What is a Theory?

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You don't know what a "postulate" is, do you?

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Wiki:

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In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths.

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Now you are probably going to argue that Wikipedia is beneath you, since they seem argue incorrectly that Stephen Hawking and not you deserves the nomination for the next Nobel prize.Instead of asking this kind of stupid questions, why don't you try to be useful for once, just quote the definition, and demonstrate that I used the term inappropriately."You don't know what XYZ means, do you?" Is that why they kicked you out of the last Stephen Hawking conference, after making abnoxious remarks to the emeritus professor?

No he didn't. I don't know if he is "smarter" than Strephen Hawking, I do know you didn't understand what he said. Would you mind arguing against what he actually said, instead of resortying back to this trather poor ad hominem?P.s.: All hail Rrhain! Champion of reason and logic!

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I hunt for the truth

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Huh? We don't have theories right now? What on earth are all those scientists doing?

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You defined the "other theory" as the overall theory that has not been contradicted by existing facts. The "perfect theory" has not been contradicted by existing facts nor will it be contradicted by future facts.I argued that it will not be possible to continue phrasing the "other theory", because it would eventually reach a level of complexity which will prevent anybody from phrasing that theory correctly.Anyway, science has not phrased the "other theory", since there enough observations that contradict existing theory. Just one example, the problem of dark matter.What's more, science has not taken into account all possible observations that could contradict its theories. More contradictions could already have occurred, without anybody noticing.

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I don't know if he is "smarter" than Strephen Hawking, I do know you didn't understand what he said.

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I was quoting. Maybe the person saying it, did not understand what he said.

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P.s.: All hail Rrhain! Champion of reason and logic!

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You're a phantastic chearleader!

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Would you mind arguing against what he actually said, instead of resortying back to this trather poor ad hominem?

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Why don't you tell him to quote definitions by himself, if he believes someone did not apply the definition correctly, instead of waiting until someone else has to put in the effort?

That's an interesting religion. Certainly not biblical. Thanks for clarifying. I will retract my guess of 'evangelical' then, and assume that you do not fall into the biblical inerrancy nonsense camp. But if you do have a bible based religion and also believe this statement you made, then your bible is thinner than other bibles, such as the kind found in motel rooms.'bounded' in mathematics - an example:
a line segment from 1 to 2 that includes its endpoints is bounded.
If it doesn't include the endpoints it is unbounded.
Both contain an infinite amount of points.
The only difference is that one contains the numbers, 1 and 2, and the other does not.Another example:
A circle in a plane with its interior is bounded. Exclude the circle and the remaining set of interior points are unbounded even though that set is smaller than the first.Another example:
A ball in 3 dimensions if it includes the points comprising the sphere is bounded, if it only includes points interior to the sphere it is unbounded.An example of a set that is infinite and both bounded and unbounded is a line segment that includes one endpoint but not the other..

Why don't you tell him to quote definitions by himself... etc. etc. blah blah blah.Here are some definitions for you. Notice that they do not rely on sophistry and philosobabble.

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Theory: a well-substantiated explanation of some aspect of the natural world; an organized system of accepted knowledge that applies in a variety of circumstances to explain a specific set of phenomena; theories can incorporate facts and laws and tested hypotheses. Theories do not grow up to be laws. Theories explain laws.

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Theory: A scientifically testable general principle or body of principles offered to explain observed phenomena. In scientific usage, a theory is distinct from a hypothesis (or conjecture) that is proposed to explain previously observed phenomena. For a hypothesis to rise to the level of theory, it must predict the existence of new phenomena that are subsequently observed. A theory can be overturned if new phenomena are observed that directly contradict the theory. Source

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When a scientific theory has a long history of being supported by verifiable evidence, it is appropriate to speak about "acceptance" of (not "belief" in) the theory; or we can say that we have "confidence" (not "faith") in the theory. It is the dependence on verifiable data and the capability of testing that distinguish scientific theories from matters of faith.

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Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.

Your nonsense is becoming more than a bit tiresome. Now you are adding inane insults against someone who does have some idea what he is talking about.You have been allowed to monopolize this thread a bit too long now.You will start to debate more forthrightly or you will be asked to stop posting to this thread.There will be only this one warning.

erikp responds to me:

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We've been through that problem before, quoting the various alternative definitions for the term "theory" and establishing that "Water boils at 100C" is a theory.

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No, we haven't. Nobody agrees with your claim that "Water boils at 100 C" is a theory. Therefore, we have not established it at all.Hint: If "Water boils at 100 C" is a theory, then there are infinitely many theories (as there are infinitely many temperatures). Thus, your "measure of falsifiability" is "infinitely falsifiable" which, by your claim, means that "measure of falsifiability" is false.Are you sure you want to insist that "Water boils at 100 C" is a theory?

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I am not going to go through all of that again, just because you did not read that part of the thread.

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(*chuckle*)I read the thread. Nobody agrees with your definitions.Thus, my question still stands:Do you even know what a theory is?While you're at it, you can then let us know what you think "incomplete" means.And are you going to retract your retraction since Dyson retracted his statement?

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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 that is your pov, quote the definition, and then demonstrate that I used the word inappropriately.

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Nice try. Answer the question:What does "unbounded" mean? Here's a hint:(0,1)
[0,1)
(0,1]
[0,1]Which of these are unbounded?

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You've already argued that Stephen Hawking is some kind of an idiot

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Incorrect. I said that Hawking was speaking outside his area of expertise. You don't go to a tax attorney for advice regarding heart surgery. It isn't that your tax attorney is an idiot. It's that cardiology is outside his area of expertise. We don't expect him to know anything about it.And, indeed, you were somewhat misquoting Hawking: He was referring to the Incompleteness Theorems as an analogy, not a direct consequence.And Dyson retracted his statement.For the exact reason I had pointed out: Physics, despite being applied mathematics, is not interchangeable with mathematics. The parts of math that physics uses have long been established and none of the undecidable statements we have found have any bearing upon physics. Thus, there is no evidence that physics has inherited the incompleteness of mathematics.Of course, this would help if you understood what "incomplete" means. I am still waiting for an answer to my direct question. I do not ask it for my health.What does "incomplete" mean?Hint: It does not mean "false." ZFC is incomplete. It is not false.

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you are the one who should receive the Nobel prize in his stead.

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(*chuckle*)You do realize that there is no Nobel Prize for math, yes? The apocryphal legend is that Nobel's wife ran off with a mathematician and that was his way of getting back at mathematicians.Instead, it's the Fields Medal.And as you will recall, it was painful to see Dyson make such an elementary mistake. You do know who Dyson is, yes? Pretty much the Euler of our lifetime.And yet, Greene and Feferman felt that they were capable of schooling Dyson...which Dyson accepted and retracted his statement.You seem to be falling for the argument from authority: Because Hawking/Dyson/Wikipedia said it, it must be true. That is a logical error. Things aren't true because a respected person says so.

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How unfortunate for you that nobody seems to agree with you.

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Huh? Dyson retracted his claim for the very reason I gave. It would seem that Dyson agrees with me.Now what?

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Everybody is obviously unjustly underestimating your amazing intelligence! Why would that be !?

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(*chuckle*)Let me see if I understand your logic: That because I insist that I am a better mathematician than you, that must mean I think I'm a better mathematician than a non-mathematician and a mathematician who has retracted his statement that you have quoted from doing a quote-mine dump from Wikipedia.I'm still waiting for a response:What does "incomplete" mean?
And "theory"?
And "unbounded"?

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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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Now you are probably going to argue that Wikipedia is beneath you

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No, I'm going to argue that you had to go to Wikipedia to give the definition. You didn't know what it was until you looked it up and yet you felt you could toss it out and expect nobody to call you on it.And note, this definition of yours contradicts your use. You claimed it was an aspect of physics. It isn't.

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why don't you try to be useful for once, just quote the definition

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Because I'm not the one tossing out these terms. You are. Therefore, you are the one who needs to show that you understand what you're talking about. Burden of proof is always on the one making the claim.Besides, I already have defined them.

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demonstrate that I used the term inappropriately.

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You mean like your confusion of "incomplete" for "false"? Why do you think I keep pointing out to you that they are called the "Incompleteness" Theorems and not the "Inconsistency" Theorems?For the umpteenth time:What does "incomplete" mean?
And "theory"?
And "ubounded"?

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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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I argued that it will not be possible to continue phrasing the "other theory"

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Indeed, but irrelevant. We are not in the future. We are in the present. We don't have these "future observations" that you keep trying to invoke to save your bacon. So how do you distinguish between them? Your "measure of falsifiability" only works in the present and it gives the same result to both: False. But the perfect theory is true, which means your "measure of falsifiability" is false.

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because it would eventually reach a level of complexity which will prevent anybody from phrasing that theory correctly.

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Why? And "complexity"? What do you mean by "complex"? It would seem that what you're trying to say is that the theory couldn't be described by a finite set of statements. Is that what you mean? That isn't "complexity."What do you think "complex" means?

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Anyway, science has not phrased the "other theory"

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Huh? We don't have theories right now? Then what on earth are scientists doing?

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since there enough observations that contradict existing theory. Just one example, the problem of dark matter.

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Huh? Since when did dark matter become a requirement for every theory? I wasn't aware that the germ theory of disease cared one whit about WIMPs and MACHOs.

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What's more, science has not taken into account all possible observations that could contradict its theories.

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Huh? Theories are specifically designed to make predictions about unmade observations. That's why "water boils at 100 C" is not a theory. It doesn't make any predictions. It's simply a statement.

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More contradictions could already have occurred, without anybody noticing.

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If nobody noticed them, how do you know they happened? You are basing quite a lot on things that have never been observed.Well, since there are infinite things that have never been observed, that means your "measure of falsifiability" will necessarily fail by its own design. It is "infinitely falsifiable," which is the trigger for it to spit out a result of "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.

I can assure you, for all intents and purposes, Hawking is a mathematician. To suggest that he doesn't understand set theory is simply laughable. He is a theoretical/mathematical physcist - definitely more physicist than mathematician if we are comparing to the likes of the real mathematical physicist heavy-weights like Atiyah, Segal, Witten, etc, and of course Penrose, which is why he will deny being a mathematician as he frequents their company BUT as far as you are concerned, he is a mathematician. The 'cosmology' we study is not built upon stars and galaxies, but on algebraic topology, differential geometry, and related fields. I'm sure you will appreciate the "connection" with set theory

cavediver responds to me:

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I can assure you, for all intents and purposes, Hawking is a mathematician.

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As an actual mathematician who hangs around with actual astrophysicists, I can assure you that while Hawking's mathematical skills are quite formidable, he is not a mathematician in the strict sense of the word.Cosmology requires a deep understanding of some higher math, yes, but it is done on a practical level, not a foundational level.There's a reason that the tensor algebra class has different versions for the physicists and the mathematicians. One is teaching you how to use them while the other is teaching you why they exist in the first place.The Incompletenesss Theorems are part of the structure of set theory, which is part of Pure Mathematics. We have long since passed the days when a physicist such as Newton would be at the forefront of pure math. This hardly means that physicists are idiots, to use erikp's word. Nor does it mean that physicists never come up with something new in the field of mathematics. Physics is applied math so clearly there will be new math discovered by physicists as they develop tools to do their jobs.But the Dyson's of this world who are both mathematician and physicist are few and far between. And even he gets it wrong. Later in this thread, you'll see: He reviews Greene's book and makes a fundamental error specifically regarding the Incompleteness Theorems. Feferman school him on his mistake and he admits his mistake.

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BUT as far as you are concerned, he is a mathematician.

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No. As far as I am concerned, he's a cosmologist. I am a mathematician.

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The 'cosmology' we study is not built upon stars and galaxies, but on algebraic topology, differential geometry, and related fields. I'm sure you will appreciate the "connection" with set theory

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Having studied all of those, being a mathematician, I see the differences between them. For a mathematician, you study set theory first. For a physicist, you never get to set theory. Set theory is pure math...about as pure as you can get. How do you prove that 1 + 1 = 2? Set theory. To get back to one of erikp's point: How does one show that 1 + 1 = 2 using gravitational theory?There is something to the cliche: Chemistry is applied physics. Physics is applied math. In chemistry, you don't really concern yourself with where the atoms come from. And yet, the work of chemists will be of immense help with answering that question and the field of physical chemistry is quite rich.But physical chemists are still chemists, not physicists.In physics, you don't really concern yourself with where the calculus comes from. And yet, the work of physicists will be of immense help with answring that question and the field of mathematical physics is quite rich.But mathematical physicists are still physicists, not mathematicians.And thus no, I do not expect Hawking to understand the field of set theory. I would hope that he knows enough to understand that since the Incompleteness Theorems describe traits of axiomatic set theories and since physics is not an axiomatic set theory, the Incompleteness Theorems would not apply.And, looking up his actual statements, it appears that he is only using them as an analogy, not as a direct implication.

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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.

I like the notion (starting with post 169) of debating whether water boils at 100C. Celsius invented a scale by saying that he would make the freezing point of water 100 and the boiling point 0. He didn’t discover it, there is no theory. He simply invented a definition. The scale was reversed after his death to make the one that we know today. (In modern usage, the Celsius scale is linked to the kelvin, which measures absolute temperatures, and the definition has become rather more complicated.)

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There is no harm in doubt and skepticism, for it is through these that new discoveries are made - Richard Feynman

There are perhaps four classes of idea where some kind of discovery, as opposed to invention or definition, is involved:1. An idea that can be, but has not yet been tested.
2. An idea that has been tested as rigorously as possible and has passed the tests.
3. An idea that has not passed the tests.
4. An idea that cannot be tested.In theology the test is based on scripture, and in philosophy on logic. The emphasis in both is usually on proof.In science the test is based on objective reality, on how the world works, and the emphasis is usually on falsification rather than proof because it is really hard to prove anything at all about the world. The first type of idea is strictly called a thesis. String Theory is, at best, a thesis, but was misnamed to make it sound cool. Most ideas end up in the third group as garbage. The last type of idea, one that cannot be tested, is known as ”not even wrong’.A good scientist will try to falsify her idea before publishing it, and will point out as many ways as possible for other people to do so. Darwin did this. He said that he could be proved wrong if we found just one species, or even a single part of an animal or plant, that can’t be explained by his idea. After 150 years and lots of attempts, no one has been able to find one. For such a counter-intuitive idea to last so long in the face of extreme skepticism by many generations of Christians, amongst others, makes it one of the strongest in science.We can never say for sure that a scientific theory is true, because we don’t have a handbook for the world. We wouldn’t need science if we did. But as the number of tested theories grows, we can be a little more certain about them, because they give the right answers and all have to work together.Many of the posts on this topic are about the meaning of words rather than the value of ideas. Modern theologians, and certainly scientists, are often much more pragmatic, so here’s a thought experiment: Suppose that your partner fell seriously ill. Would you seek the aid of scientifically trained doctors and scientific medicine? Of course. Would you pray your heart out? Of course. You would try everything that might work. But would it help to debate the meaning of life and whether we can truly ever know anything? Probably not.So why do it now?

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There is no harm in doubt and skepticism, for it is through these that new discoveries are made - Richard Feynman