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Initial post: May 18, 2013 10:08:58 PM PDT
Last edited by the author on May 18, 2013 10:16:38 PM PDT
Introduction

Our civilization depends on our ability to predict results of actions, which we do on the basis of our knowledge of how the universe works. It follows that it is important to understand what we can know, and how we can know that we know it.

I will use the following terms in this discussion:
A "thesis" is a proposition put forward for discussion. It may be true, or false, or its truth value may be undetermined or even indeterminable.
A "hypothesis" is a thesis for which there exists some known means for investigating whether it is true, or (more importantly, as we shall see later), whether it is false.
A "theory" is a hypothesis which has been tested and found to be valid over some domain of situations. (This is the scientific sense of the word.)
A theory may be said to be "persuasively demonstrated" if the domain of situations in which it has been found to be valid is "large". (How big "large" must be is something of a judgment call.)
A theory may be said to be "conclusively demonstrated" if it is persuasively demonstrated, and its domain of validity extends to domains to which it did not obviously apply when initially propounded. In other words, it predicted the existence of a new effect which was subsequently found.
A theory may be said to be "provably correct" if it is based on valid premises and the logical steps by which it is deduced from those premises are also valid. (Most scientific theories are NOT provably correct.)
A "theorem" is a theory which is provably correct. The term is more often used with mathematical or logical deductions than with science, since most scientific theories are not provably correct.

A note: Much of this material has been taken from previous posts in "Belief in the Christian god is absurd" and elsewhere. Extensive editing has been done to make the material flow more logically, further explain some concepts, and fix a minor error.

On Science

The first real description of the scientific method is attributed to Francis Bacon, Lord Verulam (1561-1626), who discussed it in his "Novum Organum" (1620). The description of a scientific statement as a provisional statement which is tentatively assumed to apply everywhere is an empirical approach, used widely because it works well. No attempt to provide any sort of theoretical basis for this approach had been made until Popper's refutability thesis, some three centuries later. But scientists didn't particularly care; the empirical approach made sense and worked, and attempting to give it a theoretical basis simply wasn't interesting. Nor was a theoretical basis even possible until recently: the mathematical tools needed to do so (information theory, set theory, and predicate calculus) simply did not exist.

Popper's thesis is that the touchstone of science is refutability: a thesis cannot convey information (in the Shannon sense) unless there exists a way to show that it is false. Popper argued vigorously for this [1, 2], but did not offer a proof that it is valid. However, it IS provable, and we shall presently examine the matter here.

It is true, of course, that people doing real science don't much care about any of this. The empirical approach has worked well for centuries, and we have never had a reason to suppose that it might not continue to do so.

Science uses both inductive and deductive logic. Inductive logic consists of conclusions, from sets of observations apparently having common properties, that there exist underlying rules which explain the supposed common properties. Since a posited property may not in fact exist, inductive conclusions are necessarily tentative. Deductive logic consists of conclusions based on prescribed premises, and conclusions drawn from these by rules of inference. If the premises are valid, and the rules correctly applied, the conclusion will be valid.

A scientific theory arises as follows:
- One constructs a thesis, possibly as an inference from observations (inductive logic), or possibly on the basis of a "What if" question, or often on the observation of a peculiar result for which the cause is not obvious.
- One attempts to devise a test of the thesis by deducing the expected results of applying the thesis to some situation. Such test must be able to show that the thesis is correct, in at least some situations, or that it is NOT correct. (As we shall see, this latter is crucial.) If no such test can be made, the thesis must be abandoned as mere speculation.
- Tests are carried out and the results examined. Whether the thesis is confirmed or refuted, our knowledge of the universe has grown.

Search key: saundersz

Posted on May 18, 2013 10:10:18 PM PDT
Proof preliminaries

In considering a proof of Popper's thesis, it is useful to take some concepts from predicate calculus. A "universal statement" is a thesis which, if true at all, applies throughout all space and time. In mathematics, some universal statements are provably correct. An example: "Every counting number has a successor." Some are provably wrong: "Every counting number has a predecessor" does not work for 1. In the real world, universal statements are generally not provably correct: there may be lurking, somewhere in the universe, an exception which has not yet been found. However, universal statements are always refutable by exhibiting a counterexample. For example, Newtonian gravity is a universal statement, which was refuted by the precession of the orbit of Mercury; Einsteinian gravity explained the discrepancy, and is universally correct so far as we know. (But, of course, it could be refuted at some time in the future.) It should be obvious that the typical scientific statement is a universal statement: we suppose that it is true throughout all space and time - until someone succeeds in showing that it isn't. (Which does not stop it from being a universal statement - it simply stops us from supposing that it continues to be a tentatively correct universal statement.) Statements such as the theory of electrostatics or electrodynamics, the laws of thermodynamics, the combination rules for chemical elements, and most other such rules are examples of universal statements which are considered to be scientific statements. (So is the ether theory, even though it was shown to be wrong.) We rely on these, for example, to do astronomy: the emission spectrum of calcium is presumed to be the same on Arcturus as it is in any earthly laboratory.

An "existential statement" is a thesis which claims that something exists; it applies to the specific example cited. If the example can be shown to be valid, the statement can be said to have been proven to be correct. An example from mathematics would be "The number 3 has a successor." True, of course; the successor is 4. (An existential statement that the successor of 3 is 5 would be an incorrect existential statement.) In the real world, we also can prove existential statements by providing appropriate evidence; we can say, for example, that the earth has a moon, or that a black sheep exists (if you can find one).

The inverse of a universal statement is an existential statement, and vice versa.

There are a few cases in which a universal statement may be proved to be correct. If the existential statement which is its inverse can be shown to be false, either by evidence or by theoretical considerations, then the universal statement must be true.

To draw any conclusions about the real world perforce requires premises about the nature of the real world; we must posit some and be prepared to defend them, even though, as universal statements, they are not provable. I use two postulates:
- The world works according to rules to which the rules of logic apply. (In other words, it acts consistently.) We rely on this many times each day, as we must; if we cannot assume that this premise is true, we cannot conclude anything about the real world -- even that the floor will be in place to support us when we get out of bed in the morning.
- Universal statements about the real world (including the one above) are generally not provable -- but can be refuted by providing a counterexample.

Posted on May 18, 2013 10:11:47 PM PDT
Last edited by the author on May 18, 2013 10:56:06 PM PDT
The General Theorem

It can be shown that the information content of any thesis derives exclusively from its refutability. In other words, if there cannot exist some means of showing that a thesis is wrong, no information can be obtained from any supposition that it is right. This result can be obtained by considering the possible functional mappings of a situation space into a result space; for the formal proof, see the Appendix.

A corollary immediately follows: if there can exist no means of showing that a thesis is false (i.e., if it is in principle irrefutable), then its information content is zero: you cannot use it for predicting anything.

The general theorem mentioned above is our basis for using science to learn about the real world. One can form a thesis, perhaps by inductive reasoning, or maybe simply by saying "Suppose..." -- and then attempt to construct a means of testing it. If such a means can be found, we have a hypothesis.

A test of a hypothesis identifies a particular point in the result space which arises from the situation in question. If the result found is within the space to which the situation point maps, then the hypothesis is confirmed with respect to that particular situation -- and, if not, it is refuted, in which case the domain of the hypothesis must be reduced to exclude the situation in which the failure occurred, and may suggest that the situation space is in fact null: i.e., the hypothesis is simply wrong. If a wide variety of tests confirm that the situation space of a hypothesis is large enough to be useful, the hypothesis can then be called a theory. Example: Newtonian mechanics works well for anything not moving at or near the speed of light, so its situation space is large and the theory can be used for predicting many things. But for work at or near light speed, relativistic mechanics is required -- and, so as we can now tell, the situation space in which these work is unbounded.

The key element of science is the need for propounded theses to be refutable. Because of the need for refutability, which only the scientific method provides, the scientific method is the only means of learning anything.

Appendix: A formal proof of the general theorem follows.

Any thesis which predicts a result of some situation can be regarded as a functional mapping from the domain of a situation space S into the realm of a result space R. For a thesis under discussion, let there be a specific situation Sx which is in S, where the thesis predicts a result Rx in R which result is a subset of R. Now Rx ideally will be a point, such that for situation Sx the thesis predicts that exactly Rx will occur, but there will be cases (such as in quantum mechanics) in which Rx will have a measure greater than zero. There is also the question of experimental error, which generally will result in a measure of Rx which is greater than zero.

Let there be an observation O which is at So in S, and has observed result Ro. Then either of two cases can arise:
- Ro is in Rx. For this case, the thesis is confirmed.
- Ro is not in Rx. This constitutes a refutation of the thesis. The set of all such refutations of So is R-Rx.

For the thesis to provide information, it must, for every Sx in S, specify an Rx in R which is a proper subset of R, and the smaller that Rx is, the more accurately the prediction can be made. If Rx is NOT a proper subset of R (i.e., is equal to R), then the thesis tells us nothing. A measure of the information derivable from the thesis is the measure of R-Rx: the larger that R-Rx is, the better the information is. Which is exactly the same as the measure of the set of refutations. Hence, the measure of the information derivable from any thesis is simply the measure of its refutability.

References:

1. Popper, The Logic of Scientific Discovery (Routledge Classics)
2. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (Routledge Classics)

Posted on May 18, 2013 10:12:34 PM PDT
Last edited by the author on Jun 4, 2013 11:14:51 PM PDT
On Evidence

Science relies on objective evidence in order to demonstrate the truth or falsity of theses. This means observation of a phenomenon, which observation can be repeatedly made by anyone who is interested, and can show, and does in fact show, that a thesis is confirmed if the observation is in accord with prediction of the thesis under consideration, and can show, and does in fact show, that a thesis is disconfirmed if it is not in such accord. Because of the need for refutability, the ability to disconfirm a thesis is absolutely essential. (Which is why anecdotal evidence is generally of slight value.)

The mind is easily fooled: we often sense things that appear to be real but aren't -- such as mirages. This is why the principle of multiple observability is important. However, there are many subjective experiences (such as dreams) which are not observable by others. These may be evidence of some things, but such evidence must be approached with some skepticism, as disconfirming such experiences may be difficult or impossible. Actions by others over a long time can be a reasonable gauge of how one's subjective experience have guided such actions.

On Scientific Publication

The rules for scientific publication are quite strict. In general, all of the following elements are required:
1. One propounds a thesis which explains or predicts some phenomenon -- the result of a situation.
2. One cites any relevant prior work relating to such thesis.
3. One deduces a prediction of the thesis, and devises a means of testing it.
4. One executes the test, and describes the results. These may show that the thesis is confirmed, or that it is wrong; in either case, something has been learned.
5. One suggests such further tests as may divulge more information about the accuracy and the domain of applicability of the thesis.
6. References are included showing justification for deductions, methods, and other germane aspects of the thesis and its tests.

The technical journals expect adherence to these rules in papers submitted for publication. Such papers are generally referred to experts in the field for review, in order to find significant errors or omissions, or necessary clarifications, before a paper is published. All of these procedures are intended to minimize the risk of errors in published material. Nevertheless, errors do sometimes occur, and any reputable journal will publish corrections or retractions of previously published material if it is appropriate to do so.

On Theology

It can be shown that belief in any god must be unfounded. For purposes of this discussion, I will take the word "god" to mean an entity which need not, and occasionally does not, follow the rules of nature which control everything else - in short, its actions are not strictly predictable. All of the following are then provably true:
- It is impossible to prove that a god does NOT exist. Such a claim would be a universal statement, and as such not provable. Universal statements are generally refutable by showing a counterexample. But, with respect to a god:
- It is impossible to prove that a god DOES exist. To show the existence of a god would require observation of a phenomenon which not only cannot occur within known natural law, but could not occur within ANY natural law, now known or not. Since it is clearly not possible to know ALL natural laws (a claim that one DID would be a universal statement), no such phenomenon can exist.
- It is impossible to derive any information from any theory of god. Information implies rules, which when applied to a situation imply a particular result. But a god need not adhere to any rules: its actions are entirely unpredictable, so the information content of a supposed godly action is zero. This is a shortcut to using the general theorem (above) that the information content of any thesis derives exclusively from its refutability: since there is no way to refute a claim that a god was NOT involved in any particular phenomenon, the information content of any thesis that one was is zero.

This has the interesting implication that theology is the only field of study in which it is impossible in principle to know ANYTHING about the subject.

Posted on May 18, 2013 10:13:20 PM PDT
Last edited by the author on May 18, 2013 10:57:59 PM PDT
The Theory of Evolution

I present here a proof that the theory of evolution is correct. Almost all scientific theories are universal statements, such as Newtonian mechanics (true at moderate speeds) and relativistic mechanics (true at all speeds), which are not provably true even though there are piles of evidence which show that they are correct. But the theory of evolution consists of existential statements only, which are provable by demonstration (and have been [1]):
- Heritable mutations occur.
- Some mutations are more beneficial to survival than the un-mutated parents.
Thus the ToE is provably correct, and of course also demonstrably correct as well. Now this proof does not (unfortunately) help us to determine the evolutionary path of any particular species: that requires actually doing some science [2].

1. Dawkins, The Greatest Show on Earth: The Evidence for Evolution.
2. See, e.g., Prothero, Evolution: What the Fossils Say and Why It Matters.

Posted on May 18, 2013 10:14:17 PM PDT
The Big Bang

I present here a synopsis of the evidence for the "big bang".

Firstly, the observed Hubble expansion of the universe, when wound backward, implies that the universe was historically hotter and denser that it is now -- and if you go back far enough, it was very dense and very hot. This would have resulted in radiation, which was predicted well before it was actually observed.

Calculations on the physics of the big bang show that it would have created hydrogen, deuterium, and lithium -- but no significant amounts of higher elements. Since lithium cannot be constructed by any nuclear process (all reactions involving it are exothermic), the existence of lithium in the universe cannot be explained in any other way -- and the measured abundance of both deuterium and lithium matches the theoretical prediction. Hence, the big bang is scientifically a done deal, and all predictions made by this theory which could have been experimentally verified have been so verified.

Posted on May 18, 2013 10:15:13 PM PDT
Afterword

Readers are invited to comment on these theses. If you consider that any of these is faulty, you should identify the particular premise or deductive conclusion which you consider to be wrong, and show by appropriate means that it is in fact wrong.

Posted on May 18, 2013 10:32:55 PM PDT
[Deleted by the author on May 19, 2013 10:48:01 AM PDT]

In reply to an earlier post on May 18, 2013 10:39:28 PM PDT
Last edited by the author on May 18, 2013 10:40:17 PM PDT
Robert A. Saunders,

How is Evolution the only hypothesis made up of existential statements when existential statements have the inverse of universal statements? This would mean that Newtonian Mechanics or any physics hypothesis, or any scientific hypothesis, consists of nothing by existential statements. What makes this even more interesting is that, existential statements aren't falsifiable, unless taken with universal statements. So you would have to hold that evolutionary hypothesis, based on nothing but existential statements, aren't falsifiable.

SCL

In reply to an earlier post on May 18, 2013 10:49:36 PM PDT
Last edited by the author on May 19, 2013 4:37:55 AM PDT
Re SCL, above: In the real world, the properties of existential and universal statements differ -- even though (actually, because) they are inverses.
You can show that an existential statement is true by exhibiting the thing which is claimed to exist.
You generally can not show that a universal statement is true, because there may be an exception that you haven't found.
You correctly note that an existential statement, once demonstrated to be true, isn't falsifiable.

The evolutionary hypothesis is not NOW falsifiable, but it was falsifiable until it was shown to be correct. Indeed, some parts of it (but not the whole thing) still are falsifiable: famously, it was noted that if a rabbit fossil were found in Cretaceous rock, evolution as we now understand it wouldn't work.

Later: Actually, an existential statement can only be refuted by showing that the claim of a specific existence is wrong. You may claim to have a unicorn in your garage, but if when I ask you to show it to me, you claim to be unable to do so because you have lost the key, I am entitled to not believe you, even without direct evidence that the alleged unicorn isn't really there.

Posted on May 18, 2013 10:50:03 PM PDT
[Deleted by the author on May 19, 2013 10:48:12 AM PDT]

In reply to an earlier post on May 18, 2013 10:57:32 PM PDT
Last edited by the author on May 18, 2013 10:59:03 PM PDT
Robert A. Saunders,

The interesting thing is that Popper, correctly, pointed out that we cannot even show that an existential statement is true, and that is why "basic statements" have to be accepted conventionally. "Basic statements", which are existential statements, contain universal concepts. And we cannot show them to hold any more than we can with a universal statement, which Popper pointed out as well. We can accept them as conventions, but this is just conjecture.

The most interesting thing is that you say that evolutionary hypothesis not NOW falsifiable. This means that evolutionary hypothesis is no longer science, but metaphysics or an analytical statement of mathematics/logic. As Popper pointed out, once you take away falsifiability, the hypothesis has forfeited its right to be called a scientific hypothesis. In the competition of scientific hypothesis, Evolutionary hypothesis has said it will no longer compete, as you say. And this would also mean that it has no content, since it isn't falsifiable now. But of course, you can saw it is not NOW falsifiable, but in the future it will be falsifiable again.

SCL

In reply to an earlier post on May 18, 2013 11:05:58 PM PDT
Last edited by the author on Jun 21, 2013 6:50:01 PM PDT
Re SCL, above: "Popper, correctly, pointed out that we cannot even show that an existential statement is true..." I must disagree with him here. We certainly can observe that the sun and moon exist; we see them, see their gravitational effects, have bounced radio waves off of both, and so on. I regarded Popper's business about "basic statements" as an unnecessary quibble, but it has been twenty years since I read him and my recollection may be faulty.

"but in the future it will be falsifiable again." Only if it can be shown that the observations which show it to be correct are all found to be erroneous. Not likely.

Posted on May 18, 2013 11:14:37 PM PDT
[Deleted by the author on May 19, 2013 10:48:24 AM PDT]

In reply to an earlier post on May 18, 2013 11:26:38 PM PDT
Last edited by the author on May 18, 2013 11:28:05 PM PDT
Robert A. Saunders,

Yes, you can see what you think is the sun or moon. But this is just a conjecture, like "All ravens are black" is a conjecture. This is also possible to be overturned in the future by the acceptance of other observations or hypothesis. And the talk of "basic statements" is just one of logic, since we have a universal statement with singular statement, and get our conclusion (i.e. results of our experiment or observation).

The interesting thing is about you bringing up future observations showing past observations to be erroneous, and not likely to happen. What Popper points out is that your point of view would be unscientific, since it would shield itself from falsifiability. The hypothesis that is least likely, i.e. not likely, is the one that says more about the world than the hypothesis that is likely. It prohibits more from happening than the likely one. And since it prohibits more, it puts its neck on the line more than the probable hypothesis.

SCL

In reply to an earlier post on May 19, 2013 4:48:41 AM PDT
Re SCL, above: "... since it would shield itself from falsifiability." Doesn't have to; if someone makes a claim that would upset an accepted thesis, you are certainly entitled to look at it, and see whether the new claim makes more sense. The special theory of relativity is a case in point. Michaelson and Morley showed a previously unknown effect that indicated that something was screwy about Newtonian physics. Hendrik Lorentz worked out a mathematical treatment to explain the observation, which required the weird-sounding idea that an object moving relatively to the observer would appear to be shortened in the direction of motion. He won a Nobel Prize in physics for this, and later on, Einstein showed that this was a natural consequence of the assumption that the speed of light is the maximum speed that information can travel. The issue in all of this is: How good is the evidence, and what does it show?

See also my edit to my post of 5-18 10:49 PM.

In reply to an earlier post on May 19, 2013 8:41:03 AM PDT
You seem to have an anti-religious bias. There's more to religion than belief in a god. There's more to the human condition than rationality. You appear to have the naÔve conviction that someday religion will disappear once everyone recognizes the truth of a mathematical proof.

Posted on May 19, 2013 9:35:18 AM PDT
Last edited by the author on May 19, 2013 9:44:41 AM PDT
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In reply to an earlier post on May 19, 2013 9:50:32 AM PDT
[Deleted by the author on May 20, 2013 4:22:57 AM PDT]

In reply to an earlier post on May 19, 2013 10:00:23 AM PDT
"A "theory" is a hypothesis which has been tested and found to be valid over some domain of situations. (This is the scientific sense of the word.)
A theory may be said to be "persuasively demonstrated" if the domain of situations in which it has been found to be valid is "large". (How big "large" must be is something of a judgment call.)
A theory may be said to be "conclusively demonstrated" if it is persuasively demonstrated, and its domain of validity extends to domains to which it did not obviously apply when initially propounded. In other words, it predicted the existence of a new effect which was subsequently found.
A theory may be said to be "provably correct" if it is based on valid premises and the logical steps by which it is deduced from those premises are also valid. (Most scientific theories are NOT provably correct.)
A "theorem" is a theory which is provably correct. The term is more often used with mathematical or logical deductions than with science, since most scientific theories are not provably correct."

Since you've got this part almost completely wrong, I won't go further.

A theory is a model of some aspect(s) of reality. It is made up of one or more (usually more) falsifiable hypotheses which have been tested and not falsified. A theory demonstrates explanatory (it provides mechanisms for a phenomena) and/or predictive (it accurately predicts what we will observe of a phenomena under new conditions) power.

A theory is, and only can be considered to be *provisionally* correct when it is tested and found to be in agreement with reality.

There is no "conclusively demonstrated", and most certainly NO "provably correct."

A theorem is *not* a theory in the sense of "a scientific theory". A theorem is "A general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths." In this case, "theorems" are what you get in formal systems with defined axioms, and defined operators over those axioms.

If you fix these errors, then perhaps we can return to the rest of your lengthy, lengthy prose.

In reply to an earlier post on May 19, 2013 10:28:38 AM PDT
Re fazakas, 5-19 8:41 AM: "You seem to have an anti-religious bias." Only because it is nonsense. Granted, people engage in religious gatherings for various purposes which they consider to be beneficial, but the irrationality of religious beliefs can, and all too frequently has, been a source of strife (e.g., Thirty Years War) and idiocy (e. g., Discovery Institute).

"There's more to the human condition than rationality." This is certainly true. We are all affected by emotions, prejudices, and any number of other irrationalities, some of which (but by no means all) cause serious problems.

"someday religion will disappear once everyone recognizes the truth of a mathematical proof." I do not expect this. But on much of the planet religion is already disappearing because people realize that it is fundamentally pointless. My point is not to extirpate religion per se -- but rather to show that it cannot be rationally supported on its own merits.

In reply to an earlier post on May 19, 2013 10:49:47 AM PDT
Last edited by the author on May 19, 2013 10:55:25 AM PDT
Re Altarriba, 2d above: Good to hear from you. I think that we are largely on the same page with respect to your concept of "theory". The words "refutable universal statement" and "provisionally correct" describe the same concept.

As for "conclusively demonstrated", what words would you use to describe the special theory of relativity? I do not intend that "conclusively demonstrated" should mean "never will be refuted"; I simply mean that the thing works so very well that a complete refutation appears to be improbable in the extreme. Newton's mechanics could have been called "conclusively demonstrated" until Einstein came along, and even Einstein didn't show that it was totally wrong: he simply showed that its domain of applicability didn't extend to things in high speed relative motion.

I accept your definition of "theorem"; there appears to be no difference in what you mean by this from what I mean.

As to evolution: you and I are looking at different aspects of the same elephant. You correctly point out that the ToE could be refuted if ALL of the observations which support it turn out to be wrong; I am saying that there exist observations which are so clear and convincing in their support of the essential concepts that a complete upset is only vanishingly probable. In short, like the mechanics example above, we may improve on the details (as, of course, we have in the 150 years since Charles did his thing), but the basic concept will stand. It's the difference between "zero" and "too small to measure".

I spent considerable time working on a response to your intelligent criticism of my posit on evolution a month or so ago, but finally dropped it in favor of re-working the entire thesis set with which I began this thread. Cheers!

In reply to an earlier post on May 19, 2013 1:11:44 PM PDT
Last edited by the author on May 19, 2013 1:12:08 PM PDT
Your statement "Religion is nonsense" is prima facie evidence for an anti-religious bias. Pointing out specific instances where religion has caused harm no more invalidates religion per se than pointing out specific instances where physics has done harm invalidates physics per se.

A similar viewpoint to yours gained fairly wide currency among intellectuals during the 1700s.......and look what happened! Romanticism. An eruption fo appreciation for the irrational which had enormous repercussions for art, literature, music, psychology, and social organization.

Irrationality is not something intrinsically bad to be extirpated. There is no simple good/bad duality of rational/irrational. Throwing out the irrational means a general impoverishment of the human condition.

In reply to an earlier post on May 19, 2013 2:01:15 PM PDT
"As for "conclusively demonstrated", what words would you use to describe the special theory of relativity?"

I'd use exactly the same words I'd use for any scientific theory: provisionally correct.

"I do not intend that "conclusively demonstrated" should mean "never will be refuted"; I simply mean that the thing works so very well that a complete refutation appears to be improbable in the extreme."

It simply doesn't matter how improbable a refutation seems to be. The conclusions of science are provisional... all of them.

"Newton's mechanics could have been called "conclusively demonstrated" until Einstein came along, and even Einstein didn't show that it was totally wrong: he simply showed that its domain of applicability didn't extend to things in high speed relative motion."

Newtonian mechanics reflects non-relativistic motion extremely well... and, still, "provisionally correct" is what it is.

"I accept your definition of "theorem"; there appears to be no difference in what you mean by this from what I mean."

Well, except that theorems aren't theories, ok.

"As to evolution: you and I are looking at different aspects of the same elephant. You correctly point out that the ToE could be refuted if ALL of the observations which support it turn out to be wrong;..."

No. I'm saying that the theory of evolution, like any other scientific theory, is *in principle* capable of refutation in the face of new evidence.

It doesn't matter how unlikely the appearance of that new evidence may be.

"... I am saying that there exist observations which are so clear and convincing in their support of the essential concepts that a complete upset is only vanishingly probable."

And I'm telling you that it doesn't matter if a "complete upset" (or a minor adjustment) are vanishingly probable or extremely likely.

You're trying to construct a special category of scientific theories.

I'm telling you to do so is not only counter-productive and justified... it's not good science, either.

*All* of science is provisional, because it is impossible, even in principle to prove that a scientific theory is false... because a scientific theory is an abstraction, a model of an actual phenomena, and not the phenomena itself, so there is always the potential that one my discover elements of that phenomena which are not included or not in agreement with the abstraction / model one has created.

So, until we figure out how to guarantee 100% accurate, complete perceptions of reality, "provisionally correct" is the best we can do... and we'd just be fooling ourselves if we asserted otherwise.

In reply to an earlier post on May 19, 2013 2:02:41 PM PDT
How about "much of religion is a relic of our much more ignorant and superstitious past"? So, I'm not saying religion offers nothing of value.

Am I being "anti-religion" now?
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