## The final theory of physics, sold here.

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The theory admits a single axiom: a formal definition of the observer, from which all known fundamental physics is entailed. The theory cannot be made simpler, it is fully comprehensive and it is constructed in an indubitable manner.

https://philpapers.org/rec/TREAMP

For those who have read a previous version posted earlier, I have re-articulated my paper thanks to the comments in the previous post. I believe it should now be crystal clear to everyone. Let me know if you have any questions, or if anything is unclear.

Some of numerous open problem that it solves are:

• Epistemic regress
• The correct definition of knowledge
• A comprehensive and infallible construction of epistemology
• Formalization of science
• Formalization of experiments
• Formalization of the scientific method
• Formalization of the observer, and subsequent integration into the formalism of physics
• The theory of quantum gravity
• The origin of the wave-function
• The origin of the Born rule, and subsequent extension thereof.
• An explanation, and resolution, of the wave-function collapse.
• The true and correct interpretation of quantum mechanics.
• The origins of the Dirac relativistic quantum physics.
• Explicitly supports Yang-Mills quantum field theory
• Explicitly entails general relativity
• Explains why the observer cannot violate the laws of physics
• Explains the origins of the laws of physics, in general
• Entails the universe from the definition of the observer
• Side-steps the Hard problem of consciousness, while retaining scientific comprehensiveness
• Finally, checkmates the solipsist position by deriving physics from the perspective of the observer, while strategically avoiding the insertion of physical baggage.
• Makes a dozen of (relatively) easily realizable falsifiable predictions

There is at least two dozen other things that it solves, but these are likely the most significant.

A formal system of science is presented as a powerful replacement for the axioms of fundamental physics. Fundamental theories of physics are typically constructed axiomatically (e.g. Dirac Von-Neumann axioms of quantum mechanics, Special theory of relativity, etc); and are justified on scientific grounds. Although well respected and crucial to the exercise, scientific grounds do not at present benefit from a formal construction. Our idea here is to design a formal system of science able to support the scientific method comprehensively. Once done, our goal will then be to derive the fundamental physics, this time not axiomatically, but as an actual theorem of the system; thereby formalizing their origin and subsequently proving physics. The formalization requirements will be quite demanding, but are responsible for making this exercise surprisingly productive and precise; correcting definitions and resolving numerous open problems spawning philosophy to physics. The first part of the paper consists of constructing an experimental basis that is purely mathematical. For this we employ the set of all halting programs and we leverage modern notions of undecidability to produce a system that never runs out of new knowledge to discover, thus supporting a perpetual application of the scientific method. The exercise culminates in a definition of the observer as a measure space over the halting programs identified by the scientific method, from which the fundamental physics is entailed as a quantum theory of computation also supporting gravity; thus for the first time integrating the observer into the formalism of physics. Finally, the compatibility of our definition with that of the observer in physics is assessed, and testable predictions are proposed for the entailed fundamental physics.
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Didn't Chris Langan already do this with his CTMU or Steven Lehar with his theory of perception
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The first part of the paper consists of constructing an experimental basis that is purely mathematical.

Pure mathematics excludes measurements. Measured quantities consist of a measured unit and a measured multiplier (number of those) units.

Physics experiments rely on measurements.

If you subtract measured units from the maths of physics, it ceases to be physics.

As an example: Certainly (x^2-Y^2) = (x+Y)(x-Y). But when you show it to a physicist, he will not find any physics in this logically otherwise true expression.
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Pure mathematics excludes measurements. Measured quantities consist of a measured unit and a measured multiplier (number of those) units.

Physics experiments rely on measurements.

If you subtract measured units from the maths of physics, it ceases to be physics.

As an example: Certainly (x^2-Y^2) = (x+Y)(x-Y). But when you show it to a physicist, he will not find any physics in this logically otherwise true expression.

Question for you; what do you think the Pythagorean theorem shows... I mean it has no units, right? a^2+b^2=c^2.
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Whatever the theorem of Pythagoras shows, is not physics. It shows relationships of lengths of sides of a right-angle triangle. That's not physics, it is, instead, descriptive geometry.

Let me ask you: what do you think people will think of your theory ex origo when in the second post in your thread you deliberately mistake descriptive geometry with physics?
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Let me ask you: what do you think people will think of your theory ex origo when in the second post in your thread you deliberately mistake descriptive geometry with physics?

What you think of t^2=x^2+y^2+z^2? Still not physics? What about ds^2 = g_(mu nu) dx^mu dx^nu? Do you seriously think that physics, at the most fundamental level is different than geometry? There is another concept that matter: information. In fact, that is what quantum gravity is; the union of *only* information and geometry.
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You win. I capitulate to your genius.
(Elegem volt ilyesmibol.)
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Reading through the first part of your paper, it strikes me that if there is any substance to it at all, you've got the solution to the P, NP problem. But I suspect you don't. My reasoning is meta-logical. If you had it, you'd know it, and you wouldn't be here.
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:smirk:
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Reading through the first part of your paper, it strikes me that if there is any substance to it at all, you've got the solution to the P, NP problem.

Glad to see you two back. I am happy to give it a shot and try to clarify things. It seems that there is a basis of misconception as you read through this, or of 'bizarre' expectations that are just slightly off... So help me understand.

What goes through your mind when you say something like this : "it strikes me that if there is any substance to it at all, you've got the solution to the P, NP problem". I do not mention the problem whatsoever in this paper. I gave a whole list of bullet points in the original post above of what I think this framework solves and not a single one refers to a computer algorithm of some kind.

When you read; a state of knowledge can be described infallibly, indempotently and immutably by the set of all programs known to have halted (forming a halting image), and that this is comprehensive due to being Turing complete. Do you think that I actually know or care which programs have halted, or that it matters that we know the specifics... ? Do you seriously think that my next step is to waste my time trying finding 'cool' programs from that set, like an intellectual peasant would...

Please... the derivation is done at a much higher level.

You can describe knowledge in such a manner (I repeat: my setup is Turing complete) irrespective of how many theorems you may or might not know right now (you can even describe an empty halting image if you know nothing). The novelty of the approach is because the knowledge of a halting program is infallible, you can construct an encyclopedia of knowledge that will *eventually* be comprehensive with no gaps in knowledge, whilst never having to fear removing or correcting a previous entry due to some future insight. Do you understand the significance of this, and what it entails... when most assumes that all "knowledge" is provisional (Karl Popper)?

The novelty of this description is that the laws of physics are entailed by that description of reality, as the rules that maximize the information in any possible state of knowledge.

Deriving the laws of physics in such a manner forces you to change what your expectations of what the laws of physics are (information maximization model of knowledge) but they map one-to-one with the fundamental physics, revealing -since they are the same- that scientists in the wild, informally (and accidentally) attempted to maximize the information of knowledge when they postulated new laws of physics from experimental data in the first place. I have simply done formally and to the highest possible degree, what everybody had been doing before accidentally or informally.
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Well that is a though question to answer. It may appear as if there is a non-vanishing amount of overlap, but at the same time there are major differences as well. For instance my definition of the observer is a singleton observer, and I do not think this is what panpsychism had in mind (pardon the pun). If you wish to dig deeper, I recommend you read the third section of the discussion of the paper where I cast it against a few philosophical frameworks.

It is more accurate to state that my model is strategically constructed to remain agnostic with respect to a plurality of philosophical framework; hence why it is a checkmate position, essentially. My definition of the observer is that it is a measure space of knowledge. Even Descartes would find it hard to find doubt in such a description (this is by design), and this definition is sufficient to entail the theory of everything in physics. Further taking the case of a solipsist as the extreme case... as long as he accepts he is a measure space of knowledge (and he should), he would understand why he is necessarily coupled to a universe obeying the laws of physics without having to attribute a physical characteristic to this universe. Likewise an objectivist would also be convinced by my derivation; as including the observer into the formalism of physics is a long-standing open problem. It works agnostically for possibly all philosophical frameworks, up to and including solipsism.

It's a checkmate position.

My framework ties in the universe, its structure and its laws, to a definition of the observer which carries no doubt, and from which it is entailed.
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Does your theory have any infallible implications for the psychology of knowledge, a suggestion of standards or principles to guide epistemic advancement (something like Ockham's Razor)?
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Does your theory have any infallible implications for the psychology of knowledge, a suggestion of standards or principles to guide epistemic advancement?

The infallible property does not refer to the method used to acquire knowledge, but to the knowledge itself once acquired. There is one and only one general method you can use to acquire knowledge such that it is comprehensive; it is a recursive enumeration of the domain of epistemology. Other than that you are free to use any insight, creativity or strategy --that is you can pick any function from an uncountably infinite set of recursively enumerable function- to perform your enumeration. The recursive enumeration is, in general, called the scientific method (definition 8 of the paper):

[Scientific method]
A function which recursively enumerates knowledge, is called a scientific method.

I then go on to describe it as follows, in the paper:

Mathematically speaking, this is a very simple definition. First, it is indeed purely mathematical, and formal, and in fact coincide with the definition of a universal function --- which is a non-controversial mathematical concept. We have previously defined knowledge as halting programs (this made it comprehensible) and it's domain as that of a universal Turing machine (this made it comprehensive). Now we simply define a recursive enumeration function for said domain and we give it a name. The notion of the scientific method, a previously informal (naive\footnote{We refer to the word naive in the mathematical sense; i.e. as a theory which is not formalized. No negative connotation are implied.}) construction, is now imported into pure mathematics and as such we have produced a net gain for science, compared to not having it.

The features of the scientific method are found implicitly in the definition. Indeed, implicit in said definition lies a requirement for the function to verify the input to be knowledge by running its corresponding program to completion, and reporting success once proven to halt. That it may or may not halt is the hypothesis, and the execution of the function is the 'experiment' which verifies the hypothesis. If an input runs for an abnormally long time, one may try a different hypothesis hoping to reach the conclusion differently. Since knowledge is element-wise infallible, each terminating experiments are formally reproducible as many times as one needs to, to be satisfied of its validity. All of the tenets of the scientific method are implicit in the definition, and its domain is that of knowledge itself, just as we would expect from the scientific method. Finally, the domain of the function is arbitrarily complex and countably infinite, therefore we never run out of new knowledge allowing for a perpetual and never ending application of the scientific method. Mathematically, it is a remarkably simple definition for such an otherwise rich concept.
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As an ex-teacher I learned the hard way that to teach you have to address your auditors on their level. If you want me to understand you, you have to dumb it down. And implicitly you acknowledge this by being here. And en passant note that most great thinkers undertake exactly this task - indeed have to. And that includes great philosophers and scientists. And it would seem the more they had to offer in substance, in many cases the better they were able to communicate their ideas. Godel, Einstein, Hawking, Heisenberg certainly among these, authors of books and papers accessible by laymen and intended to be.

You have been asked by me and others to make simple demonstrations of the power of your discoveries - I confess I gave up looking for and waiting for you to make such a demonstration. I assume you cannot. What's left - if there was anything in the first place - is the idea that if some things are true, then in principle some other things follow. The "in principle" being that some of those things just might be a very long time in following. And you have certainly been treated with respect by some here who know much more than I know, and I accord you respect on that basis.

But you haven't delivered, near as I can tell, and that's the point.

" Here, we will adopt the insight of Kirkham regarding the requirement of infallibility, whilst also resolving the non-comprehensiveness objection. To do so, we will structure our statements such that they are individually infallible,"

Great! Please exhibit one infallible statement.

Another:
"With these two features, the set of all knowledge becomes well-defined and is in fact recursively enumerable."

Hmm. Does that mean recursive? I think it doesn't - subject to correction. And that means the complement of the recursively enumerable but not recursive is itself infinitely rich.

And:

"However, it is possible to construct a logical basis for knowledge provided that such basis is recursively enumerable (and not decidable), and further the limitations induced by recursive enumeration ought to instead be seen as an opportunity; in this case, to create a formal system to map out knowledge, such that it may serve as the foundation to a formalization of science."

Well, all right.... All knowledge listable. That's a long list. Two questions: what is the criterium for inclusion on the list? I.e., what is that definition of knowledge that permits a division between knowledge and not-knowledge, and, maybe the same question, how do you know? If it's a matter of some program halting, what do you do when it doesn't halt?

And it would seem that out-of-the-gate some of this will involve processes that inevitably will simply take too long - "simple" proofs about large numbers as simple examples. And so it would seem that your claims reduce to being a variety of, "if I count until forever, then I can know everything and can solve anything." And you can't. Maybe even God can't.

But what do I know? (Ans. not much.) Refutation by demonstration then not too difficult. It's all yours....
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Alright, let me do so as explicitly as I can:

Great! Please exhibit one infallible statement.

First, the simplest infallible statement.

Let us define a program TM for a UTM:

fn main() -> bool{
return true;
}


Then, we define its input p=null (in this case the empty input). The pair (TM, p) halts on UTM, thus is an element of infallible knowledge.

Feel free to replace 'return true' with anything else you would like.

A second example I have given (in the paper and to illustrate the sacrifices entailed by comprehensible definitions) is a comprehensible (but by design non-satisfying) definition of beauty:

fn is_beautiful(painting: Painting) -> bool{
if painting.colors.len()>=3{
return true;
}
return false;
}


And a slightly more involved definition of beauty:

fn is_beautiful(painting: Painting, people: Vec<Person>) -> bool{
for person in people{
if person.is_beautiful(painting){
return true;
}
}
return false;
}


There are uncountable infinitely many comprehensible definitions.

The scientific method takes any of these definitions (or questions) as input and outputs knowledge if it halts. The scientific method cannot produce knowledge from non-comprehensible definitions.

How this corresponds to reality... I give the example of the universal verifier; a machine that can run any scientific protocol in nature, and show that an operator will model this machine and its interaction with it using the same mathematical definition as that of a program. Hence, we describe reality via the set of all experiments knowns to have terminated to date. This forms what I call an experimental image of reality.

Hmm. Does that mean recursive? I think it doesn't - subject to correction. And that means the complement of the recursively enumerable but not recursive is itself infinitely rich.

It remains forever and always recursively enumerable. Otherwise if you make it recursive you basically kill science, because there is no more need to run experiments and you will never be surprised by new knowledge, or you will never be able to waste your time investigating a non-halting question...

Well, all right.... All knowledge listable. That's a long list. Two questions: what is the criterium for inclusion on the list? I.e., what is that definition of knowledge that permits a division between knowledge and not-knowledge, and, maybe the same question, how do you know? If it's a matter of some program halting, what do you do when it doesn't halt?

If its halts its on the list, and it doesn't it ain't. Building the list is the ultimate never-ending challenge of science and epistemology! "what do you do when it doesn't halt?" You waste your time until you give up. "Is there a God?" is a question that probably doesn't halt...

And it would seem that out-of-the-gate some of this will involve processes that inevitably will simply take too long - "simple" proofs about large numbers as simple examples. And so it would seem that your claims reduce to being a variety of, "if I count until forever, then I can know everything and can solve anything." And you can't. Maybe even God can't.

Some may take too long, but thats still what reality is. I can't eliminate truth that are 'too hard' because they are still part of reality. You don't need to list the programs to get the laws of physics; you just need to be convinced that you *can* in principle describe reality in such a manner and that said description is infallible and comprehensive. Then, you use the formulation of mathematics in terms of halting image, define a measure over it, maximize its entropy and get the theory of everything. I am not interested in finding actual epistemological knowledge because that is just the job a computer could do. I wish to describe how the universe follows indubitably from this description of reality.
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My framework ties in the universe to a definition of the observer which carries no doubt.

It's a checkmate position.

What does your theory say happens to the universe if all observers disappear?
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What does your theory say happens to the universe if all observers disappear?

The universe becomes undefined/undefinable - it is defined with respect to the singleton observer.
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The universe becomes undefined/undefinable - it is defined with respect to the singleton observer.

Are you claiming that a possible world like this one but with no observers is undefined/undefinable? Wouldn't it simply be this world, but with no observers? That is to say, if all observers disappeared, the stars, planets, fundamental particles, etc. wouldn't wink out of existence but would continue to exist?
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Are you claiming that a possible world like this one but with no observers is undefined/undefinable? Wouldn't it simply be this world, but with no observers? That is to say, if all observers disappeared, the stars, planets, fundamental particles, etc. wouldn't wink out of existence but would continue to exist?

If I knew what happens, it would be definable. A world without observer is non-definable. You cannot even talk about a possible world without you (an observer) existing in the first place, to talk about it.
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If I knew what happens, it would be definable. A world without observer is non-definable. You cannot even talk about a possible world without you (an observer) existing in the first place, to talk about it.

That sounds like a cop out. Your theory should have an answer for what would happen to the universe if all observers disappeared. Either the universe would continue to exist or it wouldn't. Are you an idealist? Also, can machines be observers? Is consciousness a necessary condition for observation?
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The theory starts from emergent gravity. Gravity being the result of QM, entanglement. The metric of spacetime is a result of quantum information on surfaces and bulk. The bulk is considered an elastic medium and the tendency of information to thermalize, increase in entropy, gives rise to matter, gravity and dark matter behavior (making true dark matter superfluous). But gravity itself is not quantized.

But. This theory reverses the direction. Only after matter is created, its information can get stored on surfaces and in volumes. For example, the information on a Bekenstein surface and inside it is encoded by all matter that was present in it and by matter it is entangled with outside of it. The entropy of the Bekenstein surface around a black hole is maximal for the matter contained in it, but at the same time all black holes are different, depending on how the hole was formed. There is much more information stored on the horizon than the Bekenstein 1's and 0's, and much more than inside a Bekenstein volume, depending on the paths of the infalling particles. The soft hair is potentially infinite in form and reflects how the hole was formed, to be spit out by Hawking radiation.
Likewise, the event horizon around the universe contains 10exp120 quantum bits of information and the can contain 10exp180 (having a proposed maximum of information of 10exp120 though), but the possible dynamical information inside is virtually infinite.
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Do you seriously think that physics, at the most fundamental level is different than geometry?

It kind of is a bit, since physics is geometry _and_ analysis. But otherwise, yeah, I'm with you. My relativity professor put it best: physics is mathematics with decorative constants. Except QFT which is a weird beast.
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My relativity professor put it best: physics is mathematics with decorative constants

I love this!
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But. This theory reverses the direction. Only after matter is created, its information can get stored on surfaces and in volumes.

Yes, the theory does indeed reverses the direction. Instead of assuming a physical medium with certain properties, then constantly re-adjusting those properties as more scientific knowledge is acquired, the theory postulates the observer and derives the physics as entailed by its definition. The advantages are that the definition of the observer is one-line, and the theory of everything is derived in about three lines; and further the definition of the observer is indubitable and immutable, and constitute a checkmate argument for nearly all philosophical systems since the observer requires so little baggage to be defined it is compatible with anything up to and including solipsism.
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That sounds like a cop out. Your theory should have an answer for what would happen to the universe if all observers disappeared. Either the universe would continue to exist or it wouldn't. Are you an idealist? Also, can machines be observers? Is consciousness a necessary condition for observation?

"Are you an idealist? " No opinion, agnostic. "Also, can machines be observers?" Nope. "Is consciousness a necessary condition for observation" Yes.

"Either the universe would continue to exist or it wouldn't". It is 100%, with absolute certainty, completely undefined.

Let me give a bit more detail, otherwise we will be running in circle. You question is equivalent to asking what happens to the natural numbers if you delete Peano's axioms, or what happens to the universe if you delete the laws of physics. The system's only axiom is the existence of the singleton observer, if you delete that axiom what happens to the rest of the system is quite undefined.
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"Are you an idealist? " Nope. "Also, can machines be observers?" Nope. "Is consciousness a necessary condition for observation" Yes.

"Either the universe would continue to exist or it wouldn't". It is 100%, with absolute certainty, completely undefined.

Let me give a bit more detail, otherwise we will be running in circle. You question is equivalent to asking what happens to the natural numbers if you delete Peano's axioms, or what happens to the universe if you delete the laws of physics. The system's only axiom is the existence of the singleton observer, if you delete that axiom what happens to the rest of the system is quite undefined.

Suppose there's another universe like ours in the multiverse, but where the constants were a bit different so that planets could not form and no life ever evolved. Are you saying that because there are no observers, the ontological status of that universe is undefined?

What happens to the stuff in a room when the last person leaves? Does the bedside lamp go from existing to undefined to back to existing when a person comes back in the room?

Also, how would you test whether a machine is conscious or not?
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Suppose there's another universe like ours in the multiverse, but where the constants were a bit different so that planets could not form and no life ever evolved. Are you saying that because there are no observers, the ontological status of that universe is undefined?

That hypothetical universe only exists in your mind, when you die it dies with you.

More detail: My theory does not remove nor add, nor transform the ontology of the object, with respect to what it actually is... it is an accurate and manifest description of reality and nothing more. Consequently, if you tell me you are imagining an alternative universe, I am bound to attribute the ontology of an imagined object (consuming your brain power and memory, but nothing else) to it (because thats what it is), and thus its ontology is bound to you, since your the one imagining it.
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What happens to the stuff in a room when the last person leaves? Does the bedside lamp go from existing to undefined to back to existing when a person comes back in the room?

The best way to understand the halting image is that it includes all the knowledge presently available in the universe, regardless of whether the singleton observer is or isn't psychologically aware of it. The singleton observer is then a measure space over this halting image, and its state of knowledge is a subset of the halting image. Finally, the singleton observer being a measure space, thus allowing a measurement over any possible subdivisions of knowledge from the halting image, entails the same laws of physics irrespectively of the psychological state of knowledge of the singleton observer.
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Whew, what a read! First, utmost respect needs to go to you for the amount of dedication and work that went into this. Forgive me if I will, but I did start to skim at the point of quantum mechanics proofs. I see why you included them, and that is enough for me.

Let me see if I can translate just some of what you said in more informal English. Please correct me were I am wrong. It would be impossible for me to fully grasp a paper like yours in one read.

1. Regular ideas of knowledge point to one truth. There are inherent problems with this that you wish to attempt to solve.

2. Your idea of resolution is to treat knowledge not as a hard and fast map of "what is knowledge", but as a formula. You note that knowledge can change by the very definitions we establish, and the models that we use. The only way to accurately cover knowledge, is to incorporate them into a system of, lets call it "contexts". In a simple sense, the science of English and the science of Spainish are identical when translated.

3. You go even further however. You note that due to different observers and models, observers and models might conclude results that are logical within their own model, but perhaps contradict in other models. For example, what is "heavy" for a person who weighs 100 pounds versus someone who lifts weights for a living and weighs 200 pounds are different, but consistently valid within their own models.

4. A key with the current view of science is it has no means to handle the differences in 2 and 3. But if we view science as a formula of knowledge, one that consists of the entirety of observers and models, we can have co-existing conclusions in particular times. So for example in the early 1900's, the "accepted" view of physics might have been at odds with several other views of physics. But those other views of physics were part of the ongoing discoveries that lead to the views of physics today. And today there are plenty of other models and observers who have their own complete ideas of science that may or may not conflict with "accepted" science. This again leads credence to your idea that science and knowledge are a system, and not an answer.

5. Now here is where I know I need your clarification (opposed to not knowing for the previous points). As observers are necessary within your model, you run into the problem of...something. To rectify this you propose a universal observer in a mathematical sense. Could you try to sum up what the problem was that made you feel the need to include a universal observer? Thanks!
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That sounds like a cop out.

I can understand why it may feel that way, but that is the price to pay to correctly model reality. All paradoxes are ultimately the consequence of describing reality slightly differently than what it is, because people seem unsatisfied with simply describing it. For instance, one imagines alternative universes, and demands to know why they may or may not be real, thus creating paradoxes. However, in reality, the ontology is already set in stone; those universe you imagine exists in your imagination, and the one thats in front of you exists, well in front of you. There is no paradox if you content yourself with describing reality without putting any emotion or preferences into it no matter how "dry" it may feel.

Another one is the hard problem of consciousness; but everyone already knows from the philosophical zombie problem that the consciousness in others cannot be proven; yet since most simply cannot accept it emotionally, and thus they postulate the consciousness of others, then demand a theory able to convert their postulate into a theorem. The paradox dissolves automatically with a pure non-preferential description of reality; there exists a singleton observer, obtained via postulation, which is conscious, and all others are at best hypothetically conscious from his or her perspective.

Yet another is the independent existence of the physical universe, or realism. Almost everyone that I have met who is a realist will readily admit that they have no proof against solipsism, but do they accept the lack of proof and adjust their description of reality to be agnostic... absolutely not. Yet, here again, the brute and non-preferential description of reality wins the day. This one took me many decades and thus is highly non trivial, but my theory derives the theory of everything in a solipsist-objectivist agnostic manner, and consequently dissolves the paradox in this case.

This is how progress is made; dissolution of paradoxes by being content with describing reality. It may seem like a cop out, but thats the cop out chosen by reality, not by me. Don't kill the describer
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