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Author | Topic: What is a Theory? | |||||||||||||||||||||||||||||||||||
erikp Member (Idle past 5549 days) Posts: 71 Joined: |
>>> Its the same as gravity. That gravity exists is an observed fact.
Bad analogy. A theory is proven not when some observations support it, but when all possible observations support it. Since gravity makes statements that covers future observations, gravity is not yet fully observed, and therefore, unproven, and absolutely not a fact. Futhermore, Gdel's incompleteness theorem deducts that there must be observations that do not fit the theory of gravity at all. That is also what Popper clearly states: one day or the other, gravity theory will prove to be false. So, the correct status for gravity theory is necessarily: unproven, false. Scientific breakthroughs do not occur when a theory is proven to be true -- which is only possible if the theory does not cover any future observations, and therefore is pretty useless -- but when a theory is proven to be false. 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. It will remain unproven and false, until someone finally manages to prove that it is false. The job of the scientist is, therefore, not to attempt in any way to prove that scientific theories are true. On the contrary, his job is to prove that they are false (which we know they are, anyway).
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
>> It will remain unproven and false, until someone finally manages to prove that it is false.
>>> You do realize that the above sentence contradicts itself, yes? The sentence does not contradict itself. Theories go from unprovenly false to provenly false. Scientific progress is the result of proving that what we know is wrong. 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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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
>>> 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.
The requirement that something can be represented as a number, is nothing more than requiring that you can create a digital representation of it. What then applies to the numbers, applies to the original thing too.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
>>> Have you been on an airplane? How does that jive with your theory that nothing is fixed and certain?
The safety of an airplane is vested in the fact that it is very hard to prove that the airplane is actually unsafe. The safety of an airplane, however, has never been and will never be proven. >>> I imagine you would never board something that stays airborne on incorrect physical principles and theories. These physical principles and theories are indeed incorrect, but nobody has been able to prove it. That is why we use them. These incorrect theories are still very useful. >>> That doesn't mean that all of our theories are correct, but that there most certainly is a path for us to follow. All these theories are incorrect. Science as a whole must necessarily be incorrect. The value of science, however, derives from the fact that it is very hard to prove that it is incorrect; and that nobody has been able to do it up till now, for the existing body of science. >>> It is my belief that this path will yield us the answers we are looking for. I didn't say that science is not useful. On the contrary. It is very useful. But that doesn't make it correct.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote: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. This is obvious. 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, ...) Gdel does not derive addition from it. 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.
quote:The fact the theorem can be written in text, is a more than sufficient proof that the theorem can be represented as a number. A=65, B=66, ... Just use the standard ascii character code, and you can see the entire theory appear as a number. I don't think that the gravity theorem has axiomatic proof associated to it (it is very much itself an axiom). I already admitted that Gdel's theorem is heavily dependent on axiomatic proof, while the true proof for gravity is not axiomatic but the fact that no observation in the collection of possible observations contradicts it. 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). 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.
quote: Since physics does not necessarily depend on axiomatic reduction, I agree. Its incompleteness must have another source. 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." 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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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:True.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:Completely besides the point. 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. This is one way to demonstrate that a theory is false, without disproving it directly. 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. 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). These principles cannot be generalized, however, because axiomatic reduction does indeed not amount to "proof". It simply relegates the burden of proof to the axioms themselves, which remain necessarily unproven. Formal proof for the hypothesis that science is necessarily false, would otherwise be very useful.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:Popper implies that a falsifiable theory will eventually be falsified. There is indeed no proof for this statement. quote:If every falsifiable theory will eventually be falsified, it means that every falsifiable theory will eventually be proven to be false. That means that the correct status of scientific theories is: unproven, false. This is important. Too many people use the phrase "scientifically proven", even though, not one single theory has ever been "scientifically proven". Furthermore, if the falsification process will inevitably end with the proof that the theory is false, we know that all scientific theories will only be useful for some time, after which they will be discarded. I concede the point, however, that the statement that every falsifiable theory will eventually be falsified, is remains unproven. It requires proving that every collection of future observations for a theory, must contain at least one observation that will contradict the theory. It is not trivial to prove this.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:All cases are equivalent. "Water boils at 100 C" has always been unproven, and presumably false, but it took a long time to discover that "Water boils at 70 C if you reduce the pressure sufficiently", and that the boiling point for water was replace by a formula in terms of atmospheric pressure. That theory or any further refined theory is, of course, still false. Whatever theory currently describes the boiling point for water, it will still be false, but we simply don't know why, and that is why we keep using that theory, until the next iteration of refinement produces yet another theory. Even though formally unproven, the point of view that every falsifiable theory will eventually be falsified, and therefore false, is in my opinion, absolutely reasonable. In those terms, science is necessarily: unproven, false. Edited by erikp, : unmatched quote
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:Exactly. We use theories that are (currently) impossible to prove false; but which are (necessarily) false. The state of the art moves forward, and science progresses when someone finally makes the observation necessary to prove what we knew all along, but never managed to prove: that the theory is simply false.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:The theory that says that "water boils at 100 C" is simply false. According to the definition of "false", one observation that contradicts the theory is sufficient to prove it false. Well, one can clearly observe that water boils at 70 C when atmospheric pressure has been reduced sufficiently. Therefore, applying the definition, the theory is incontrovertibly false. Note that 999 999 999 999 observations may not contradict, and therefore support the theory; it doesn't matter. That one observation that does contradict it, irrevocably falsifies the theory. And the theory is then simply false, regardless of how long anybody or how many people may have thought it was true.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:What is the definition for "normal circumstances"? In absence of a definition for that term, your statement is simply open-ended. If you do define the term, however, we are inevitably back to the formula that describes the boiling point for water according to the current state of the art. That formula is wrong, but we just still don't know why. The next iteration of that formula will be wrong too. Science will remain: unproven, false.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:Given the definition of "true" and "false", "incomplete" means "false". true: all possible observations concur with the theory.false: one observation contradicts the theory. An incomplete theory is false, because there will be at least one observation that will contradict it -- there where the theory is incomplete. If all theories are incomplete, they are all false. Gdel already proves that all axiomatic theories capable of expression basic arithmetic are incomplete (and therefore false). Even though it is not proven that all non-axiomatic theories of sufficient complexity, that is, falsifiable by an infinite number of future observations, are also incomplete, and therefore false, it is certainly reasonable to assume this. Since "incomplete" in this context means "false", the entire body of science must be deemed to be false. However, nobody is currently able to demonstrate this statement, by making the observations that will prove it. Edited by erikp, : No reason given.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:Not one theory in the current body of science claims this. What's more, Gdel's second incompleteness theory, which is supported by formal proof, says that a (sufficiently complex, in terms of Gdel) theory that makes statements concerning its own consistency (truth), is necessarily inconsistent (false). A (sufficiently complex, in terms of Gdel) theory can therefore not claim its own truth. In addition to that, any sufficiently complex theory is falsifiable by an infinite number of future statements, and is therefore eternally unproven. In those circumstances, how could anybody ever claim the ultimate truth of such theory? There are true theories, however. A theory falsifiable by a finite number of facts, can be completely true, and will be proven after observing the last fact. A theory falsifiable by 10 facts and not falsified by any of them, is true. The same for 9,8,7,6,5,...,2,1 facts. What about zero facts? The principle of continuity demands that a theory falsifiable by zero facts and (obviously) not falsified by them, is true. Therefore, unfalsifiable theories must be considered: true. The ultimate truth can therefore not be a theory falsifiable by an infinite number of future facts, by its own rules unable to claim its own truth (science), but rather a correctly stated (that is, by enforcing its unfalsifiability) unfalsifiable theory. A true theory can therefore only consist of (necessarily past) facts and unfalsifiable claims (religion). Edited by erikp, : Add conclusion Edited by erikp, : No reason given.
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erikp Member (Idle past 5549 days) Posts: 71 Joined: |
quote:The value of knowledge does not reside in its truth, but in the fact that it is very hard to prove that it is false. Therefore, we only keep using these false claims (knowledge), as long as nobody manages to prove their falsehood. As soon as someone proves the falsehood of any such claim, however, we discontinue its use. There is no other way around it, than doing exactly that.
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