Do science and religion have rights to some "explanatory space"?

Science and religion do not overlap and may not overlap.Both Popper and Gdel demonstrate that the status required for scientific theorems is: unproven false. Only observations from reality have the status: proven true.If a scientific theorem has the status "proven", it means that it does not cover any possible future observations. That would simply make the scientific theorem useless for any practical purpose.Popper and Gdel also demonstrate that every scientific theorem that is applicable to an unending stream of future observations, will eventually prove to be false. There are --always-- observations possible that will sooner or later contradict the theorem. The status of every scientific theorem currently in use is simply: false (but hard to prove so).The only theorems that can be true, are theorems for which it is impossible to make observations. The status of such theorem would be: unproven true.We can summarize it as following:Reality: proven true
Errors: proven false
Science: unproven false
Religion: unproven trueScience is therefore false, but hard to prove so; but sooner or later every scientific statement will turn out to be an error [Popper, Gdel]. Religion, however, is true, but impossible to prove so.Therefore, as long as religious statements (theorems) are phrased as such that they impossibly be contradicted by future observations, the statements -- but also their antithesis -- must be considered to be true, though unproven. Any religious statement, however, that could be contradicted by future observations, is not a valid religious statement.In my impression, both the Bible and the Koran, manage to stay clear of making unproven false statements (that is, scientific statements) by staying clear of phrasing statements that could be contradicted by future observations.Religion may only contain proven true (facts, observations) and unproven/unprovable true statements (religious imperatives).

>>> any a fine hypothesis has fallen victim to stubborn little facts that can't be explained, and just refuse to go away.Gdel's incompleteness theorem deducts that these little facts must exists. Science must be necessarily false. In other words, everything we know, is actually wrong. We simply haven't been able to figure out why.How mankind came into existence, however, is a valid religious subject (unproven true), because all facts lie in the past. The same can be said for the beginning of the universe.The fact that science covers future observations, makes it false and unproven, but at the same time, very useful.

>>> I think that your terminology is a bit unclear.Ok. Every future statement is unproven. If I say that the sun comes up every morning, I am making a future statement, and therefore an unproven statement. Only facts (observations) are proven and true. Unfortunately, facts/observations always lie in the past.The situation is even worse than that. Gdel's incompleteness theorem clearly deducts that there will always be facts that will not fit the theorem. One such fact, however, makes the theorem already false. Therefore, all scientific theorems more complex that the Gdel treshold, are necessarily false.Now hold your breath: All scientific theorems are therefore unproven and false.And this exactly what Popper states too. Scientific theorems deduct their usefulness solely from the fact that it is hard to prove that they are false, and that we are therefore still unable to do it.>>> But what is really confusing is your "unproven true" category.Only theorems that cannot be contradicted by (future) observations can be true. All other theorems are necessarily false, because every falsifiable statement will eventually be falsified.>>> And as a consequence of that it follows that no statement in this category can be proven true or false. Perhaps it would be better to label the category "unknowable" ?Not really. As long as a theorem is not contradicted by reality, we keep labeling it as true. That's what we do for scientific theorems, even though we should know better (since they are all false). So, how do you label a statement that can impossibly be contradicted by reality? True or false? I would say: true.

>>> ... so long as Biblical creationists are allowed to air the science related Biblical fundamentals.They don't.It is indeed the prerogative of science to establish systems of unproven, false statements, whose usefulness derives from the fact that nobody has managed (as yet) to prove that the statements are false.Religion concerns statements that cannot be contradicted by future facts in reality. For example, "the sun comes up every morning" is not a valid religious statement. It is unproven (concerns future facts) and it is necessarily false (Gdel).Only proven and unproven true statements are the domain of religion.Biblical creationists do not air scientific statements, because the creation of the universe (or mankind) do not cover future facts, and therefore cannot be contradicted by future facts.

>>> We do not accept a statement as true simply because it has not been proven false - but because it could be proven false and has not been.... but it will be. So, it is not true. It is false. We simply don't know how and why.>>> I'll also ass that your understanding of Gdel's theorem is a bit dodgy, too. For instance it only applies to systems capable of handling arithmetic.That includes every system that has -- or could have -- a digital representation. Do you know of many systems that handle observations that do not -- or cannot -- have a digital representation? I don't know of any myself.>>> That is simply not true. There certainly can be falsifiable statements that will not be falsified. Indeed, if a statement and it's negation are both falsifiable it is necessarily the case that only one will be falsified.Point conceded. Only one will be falsified.> So, how do you label a statement that can impossibly be contradicted by reality?
>> I would label it unfalsifiable. If it's negation was also unfalsifiable I would label it unknowable. I certainly wouldn't call it true because there would be no basis for doing so.Ok. We have an issue here:(1) Every statement that cannot be proven to be true, is false
(2) Every statement that cannot be proven to be false, is trueWhat is the correct default?The scientific method is necessarily (2). Every statement that potentially covers future observations cannot be proven to be true. In order to be useful and predict events in the future, the scientific method must accept these statements "to be true", even though they are correctly suspected to be false.Consequently, we have to label statements that cannot be proven to be false: true.

>>> No, it does not. Systems that lack the richness required to construct the representations needed for the proof are unaffected by the Theorem.Such systems are too simple to be useful. Do you know of any scientific theorem which is so simple that it would be unaffected?>>> No. The scientific method says that unfalsifiable statements should be binned.It says that unfalsifiable statements are not part of science. And I agree with that.But then again, the beginning of the universe is also unfalsifiable, as what happened at that point in time, cannot be contradicted by future facts. This is a problem, because science does conjecture theories about it.>>> No, only statements shown to be very close to the truth (i.e. we have grounds for thinking that they will be true in almost every case, even if there may be unforseen cases where they are not) are taken as true.These statements are not "very close to the truth". They will remain unproven and false, until they are finally proven false [Popper].Anyway, it is not because a statement is hard to disprove, that the statement is true. It is still false.

>> Such systems are too simple to be useful. Do you know of any scientific theorem which is so simple that it would be unaffected?
>>>> I don't know of even one that WOULD definitely be affected. Can you give me an example and show how Gdel's proof applies ?For Gdel's proof to apply, it must be possible to represent the statements in the theory with natural numbers. Therefore, any theory that has a digital representation is already represented with natural numbers. Any theory, for which the statements can be represented on a computer, satisfies this criterion.Now, instead of using the axiomatic reduction of the statement as proof, we define its collection of all possible observations as proof. Each potential observation can be represented as a number too. The Gdel number for the proof is then the number representing its collection of possible observations (Y) for statement (X).We must therefore show that for any such given statement X, the number Y (its proof) does not exist. That would prove that all such statements X are false.This is what Popper says; and what Gdel implies, even though the latter uses axiomatic reduction as proof instead of collections of observations. Proof for this theorem, requires demonstrating formally that both are equivalent.

>>>> In other words you are vaguely presenting something that looks a bit like Gdel's proof - but leaves out the essential element, among other fatal flaws.Gdel uses axiomatic reduction as proof mechanism, while I used not contradicting the observations as proof mechanism. It is indeed not exactly the same. So, that is indeed something that I did not prove.

>>> Gdel used natural numbers because he was working with mathematics - that was the system he was interested in.Not true. As long as you can represent anything as natural numbers, the theory applies. Gdel represents statements as natural numbers, because then he can apply number theory to theorems.

>>> Two contradictory unprovable statements could not both be true. To regard two such statements as both being true is to embrace absurdity. In the real world, two mutually contradictory statements cannot, by definition, both be true. In your world, they both have to be considered be true.By defining "true" as "can impossibly be contradicted by facts" (past or future), a thesis and its antithesis can both be true at the same time.>>> A theory that accurately describes reality would be correct.A theory cannot accurately describe reality. If it does, it just means that we haven't been diligent enough in making contradicting observations.>>> We are being watched by the invisible and undetectable eyes of the machine elves from the other side.I need more information to reject this statement and let you elaborate. I have to wait until your description finally contains something falsifiable, and then produce the contradicting observation."eyes", "machine", "elves", however, come dangerously close to something that can be falsified.But then again, as long as your elaboration of the theory stays clear from becoming falsifiable, both your theory and the antithesis for your theory remain: unproven true.But then again, you will quickly notice that it is not easy at all to keep producing unproven true statements for hundreds of pages ...

When is a theory "true" and when is it "false"? This question goes straight to the core of the problem.What's more, this is an issue of definition. Assuming the following definitions of true and false:A theory is false, if at least one observation contradicts it.
A theory is true, if all possible observations concur with it.If it is not possible to make any observations for the theory, all possible observations necessarily concur with it, and therefore, the theory must be considered to be true.If it is not possible to make any observations for the theory, it is not possible to make them for the antithesis too. Consequently, the antithesis is also true.I admit that this is a borderline case, but it concurs with the definitions stated. So, in this borderline case, both the thesis as the antithesis are true.Science if full of strange results in borderline cases. What's so new about that?The remainder of your answer lacks scientific rigor.Edited by erikp, : Explaining why I don't answer the remainder of the post.

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That definition of "true" is in fact the definition of "unfalsifiable".

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A fact by itself is also true, since the observation obviously cannot contradict itself. Therefore, my hypothesis is indeed that only facts and unfalsifiable theories can be true.

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the definition is obviously faulty

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This the standard definition in science for truth/untruth. The benchmark for truth/untruth is necessarily: reality, that is, facts. But then again, according to the same definition, unfalsifiable theories are simply true.

Given the stated definitions of "true" and "false", the remainder simply follows. The proper way to discard the remainder, consists in rejecting the stated definitions. On what grounds can you reject these definitions?