What is a Theory?

erikp writes:

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Futhermore, Gdel's incompleteness theorem deducts that there must be observations that do not fit the theory of gravity at all.

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Incorrect. It sounds like you were given a quick summary of the Incompleteness Theorems but have not done the foundational mathematical work to derive them on your own. In short, you're applying a conclusion of Set Theory to something that is not Set Theory and are expecting it to behave the same way.This is the same fallacious reasoning that has professors of the Humanities trying to claim that the Heisenberg Uncertainty Principle has some effect upon human behaviour.The short summary of the first Incompleteness Theorem states that in an axiomatic description of set theory sufficiently powerful enough to model arithmetic, there will be statements within that theory that cannot be proven by those axioms.The last time I checked, gravitational theory was not an axiomatic set theory let alone one powerful enough to model arithmetic. Therefore, the Incompleteness Theorems do not apply.

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That is also what Popper clearly states: one day or the other, gravity theory will prove to be false.

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Incorrect. Gravitational theory may be absolutely perfect exactly as we have it. However, due to the observational nature of science, we will never know. In order to demonstrate it, we would need to be able to make all possible observations, which cannot be done. This doesn't mean our model is destined to be false. It simply means we will never know if it is true.

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So, the correct status for gravity theory is necessarily: unproven, false.

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Incorrect. Instead, the status of gravitational theory is the same as that of every one solid theory we have: Consistent with the observations we have and satisfying the predictions we have demanded of it.

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It is very hard (has it been done yet?) to prove that gravity is false. That is why it is such a good theory. But that still does not make the theory true.

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Indeed, but that also doesn't make it false. Instead, what we have is a theory that is consistent with all the observations we have made. We might have it exactly right, but we'll never be able to know for sure. Being unable to show it true does not mean it is false.

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It will remain unproven and false, until someone finally manages to prove that it is false.

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You do realize that the above sentence contradicts itself, yes?

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp and I respond to each other:

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Theories go from unprovenly false to provenly false.

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That isn't what you said. What you said was: But there is no evidence for it being false, therefore we cannot claim that it is. Again, the theory might be absolutely perfect. However, we will never be able to know that for that would require us being able to make every possible observation, which cannot be done.This does not make the theory false. Just because you cannot show it to be true does not mean that it is false. Since you mentioned the Incompleteness Theorems, surely you know about the Continuum Hypothesis and how it relates.Without getting into what the Continuum Hypothesis is, the point is that Godel showed that if we assume it to be true, then we do not reach any contradiction with the axioms of set theory. But just because we don't have a contradiction doesn't mean it is actually true. Cohen showed that if we assume it to be false, we also do not reach any contradiction with the axioms of set theory.Just because you can't prove it true doesn't mean it is false.

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Scientific progress is the result of proving that what we know is wrong.

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In part. Another part of scientific progress is the result of finding new applications for known processes. To hook into a recent Nova special, the Nobel Prize was given out for the work in reaching the coldest temperatures ever recorded. We're only a few picodegrees away from absolute zero...something that we will never be able to reach. We made magnificent progress not by proving something wrong but by extending what we already knew.Oh, showing things to be wrong is a wonderful thing, don't get me wrong. When we find that what we thought we knew isn't true, it opens up whole new avenues of exploration. But that isn't the end-all, be-all of science.

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As soon as someone finally finds an observation that contradicts the theory, the theory will finally be proven to be false, because proof of falsehood only requires one observation that contradicts the theory.

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Indeed. Do you have any evidence that such an observation has been found? Your claim rests upon the phrase, "as soon as." Well, we haven't hit that. What happens if we never do? Again, our theory might be exactly right, but we'll never know for sure because we'll never be able to make every possible observation. But just because we can't make every observation doesn't mean we have failed in the ones we have made.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp responds to me:

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The requirement that something can be represented as a number, is nothing more than requiring that you can create a digital representation of it.

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Incorrect. Number is much more complicated than that. If you think that gravitational theory is equivalent to set theory, then surely you can tell us how to derive addition from it. You'll need to develop the relationships of equality, commutativity, etc. and all the other aspects of arithmetic that will result in it satisfying the requirements of the first Incompleteness Theorem.

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What then applies to the numbers, applies to the original thing too.

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But where is your proof that gravity is equivalent to a number?Hint: Just because we know that there are statements that cannot be proven in our set theory doesn't mean that any collection of statements must include such an unprovable statement. The Continuum Hypothesis is unprovable, but that there is no largest prime is trival to prove.What that means: Just because physics is applied math doesn't mean that the findings of physics are subject to the incompleteness of math.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp, I know you're new, so here's some helpful guidelines for posting:There are "dBCodes" that can be used to help quote things. This will prevent you from having to manually insert brackets. They can be nested in case you need to quote both sides of a conversation.To do a simple quotation, use the [quote] and [/quote] tags. If you put in:[quote]Quoted text.[/quote]It will show up as:

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Quoted text.

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Again, you can nest the quotes:[quote][quote]Starting quote.[/quote]
Response quote.[/quote]To get:

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Starting quote.

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Response quote.

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For a little fancier quotation that allows you to put in an attribute, use the [qs] and [/qs] tags:[qs]Quoted text.[/qs]Becomes: To nest:[qs][qs]Starting quote.[/qs]
Response quote.[/qs]Becomes: To add the attribution, use [qs=Name of person] (which can also be nested):[qs=Steven Hawking][qs=Albert Einstein]God does not play dice with the universe.[/qs]
Not only does god play dice with the universe, he throws them where we can't see them[/qs]Will become: Note, the attribution option is only available for [qs], not [quote]

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp responds to me:

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Gravitational theory can be represented as a number. If it has an axiomatic proof (which I doubt ...), this proof can be represented as a number too.

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Um, that doesn't answer the question. How? How can gravitational theory be used to derive "1 + 1 = 2"? Be specific.Note, you directly contradict the requirements of the Incompleteness Theorems in your statement. The theorem states that given an axiomatic set theory sophisticated enough to model arithmetic, there will be statements that are unprovable.If gravitational theory is not axiomatic, how can it be subject to incompleteness?Of course, this still doesn't handle another issue that I neglected to mention: You keep saying, "false," but the Incompleteness Theorems aren't about false. They're about being unable to prove a truth value.The Continuum Hypothesis is either true or false. We just don't know which and can never know given our current axiomatic set theory.

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This is obvious.

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Incorrect. It is anything but obvious. What is a number in gravitational terms? I don't see it and I'm a mathematician. It would help if you could provide specifics.

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Anything that can be represented in text, can be represented as a number, since every letter in the text is mapped to a number (ascii, unicode, ...)

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Irrelevant. Please stick to the topic. You are insisting that gravitational theory is subject to the Incompleteness Theorems. The question is not whether or not a peculiar coincidence of symbology can be represented by another symbol. It's whether or not gravity, in and of itself, can represent a number.

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Gdel does not derive addition from it.

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I didn't say he did. You really don't know what you're talking about, do you?

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He analyses the tuples (T,PROOF(T)), which simply associates each numerically represented theorem T with its proof PROOF(T). Then he demonstrates that there are theorems T that are associated with themselves (fixed points), while claiming that they are unprovable.

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Irrelevant. You still haven't managed to show that gravitational theory is a set theory sufficiently powerful enough to model arithmetic. Until you do, you're just engaging in mental masturbation.

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The fact the theorem can be written in text, is a more than sufficient proof that the theorem can be represented as a number.

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Irrelevant. It is not sufficient that you can replace one symbol with another. The Incompletness Theorems are about axiomatic systems of set theory. Where is the evidence that gravitational theory is an axiomatic system of set theory? You claim in your own words that it isn't axiomatic.Then how do the Incompleteness Theorems apply?

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The problem consists in demonstrating that this contradicting observation -- in a set of given conditions of minimal complexity -- must exist, without having to pinpoint it (without the need to disprove the theory).

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Word salad doesn't help. So far, you still haven't shown gravitational theory to be an axiomatic system of set theory sufficiently powerful enough to model arithmetic.You admit that gravitational theory isn't axiomatic. Then how do the Incompleteness Theorems apply?

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This requires something similar to Gdel's incompleteness theorem, but not exactly the same, since we need to reject axiomatic reduction as a mechanism to prove theorems.

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But the Incompleteness Theorems are all about axiomatic set theories. If you're going to abandon the entire foundation, then why on earth do you expect the results of that foundation to apply?

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Since physics does not necessarily depend on axiomatic reduction, I agree. Its incompleteness must have another source.

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Why? There are complete and consistent axiomatic systems. Presburger arithmetic, for example, is both complete and consistent. It's even decidable. However, it isn't powerful enough to model arithmetic: There is no multiplication.Why do you assume that gravitational theory is powerful enough to model arithmetic? Not all systems can do that.

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The statement to prove is: "within the collection of possible observations for a statement, there will always be at least one that contradicts the statement."

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And where is the axiomatic system we are going to be analysing this statement within? The Incompleteness Theorems are about axiomatic systems. If there is no axiomatic system, why on earth would we insist that they apply?

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It looks indeed very much like Gdel's theorem, but it is not exactly the same. So, I concede this point.

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Do you really? I need you to state it unequivocally: Gravitational theory has nothing to do with the Incompletness Theorems. Gravitational theory just might be absolutely correct.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp writes:

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The point is that it is sufficient to demonstrate that a theory can be rephrased as a set theory sufficiently powerful to model arithmetic, to demonstrate that it necessarily contains false statements.

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Incorrect. You really don't know what "incomplete" means, do you? It does not mean "false." It means that there is no way to come up with any truth value.The Continuum Hypothesis is undecidable. Assuming it is true does not lead to a contradiction. Assuming it is false does not lead to a contradiction. There is no way to decide the truth value under ZFC.

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This is one way to demonstrate that a theory is false, without disproving it directly.

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Incorrect. Incompleteness doesn't say anything about a theory being "false." It has everything to do with it being "incomplete." That's why they're called the "Incompleteness" Theorems, not the "Inconsistency" Theorems.

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A more interesting way would consist in demonstrating (for example, using a fixed point theorem similar to Gdel) that the collection of possible observations for particular kinds of statements must necessarily contain contradictions. This has not been proven as yet.

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Since it's a pile of crap. The Incompleteness Theorems do not claim an axiomatic set theory sufficiently powerful to model arithmetic include false statements. On the contrary, they state that such theories contain statements that cannot be decided.Do you even know what "incomplete" means? Presburger arithmetic is complete and consistent. So what does this do to your claim that it contains false statements?

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Gdel's work is very interesting, as it shows the limitations of mathematics and other formal axiomatic systems (the fact that they are necessarily false).

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Incorrect. Godel's work has to do with incompleteness. Do you even know what that word means? How do you reconcile your statement with Presburger arithmetic which is complete, consistent, and decidable?

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Formal proof for the hypothesis that science is necessarily false, would otherwise be very useful.

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And you understanding what any of those words means would be even more useful.What does "incomplete" mean?

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

Parasomnium writes:

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This thread could do with two consecutive days of Rrhain.

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I swear I felt my ears burning. On a lark, I look through an old thread that has a white dot and I find my name.Is erikp still at it, trying to claim that the idea something can conceivably be false necessarily means it is?I'm not sure what else I could do. He seems to be intent upon twisting the definition of every single word. First it was "incomplete," now it's "theory": That's because "Water boils at 100 C" isn't a theory. It's a derived conclusion. That you can reduce the atmospheric pressure and make water boil at a lower temperature isn't a violation of any theory. In fact, it is corroborating evidence of theories of physical chemistry: PV = nRT and all that. The statement that "Water boils at 100 C" has unstated premises, the big one being "At standard pressure."That's why real chemists always calibrate their equipment before using it. Just because water boiled at this particular level on the thermometer today doesn't mean it's going to boil at the same particular level tomorrow. Sometimes that precision is extremely important so you always check to see where you are.The theory isn't "Water boils at 100 C." Instead, the theory is "Liquids at a given pressure will always boil at a specific temperature." Other theories (such as molecular theory) will explain why water boils at such a high temperature (hydrogen bonding).Here's the problem: Of course, nobody who actually works in science or mathematics uses the definitions of "proven/unproven" or "true/false" that he provides. How do you get past that? Until he can grasp the concept that because something is potentially false doesn't mean that it necessarily is false, no progress will ever be made.F'rinstance, the Poincaré Conjecture. When it was first proposed, it might have been true. It might have been false. The fact that we didn't know didn't make it false. And, in fact, it's true.Of course, that's an example from mathematics where things can actually be proven true because you can, indeed, make all observations possible. Science, alas, doesn't work that way. It's an observational process which means we can never know for certain if our theories are true.Our understanding of gravity may be absolutely perfect, but we will never be able to declare it true because that requires perfect observation which we can never have. The best we can hope for is the claim that it is accurate.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp responds to Parasomnium:

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"Magnitude of falsifiability" (MoF) can be defined, and can therefore not be rejected without justification.

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Incorrect. Just because a bogus thought can be quantified doesn't mean we need to examine every little inch of it. Once you recognize it is bogus, you can pass it by.And "magnitude of falsifiability" is simply bogus. Science does not work that way. Therefore, we can reject it out of hand. For example:

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Given a random theory

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Theories are not random variables. They cannot be modeled as random variables. Therefore, attempting to apply statistics to them is a failed experiment.

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What does that say about the likelihood that a random infinitely falsifiable theory will be contradicted by the facts?

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Since theories are necessarily based upon the facts, the "likelihood" that a theory "will be contradicted by the facts" is necessarily 0. If a theory is contradicted by the facts, it is not a theory.Are you claiming you have facts that contradict the theory? Then bring them forward and show them. If you are waiting for future observations not yet made to come forward and rescue you, then you don't have any facts.Ergo, your "magnitude of falsifiability" is bogus and is rejected out of hand.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp writes:

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This relationship is:

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P(C|MoF=k) = 1 - 0.5^k.

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And is completely bogus. Theories are not random variables. In order for something to be a theory, it must necessarily be in compliance with the facts.Observations you have not made that you are depending upon coming along to rescue you are not facts.Therefore, this "magnitude of falsifiability" is nothing but a straw you are grasping at to save you from drowning.

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All of this supports my case: infinitely falsifiable theories are presumably false.

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Incorrect. Until you actually run through it, you haven't shown the theory to be false. Something potentially being false does not mean it is. It doesn't matter how many possible ways a theory might be proven false, even an infinite number of them. The only way to show a theory false is to bring forth the observation.Wishful thinking about unmade observations are not facts.

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Science must be unproven and false in order to be useful.

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Huh? The only way to get to Mars using gravitational theory is if it's wrong? The reason why we had so many failures of probes making it to Mars is because our theory of gravity is actually correct?That makes no sense.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

OK, let's see if this will help erikp understand. We'll do it via indirect proof:Assume this "measure of falsifiability" claim of yours is true.Suppose you have a theory that is perfect. We'll call it the "perfect theory." It accurately describes the outcome of any and all scenarios that could ever come down the pike.Since we cannot actually throw all possible scenarios at the theory, how do you distinguish it from any other theory (which we'll call the "other theory") you might care to name? Theories necessarily conform to all the observations we have ever made. If they don't, they aren't theories.So given that the "perfect theory" will conform to all the observations we have ever made concerning it (because it is true) and the "other theory" also conforms to all the observations we have ever made (because it is a theory), how do you tell which one is true and which one is false?Your "measure of falsifiability" claim insists that the "perfect theory" is false. But it isn't false. It's true. This is a contradiction which necessarily means that your "measure of falsifiability" is not true.QED

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp responds to me:

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Every theory that goes into building and operating these probes is false, but very hard -- currently impossible -- to prove so.

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How do you know? Since you cannot bring forth an observation that shows it to be false, how do you justify concluding that it is? Again, your "measure of falsifiability" cannot distinguish between a "perfect theory" and any "other theory." It declares the "perfect theory" to be false, which is a contradiction.Ergo, "measure of falsifiability" is false.QED

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In those circumstances, we can reasonably expect these probes to work, because nobody can tell us why they wouldn't.

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Which is the very point. If you cannot show why it wouldn't, where is the justification for claiming that it won't? Your "measure of falsifiability" returns a value of "false" for a "perfect theory" that is true. That's a contradiction which necessarily means your "measure of falsifiability" is false.QED

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But that still does not make any of these theories true.

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Irrelevant. Since you cannot show it to be false, where do you find justification for claiming that it is?Be specific. Your "measure of falsifiability" is false, therefore what else is left?

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They are still false. One day or the other, someone may also finally be able to tell us why exactly they are false.

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Says who? You? Why should we believe you? Your "measure of falsifiability" claims that a "perfect theory" is false even though it is true. This is a contradiction which necessarily means that this "measure of falsifiability" is itself false.QED

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp responds to me:

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Bringing forth the observations that will contradict the current body of science in use, is very hard -- currently impossible.

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Which means that the theory isn't false. Fantasy observations that you wish would be made but don't exist are not facts. Until you actually show why it is false, you have no justification for declaring it to be so.Again, your "measure of falsifiability" declares a "perfect theory" to be false, which is a contradiction. Thus, this "measure of falsifiability" is itself false.QED

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So, I repeat, the current body of science is entirely false, but it is currently impossible to know why.

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But you still haven't shown why. Your "measure of falsifiability" is false.So where is your justification?

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp responds to me:

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Theories necessarily conform to all the observations we have ever made.

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In order to be true, it is not sufficient that a theory conforms to all the observations we have ever made. It must also conform to all possible future observations we could ever make.

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Irrelevant. We're not talking about future observations. They haven't been made. We're talking about what allows us to call something a theory. A theory necessarily conforms to all observations we have ever made.Simple question: Do you agree that a theory necessarily conforms to all observations we have ever made. For right now, I am ignoring any future observations that might be made. I am simply asking if a theory must conform to all observations we have.If you do agree, then since the "other theory" necessarily conforms to all observations we have ever made (because it is a theory) and since the "perfect theory" also conforms to all theories we have ever made (because it is true), how do you distinguish between the two of them? The only thing we have to go on are the observations we have made.Since your "measure of falsifiability" declares a true theory to be "false," that necessarily means your "measure of falsifiability" is false.So how do you distinguish them?

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Your "measure of falsifiability" claim insists that the "perfect theory" is false. But it isn't false. It's true.

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There is absolutely no way to know if an infinitely falsifiable theory is "perfect", because there are still an infinite number of new observations possible to which this theory also has to conform in order to be perfect.

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Irrelevant. That's how indirect proof works. You start with assumptions and see if you lead yourself to a contradiction. If you do, then your assumptions are necessarily false.Your "measure of falsifiability" declares a true theory to be false. That is a contradiction. Therefore, the asusmption that the "measure of falsfiability" is true is actually false.How do you tell the difference between a true theory and a false one given that you only have our current observations to go off of? A true theory conforms to all of them because it is true. A false theory conforms to all of them because it is a theory.Since your method returns a value of "false" for a true theory, your method is false. So what's left?

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Suppose you have a theory that is perfect.

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If that theory exists, it will be infinitely falsifiable, and therefore, there is no way to know that it is perfect.

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Irrelevant. It is true. The fact that you cannot know it is true doesn't change that. Your "measure of falsifiability," however, declares it to be false.Ergo, your "measure of falsifiability" is necessarily false.So how do you tell the difference between a true theory and a false one?

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp responds to me:

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If it is infinitely falsifiable, the theory is presumably false.

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But the theory is true. Therefore your "measure of falsifiability" is itself false. Thus, your claim that all theories are false is also false.How do you distinguish between the "perfect theory" that is true and the "other theory" which is false?

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That has nothing to do with the truth or falsehood of any claim made by the theory

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So how do you distinguish the "perfect theory" from the "other theory"? If it isn't by throwing scenarios at them and seeing which one deviates from the observed results, how is it? All we have are the observations. Both the perfect theory and the other theory are in concordance with all current observations. The first because it is true. The latter because it is a theory.So how do you distinguish between them? Your "measure of falsifiability" declares the perfect theory to be false which is a contradiction. Therefore, the "measure of falsifiability" is false.

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However, it does not matter how likely an observation will contradict the theory.

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I never said it did. You're avoiding the question. For the umpteenth time:How do you distinguish the "perfect theory" from the "other theory"? If it isn't by throwing scenarios at them and seeing which one deviates from the observed results, how is it? All we have are the observations. Both the perfect theory and the other theory are in concordance with all current observations. The first because it is true. The latter because it is a theory.So how do you distinguish between them? Your "measure of falsifiability" declares the perfect theory to be false which is a contradiction. Therefore, the "measure of falsifiability" is false.

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This perfect theory would have to take everything into account. It would be the Theory of Everything.

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No, not the theory of everything. Just the perfect theory for the subject that it covers. There are theories in chemistry, but chemistry isn't really concerned with where the atoms come from. That's a question for physics. Suppose we have a perfect theory of gases. Since it is true, it conforms to all observations we have made. But current theory of gases also conforms to all obserations we have made.So how do you tell the two of them apart?Stop avoiding the question:How do you distinguish the "perfect theory" from the "other theory"? If it isn't by throwing scenarios at them and seeing which one deviates from the observed results, how is it? All we have are the observations. Both the perfect theory and the other theory are in concordance with all current observations. The first because it is true. The latter because it is a theory.So how do you distinguish between them? Your "measure of falsifiability" declares the perfect theory to be false which is a contradiction. Therefore, the "measure of falsifiability" is false.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

erikp responds to me:

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If you can convince Stephen Hawking

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Ahem.Stephen Hawking is a cosmologist, not a mathematician. I would not expect him to understand the field of set theory.I'm still waiting for you to explain how gravitational theory is an axiomatic set theory. If I recall correctly, you agreed that it isn't. Therefore, how could incompleteness possibly apply since incompleteness is a trait of axiomatic set theories.And on top of that, incompleteness doesn't declare an axiomatic set theory to be false. Instead, it declares it to be incomplete, meaning there will be some statements that cannot be decided.The continuum has a size. We just don't know what it is and can never know given our current axioms of set theory. That doesn't make set theory wrong. It simply makes it incomplete.

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But then again, you would first have to demonstrate that Gdel was wrong.

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Incorrect. I am not saying Godel was wrong.I'm saying you don't understand what Godel said. We've been through this. Do we really need to go over it again? You seem to think that the Incompleteness Theorems apply to gravitational theory. You have yet to explain how gravitational theory is an axiomatic set theory.Incompleteness is a trait of axiomatic set theories. Until you explain how gravitational theory is an axiomatic set theory, then incompleteness does not apply.Why isn't gravitational theory like Presburger arithmetic? Presburder arithmetic is complete, consistent, and decidable. But doesn't that contradict the Incompleteness Theorems?Of course not. Presburger arithmetic is not complex enough to model simple arithmetic, which is when incompleteness kicks in. Since Presburger arithmetic does not meet the standards for the Incompleteness Theorems (an axiomatic set theory sufficiently powerful to model simple arithmetic), it is not constrained by them.I'm still waiting for you to explain how gravitational theory can be used to prove that 1 + 1 = 2. Russell had to take 65,000 steps to do it and that was using math. Your declaration that it can be done is insufficient.And of course, all of this is naught but a distraction. Hawking isn't here. You are. Therefore, you need to justify your claims. Your attempts to push your feelings onto Hawking is projection in the extreme.Now, stop avoiding the question:How do you distinguish the "perfect theory" from the "other theory"? If it isn't by throwing scenarios at them and seeing which one deviates from the observed results, how is it done? All we have are the observations. Both the perfect theory and the other theory are in concordance with all current observations. The first because it is true. The second because it is a theory.So how do you distinguish between them? Your "measure of falsifiability" declares the perfect theory to be false which is a contradiction. Therefore, the "measure of falsifiability" is false.How many times do I have to ask before I get an answer?

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.