What is a Theory?

If it is a key concept, then why did we have to wait for 100+ messages before it entered the conversation? And I might mention that it wasn't even you who brought it up, but me. Furthermore, I also stated that science doesn't deal with it, because it's a non-item. Now all of a sudden you latch onto it as a key concept. Sounds like a bit of an ad hoc argument to me, which makes your theory about unfalsifiable theories unfalsifiable itself, and therefore, in your opinion, true, while the world at large just shrugs its shoulders and carries on not bothering any more.The Rrhain shower was short but refreshing.

---

"Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science." - Charles Darwin.

quote:

---

If it is a key concept, then why did we have to wait for 100+ messages before it entered the conversation? And I might mention that it wasn't even you who brought it up, but me.

---

Indeed. I didn't think of quantifying falsifiability, until you brought up that you thought it had no use, so that I could conclude that it does have use.There is indeed a positive relationship between falsifiability of a theory, that is, the number of potential (future) facts k that could contradict it, and the likelihood that the theory will be contradicted P(C|MoF=k).This relationship is:P(C|MoF=k) = 1 - 0.5^k.And this relationship suggests that infinitely falsifiable theories can most reasonably be expected to be contradicted.All of this supports my case: infinitely falsifiable theories are presumably false. And therefore, supported by the relationship that we established, I can comfortably re-iterate my initial point:Science must be unproven and false in order to be useful.

erikp responds to Parasomnium:

quote:

---

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

---

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:

quote:

---

Given a random theory

---

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

quote:

---

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

---

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.

---

Rrhain

---

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:

quote:

---

This relationship is:

​

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

---

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.

quote:

---

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

---

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.

quote:

---

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

---

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.

---

Rrhain

---

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.

quote:

---

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

---

Theories can perfectly well be represented by numbers. If theories represent a number, a number can represent a theory. That is exactly the gist of Gdel's (axiomatic) proof. Wiki(Gdel):

quote:

---

In order to prove the first incompleteness theorem, Gdel represented statements by numbers. Then the theory at hand, which is assumed to prove certain facts about numbers, also proves facts about its own statements. Questions about the provability of statements are represented as questions about the properties of numbers, which would be decidable by the theory if it were complete. In these terms, the Gdel sentence states that no natural number exists with a certain, strange property. A number with this property would encode a proof of the inconsistency of the theory. If there were such a number then the theory would be inconsistent, contrary to the consistency hypothesis. So, assuming the theory is consistent (as done in the theorem's hypothesis) there is no such number.

---

If a statement can be represented by a number, a theory, that is, a collection (a set) of statements can be represented by a number too:

quote:

---

a (formal) theory is a set of statements expressed in a particular formal language.

---

Therefore, the overall set of theories, T, can be represented as a set of numbers. Like in Gdel's proof, the properties of these numbers translate to properties of the theories they represent.Futher, nothing prevents anybody from taking a random sample of numbers and therefore a random sample of theories, and make valid statistical inferences, based on the sample, about the population of theories.Furthermore, for the population of theories, the observations (facts) that can contradict them, can be observed. The occurrence of these facts is a random process, that can perfectly well be sampled and modeled by statistics.

quote:

---

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?

---

Every theory that goes into building and operating these probes is false, but very hard -- currently impossible -- to prove so. In those circumstances, we can reasonably expect these probes to work, because nobody can tell us why they wouldn't. But that still does not make any of these theories true. They are still false. One day or the other, someone may also finally be able to tell us why exactly they are false.

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

---

Rrhain

---

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.

quote:

---

The only way to show a theory false is to bring forth the observation.

---

Indeed. Bringing forth the observations that will contradict the current body of science in use, is very hard -- currently impossible. So, I repeat, the current body of science is entirely false, but it is currently impossible to know why.

erikp responds to me:

quote:

---

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

---

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

quote:

---

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

---

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

quote:

---

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

---

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?

quote:

---

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

---

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

---

Rrhain

---

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.

What a gem of an argument, thanks!(Not that it will convince Erik, of course...)Edited by Parasomnium, : No reason given.

erikp responds to me:

quote:

---

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

---

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

quote:

---

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

---

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

---

Rrhain

---

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.

quote:

---

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

---

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.

quote:

---

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

---

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.

quote:

---

Suppose you have a theory that is perfect.

---

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

quote:

---

Which means that the theory isn't false.

---

If it is infinitely falsifiable, the theory is presumably false. That has nothing to do with the truth or falsehood of any claim made by the theory, but only with the fact that the number of potential observations is infinite.I stated that:P(k) = 1 - 0.5^kgiving the observation 1 chance out of 2 to contradict the theory (absence of any further information).However, it does not matter how likely an observation will contradict the theory. It could be extremely small:P(k) = 1 - (1-0.00000000000000001)^kFor an infinite number of observations this likelihood will still go to 1 (=always).P(k) = 1 - (1-a)^k, with a the likelihood that 1 observation contradicts the theory.lim (k --> inf) P(k) = 1, on the condition that a is not exactly zero.The perfect theory requires that a would be exactly zero. This perfect theory would have to take everything into account. It would be the Theory of Everything.Concerning the Theory of Everything, Stephen Hawking (Wiki, Theory of Everything):

quote:

---

Stephen Hawking was originally a believer in the Theory of Everything but, after considering Gdel's Theorem, concluded that one was not obtainable.

​

"Some people will be very disappointed if there is not an ultimate theory, that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind."

---

erikp responds to me:

quote:

---

quote:

---

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

---

​

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.

---

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?

quote:

---

quote:

---

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

---

​

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.

---

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?

quote:

---

quote:

---

Suppose you have a theory that is perfect.

---

​

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

---

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?

---

Rrhain

---

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.

Rrhain writes:

quote:

---

{about perfect and other theories}

---

quote:

---

What a gem of an argument, thanks! (Not that it will convince Erik, of course...)

---

If you can convince Stephen Hawking, I will be convinced too. But then again, you would first have to demonstrate that Gdel was wrong. Wiki:

quote:

---

Stephen Hawking was originally a believer in the Theory of Everything but, after considering Gdel's Theorem, concluded that one was not obtainable.

---