Some people do not understand Counterfactual Definiteness

[Justo]

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You can call it counterfactual if you like. So what? It is what it is. The maths are legal, and we are working within a mathematical model. If you get conclusions (about relations between correlations observed in different experiments) that do not hold in reality then you know the model does not describe reality.

So nothing, you are saying just what I said: you can do any legal mathematical operation. For instance, if you add and subtract A(a,\lamda), does it mean that you really have to measure A(a,\lambda)? If we cannot do legal mathematical operations with an expression that has some physical meaning, mathematics would be useless for physics. That is exactly what many Bell deniers do.

Of course, we have to start with a mathematical expression that does have a physical meaning. In this case in the integral giving the value of P(a,b).

[Justo]

The statement is a conditional statement. Nobody is suggesting that it is a counterfactual statement. It only becomes counterfactual in the specific context in which is fact and it is no longer possible for to be true. Counterfactual Definiteness means the statement is valid and as a result of is definite even in the context in which is counterfactual. If you disagree, please provide your definition.

You are saying that becomes a conterfactual statement. It is not a "counterfactual conditional". Please google counterfactual conditional.

You didn't answer the question. You just made an empty proclamation that is unfounded. What is the basis for factoring?

Yes responded to that and also Richard Gill. The basis is mathematics.

[gill1109]

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You can call it counterfactual if you like. So what? It is what it is. The maths are legal, and we are working within a mathematical model. If you get conclusions (about relations between correlations observed in different experiments) that do not hold in reality then you know the model does not describe reality.

So nothing, you are saying just what I said: you can do any legal mathematical operation. For instance, if you add and subtract A(a,\lamda), does it mean that you really have to measure A(a,\lambda)? If we cannot do legal mathematical operations with an expression that has some physical meaning, mathematics would be useless for physics. That is exactly what many Bell deniers do.

Of course, we have to start with a mathematical expression that does have a physical meaning. In this case in the integral giving the value of P(a,b).

Exactly. I was agreeing with you, Justo.

I have been looking at the Wikipedia page on counterfactual definiteness and the long sequence of papers by Henry Stapp and Abner Shimony on Henry Stapp's introduction of the term "counterfactual definiteness" and his later attempt to weaken the concept and/or drop the term, and to replace it by something weaker but without losing the conclusion of Bell's theorem. The more I think about it, the more I think that "counterfactual definiteness" is an unfortunate pair of words. The assumption is not supposed to entail that outcomes of unperformed measurements *are* real, but only that what can imagine them to be real, in the sense that one can put down mathematical models in which they exist mathematically - which is not to say that they exist in reality.

I would suggest that anyone who finds the term unsatisfactory should simply not use it. Personally, I like to use it, because Boris Tsirelson liked it, and because I very much respect that guy. He was a mathematician and I am a mathematician. We both mean by counterfactual definiteness the possibility to find a mathematical model in which those outcomes of all possible experiments do exist alongside of the experiment actually chosen. The assumption becomes meaningful when complemented with assumptions of locality and of no-conspiracy; because locality applies to those counterfactual outcomes as well. They are localized to the same place where the factual outcomes reside.

The basis is mathematics. Leave philosophy to the philosophers.

By the way, suppose we agree that counterfactual definiteness plus locality should mean the mathematical existence of the pair of functions ((A(a): a in {possible Alice's settings}), (B(b): b in {possible Bob's settings})) = (A(.),B(.)). Then you could define lambda = the pair of functions (A(.),B(.)). Finally define A(a, lambda) = first component of (A(.),B(.)) [which is a function defined on the set of possible settings] evaluated at a. We see that locality plus counterfactual definiteness is *equivalent* to local hidden variables is *equivalent* to local realism.

If we stick to mathematics things are very clear.

If we move to philosophy we will never be finished.

[Juso]

Exactly. I was agreeing with you, Justo.

Yes, I'm sorry. I later realized that you were responding to minkwe. Anyway, I just strengthened your point.

[Joy Christian]

The basis is mathematics.

The issue of counterfactual definiteness is a side issue. Whichever side wins in the debate about it will not affect the fact that Bell's theorem is a fundamentally flawed argument.

The flaw in Bell's theorem was pointed out by Einstein in the mid-1930s when Bell was hardly seven years old. It is so basic that it is mindboggling why it has not been recognized before.

The flaw has to do with the assumption of the additivity of expectation values in any derivation of a Bell-type inequality. That assumption is illegal for hidden variable theories of any kind, as pointed out by Einstein in the mid-1930s, and independently by Bell himself just before 1964, in the context of von Neumann's theorem against hidden variables.

And this is the point that mathematicians will never understand. Just because the additivity of expectation values follows by following mathematics does not mean that it is meaningful physically. Einstein saw that clearly, and so did Bell in the above-mentioned context. Consequently, what is ruled out by the Bell-test experiments is not local realism but additivity of expectation values --- which is not permissible for hidden variable theories to begin with. That is the sad end of the sordid saga of Bell's theorem: https://arxiv.org/pdf/1704.02876.pdf.
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[Justo]

The issue of counterfactual definiteness is a side issue. Whichever side wins in the debate about it will not affect the fact that Bell's theorem is a fundamentally flawed argument.

I think that Joy Christian has previously criticized the Bell theorem on the basis of counterfactual definiteness. The fact that he now doesn't do it anymore is a sign of change. That is a good sign and speaks highly of himself. I know of people that keep repeating the same mistakes about the Bell theorem for forty and even fifty years.
Unfortunately, I am afraid that now he moved to another mistake. Claiming that Bell's theorem is nonsense is by itself a big issue. He now is making a very puzzling claim, that Bell correctly identified von Neumann's error(which is true) and then went on to commit the same silly mistake when formulating his theorem.

I only would like to contribute with the following thought. If Joy Christian is really correct about his criticisms, he will be recognized as a martyr someday. I do not believe in conspiracies. In science, the truth prevails sooner or later.
Although in science there should be no place for authority other than the truth, I would like to know of someone of outstanding intellectual authority saying the Bell theorem is terribly flawed. I know of two examples not saying that, Richard Feynman dismissed the importance of the theorem saying that it is only a mathematical proof of things we already know. On the other hand, another novel laureate, Gerard 't Hooft was led to accept superdetermism instead of considering Bell's theorem as flawed.

[minkwe]

Yes responded to that and also Richard Gill. The basis is mathematics.

You probably don't understand the question.

In order to factor A from AB - AC into A(B-C), you imply that the A term in AB is exactly the same A term in AC. So then how can it be the same A term if AB and AC can never be measured on the same particle pair simultaneously. The basis for factoring is the assumption of counterfactual definiteness. The assumption that although the experiment AB was performed, the results of the counterfactual measurement AC is definite and unaffected by the measurement actually performed.

Within the integral, AB is a result from one particle pair measured at settings (a,b). Now answer this -- is AC a result from the same particle pair or a different pair measured at (a,c)? Do you understand the difference?

Simply saying the basis is mathematics is quite naive of the physical implications of the mathematical operation.

[minkwe]

The statement is a conditional statement. Nobody is suggesting that it is a counterfactual statement. It only becomes counterfactual in the specific context in which is fact and it is no longer possible for to be true. Counterfactual Definiteness means the statement is valid and as a result of is definite even in the context in which is counterfactual. If you disagree, please provide your definition.

You are saying that becomes a conterfactual statement. It is not a "counterfactual conditional". Please google counterfactual conditional.

I've not used the phrase "counterfactual conditional". You need to define what you understand by "Counterfactual definiteness".

[gill1109]

Yes responded to that and also Richard Gill. The basis is mathematics.

You probably don't understand the question.

In order to factor A from AB - AC into A(B-C), you imply that the A term in AB is exactly the same A term in AC. So then how can it be the same A term if AB and AC can never be measured on the same particle pair simultaneously. The basis for factoring is the assumption of counterfactual definiteness. The assumption that although the experiment AB was performed, the results of the counterfactual measurement AC is definite and unaffected by the measurement actually performed.

Within the integral, AB is a result from one particle pair measured at settings (a,b). Now answer this -- is AC a result from the same particle pair or a different pair measured at (a,c)? Do you understand the difference?

Simply saying the basis is mathematics is quite naive of the physical implications of the mathematical operation.

It is not naive. You are inside mathematics. You are discussing the consequences of a mathematical theory. A, B and C are functions defined on the same set and taking values +/-1. Within those assumptions you do valid mathematics.

You do make the assumption that when you do the experiment (A, B) you do not change the results you would get for (A, C). You make this assumption via the no-conspiracy assumption which basically comes down to the assumption that the probability distribution of lambda does not depend on which experiment you choose to do. Bell's theorem needs locality, realism, and no-conspiracy.

You can have physical objections to the assumptions. You can believe in super-determinism. Which measurements were going to be performed was already fixed at the time of the big bang. So there are no functions A, B, C since the experiment which was going to be done was fixed in advance along with properties of the particles, measurement devices etc. Like those people who believe the world was created 4000 years ago with the fossils deliberately put in the earth in order to test our faith in the bible.

[minkwe]

It is not naive. You are inside mathematics. You are discussing the consequences of a mathematical theory. A, B and C are functions defined on the same set and taking values +/-1. Within those assumptions you do valid mathematics

Bell's theorem is a theorem about physics not mathematics. P(a,b) is the result of an experiment in a physical system. The factoring within the integral has a physical implication. It is naive to ignore that.

You do make the assumption that when you do the experiment (A, B) you do not change the results you would get for (A, C).

Yes but we are not talking about P(a,b), we are talking about the (A, B) result from a single particle pair within the integral. There is no probability involved in the factoring. All you have are functions acting on a set of particle and instrument properties. The assumption is that all three functions are acting on the same set. That is the justification for doing the mathematics under the integral. Anything else would be mathematically invalid. You can't do the factoring if A & B act on one set, while A & C act on another. But since physically, A & B is mutually exclusive with A & C, then physically, the mathematical operation that Bell performed in 14b amounts to an assumption of counterfactual definiteness. Do you disagree with this?

The point is that Justo claims there is nothing about CFD in Bell's theorem. Surely you disagree with him since you've also made the claim that CFD is an assumption. I've shown where CFD is invoked in Bell's derivation in equation 14a. Do you object to that?

[Heinera]

Bell's theorem is a theorem about physics not mathematics.

It's of course a theorem about mathematics (like any theorem; "theorem" is a mathematical term). Bell arrived at his conclusion without doing a single physical experiment. The theorem says that a certain class of mathematical models cannot produce a certain numerical result.

P(a,b) is the result of an experiment in a physical system.

No, P(a,b) is a mathematical function, which we interpret as giving a prediction for a particular outcome in a certain thought experiment.

[minkwe]

Bell's theorem is a theorem about physics not mathematics.

It's of course a theorem about mathematics (like any theorem; itself a mathematical term). Bell arrived at his conclusion without doing a single physical experiment. The theorem says that a certain class of mathematical models cannot produce a certain numerical result.

P(a,b) is the result of an experiment in a physical system.

No, P(a,b) is a mathematical function, which we interpret as giving a prediction for a particular outcome in a certain thought experiment.

A theorem can be formulated in mathematics, that doesn't mean it is a theorem about mathematics. Please understand the difference. Just because P(a,b) is a mathematical function does not mean it is not the result of an experiment in a physical system. You've just demonstrated why some mathematicians are incapable of doing physics. Next, you will claim from the left side of your mouth that locality is one of Bell's assumptions.

[Joy Christian]

The issue of counterfactual definiteness is a side issue. Whichever side wins in the debate about it will not affect the fact that Bell's theorem is a fundamentally flawed argument.

The flaw in Bell's theorem was pointed out by Einstein in the mid-1930s when Bell was hardly seven years old. It is so basic that it is mindboggling why it has not been recognized before.

The flaw has to do with the assumption of the additivity of expectation values in any derivation of a Bell-type inequality. That assumption is illegal for hidden variable theories of any kind, as pointed out by Einstein in the mid-1930s, and independently by Bell himself just before 1964, in the context of von Neumann's theorem against hidden variables.

And this is the point that mathematicians will never understand. Just because the additivity of expectation values follows by following mathematics does not mean that it is meaningful physically. Einstein saw that clearly, and so did Bell in the above-mentioned context. Consequently, what is ruled out by the Bell-test experiments is not local realism but additivity of expectation values --- which is not permissible for hidden variable theories to begin with. That is the sad end of the sordid saga of Bell's theorem: https://arxiv.org/pdf/1704.02876.pdf.

He now is making a very puzzling claim, that Bell correctly identified von Neumann's error (which is true) and then went on to commit the same silly mistake when formulating his theorem.

That is precisely what I am claiming. Just as von Neumann turned out not to be infallible, Bell too was not infallible.

The reason why Bell made the mistake is that he did not identify the additivity of expectation values as one of the assumptions on which the conclusion of his theorem inevitably depends.

By contrast, being a mathematician, von Neumann identified his assumption of the additivity of expectation values explicitly in the statement of his theorem --- see his premise B'. Because of the clear list of four explicit assumptions written down by von Neumann before proving his theorem, it was easy for several people, besides Einstein and Bell, to identify the faulty one.

Bell, on the other hand, was not a mathematician and his 1964 theorem does not have an explicit list of clearly stated assumptions. It is therefore difficult to understand what exactly is being assumed and proved in his theorem. The fumbling history of the defenders and antagonists of Bell's theorem is a testimony to this fact.

So, the first obligation of the proponents of Bell's theorem is to acknowledge that the additivity of expectation values is one of the implicit assumptions on which Bell's theorem depends.
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[Heinera]

A theorem can be formulated in mathematics, that doesn't mean it is a theorem about mathematics.

Any theorem is about mathematics by the very definition of the term.

Just because P(a,b) is a mathematical function does not mean it is not the result of an experiment in a physical system.

Actually performing any experiments is completely irrelevant to Bell's theorem. He certainly didn't perform any himself.

[Joy Christian]

Any theorem is about mathematics by the very definition of the term.

Bell's theorem is not a theorem at all. It is a word-salad.

And by the way, Heinera, I am still waiting for the bibliographical information on just one of your published papers on any subject. Don't take too long to supply that information here.
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[Heinera]

And by the way, Heinera, I am still waiting for the bibliographical information on just one of your published papers on any subject. Don't take too long to supply that information here.
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Google is your friend (and I've had none retracted, so they should still be there).

[Joy Christian]

And by the way, Heinera, I am still waiting for the bibliographical information on just one of your published papers on any subject. Don't take too long to supply that information here.
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Google is your friend (and I've had none retracted, so they should still be there).

I cannot find a single one by googling. I assume therefore that you have published none. Just as I thought.
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[Heinera]

And by the way, Heinera, I am still waiting for the bibliographical information on just one of your published papers on any subject. Don't take too long to supply that information here.
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Google is your friend (and I've had none retracted, so they should still be there).

I cannot find a single one by googling. I assume therefore that you have published none. Just as I thought.
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Well, I really can't take responsibility for your skills with Googling.

[Joy Christian]

And by the way, Heinera, I am still waiting for the bibliographical information on just one of your published papers on any subject. Don't take too long to supply that information here.
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Google is your friend (and I've had none retracted, so they should still be there).

I cannot find a single one by googling. I assume therefore that you have published none. Just as I thought.
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Well, I really can't take responsibility for your skills with Googling.

And you expect the readers to believe that? The fact is that you made an empty boast and have been caught out.
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[Heinera]

And you expect the readers to believe that? The fact is that you made an empty boast and have been caught out.
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Hahaha! First, I've never boasted about my handful of published papers; and second, there are at least ten others with the same name as me that has published (I guess a hundred papers between the lot of us), so you must really stink at googling.