaviour of nature. How could this be related to your result that a model facilitated by human consciousness can at all capture some coarse-grained truths about external reality? It is because such coarse-grained models indeed are able to incorporate some coarse-grained truths of external reality and therefore aren’t anymore merely models, but truths. The latter surely only if we exclude that there could be possible some miracles that could immediately contradict these truths, miracles either produced by God or by some random ex nihilo creation. If we exclude the latter two options, then our coarse-grained truths are at least true as long as as our accompanied laws of nature are true.

The question then is under what conditions these laws of nature could be only temorarily true. It could well be that these laws of nature can change with time (albeit surely within some rather large time-spans). I cannot exclude this possibility. At least in my essay I gave a minimal interpretation of what it could reasonably mean that those laws of nature could only be temporarily true. This would be the case if mathematics itself would be only temporarily true.

Regarding to the empirical content of physical theories and Popper, I would say that falsifying a certain prediction of a theory falsifies the theory as it stands. Surely there is the possibility to adapt the theory somewhat to incorporate the result of some experiment. One then had to look for another prediction of the adapted theory to be tested for its empirical content. As far as explanations are involved in the original, non-adapted version of the theory, I think it is not always easy to hold such explanations when the theory is adapted to the result of the first experiment. At least if such an explanation is equal to a fundamental principle one assumes to have discovered in nature. So, generally, I think that the falsificationist credo crititcally hinges on whether or not a certain theory has stated such a fundamental principle – or has stated rather a trivial prediction which is rather non-conclusive to decide whether or not the theory has any empirical content.

Concering what you wrote as

“However, I think you're selling logic short. Not all logic is deterministic---there are probabilistic logics, fuzzy logic, etc. Some systems of logic (paraconsistent logics) are even capable of dealing with inconsistencies---although they're a little out there for my taste. I'd want to keep the principle of explosion. And your leap from the examples you give to stipulating that 'every rule has an exception' seems a little quick, and far, to me.”

I am aware of these logical systems. They are all concerned with issues like consistency and provability. Using one or the other of these systems surely depends on situative circumstances, not on eternal truths, as long as one does not mix them up into a kind of eternally fixed, logico-mathematical landscape of exclusively only relative truths. But even in doing so, the truth that all truths are somehwat relative must then itself be a fundamental truth. As I tried to lay out in footenote 6 of my essay, it seems to me to be impossible to unequivocally prove such a logico-mathematical landscape to have any ontological reality other than existing in the minds of people that believe in it. Even for the case that such a logico-mathematical landscape unavoidably necessitates the existence of consciousness, the fact of the latter’s existence cannot be modeled other then by admitting that there is consciousness which is able to assume something non-conclusive about itself, namely that it should be a product of the assumed logico-mathematical landscape. Stated differently: I think that such a logico-mathematical landscape does merely exist in the imagination of someone who states that it must exist independently of him / her. It is a model of what lies at the very foundations of ultimate reality and the fact that a model is in fact a step-by-step description, as well as mathematics is, the believer in such a logico-mathematical landscape step-by-step infers that heself must be part of such a landscape, since all he has at hand are step-by-step descriptions which lead him in a self-confirming manner to the conclusion that step-by-step descriptions must be the ultimate foundation of reality. On the basis that such step-by-step description is not possible for the believer’s own realm of consciousness, he concludes that such a step-by-step description nonetheless must nonethless exist objectively when adding an additional realm of step-by-step dynamics by means of a dynamically behaving logico-mathematical landscape. The latter then surely contains the exact step-by-step description of the believer’s own contents of consciousness – including the assumption that such an additional realm has to exist ‘independent’ of whether or not he believes in it.

The crucial point here is, that in the framework of such a believer, his own belief in his very framework has been brought about by his very framework in manner that is in no way controllable by himself, because neither a deterministic step-by-step dynamics nor ex nihilo creations nor pseudo-randomness leave any room for a kind of limited free-will that is able to decide between two mutually exclusive alternatives. The framework may be consistent, but is incompatible with the kind of free-will I mentioned and with every-day life that demands that we are fully responsible for deciding between two mutually exclusive alternatives.

In my essay, I take consciousness serious in regards to every-day experience and responsibility in the sense that I assume it as a thing that at least has its roots not in the realm of time and space, and also not in the realm of some eternal mathematical landscape.

As you may have noticed, I purport the view that mathematics is merely of temporal truth, since in my framework the existence of mathematics is the result of a free-will based decision of an observer that I identify with the more traditional concept of God (hence, not some artifical God, produced by some omegapoint or something like that). My concept of God is that whatever we call this God, it is fundamentally non-formalizable truth far beyond ex nihilo randomness or mathematically tracable relationships. Of course, the fundamental relationships that are true in the realm of such a God are at the one hand indeed anthropically inferred truths, as for example the existence of love and some kind of free-will, but on the other hand go parallel with the absence of any necessity to describe the real intentions of such a God exhaustively in terms of step-by-step descriptions – with the exception that these intentions can to different degrees be *felt* by human beings. For example when they share love, are happy or even lucky.

Regarding my Rule F, I invented it as a reductio ad absurdum for every attempt to take a viable TOE that exlusively only follows the path of mathematical step-by-step descriptions to ever say something conclusively why human beings have at all the experiences they have, why they at all are existent and feel what they feel. I think as long as such questions are not considered to be valid, one cuts out an important factor of reality. Surely, no TOE in the sense of a scientific, physical explanation of existence is ever conducted to answer those questions, because they are theological in nature. But on the other hand, as I hopefully made clear, the assumption of an eternal realm of mathematics together with some ex nihilo creations is likewise a kind of theological explanation, because they purport to explain human feelings as the result of some mathematical dynamics without ever being able to unequivocally proving it. Every such purported proof must, in my opinion remain in the realm of mere correlations between some brain activities and some mathematical descriptions of what one assumes is causing certain Qualia.

My rule F can be stated without the flavour of self-reference by simply saying “No rule without an exception, but not for rule F” (in a comment above to Lawrence Crowell I explained how to better grasp the content of such a rule, for its only content is about rules and exceptions, means content and form are interchangeable without altering the invariant truth of it). I do not purport that such a rule indeed does exist (although I cannot exclude it), this rule is just a placeholder to question our rigid rule-dependend models of reality and suggest that this thinking can be transcended. In my essay, I made such an attempt to transcend it by pointing to the question what truth is and in which sense its existence is necessary to sufficiently explain existence itself. Self-evidently my conclusion is that at the very foundation of ultimate reality, there should be some fundamental truth, if we at all are able to speak meaningfully about ultimate reality. And self-evidently existence itself is a truth. And self-evidently, if ‘nothing’ would be indeed possible, this would be also a truth. I further think that ‘nothing’ as I defined it in my essay and an assumed eternally existing mathematical lanscape are completely equivalent when it comes to the question ‘what is the ultimate truth?’. I conclude this because although the popularily purported view of ultimate reality being a mathematical landscape that must be considered as eternal, the latter is the very reason that the whole content of this mathematical landscape, as well as its included properties of conistency, inconsistency, provability and unprovability are at the end of the day not only not just relative truths, but by the very definition of ‘relative truth’ as abstract relationships that make no distinction between consistency and inconsistency – they are as random as the existence of such a mathematical landscape itself. With randomness I mean here that there is no cause (none of the four Aristotelian causes) that could support this landscape’s existence to be eternal and reasonable. Note that these conclusions are made from the bird’s perspective, looking at this landscape at a whole (from the frog’s perspective there are indeed reasons to assume such a landscape, namely the fact that nature can be at all desribed mathematically). From this bird’s perspective I conclude that, although mathematics is concerned with symbol manipuation, nothing within this whole landscape necessitates that there should be a criterion like consistency or inconsistency. I could well also assume that there is an eternal landscape that produces arbitrary different symbols, phenomena and subjective impressions no observer could extract any meaning out of them (like the stone you mentioned in your reply to my comment on your essay page) which are *not* concatenated or permutated, but appear to a potential observer as far beyond our notion of randomness. For excluding the latter scenario (furtherly called ‘weird scenario’), platonists had to explain why mathematics comes with the feature of consistency and inconsistency at all. Obviously, my statement that “appear to a potential observer as far beyond our notion of randomness” presupposes that we have this model of randomness at hand, to compare it with the latter scenario. Therefore, by comparing this scenario with the contents of a traditional platonic realm with some randomness in it or not, I see only empirical arguments against the ‘weired scenario’, but no logical ones. The reason why there aren’t such logical arguments at hand is rooted in the problem of induction – the observation of an observed rule does not imply that this rule is eternal or fundamental. Therefore the assumption of the existence of an eternal platonic realm is just an induction, an extrapolation. What guarantees that this platonic realm does not suddenly chance into a ‘weird scenario’? I think the only answer that one can give to this question is that logics – altough necessarily not in its antivalent form – must play a crucial role at the heart of ultimate reality. Dropping the assumption that there is a realm of existence without antivalent logics (in the sense of a realm of fundamental truths as outlined in my essay), leaves us with antivalent thinking and the possibility of the ‘weird scenario’. This ‘weird scenario’ then could be equivalently be considered as ‘nothing’ – playing some weird tricks on us by ‘randomly’ producing a seemingly consistent world. So the asumption of an eternal platonic realm of mathematics – with or without randomness – is just an extrapolation, an induction, as well as its feature of consistency and its very unchangeable properties are: if mathematical values can be created ex nihilo, can they also again vanish into ‘nothing’, one is tempted to ask. More serious, if mathematical consistency depends on some values created ex nihilo, can the very feature of mathematics, namely consistency, also vanish into ‘nothing’? What guarantees that this landscape isn’t just a lucky fluke – together with our universe? Well, these have been the questions I was concerned about in my essay, albeit due to restrictions of characters, I couldn’t write them all down, but have done it with this rather epic comment!

Firstly I want to mention that I do not believe in mathematical infinities as ontologically real facts – be it physically or as a platonic fact. This concept of infinities is suspect to me, I view the notion of ‘infinite’ as an alternative term for ‘undefined’.

Although I did not explicitely write about the issue of infinity in my essay, an aspect of it seems to me the problem of infinite recursive reasoning, especially about what is fundamentally true in physics and nature.

To remove any misunderstandings, I certainly believe two things: firstly that there is a true ontology behind all phenomena and hence I consider it as true that “this machine halts” should be either true or false – as long as if follows the valid definitions of turings halting problem and all the subsequent consequences derived from it. Even for the case of Chaitin’s results I would say that a machine defined according to his framework must either halt or not – to whatever objective reasons.

So truth is not exclusively a subjective, relative concept, in my opinion. The question is rather whether or not our contemporary picture of reality as exclusively only following the first three causes of Aristotle (as mention in my essay and in footenote 2) is complete or not. And surely, I think that also this question has a definite answer, independent of whether I can know it or not.

I think that for coming closer to truth for whether or not the ontological reality merely encompasses the first three Aristotelian causes, one has to consider the possibility that the first three causes of Aristotle are merely limiting cases of the fourth cause Aristotle gives.

As you surely are aware of, the question about the truth or falsity of any theory that purports to having captured all ‘necessary’ ingredients to be a complete theory for at least all physical phenomena (and therefore for the contemporarily purported ontological framework of exclusively *non-subjective* causes) must necessarily be causally closed. With ‘causally closed’ I do not only mean that it encompasses all three Aristotelian causes, it even may incorporate true irreducible randomness – the latter in the sense of some timeless or time-dependent quantum fluctuations.

According to the picture of such a causally closed system, one cannot label other reasons for the modal ontology for whole existence (ultimate reality) than merely refer to either randomness – which must then be governed by some eternal mathematics (probabilities etc.) or to a strict determinism, or eventually to both.

Nevertheless, as you rightfully wrote in your own essay, understanding something is (at least in parts) equivalent to give a step-by-step description. By such a step-by-step analysis I come to the conclusion that for the cases that such a causally closed explanation for the ontological status of ultimate reality should be fundamentally true, it implies the following truths:

1. If someone claims that ultimate reality is strictly deterministic, this implies that she or he had to come to this conclusion just the way she / he did, and no jota other. It further implies that consciousness is an inevitably ontological phenomenon. It also implies that I had no other chance then to write exactly these lines of reasoning to you.

2. If someone claims that ultimate reality is irreducibly random at its core (‘quantum fluctuations and the like), this either necessitates an eternal realm where at least the probabilistic framework of mathematics resides, or – vaguely in the spirit of the MUH – it implies that ‘quantum fluctuations and the like’ *are* in some sense the mathematics with which we assumed to merely *describe* those fluctuations. In fact, this mathematics then couldn’t be anymore the traditionally fixed mathematics, but must have a random element. Hence, this kind of ‘platonic realm’ would be kind of dynamical in which mathematical truths are randomly generated by the mysterious power of mathematics to generate truly random values. Alternatively one could understand randomness in mathematics as an infinite sea of prefixed mathematical relations of any conceivable combination. So, if someone claims that ultimate reality is irreducibly random, what she / he means is either irreducible randomness in the absence of any platonic mathematical realm (ex nihilo truths), or that there has to exist an eternal platonic mathematical realm consisting of infinitely many prefixed mathematical relations of any conceivable combinations.

3. If someone claims that ultimate reality is a mixture of determinism and irreducible randomness, this necessitates that either this mixture came about ex nihilo, or that determinism and ‘irreducible’ randomness can be reduced to an eternally existing platonic mathematical realm consisting of infinitely many prefixed mathematical relations of any conceivable combinations. Alternatively one could interpret the mentioned claim as being a mixture of eternally prefixed mathematical relations and some ex nihilo created new mathematical relationships. This would necessitate that the eternal prefixed part of mathematics cannot be complete, since otherwise every ‘new ex nihilo created’ mathematical relationship would already be contained within the eternal prefixed part of the platonic mathematical realm. It is obvious that the latter possibility is completely indistinguishable from an infinite, prefixed platonic realm of mathematics. Any purported claim that it should nonetheless be distinguishable due to the very fact that there is indeed a dynamical external world out there that ‘proves’ that the platonic mathematical realm has to be understood as a *dynamical* realm – is anthropical reasoning, based on the fact that mathematics is indeed able to give a *coarse-grained* step-by-step description of some physical dynamics.

Let me resume point 3 a bit more detailed.

If it is true that the real meaning of mathematics has to be understood as a dynamical realm of mathematical relationships, this necessitates ex nihilo creations of mathematical relationships which are genuinly irreducibly random. The latter in the sense that every such creation at point t in time could have reasonably been also another relationship, other than that which has been created ex nihilo. So, if it is indeed true – and for the sake of my following arguments I will adopt the truth of the claim – that the real meaning of mathematics is that the latter is of a dynamical ontology which executes ex nihilo creations, then the big question is how this dynamics and especially its ex nihilo creative part is able to facilitate at all observers which can capture this truth. Surely and obviously, this must be impossible, since all we are talking about here is conditionally restricted by merely assuming that the claim in question is indeed true. We are not talking about that we unequivocally have found that this claim *must* be true. It does not help to push the lack of objectifiability for this claim a level up the chain of step-by-step descriptions. Even if we *assume* that there is a multiverse out there and in some multiverses observers indeed unequivocally can capture the truth of the claim in question – this would again not only be merely an assumption, but due to the very axioms of the claim in question, in every ‘branch’ of such a multiverse, observers could merely conclude what we conclude in our branch.

To make my long story short here: For explaining what generated some dynamics for a physical world to exist at all, one is left with some mysterious power of mathematics to do that and / or with some creation ex nihilo.

If we allow ex nihilo creations, we either allow the existence of a God in the traditional sense, or we allow what I called in my essay ‘nothing’ as an ontological fact. So the only way to escape both possibilities is to adopt that there necessarily has to exist something eternally from which the existence of our physical world can be derived. This could be the mysterious power of a platonic realm of mathematics – or simply the eternal existence of physical stuff, for example some steady-state universe.

Surely one can also assume that an eternally existing, finite landscape of platonical mathematical relationships, together with some ex nihilo creation, should be the ontologically real deal. But in my opinion, this would merely increase the mysterium of existence – especially the mysterium why there should be eternal existence of something and at the same time there should be the fact of ex nihilo creations.

In a very deep sense, the combination of eternal mathematics with ex nihilo creations merely resembles what human beings have figured out millennia ago, namely the possibility that there could exist an eternal thing – God – that is able to bring about some ex nihilo creation. Albeit the eternal realm of mathematics together with some ex nihilo creation of randomness seems to be able to explain some coarse-grained regularities of nature, I think it completely fails to explain the existence of consciousness and its ability to indeed capture some coarse-grained truths about ontological reality. Take for example the truth that every object falls down to earth or all the other physical facts that enable us to build all sorts of machines that follow in their behaviour at least a coarse-grained model we have about the behaviour of nature. How could this be related to your result that a model facilitated by human consciousness can at all capture some coarse-grained truths about external reality? It is because such coarse-grained models indeed are able to incorporate some coarse-grained truths of external reality and therefore aren’t anymore merely models, but truths. The latter surely only if we exclude that there could be possible some miracles that could immediately contradict these truths, miracles either produced by God or by some random ex nihilo creation. If we exclude the latter two options, then our coarse-grained truths are at least true as long as as our accompanied laws of nature are true.

The question then is under what conditions these laws of nature could be only temorarily true. It could well be that these laws of nature can change with time (albeit surely within some rather large time-spans). I cannot exclude this possibility. At least in my essay I gave a minimal interpretation of what it could reasonably mean that those laws of nature could only be temporarily true. This would be the case if mathematics itself would be only temporarily true.

Regarding to the empirical content of physical theories and Popper, I would say that falsifying a certain prediction of a theory falsifies the theory as it stands. Surely there is the possibility to adapt the theory somewhat to incorporate the result of some experiment. One then had to look for another prediction of the adapted theory to be tested for its empirical content. As far as explanations are involved in the original, non-adapted version of the theory, I think it is not always easy to hold such explanations when the theory is adapted to the result of the first experiment. At least if such an explanation is equal to a fundamental principle one assumes to have discovered in nature. So, generally, I think that the falsificationist credo crititcally hinges on whether or not a certain theory has stated such a fundamental principle – or has stated rather a trivial prediction which is rather non-conclusive to decide whether or not the theory has any empirical content.

Concering what you wrote as

“However, I think you're selling logic short. Not all logic is deterministic---there are probabilistic logics, fuzzy logic, etc. Some systems of logic (paraconsistent logics) are even capable of dealing with inconsistencies---although they're a little out there for my taste. I'd want to keep the principle of explosion. And your leap from the examples you give to stipulating that 'every rule has an exception' seems a little quick, and far, to me.”

I am aware of these logical systems. They are all concerned with issues like consistency and provability. Using one or the other of these systems surely depends on situative circumstances, not on eternal truths, as long as one does not mix them up into a kind of eternally fixed, logico-mathematical landscape of exclusively only relative truths. But even in doing so, the truth that all truths are somehwat relative must then itself be a fundamental truth. As I tried to lay out in footenote 6 of my essay, it seems to me to be impossible to unequivocally prove such a logico-mathematical landscape to have any ontological reality other than existing in the minds of people that believe in it. Even for the case that such a logico-mathematical landscape unavoidably necessitates the existence of consciousness, the fact of the latter’s existence cannot be modeled other then by admitting that there is consciousness which is able to assume something non-conclusive about itself, namely that it should be a product of the assumed logico-mathematical landscape. Stated differently: I think that such a logico-mathematical landscape does merely exist in the imagination of someone who states that it must exist independently of him / her. It is a model of what lies at the very foundations of ultimate reality and the fact that a model is in fact a step-by-step description, as well as mathematics is, the believer in such a logico-mathematical landscape step-by-step infers that heself must be part of such a landscape, since all he has at hand are step-by-step descriptions which lead him in a self-confirming manner to the conclusion that step-by-step descriptions must be the ultimate foundation of reality. On the basis that such step-by-step description is not possible for the believer’s own realm of consciousness, he concludes that such a step-by-step description nonetheless must nonethless exist objectively when adding an additional realm of step-by-step dynamics by means of a dynamically behaving logico-mathematical landscape. The latter then surely contains the exact step-by-step description of the believer’s own contents of consciousness – including the assumption that such an additional realm has to exist ‘independent’ of whether or not he believes in it.

The crucial point here is, that in the framework of such a believer, his own belief in his very framework has been brought about by his very framework in manner that is in no way controllable by himself, because neither a deterministic step-by-step dynamics nor ex nihilo creations nor pseudo-randomness leave any room for a kind of limited free-will that is able to decide between two mutually exclusive alternatives. The framework may be consistent, but is incompatible with the kind of free-will I mentioned and with every-day life that demands that we are fully responsible for deciding between two mutually exclusive alternatives.

In my essay, I take consciousness serious in regards to every-day experience and responsibility in the sense that I assume it as a thing that at least has its roots not in the realm of time and space, and also not in the realm of some eternal mathematical landscape.

As you may have noticed, I purport the view that mathematics is merely of temporal truth, since in my framework the existence of mathematics is the result of a free-will based decision of an observer that I identify with the more traditional concept of God (hence, not some artifical God, produced by some omegapoint or something like that). My concept of God is that whatever we call this God, it is fundamentally non-formalizable truth far beyond ex nihilo randomness or mathematically tracable relationships. Of course, the fundamental relationships that are true in the realm of such a God are at the one hand indeed anthropically inferred truths, as for example the existence of love and some kind of free-will, but on the other hand go parallel with the absence of any necessity to describe the real intentions of such a God exhaustively in terms of step-by-step descriptions – with the exception that these intentions can to different degrees be *felt* by human beings. For example when they share love, are happy or even lucky.

Regarding my Rule F, I invented it as a reductio ad absurdum for every attempt to take a viable TOE that exlusively only follows the path of mathematical step-by-step descriptions to ever say something conclusively why human beings have at all the experiences they have, why they at all are existent and feel what they feel. I think as long as such questions are not considered to be valid, one cuts out an important factor of reality. Surely, no TOE in the sense of a scientific, physical explanation of existence is ever conducted to answer those questions, because they are theological in nature. But on the other hand, as I hopefully made clear, the assumption of an eternal realm of mathematics together with some ex nihilo creations is likewise a kind of theological explanation, because they purport to explain human feelings as the result of some mathematical dynamics without ever being able to unequivocally proving it. Every such purported proof must, in my opinion remain in the realm of mere correlations between some brain activities and some mathematical descriptions of what one assumes is causing certain Qualia.

My rule F can be stated without the flavour of self-reference by simply saying “No rule without an exception, but not for rule F” (in a comment above to Lawrence Crowell I explained how to better grasp the content of such a rule, for its only content is about rules and exceptions, means content and form are interchangeable without altering the invariant truth of it). I do not purport that such a rule indeed does exist (although I cannot exclude it), this rule is just a placeholder to question our rigid rule-dependend models of reality and suggest that this thinking can be transcended. In my essay, I made such an attempt to transcend it by pointing to the question what truth is and in which sense its existence is necessary to sufficiently explain existence itself. Self-evidently my conclusion is that at the very foundation of ultimate reality, there should be some fundamental truth, if we at all are able to speak meaningfully about ultimate reality. And self-evidently existence itself is a truth. And self-evidently, if ‘nothing’ would be indeed possible, this would be also a truth. I further think that ‘nothing’ as I defined it in my essay and an assumed eternally existing mathematical lanscape are completely equivalent when it comes to the question ‘what is the ultimate truth?’. I conclude this because although the popularily purported view of ultimate reality being a mathematical landscape that must be considered as eternal, the latter is the very reason that the whole content of this mathematical landscape, as well as its included properties of conistency, inconsistency, provability and unprovability are at the end of the day not only not just relative truths, but by the very definition of ‘relative truth’ as abstract relationships that make no distinction between consistency and inconsistency – they are as random as the existence of such a mathematical landscape itself. With randomness I mean here that there is no cause (none of the four Aristotelian causes) that could support this landscape’s existence to be eternal and reasonable. Note that these conclusions are made from the bird’s perspective, looking at this landscape at a whole (from the frog’s perspective there are indeed reasons to assume such a landscape, namely the fact that nature can be at all desribed mathematically). From this bird’s perspective I conclude that, although mathematics is concerned with symbol manipuation, nothing within this whole landscape necessitates that there should be a criterion like consistency or inconsistency. I could well also assume that there is an eternal landscape that produces arbitrary different symbols, phenomena and subjective impressions no observer could extract any meaning out of them (like the stone you mentioned in your reply to my comment on your essay page) which are *not* concatenated or permutated, but appear to a potential observer as far beyond our notion of randomness. For excluding the latter scenario (furtherly called ‘weird scenario’), platonists had to explain why mathematics comes with the feature of consistency and inconsistency at all. Obviously, my statement that “appear to a potential observer as far beyond our notion of randomness” presupposes that we have this model of randomness at hand, to compare it with the latter scenario. Therefore, by comparing this scenario with the contents of a traditional platonic realm with some randomness in it or not, I see only empirical arguments against the ‘weired scenario’, but no logical ones. The reason why there aren’t such logical arguments at hand is rooted in the problem of induction – the observation of an observed rule does not imply that this rule is eternal or fundamental. Therefore the assumption of the existence of an eternal platonic realm is just an induction, an extrapolation. What guarantees that this platonic realm does not suddenly chance into a ‘weird scenario’? I think the only answer that one can give to this question is that logics – altough necessarily not in its antivalent form – must play a crucial role at the heart of ultimate reality. Dropping the assumption that there is a realm of existence without antivalent logics (in the sense of a realm of fundamental truths as outlined in my essay), leaves us with antivalent thinking and the possibility of the ‘weird scenario’. This ‘weird scenario’ then could be equivalently be considered as ‘nothing’ – playing some weird tricks on us by ‘randomly’ producing a seemingly consistent world. So the asumption of an eternal platonic realm of mathematics – with or without randomness – is just an extrapolation, an induction, as well as its feature of consistency and its very unchangeable properties are: if mathematical values can be created ex nihilo, can they also again vanish into ‘nothing’, one is tempted to ask. More serious, if mathematical consistency depends on some values created ex nihilo, can the very feature of mathematics, namely consistency, also vanish into ‘nothing’? What guarantees that this landscape isn’t just a lucky fluke – together with our universe? Well, these have been the questions I was concerned about in my essay, albeit due to restrictions of characters, I couldn’t write them all down, but have done it with this rather epic comment!

Hi Stefan,

about:

If it would be possible that there existed nothing rather than something at all (for example prior to the appearance of time 13.8 billion years ago before the big bang),

I think:

If nothing is surrounded by anything then that is something. Nothing surrounded with nothing (before the Big Bang) is a singularity (undefined state). Accordingly, Big Bang is false theory.

I agree with this:

We see that the term ‘fundamental’ can also mean that there necessarily should be exclusively only one origin for all existence.

For me, "meta rule" is the relationship between the entities, which must exist.

About Newton: Inded, originaly Newton wrote about surfaces not distances.

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about:

If it would be possible that there existed nothing rather than something at all (for example prior to the appearance of time 13.8 billion years ago before the big bang),

I think:

If nothing is surrounded by anything then that is something. Nothing surrounded with nothing (before the Big Bang) is a singularity (undefined state). Accordingly, Big Bang is false theory.

I agree with this:

We see that the term ‘fundamental’ can also mean that there necessarily should be exclusively only one origin for all existence.

For me, "meta rule" is the relationship between the entities, which must exist.

About Newton: Inded, originaly Newton wrote about surfaces not distances.

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Hi Branco, thanks for your comment.

Regarding

“If nothing is surrounded by anything then that is something.”

That’s also my point of view.

“Nothing surrounded with nothing (before the Big Bang) is a singularity (undefined state). Accordingly, Big Bang is false theory.“

Well, nothing, according to my essay, can be defined. It ‘is’ simply total non-existence. As I defined it, there doesn’t even exist a singularity – if you mean by ‘singularity’ the traditional meaning of a kind of black hole’s internal structure or some GR-singularity.

If there has been nothing (again as I defined it) before the Big Bang, this simply means that ‘nothing’ as I defined it is possible. The consequences would be that one cannot exclude that such a ‘nothing’ has produced a Big Bang. Nothing can produce everything – if one believes in it. And if one believes in such a ‘nothing’, how can one exclude that the things which it has produced by it cannot vanish again into ‘nothing’ – perhaps in the next 3 minutes?

To stay on logical grounds, ‘nothing’ has nothing to do with the possibility that there could have been a Big Bang – except for the case that someone seriously believes in ‘nothing’.

Regarding

“If nothing is surrounded by anything then that is something.”

That’s also my point of view.

“Nothing surrounded with nothing (before the Big Bang) is a singularity (undefined state). Accordingly, Big Bang is false theory.“

Well, nothing, according to my essay, can be defined. It ‘is’ simply total non-existence. As I defined it, there doesn’t even exist a singularity – if you mean by ‘singularity’ the traditional meaning of a kind of black hole’s internal structure or some GR-singularity.

If there has been nothing (again as I defined it) before the Big Bang, this simply means that ‘nothing’ as I defined it is possible. The consequences would be that one cannot exclude that such a ‘nothing’ has produced a Big Bang. Nothing can produce everything – if one believes in it. And if one believes in such a ‘nothing’, how can one exclude that the things which it has produced by it cannot vanish again into ‘nothing’ – perhaps in the next 3 minutes?

To stay on logical grounds, ‘nothing’ has nothing to do with the possibility that there could have been a Big Bang – except for the case that someone seriously believes in ‘nothing’.

Dear Stefan Weckbach,

You wrote: “The term ‘fundamental’ implies that something should have as much as possible universal validity for the range of its applications.”

My research has concluded that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

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You wrote: “The term ‘fundamental’ implies that something should have as much as possible universal validity for the range of its applications.”

My research has concluded that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

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Dear Stefan,

I agree with or at least can make sense of much you say in your essay. But I'm still failing to integrate a great many of reasonable logical arguments into some big picture. So, I'd very much appreciate your answer to two questions:

First, Hegel did away with classical logic for the reason of its artificial separation of form and contents. Haven't computation and AI in particular - which are based on this separation - shown that the recombination of form and contents to meaning is illusive? In other words, do you think you have solved in your essay logic's grounding problem?

Second, do you think that logic might exist in the absence of time?

Heinrich

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I agree with or at least can make sense of much you say in your essay. But I'm still failing to integrate a great many of reasonable logical arguments into some big picture. So, I'd very much appreciate your answer to two questions:

First, Hegel did away with classical logic for the reason of its artificial separation of form and contents. Haven't computation and AI in particular - which are based on this separation - shown that the recombination of form and contents to meaning is illusive? In other words, do you think you have solved in your essay logic's grounding problem?

Second, do you think that logic might exist in the absence of time?

Heinrich

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Hi Heinrich,

thank you for having read my essay and for commenting it. Thanks also for your very reasonable questions.

The problem of how meaning came into the world can surely be labeled a big puzzle. Although subjective observers have the – subjective – impression that many things mean very much to them, the very quest of what meaning should really mean would need to reconcile consciousness / Qualia with the external world – in the one and only possible meaningfull way.

Maybe the latter can be achieved in the future in a more stringent manner than merely assuming that form and content are – seen from a bird’s view – identical. This would be the Tegmark’s MUH view and maybe also the one AI purports. The problem with this is that we have to wait until some AI shows to us that *objective* meaning can indeed emerge from a pure formal system in the one and only possible meaningfull manner.

I think by pondering about how this could be and – by using the terms “objective meaning” without yet having grasped what meaning itself definitely could be at its core – one wanders around in the confusing realms of possible meanings of the very term meaning. One may even be tempted to consider this term as purely self-referencing – exactly in the sense I introduced the Rule F in my essay, where rule F is a purely formal description where content and form coincide (since Rule F is exlusively only about formal aspects of other rules – without defining their contents).

I think the grounding problem hasn’t been solved yet, even not by my own approach. The grounding problem – so I think – is a variant of Gödel incompleteness. My own has at its basis two strategies. Firstly, it tries to take all the hitherto known formal aspects of the world and re-arrange them in an as much as possible coherent manner so that a new (hopefully more general) meaning of the relation between form and content can be inferred.

Secondly, by doing the first step, one has to consider that the very subjects we are talking about here, namely formal systems, may not be sufficient to solve the grounding problem. Surely, one always can say that there is no meaning at all in the overall scheme of affairs independent of human observers. Or alternatively, that formal systems (like a landscape of mathematics) must necessarily somewhat incorporate something that at least generates the illusion of meaning – and with that also the illusion of this landscape’s own ‘real’ meaning (in the sense of being most fundamental). This is a crucial point, since it implies that one cannot objectively determine some real meaning for the existence of such a mathematical landscape but only subjective musings. Surely, the one and only objective meaning of such a landscape could be ‘found’ (defined) by defining this landscape as the ultimate source of reality. But this is just an alternative strategy to say that all that exists must necessarily be exclusivel only formal systems. As I outlined in my essay, I doubt this assumption.

I think that all boils down to Gödel and the impossibility to unequivocally prove some fundamental statements about the world. In my approach, I have compressed these ambiguities by saying they are merely a characteristic of a temporal world with antivalent logics in it. The realm of fundamental truth I spoke of is the necessary alternative for a worldview that is fundamentally based on self-referential ambiguities, leading either to a kind of nihilism (‘nothing’ has indeed produced logics and all the rest) or to the mathematical landscape (where meaning is fundamentally illusionary – except for the case that if one believes this, this would be the only objective definition of meaning and therefore wouldn’t be anymore illusionary). Since I doubt that such mere formally self-confirming logical figures can say anything about the real nature of nature, I surely do not claim that my proposal must be an exception of that. But I think it is a viable possibility. The realm of fundamental truth I spoke of would then be a realm of conscious creativity, where things can be constructed into existence according to the very fundamental rules this realm allows one to construct such extensions. The latter must be then understood as deeply connected with Qualia and consciousness – what is constructed would be of phenomenological content (in this realm content is a valid concept), it cannot alter or annihilate the very basis of this realm nor its fundamental truths. Stated differently: what is considered in our world as a fundamental distinction – namely the subjective and the objective – coincide in the realm of truth and the content of these phenomenological appearances can be totally shared amongst other conscious beings in this realm – beings that are tuned in to the emotional content of such phenomena (in this sense ‘time’ in those realms are a matter of emotional alignments).

Having said all this, I would like to add that in the phenomenological realm of fundamental truth, there is also a kind of time, but I assume that it is more a kind of ‘many-fingered’ time. I further assume that this kind of time can only vanish if one could enter the inner core of what consistutes this realm at all, namely what I called in my essay the ‘most objective subject’. I do not know whether or not by entering it (if possible at all), the individual consicousness must totally vanish, and I think these are more theological questions not answerable by pure logic.

According to logics itself, I think that in the mentioned realms logic may be organized different than in our realm here. I do not say that there isn’t any logic at all in these realms – and to be honest – I not even no for sure what a realm without any logics would look like. So, surely in the realms I suggest there is structure and rules, but these structures and rules are axiomatically based on emotional truths rather than on mere formal truths. So what my approach implies is that logics could merely be a reduced version of such rules and structures, what would mean that the reduction of form and content into a concept of ‘the meaning of meaninglessness’ (in the sense of a provable nihilism, purported by many scientists) is – according to my approach – a meaningfull example of how the phenomenological realm of fundamental truths can create consistent intersubjective worlds. I think that is part of the big picture I have to offer: By choosing some suitable axioms on the basis of some free will one can effectively reduce one’s own freedom by claiming that there is no such thing as free will (or consciousness, or meaning etc.). Do we at all have the choice to choose our starting axioms? I think we have, but cannot prove it.

thank you for having read my essay and for commenting it. Thanks also for your very reasonable questions.

The problem of how meaning came into the world can surely be labeled a big puzzle. Although subjective observers have the – subjective – impression that many things mean very much to them, the very quest of what meaning should really mean would need to reconcile consciousness / Qualia with the external world – in the one and only possible meaningfull way.

Maybe the latter can be achieved in the future in a more stringent manner than merely assuming that form and content are – seen from a bird’s view – identical. This would be the Tegmark’s MUH view and maybe also the one AI purports. The problem with this is that we have to wait until some AI shows to us that *objective* meaning can indeed emerge from a pure formal system in the one and only possible meaningfull manner.

I think by pondering about how this could be and – by using the terms “objective meaning” without yet having grasped what meaning itself definitely could be at its core – one wanders around in the confusing realms of possible meanings of the very term meaning. One may even be tempted to consider this term as purely self-referencing – exactly in the sense I introduced the Rule F in my essay, where rule F is a purely formal description where content and form coincide (since Rule F is exlusively only about formal aspects of other rules – without defining their contents).

I think the grounding problem hasn’t been solved yet, even not by my own approach. The grounding problem – so I think – is a variant of Gödel incompleteness. My own has at its basis two strategies. Firstly, it tries to take all the hitherto known formal aspects of the world and re-arrange them in an as much as possible coherent manner so that a new (hopefully more general) meaning of the relation between form and content can be inferred.

Secondly, by doing the first step, one has to consider that the very subjects we are talking about here, namely formal systems, may not be sufficient to solve the grounding problem. Surely, one always can say that there is no meaning at all in the overall scheme of affairs independent of human observers. Or alternatively, that formal systems (like a landscape of mathematics) must necessarily somewhat incorporate something that at least generates the illusion of meaning – and with that also the illusion of this landscape’s own ‘real’ meaning (in the sense of being most fundamental). This is a crucial point, since it implies that one cannot objectively determine some real meaning for the existence of such a mathematical landscape but only subjective musings. Surely, the one and only objective meaning of such a landscape could be ‘found’ (defined) by defining this landscape as the ultimate source of reality. But this is just an alternative strategy to say that all that exists must necessarily be exclusivel only formal systems. As I outlined in my essay, I doubt this assumption.

I think that all boils down to Gödel and the impossibility to unequivocally prove some fundamental statements about the world. In my approach, I have compressed these ambiguities by saying they are merely a characteristic of a temporal world with antivalent logics in it. The realm of fundamental truth I spoke of is the necessary alternative for a worldview that is fundamentally based on self-referential ambiguities, leading either to a kind of nihilism (‘nothing’ has indeed produced logics and all the rest) or to the mathematical landscape (where meaning is fundamentally illusionary – except for the case that if one believes this, this would be the only objective definition of meaning and therefore wouldn’t be anymore illusionary). Since I doubt that such mere formally self-confirming logical figures can say anything about the real nature of nature, I surely do not claim that my proposal must be an exception of that. But I think it is a viable possibility. The realm of fundamental truth I spoke of would then be a realm of conscious creativity, where things can be constructed into existence according to the very fundamental rules this realm allows one to construct such extensions. The latter must be then understood as deeply connected with Qualia and consciousness – what is constructed would be of phenomenological content (in this realm content is a valid concept), it cannot alter or annihilate the very basis of this realm nor its fundamental truths. Stated differently: what is considered in our world as a fundamental distinction – namely the subjective and the objective – coincide in the realm of truth and the content of these phenomenological appearances can be totally shared amongst other conscious beings in this realm – beings that are tuned in to the emotional content of such phenomena (in this sense ‘time’ in those realms are a matter of emotional alignments).

Having said all this, I would like to add that in the phenomenological realm of fundamental truth, there is also a kind of time, but I assume that it is more a kind of ‘many-fingered’ time. I further assume that this kind of time can only vanish if one could enter the inner core of what consistutes this realm at all, namely what I called in my essay the ‘most objective subject’. I do not know whether or not by entering it (if possible at all), the individual consicousness must totally vanish, and I think these are more theological questions not answerable by pure logic.

According to logics itself, I think that in the mentioned realms logic may be organized different than in our realm here. I do not say that there isn’t any logic at all in these realms – and to be honest – I not even no for sure what a realm without any logics would look like. So, surely in the realms I suggest there is structure and rules, but these structures and rules are axiomatically based on emotional truths rather than on mere formal truths. So what my approach implies is that logics could merely be a reduced version of such rules and structures, what would mean that the reduction of form and content into a concept of ‘the meaning of meaninglessness’ (in the sense of a provable nihilism, purported by many scientists) is – according to my approach – a meaningfull example of how the phenomenological realm of fundamental truths can create consistent intersubjective worlds. I think that is part of the big picture I have to offer: By choosing some suitable axioms on the basis of some free will one can effectively reduce one’s own freedom by claiming that there is no such thing as free will (or consciousness, or meaning etc.). Do we at all have the choice to choose our starting axioms? I think we have, but cannot prove it.

Dear Stefan,

Very important, deep essay and discussion. This is a very good conclusion: "This 'principle' says, in my opinion, that the ultimate reality is not just one of the formal systems."

I believe that the dialectical logic of the "coincidence of opposites" in the spirit of the Cusa should continue to work. This is the logic of "grasping" the absolute forms of existence of matter, its unification over all levels of the Universum's existence for building a "house" in which a self-developing "soul of matter" lives. I agree with the constructive deduction of Alexander Zenkin in article SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS : "The truth should be drawn ..." My high rating for deep ideas in your essay and discussion. I invite you also to evaluate my logic and ontological construction.

Yours faithfully,

Vladimir

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Very important, deep essay and discussion. This is a very good conclusion: "This 'principle' says, in my opinion, that the ultimate reality is not just one of the formal systems."

I believe that the dialectical logic of the "coincidence of opposites" in the spirit of the Cusa should continue to work. This is the logic of "grasping" the absolute forms of existence of matter, its unification over all levels of the Universum's existence for building a "house" in which a self-developing "soul of matter" lives. I agree with the constructive deduction of Alexander Zenkin in article SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS : "The truth should be drawn ..." My high rating for deep ideas in your essay and discussion. I invite you also to evaluate my logic and ontological construction.

Yours faithfully,

Vladimir

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Dear Vladimir,

I am happy that you enjoyed my essay much. Cusa’s lines out thought are very interesting and I will delf into your essay as soon as I can. Since the weekend I have a flue and it got more severe today. Therefore I am not able to concentrate for much long by reading an essay. I bookmarked your essay for studying it when I am again more healthy and can give longer comments without being exhausted. I think at the beginning of next week I will be able to again wrap my head around other essays. Thanks again for visiting my site,

Stefan Weckbach

I am happy that you enjoyed my essay much. Cusa’s lines out thought are very interesting and I will delf into your essay as soon as I can. Since the weekend I have a flue and it got more severe today. Therefore I am not able to concentrate for much long by reading an essay. I bookmarked your essay for studying it when I am again more healthy and can give longer comments without being exhausted. I think at the beginning of next week I will be able to again wrap my head around other essays. Thanks again for visiting my site,

Stefan Weckbach

Stefan,

Excellent essay, well written, argued & constructed, interesting, important subject and good analysis. It ticks all the boxes for me so I'm not sure why it's not higher yet. My score will help when I start applying them. Perhaps too philosophical for some? But Vladimir's is far more so and well supported. Perhaps some dislike frogs, birds*and* turtles in the pie!

I don't entirely agree with all, and have some questions. Firstly, in principle, I agree a sub matter 'space', and that recursion and Godel don't give us a full understanding. I also like the idea of an ultimate 'hard deck', assumedly completely inaccessible to us. But I disagree there can be 100% 'False' before we hit it, just Bayesian sine curve distributions (helical in 3D).

I also disagree circles can exposing nature as they're only 2D. I suggest a sphere is required, and one in motion at that. I've found a new analysis of that to be very powerful in my own essay. Indeed with your interest in QM I hope you'll read it carefully as an extraordinary result needs falsification. I hope we can discuss it. (see also Declan's for the matching code).

Very well done for yours.

Best of luck getting back up where it belongs.

Peter

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Excellent essay, well written, argued & constructed, interesting, important subject and good analysis. It ticks all the boxes for me so I'm not sure why it's not higher yet. My score will help when I start applying them. Perhaps too philosophical for some? But Vladimir's is far more so and well supported. Perhaps some dislike frogs, birds

I don't entirely agree with all, and have some questions. Firstly, in principle, I agree a sub matter 'space', and that recursion and Godel don't give us a full understanding. I also like the idea of an ultimate 'hard deck', assumedly completely inaccessible to us. But I disagree there can be 100% 'False' before we hit it, just Bayesian sine curve distributions (helical in 3D).

I also disagree circles can exposing nature as they're only 2D. I suggest a sphere is required, and one in motion at that. I've found a new analysis of that to be very powerful in my own essay. Indeed with your interest in QM I hope you'll read it carefully as an extraordinary result needs falsification. I hope we can discuss it. (see also Declan's for the matching code).

Very well done for yours.

Best of luck getting back up where it belongs.

Peter

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Dear Peter,

thanks for reading and commenting my essay.

My ‘cirlce’ is merely a metaphor, it isn’t intended to catch any ontology of the referred realm other than its completeness regarding its self-contained truth.

My esssay is not interested in entanglement and non-locality questions, indeed it is agnostic about that. So I will not comment on yours.

I am interested in the more fundamental questions this time.

Best wishes,

Stefan Weckbach

thanks for reading and commenting my essay.

My ‘cirlce’ is merely a metaphor, it isn’t intended to catch any ontology of the referred realm other than its completeness regarding its self-contained truth.

My esssay is not interested in entanglement and non-locality questions, indeed it is agnostic about that. So I will not comment on yours.

I am interested in the more fundamental questions this time.

Best wishes,

Stefan Weckbach

Hi Stefan Weckbach

Very interesting result “One of our main results is that what seems to be fundamental from a viewpoint within a certain system can be fundamentally meaningless from a viewpoint outside this system and vice versa.” And so no rule without an exception, except this rule." wonderful Stefan Weckbach!..….. very nice idea…. I highly appreciate your essay and hope for...

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Very interesting result “One of our main results is that what seems to be fundamental from a viewpoint within a certain system can be fundamentally meaningless from a viewpoint outside this system and vice versa.” And so no rule without an exception, except this rule." wonderful Stefan Weckbach!..….. very nice idea…. I highly appreciate your essay and hope for...

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Dear Stefan,

finally I read your essay; it's very complex and has many points of interest.

I find your Rule F is very interesting. Rule F: “No rule without an exception. Except rule F.”

We can read rule F as a whole, then, as you said, assuming its truth, there should be exactly one rule without an exception.

But if we consider it composed “(a) No rule without an exception (b) Except rule F.”, then the second part could apply to the first part, and the rule would be self-contradictory. But since you call Rule F (a+b), it seems working to me. Very nice.

Sadly I didn't get this:

The essence of truth is that it is a self-evident default state. Because whatever falseness may be a fact, this fact must be considered a truth, but not vice versa.

Could you please make an example?

Your essay worths an higher rate for sure. All the best!

Francesco

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finally I read your essay; it's very complex and has many points of interest.

I find your Rule F is very interesting. Rule F: “No rule without an exception. Except rule F.”

We can read rule F as a whole, then, as you said, assuming its truth, there should be exactly one rule without an exception.

But if we consider it composed “(a) No rule without an exception (b) Except rule F.”, then the second part could apply to the first part, and the rule would be self-contradictory. But since you call Rule F (a+b), it seems working to me. Very nice.

Sadly I didn't get this:

The essence of truth is that it is a self-evident default state. Because whatever falseness may be a fact, this fact must be considered a truth, but not vice versa.

Could you please make an example?

Your essay worths an higher rate for sure. All the best!

Francesco

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Dear Francesco,

Thankyou for reading and commenting on my essay, much appreachiated.

I introduced rule F as the compressed, extreme case of an assumed to be found ‘TOE’ and examine with this rule F what such a TOE could mean for our quest about “what is fundamental”. Surely, the term “except” in the b)-part of rule F can be misleading, but it mustn’t. One can understand the b)-part as “but not for rule F.” without changing the term “except”. Since rule F is the whole lot only about rules and exceptions, but makes no reference to the contents of such exceptions, the term “except” in the b)-part is just a negation of the a)-part for *exclusively only* a very special rule, namely rule F itself. As I annotated in the essay, formally this is a double negation, referring to a default state that has no exceptions.

According to your question:

I consider it a false statement that I am non-existent at the moment – so I consider it a *truth* that “I am non-existent at the moment” is indeed a false statement.

Another example would be that I consider it a false statement that my computer monitor is a living elephant (like the ones in the zoo). So I consider it a truth that “my computer monitor is a living elephant” is indeed a false statement.

But vice versa, I would enter into some problems. If I consider that my computer monitor is indeed a living elephant (and therefore the truth of the starting premise is doubted), I think I had to go to a doctor. Similarily, if I consider myself to be non-existent at the moment, I had to go to a doctor. Even when I am dead, I cannot consider myself as being non-existent, because non-existent things cannot consider anything.

Francesco, if you have further questions, just ask and I will respond. Best wishes, Stefan.

Thankyou for reading and commenting on my essay, much appreachiated.

I introduced rule F as the compressed, extreme case of an assumed to be found ‘TOE’ and examine with this rule F what such a TOE could mean for our quest about “what is fundamental”. Surely, the term “except” in the b)-part of rule F can be misleading, but it mustn’t. One can understand the b)-part as “but not for rule F.” without changing the term “except”. Since rule F is the whole lot only about rules and exceptions, but makes no reference to the contents of such exceptions, the term “except” in the b)-part is just a negation of the a)-part for *exclusively only* a very special rule, namely rule F itself. As I annotated in the essay, formally this is a double negation, referring to a default state that has no exceptions.

According to your question:

I consider it a false statement that I am non-existent at the moment – so I consider it a *truth* that “I am non-existent at the moment” is indeed a false statement.

Another example would be that I consider it a false statement that my computer monitor is a living elephant (like the ones in the zoo). So I consider it a truth that “my computer monitor is a living elephant” is indeed a false statement.

But vice versa, I would enter into some problems. If I consider that my computer monitor is indeed a living elephant (and therefore the truth of the starting premise is doubted), I think I had to go to a doctor. Similarily, if I consider myself to be non-existent at the moment, I had to go to a doctor. Even when I am dead, I cannot consider myself as being non-existent, because non-existent things cannot consider anything.

Francesco, if you have further questions, just ask and I will respond. Best wishes, Stefan.

Dear Fellow Essayists

This will be my final plea for fair treatment.,

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Only the truth can set you free.

Joe Fisher, Realist

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This will be my final plea for fair treatment.,

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Only the truth can set you free.

Joe Fisher, Realist

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Dear Stefan,

You say that "rule F' is logically consistent. It is just an arbitrary statement, and does not come from any logical reasoning. Such arbitrary statements (whether true or false) are 'basic assumptions' from which we start our arguments. Logical consistency comes only later: our arguments should be consistent with the basic assumptions. Such 'arbitrary basic-assumptions' are unavoidable in all logical arguments, and so in a way, all logical arguments are 'incomplete' as Godel has stated.

What do you mean by 'rules' in physics? What we observe is matter getting added up in different forms; if it is spherical, mathematics gives a short-cut to calculate its volume and mass. General Relativity and Quantum Mechanics provide equations to elucidate certain results (that are factually correct) in certain areas. Such equations are mathematical short-cuts to calculate the adding up of mass, volume, force and energy. So the law of addition alone is required to explain everything in physics.

However, the pattern of adding up is not the same for mass, volume, energy and force. For example, if matter comes in spherical balls, and we pack it into larger spheres, and these larger spheres into still larger spheres, the mass- volume ratio will not be the same. But the rule followed is law of addition. In the case of force and energy, the adding up is more complex. Thus in fact, there is just one law (the law of addition), and a large number of short-cuts applicable to different circumstances.

Jose P Koshy

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You say that "rule F' is logically consistent. It is just an arbitrary statement, and does not come from any logical reasoning. Such arbitrary statements (whether true or false) are 'basic assumptions' from which we start our arguments. Logical consistency comes only later: our arguments should be consistent with the basic assumptions. Such 'arbitrary basic-assumptions' are unavoidable in all logical arguments, and so in a way, all logical arguments are 'incomplete' as Godel has stated.

What do you mean by 'rules' in physics? What we observe is matter getting added up in different forms; if it is spherical, mathematics gives a short-cut to calculate its volume and mass. General Relativity and Quantum Mechanics provide equations to elucidate certain results (that are factually correct) in certain areas. Such equations are mathematical short-cuts to calculate the adding up of mass, volume, force and energy. So the law of addition alone is required to explain everything in physics.

However, the pattern of adding up is not the same for mass, volume, energy and force. For example, if matter comes in spherical balls, and we pack it into larger spheres, and these larger spheres into still larger spheres, the mass- volume ratio will not be the same. But the rule followed is law of addition. In the case of force and energy, the adding up is more complex. Thus in fact, there is just one law (the law of addition), and a large number of short-cuts applicable to different circumstances.

Jose P Koshy

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Hi Jose, thanks for reading and commenting. I did not state that Rule F isn’t arbitrary; it is as arbitrary as E = m(c x c). Why not E = m (c x c):2? Elsewhere on this site I wrote that Rule F is just a gedankenexperiment and I think I made it clear in my essay that even for the case that such a strange Rule F would reflect something fundamental in nature, this Rule F would remain mysterious and arbitrary. The point is therefore, even if you find a “theory of everything” (in the sense of a set of mathematical relationships that unite GR with QM and explain [away] all the rest – dark matter, dark energy, cosmological constant etc.) you also end up with arbitrariness – in relation to that set of rules instead of other possible ones. Nothing within the relationship of these mathematical rules tells you that the world must be such that it only obeys those rules, instead of possibly some others. You only end up with consistency and the *induction* that these rules govern all things in the microscopic as well as in the macroscopic realms. But you can never prove your induction to indeed meet reality, since such a TOE remains in the realm of coarse-grained experimental verification. Does the water-vortex in your shower really obey infinitesimally the laws of motion together with the laws of gravity – nobody can ever prove this, since every new instant of that votex is different from any other such instant.

By rules in physics I mean for example F = ma. Or E = m (c x c). My Rule F is only a gedankenexperiment, an idealized TOE that compresses all rules into one to show that such a TOE may be self-consistent, but merely ‘explains’ terms like energy, force, space, time in terms of those other terms. What remains unexplained is what these terms refer to in the first place. Since you argue with matter, I ask why matter and energy are equivalent. So the question of what is matter is rephrased by the question what is energy. You may say energy is a kind of vibration. Well, maybe, but what does vibrate? You may say fields do vibrate, well maybe, but what are the fields made of? Every TOE comes to a point where we are forced to ask whether or not we are further talking about physical things at all.

If it were true that the law of addition is sufficient to explain everything in physics, then consciousness must be an unphysical phenomenon. I also cannot see how space can be a physical phenomenon, since adding up infinitesimally small pieces of space to come to a kind of planck-area seems to make no sense to me – unless one presupposes space to be some magical kind of Cantor-dust. Not to speak about the question whether or not one has to take the mathematics behind any TOE seriously such that one assumes that nature incorporates and executes the physical constants to an infinity of decimal places. In my opinion there is something wrong with assuming that physical relationships and mathematical relationships are in a one-to-one correspondence. Infinities cannot be part of the very fabric of reality, since otherwise every rule of addition wouldn’t come to an end even for the tiniest changes in nature.

But you are surely right that mathematical rules are indeed short-cuts, since they indeed compress a wide range of phenomena into a small piece of algorithm. The problem is really the initial conditions. Are the latter of infinite precission or merely of a finite precision? And if merely of finite precision, at which mathematical resolution do the physical constants stop to have any impact on the course of events? Since we know from chaos theory, even the tiniest differences can make a huge difference after some time-evolution. I think that mathematics isn’t able to describe such dynamics in nature, not because deterministic chaos wouldn’t be possible, but because such tiny dynamics simply doesn’t exist. The gap that remains must be bridged by some other means than classical causality and classical determinism. Please do not misunderstand me, I do not generally deny causality, that be far away from me. But I doubt that ‘reason’ and ‘causality’ must be one and the same thing under every circumstance. My essay was intended to expose all these questions I outlined here, surely in a rather compressed form due to character restrictions and with the focus on the mutual exclusiveness of some ‘ex nihilo creation’ versus reasonable (logical) thinking.

Thank you again for your comment Jose!

Best wishes,

Stefan Weckbach

By rules in physics I mean for example F = ma. Or E = m (c x c). My Rule F is only a gedankenexperiment, an idealized TOE that compresses all rules into one to show that such a TOE may be self-consistent, but merely ‘explains’ terms like energy, force, space, time in terms of those other terms. What remains unexplained is what these terms refer to in the first place. Since you argue with matter, I ask why matter and energy are equivalent. So the question of what is matter is rephrased by the question what is energy. You may say energy is a kind of vibration. Well, maybe, but what does vibrate? You may say fields do vibrate, well maybe, but what are the fields made of? Every TOE comes to a point where we are forced to ask whether or not we are further talking about physical things at all.

If it were true that the law of addition is sufficient to explain everything in physics, then consciousness must be an unphysical phenomenon. I also cannot see how space can be a physical phenomenon, since adding up infinitesimally small pieces of space to come to a kind of planck-area seems to make no sense to me – unless one presupposes space to be some magical kind of Cantor-dust. Not to speak about the question whether or not one has to take the mathematics behind any TOE seriously such that one assumes that nature incorporates and executes the physical constants to an infinity of decimal places. In my opinion there is something wrong with assuming that physical relationships and mathematical relationships are in a one-to-one correspondence. Infinities cannot be part of the very fabric of reality, since otherwise every rule of addition wouldn’t come to an end even for the tiniest changes in nature.

But you are surely right that mathematical rules are indeed short-cuts, since they indeed compress a wide range of phenomena into a small piece of algorithm. The problem is really the initial conditions. Are the latter of infinite precission or merely of a finite precision? And if merely of finite precision, at which mathematical resolution do the physical constants stop to have any impact on the course of events? Since we know from chaos theory, even the tiniest differences can make a huge difference after some time-evolution. I think that mathematics isn’t able to describe such dynamics in nature, not because deterministic chaos wouldn’t be possible, but because such tiny dynamics simply doesn’t exist. The gap that remains must be bridged by some other means than classical causality and classical determinism. Please do not misunderstand me, I do not generally deny causality, that be far away from me. But I doubt that ‘reason’ and ‘causality’ must be one and the same thing under every circumstance. My essay was intended to expose all these questions I outlined here, surely in a rather compressed form due to character restrictions and with the focus on the mutual exclusiveness of some ‘ex nihilo creation’ versus reasonable (logical) thinking.

Thank you again for your comment Jose!

Best wishes,

Stefan Weckbach

Dear Stefan,

From what you have written above, it is not clear whether you consider infinity as part of reality. In my opinion, infinity is not part of reality. Infinite space and infinite time are not part of our reality, but just an arena. But space occupied by matter and time taken for any process involving matter are parts of our reality.

Regarding energy, I do not visualize matter- energy conversion. Energy according to my model is 'motion of matter'. We need not take QM or GR as correct theories; new theories may come. Any theory is based on some arbitrary assumptions. These assumptions cannot be explained from within the theory. So any theory of everything will have one defect, which we can call 'Godel's incompleteness'.

Chaos and Determinism are diametrically opposite; there cannot be a deterministic chaos. Anyway that depends on how you define chaos. In my opinion, chaos is lawlessness. The validity of chaos theory is questionable.

What do you mean by physical relationship? To me physical relationship occurs due to the physical properties of bodies. The extent to which such relations go depends entirely on mathematical laws. So I do agree with your opinion that physical relationship and mathematical relationship have no one-to-one correspondence. And that explains why consciousness is a physical phenomenon.

Atoms just add up forming three-dimensional structures, mathematics deciding their relative positions (given the properties of each atom). The resultant structure has some emergent properties that can be explained based on mass, volume, energy an force. Consciousness is one such emergent physical property.

I agree with you that 'classical causality' and 'classical determinism' are not enough to explain everything. However, the term 'classical' means only the 'present form' and not any particular style. I do not argue for any 'magical' causality/determinism. Some corrections in their definitions are required.

Jose P Koshy

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From what you have written above, it is not clear whether you consider infinity as part of reality. In my opinion, infinity is not part of reality. Infinite space and infinite time are not part of our reality, but just an arena. But space occupied by matter and time taken for any process involving matter are parts of our reality.

Regarding energy, I do not visualize matter- energy conversion. Energy according to my model is 'motion of matter'. We need not take QM or GR as correct theories; new theories may come. Any theory is based on some arbitrary assumptions. These assumptions cannot be explained from within the theory. So any theory of everything will have one defect, which we can call 'Godel's incompleteness'.

Chaos and Determinism are diametrically opposite; there cannot be a deterministic chaos. Anyway that depends on how you define chaos. In my opinion, chaos is lawlessness. The validity of chaos theory is questionable.

What do you mean by physical relationship? To me physical relationship occurs due to the physical properties of bodies. The extent to which such relations go depends entirely on mathematical laws. So I do agree with your opinion that physical relationship and mathematical relationship have no one-to-one correspondence. And that explains why consciousness is a physical phenomenon.

Atoms just add up forming three-dimensional structures, mathematics deciding their relative positions (given the properties of each atom). The resultant structure has some emergent properties that can be explained based on mass, volume, energy an force. Consciousness is one such emergent physical property.

I agree with you that 'classical causality' and 'classical determinism' are not enough to explain everything. However, the term 'classical' means only the 'present form' and not any particular style. I do not argue for any 'magical' causality/determinism. Some corrections in their definitions are required.

Jose P Koshy

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Dear Jose,

thanks again for your reply.

Yes, I would agree that space and time are needed for processes involving matter. I also do not consider infinity as something which is physically realized.

In my considerations about fundamentals, I can only take into account what we know today works reliably, which seems to be GR and QM. By physical relationships I mean not only the properties matter has – according to our hitherto establishes theories – but also how matter behaves when it meets other matter. Or alternatively, how matter behaves when it does not meet other matter.

Yes, the terminus ‘deterministic chaos’ is a little bit misleading and I agree that ‘chaos’ is synonym with lawlessness. But that is not what I intended with deterministic chaos. I intended to say that deterministic chaos (in the sense of chaos theory) is hard to differentiate from a probabilistic interpretation of QM.

I think I do not agree that if mathematical relationships and physical relationships have no one-to-one correspondence, then consciousness must be a physical phenomenon. I cannot see any necessity for this conclusion. Also I cannot see how mathematics or the physics of matter or both could in any way elucidate that ‘matter’ (or mathematics) should be capable of becoming aware of an external world (say, of other matter particles, brains etc.) and should additionally be able to fully understand all this – on the basis of three-dimensional matter structures. Surely, animals are aware too, but do not understand all this. But if I take your claims serious that human beings can understand all this – by means of some law of addition with some ‘emergence’ mixed in – what would THIS then MEAN for our worldview? Would it be deeply natural that nature MUST come to a point where it becomes aware of itself (‘itself’ as defined in our theories) and additionally aware of the fact that it must become aware of itself at some point in time? I deeply suspect that what we as ‘nature’ are factually aware of in reference to ‘nature’, is not the complete, ultimate nature, but merely our pictures we make ourselves from nature.

I do not claim that consciousness is a-natural or something like this. I merely state that what is natural is at the foremost a matter of personal taste. For some it is natural that mathematics is indeed the thing we only think it describes it (the MUH for example). I purport the view that we should not exclude other possibilities and options. As you may know – and as I have outlined in the last essay contest – the phenomenon of near-death experiences can give us a totally other perspective on matter and consciousness. Albeit it is not clear at all how a consciousness that is considered independent of any brain can interact or perceive a physical world, it nonetheless is the case – at least for me. And believe me, I have studied hundreds of such experiences, I studied what they may say about the mind-body problem and also studied what they teleologically may say about the existence of a physical world. The crucial point is, that there are many cases where information was brought back from such experiences that couldn’t be achieved by the physical senses at all. One cannot explain this by statistical randomness and probability, since there are no reports out there that could underpin such an interpretation (in terms of information brought back that could be falsified – what should be the case for a statistical interpretation). What I consider is that consciousness is natural, but our framework what is allowed to be natural at all is too narrow still.

If you have any further questions, just ask and I reply.

Best wishes,

Stefan Weckbach

thanks again for your reply.

Yes, I would agree that space and time are needed for processes involving matter. I also do not consider infinity as something which is physically realized.

In my considerations about fundamentals, I can only take into account what we know today works reliably, which seems to be GR and QM. By physical relationships I mean not only the properties matter has – according to our hitherto establishes theories – but also how matter behaves when it meets other matter. Or alternatively, how matter behaves when it does not meet other matter.

Yes, the terminus ‘deterministic chaos’ is a little bit misleading and I agree that ‘chaos’ is synonym with lawlessness. But that is not what I intended with deterministic chaos. I intended to say that deterministic chaos (in the sense of chaos theory) is hard to differentiate from a probabilistic interpretation of QM.

I think I do not agree that if mathematical relationships and physical relationships have no one-to-one correspondence, then consciousness must be a physical phenomenon. I cannot see any necessity for this conclusion. Also I cannot see how mathematics or the physics of matter or both could in any way elucidate that ‘matter’ (or mathematics) should be capable of becoming aware of an external world (say, of other matter particles, brains etc.) and should additionally be able to fully understand all this – on the basis of three-dimensional matter structures. Surely, animals are aware too, but do not understand all this. But if I take your claims serious that human beings can understand all this – by means of some law of addition with some ‘emergence’ mixed in – what would THIS then MEAN for our worldview? Would it be deeply natural that nature MUST come to a point where it becomes aware of itself (‘itself’ as defined in our theories) and additionally aware of the fact that it must become aware of itself at some point in time? I deeply suspect that what we as ‘nature’ are factually aware of in reference to ‘nature’, is not the complete, ultimate nature, but merely our pictures we make ourselves from nature.

I do not claim that consciousness is a-natural or something like this. I merely state that what is natural is at the foremost a matter of personal taste. For some it is natural that mathematics is indeed the thing we only think it describes it (the MUH for example). I purport the view that we should not exclude other possibilities and options. As you may know – and as I have outlined in the last essay contest – the phenomenon of near-death experiences can give us a totally other perspective on matter and consciousness. Albeit it is not clear at all how a consciousness that is considered independent of any brain can interact or perceive a physical world, it nonetheless is the case – at least for me. And believe me, I have studied hundreds of such experiences, I studied what they may say about the mind-body problem and also studied what they teleologically may say about the existence of a physical world. The crucial point is, that there are many cases where information was brought back from such experiences that couldn’t be achieved by the physical senses at all. One cannot explain this by statistical randomness and probability, since there are no reports out there that could underpin such an interpretation (in terms of information brought back that could be falsified – what should be the case for a statistical interpretation). What I consider is that consciousness is natural, but our framework what is allowed to be natural at all is too narrow still.

If you have any further questions, just ask and I reply.

Best wishes,

Stefan Weckbach

Dear Stefan Weckbach,

In a last comment on my own essay, I am arguing that the frog's view is fundamental to the bird's view. This summarizes my effort.

Eckard Blumschein

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In a last comment on my own essay, I am arguing that the frog's view is fundamental to the bird's view. This summarizes my effort.

Eckard Blumschein

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Dear Eckhard,

thank you for your comment. The big question is if there is any such ‘thing’ as a bird’s view. This critically hinges on whether or not one assumes consistent logics to be more fundamental than inconsistent logics.

I differentiate ‘inconsistent logic’ (principle of explosion) from some consistent one by arguing that the former allows one to ‘prove’ everything, even itself to be consistent – and inconsistent – at the same time.

If one can ‘prove’ everything – then one can ‘prove’ nothing. Even that “nothing” I referred in my essay.

Since your comment was not about my essay, but about yours, I cannot comment on it, because I am not competent enough to judge it. I can only say something about my view on bird’s and frog’s.

If reality is rational and reasonable, these attributes necessarily have also to reside in a yet undefined realm that facilitated our universe in the first place. This is independent of our universe being eternal or only temporal, since both possibilities do not exclude a realm beyond our spatio-temporal universe.

If reality (whatever it is) has no objective reason to be like it is (and to be at all existent), then no infinity of arguments can make it rational or reasonable. It even could be then that parts of it spontaneously vanish into “nothing” or some other parts spontaneously emerge out of “nothing”. Either way, a reality that is not considered by an observer as rational and reasonably facilitated is by definition an irrational universe and then there is no reason for us to demand its rational behaviour. This statement is surely inconsistent, since if the universe where indeed irrational, why should it allow at all rational thoughts about its irrationality?

Here is why I claim that a real bird’s view is possible and that this implies a realm of fundamental truths – truths which do not irrationally change due to the universe being irrational itself. Even if such truths do not change within an irrational universe (due to the latter being irrational and therefore nothing can be predicted or deduced in it with absolute certainty), a human being equipped with some rational thoughts in such an irrational universe is forced to conclude that the very term ‘truth’ is only a fiction – as is the whole irrational universe, but cannot prove it, because it seems that he has captured a real truths by means of rational thinking. Hence, if one considers existence to be an irrational state of affairs (as is "nothing" too!), then every thought about something will at the end of the day turn out to be deeply irrational.

Surely i do not buy into such an irrational world view. The only premise for my claim that a bird’s view is possible is the claim that deep rationality governs all of reality. By rationality I do not mean necessarily maths equations, determinism and such, but moreover that there are explanations for reality to be like it is – explanations that may or may not be understandable by human minds.

So, I regard explanations as being existent independent of observers that may or may not be able to catch them. If there are no unchangeable, eternal truths, then there aren’t independent explanations out there – but all explanations are man-made delusions. Since the latter is a deeply unscientific and solipsistic point of view, I do not subscribe to it but make my case for a fundamental realm of truths.

If my lines of reasoning are correct, then I further conclude that the human ability to at least infer this realm of fundamental truth is itself possible due to the rationality of reality – and that rationality must have something to do with being able to meaningfully speak about truths. Surely, the latter is only possible because conscious observers are possible. But nothing in an irrational universe demands that these observers should at all be able to speak about ‘truth’ in an absolute, eternal sense. And surely, the assumption of an irrational universe together with a delusion that only mimicks its rationality might be possible logically.

But these are conspiratory theories which mix the rational with the irrational, the consistency with the principle of explosion and make every rational thought delusionary at the end of the day. In my view, rationality and reasonable behaviour aren’t dividable. Even if there are no physical causes for some yet to be explained phenomena in nature, I would bet that there are nonetheless reasonable reasons for these phenomena. How could it be other for a scientific worldview, I am tempted to ask.

Since every final explanation for there being something at all rather than nothing must assume something that is no more further reducible to some other components, one is left with either a mechanical ‘first cause’ – what does not make any sense, because every mechanical cause needs a predecessor. Or one assumes existence as a brute fact, limiting rationality to an ‘anthropic’ realm, the latter understood as the realm of self-consistent systems. With that one states that self-consistence is at the bottom of all, leaving out the fact that there are many self-consistent systems possible other than reality being the way ‘it is’ (nobody really knows what reality ‘really’ is!, surely I too do not know).

The third alternative is to assume a non-mechanical cause which is also a brute fact. This would be the concept of God. For me it has the advantage to at least explain in a coarse-grained manner why the universe is like it is and is not of the kind of some other self-consistent system that is thinkable in mathematics. Surely, the existence of God must remain a brute fact, not furtherly decomposable into other factors. But this is the case with all explanations human beings can think of.

My minimal interpretation that I purported in my essay does not explicitely mention God, since this term is highly controversial as well as ambigous, depending on what religious background (if any) the reader has. I have limited myself to reduce the whole problem to that of rationality versus irrationality, of mechanical reasoning versus non-mechanical resoning (means mathematics versus non-formalizability).

I am absolutely sure that you subscribe also to rationality and that your essay develops along the lines of rationality and the law of non-contradiction. But I cannot vote or comment it, because there are other people that do understand your approach better than me, so it makes no sense to delf into it with my baggage of half-knowledge about your topic.

I nonetheless wish you all the best and that there will be people at the end of the contest that honor your results, since I believe that most of our essays consist of hard mental work and much time of processing ideas and carfully evaluating them.

Best wishes from germany,

Stefan Weckbach

thank you for your comment. The big question is if there is any such ‘thing’ as a bird’s view. This critically hinges on whether or not one assumes consistent logics to be more fundamental than inconsistent logics.

I differentiate ‘inconsistent logic’ (principle of explosion) from some consistent one by arguing that the former allows one to ‘prove’ everything, even itself to be consistent – and inconsistent – at the same time.

If one can ‘prove’ everything – then one can ‘prove’ nothing. Even that “nothing” I referred in my essay.

Since your comment was not about my essay, but about yours, I cannot comment on it, because I am not competent enough to judge it. I can only say something about my view on bird’s and frog’s.

If reality is rational and reasonable, these attributes necessarily have also to reside in a yet undefined realm that facilitated our universe in the first place. This is independent of our universe being eternal or only temporal, since both possibilities do not exclude a realm beyond our spatio-temporal universe.

If reality (whatever it is) has no objective reason to be like it is (and to be at all existent), then no infinity of arguments can make it rational or reasonable. It even could be then that parts of it spontaneously vanish into “nothing” or some other parts spontaneously emerge out of “nothing”. Either way, a reality that is not considered by an observer as rational and reasonably facilitated is by definition an irrational universe and then there is no reason for us to demand its rational behaviour. This statement is surely inconsistent, since if the universe where indeed irrational, why should it allow at all rational thoughts about its irrationality?

Here is why I claim that a real bird’s view is possible and that this implies a realm of fundamental truths – truths which do not irrationally change due to the universe being irrational itself. Even if such truths do not change within an irrational universe (due to the latter being irrational and therefore nothing can be predicted or deduced in it with absolute certainty), a human being equipped with some rational thoughts in such an irrational universe is forced to conclude that the very term ‘truth’ is only a fiction – as is the whole irrational universe, but cannot prove it, because it seems that he has captured a real truths by means of rational thinking. Hence, if one considers existence to be an irrational state of affairs (as is "nothing" too!), then every thought about something will at the end of the day turn out to be deeply irrational.

Surely i do not buy into such an irrational world view. The only premise for my claim that a bird’s view is possible is the claim that deep rationality governs all of reality. By rationality I do not mean necessarily maths equations, determinism and such, but moreover that there are explanations for reality to be like it is – explanations that may or may not be understandable by human minds.

So, I regard explanations as being existent independent of observers that may or may not be able to catch them. If there are no unchangeable, eternal truths, then there aren’t independent explanations out there – but all explanations are man-made delusions. Since the latter is a deeply unscientific and solipsistic point of view, I do not subscribe to it but make my case for a fundamental realm of truths.

If my lines of reasoning are correct, then I further conclude that the human ability to at least infer this realm of fundamental truth is itself possible due to the rationality of reality – and that rationality must have something to do with being able to meaningfully speak about truths. Surely, the latter is only possible because conscious observers are possible. But nothing in an irrational universe demands that these observers should at all be able to speak about ‘truth’ in an absolute, eternal sense. And surely, the assumption of an irrational universe together with a delusion that only mimicks its rationality might be possible logically.

But these are conspiratory theories which mix the rational with the irrational, the consistency with the principle of explosion and make every rational thought delusionary at the end of the day. In my view, rationality and reasonable behaviour aren’t dividable. Even if there are no physical causes for some yet to be explained phenomena in nature, I would bet that there are nonetheless reasonable reasons for these phenomena. How could it be other for a scientific worldview, I am tempted to ask.

Since every final explanation for there being something at all rather than nothing must assume something that is no more further reducible to some other components, one is left with either a mechanical ‘first cause’ – what does not make any sense, because every mechanical cause needs a predecessor. Or one assumes existence as a brute fact, limiting rationality to an ‘anthropic’ realm, the latter understood as the realm of self-consistent systems. With that one states that self-consistence is at the bottom of all, leaving out the fact that there are many self-consistent systems possible other than reality being the way ‘it is’ (nobody really knows what reality ‘really’ is!, surely I too do not know).

The third alternative is to assume a non-mechanical cause which is also a brute fact. This would be the concept of God. For me it has the advantage to at least explain in a coarse-grained manner why the universe is like it is and is not of the kind of some other self-consistent system that is thinkable in mathematics. Surely, the existence of God must remain a brute fact, not furtherly decomposable into other factors. But this is the case with all explanations human beings can think of.

My minimal interpretation that I purported in my essay does not explicitely mention God, since this term is highly controversial as well as ambigous, depending on what religious background (if any) the reader has. I have limited myself to reduce the whole problem to that of rationality versus irrationality, of mechanical reasoning versus non-mechanical resoning (means mathematics versus non-formalizability).

I am absolutely sure that you subscribe also to rationality and that your essay develops along the lines of rationality and the law of non-contradiction. But I cannot vote or comment it, because there are other people that do understand your approach better than me, so it makes no sense to delf into it with my baggage of half-knowledge about your topic.

I nonetheless wish you all the best and that there will be people at the end of the contest that honor your results, since I believe that most of our essays consist of hard mental work and much time of processing ideas and carfully evaluating them.

Best wishes from germany,

Stefan Weckbach

Dear Stefan,

Please find a brief attempt to explain peculiarities of my essay at 3009.

Notice, I am distinguishing between pragmatic mathematical infinities and the logical infinity. Don't be a coward. We both will anyway not win the contest.

Greetings from Germany too,

Yours, Eckard

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Please find a brief attempt to explain peculiarities of my essay at 3009.

Notice, I am distinguishing between pragmatic mathematical infinities and the logical infinity. Don't be a coward. We both will anyway not win the contest.

Greetings from Germany too,

Yours, Eckard

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Dear Eckhard,

I read your essay and cannot see how you answer the question “what is fundamental”. Since I am not clear about this, I may ask you, do you think that some fundamental truth can be found in mathematics itself or in physical theories themselves or in the existence of the universe itself, in matter or in the fact that matter can become conscious at some point in time?

Sorry, I simply couldn’t find a clear statement in your essay regarding the contest’s question. You mention many concepts and scientists, but your take on the main question remains unclear to me.

This does not mean in any way to me that you haven't said something important about some of the issues you raised.

Best wishes,

Stefan Weckbach

I read your essay and cannot see how you answer the question “what is fundamental”. Since I am not clear about this, I may ask you, do you think that some fundamental truth can be found in mathematics itself or in physical theories themselves or in the existence of the universe itself, in matter or in the fact that matter can become conscious at some point in time?

Sorry, I simply couldn’t find a clear statement in your essay regarding the contest’s question. You mention many concepts and scientists, but your take on the main question remains unclear to me.

This does not mean in any way to me that you haven't said something important about some of the issues you raised.

Best wishes,

Stefan Weckbach

Dear all,

I have the impression, Stefan Weckbach doesn't notice those who dare challenging something, e.g. Klingman, Traill, and Kadin. Shouldn't we try reading and digesting much more than writing?

In order to avoid misjudgement of such essays including mine, I would like to remind of suspected fundamental (in the sense of perhaps important) mistakes and their possible consequences.

What about me, as an advocate of conciseness, I have to stress that I nonetheless like using i, Nabla, and box as elegant "bird's" tools.

Eckard (not Eckhard)

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I have the impression, Stefan Weckbach doesn't notice those who dare challenging something, e.g. Klingman, Traill, and Kadin. Shouldn't we try reading and digesting much more than writing?

In order to avoid misjudgement of such essays including mine, I would like to remind of suspected fundamental (in the sense of perhaps important) mistakes and their possible consequences.

What about me, as an advocate of conciseness, I have to stress that I nonetheless like using i, Nabla, and box as elegant "bird's" tools.

Eckard (not Eckhard)

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Dear Eckard,

please excuse me for having mispelled your name several times!

There are so many people in this essay contest who dare challenging something, “nothing” or everything. So please excuse me for being not motivated to involve myself in every challenge that is considered by someone as fundamentally important. It may be so, but surely I am not the final judge, nor does some abritrary voting alter the arguments involed in these multitudes of approaches.

There are lots of people that read and commented on Klingman, Traill and Kadin, I prefer to comment on things that my own essay may necessarily imply or exclude to see where that may lead. Diving into the things I consider as important is hard enough for me, my concentration and motivation for evaluating all the assumed to be existent details of various approaches is indeed limited. Since there are over 250 entries (estimated), everbody’s entry should receive a good portion of attention, if the author isn’t permanently absent from his / her own essay commentary page.

And I suspect that even the FQXi stuff and members are listening quite interestingly, so to speak, and indeed follow your advice for more reading and digesting instead of writing and commenting. According to the oppulent meal served by over 250 authors, the important readers of the FQXi memberships may well be not yet be finished with their digesting processes. I would just have some more patience, because anyways you can’t force someone to be convinced of something.

Best wishes,

Stefan

please excuse me for having mispelled your name several times!

There are so many people in this essay contest who dare challenging something, “nothing” or everything. So please excuse me for being not motivated to involve myself in every challenge that is considered by someone as fundamentally important. It may be so, but surely I am not the final judge, nor does some abritrary voting alter the arguments involed in these multitudes of approaches.

There are lots of people that read and commented on Klingman, Traill and Kadin, I prefer to comment on things that my own essay may necessarily imply or exclude to see where that may lead. Diving into the things I consider as important is hard enough for me, my concentration and motivation for evaluating all the assumed to be existent details of various approaches is indeed limited. Since there are over 250 entries (estimated), everbody’s entry should receive a good portion of attention, if the author isn’t permanently absent from his / her own essay commentary page.

And I suspect that even the FQXi stuff and members are listening quite interestingly, so to speak, and indeed follow your advice for more reading and digesting instead of writing and commenting. According to the oppulent meal served by over 250 authors, the important readers of the FQXi memberships may well be not yet be finished with their digesting processes. I would just have some more patience, because anyways you can’t force someone to be convinced of something.

Best wishes,

Stefan

Dear anonymous 1-bomber, fear, anger and irrationality are not a healthy combination. Calm down and reflect your own emotions, before proceeding with further votings. Please! Thank you.

Hello Stefan,

Congratulations for your essay, I liked it,

good luck in this contest,

Best Reagrds

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Congratulations for your essay, I liked it,

good luck in this contest,

Best Reagrds

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Hi Steve,

happy that you read and liked it!

Thanks for your good wishes wich I want to reciproke!

Stefan Weckbach

happy that you read and liked it!

Thanks for your good wishes wich I want to reciproke!

Stefan Weckbach

You are welcome,

I have always liked your lines of reasonings in physics and philosophy,

friendly

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I have always liked your lines of reasonings in physics and philosophy,

friendly

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Dear Stefan,

I highly appreciate your beautifully written essay.

It is so close to me. «The laws of physics seem to imply exclusively only deterministical processes in nature, and thisautomatically suggests that nature obviously acts according to some fundamental rationality,tacitly suggesting that the principle of physical causation must be absolutely exclusive. Moreover, the assumption of the predominant deterministic behaviour of nature seems to be reassured by the very tool science operates with, namely by logic».

I hope that my modest achievements can be information for reflection for you.

Vladimir Fedorov

https://fqxi.org/community/forum/topic/3080

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I highly appreciate your beautifully written essay.

It is so close to me. «The laws of physics seem to imply exclusively only deterministical processes in nature, and thisautomatically suggests that nature obviously acts according to some fundamental rationality,tacitly suggesting that the principle of physical causation must be absolutely exclusive. Moreover, the assumption of the predominant deterministic behaviour of nature seems to be reassured by the very tool science operates with, namely by logic».

I hope that my modest achievements can be information for reflection for you.

Vladimir Fedorov

https://fqxi.org/community/forum/topic/3080

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I attach an addendum to my essay that can be read on page 9 of the attachment below. There I have summarized the main points I want to make with my essay about the contest's question. Its easy to read, since i used bullets to make these points.

Best wishes and thanks to all the readers, commentators and raters of my essay!

Stefan Weckbach

Best wishes and thanks to all the readers, commentators and raters of my essay!

Stefan Weckbach

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