Some people do not understand Counterfactual Definiteness

[gill1109]

Your question does not make any sense to me, sorry.

https://arxiv.org/pdf/1207.5103.pdf "Statistics, Causality and Bell's theorem", you reveal this deficiency very cleary:

In a nut-shell, the inequality is an empirically verifiable consequence of the idea that the outcome of one measurement on one system cannot depend on which measurement is performed on the other. This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

I think you understand the question very well, you just don't want to answer.

It’s Christmas Eve and I’m busy with my family. We haven’t been near to our children and grandchildren for a year. I shall be delighted to figure out what you are saying with your coin example, but maybe it will only be in a few days from now.

Please explain what you mean by your question which of three correlations is counterfactual. Honestly, it makes no sense to me. What context do you want me to understand, for those correlations? Three correlations measured separately could in principle be anything. But three correlations of a particular mathematical form can’t necessarily be anything. For instance, if there are functions A and B and a probability distribution rho such that ... then there are constraints on those correlations. See Boole (1853), end of Section 11 of Chapter XIX, where the general method of that chapter is applied to Example 7, Case III of Chapter XVIII. George Boole, founder of modern logic and probability theory, shows that in the three correlations situation the six one-sided three-correlation Bell (1964) inequalities are necessary and sufficient for existence of the counterfactual variables which local realism (as formulated by Bell) allows mathematically to be constructed. See https://www.gutenberg.org/files/15114/15114-pdf.pdf (Boole, 1853) and https://arxiv.org/pdf/2012.00719.pdf (Gill and Karakozak, 2020).

It’s true that many people do not understand counterfactual definiteness.

[gill1109]

I think a discussion about the meaning of Counterfactual Definiteness (CFD) is badly needed. Like many other concepts such as "randomness", "locality", "realism". etc, the concept of "counterfactual definiteness" (CFD) has been bastardized by many in the quantum foundations community. One of the reasons nobody understands QM is because the meanings of words are free for all. It's the wild-wild west and don't even get me started about "virtual" particles. A careful look at CFD will reveal that it does not mean what most people in the Bell community mistakenly think it means.

In discussions about the foundations of quantum physics, “counterfactual definiteness” is a term which has been used for a long time by the community of scholars in this area with a very definite meaning. Moreover, it is generally agreed that Bell’s theorem states that quantum mechanics is incompatible with locality + counterfactual definiteness + no conspiracy.

Counterfactual definiteness means, in discussions of Bell’s theorem, that measurements which are not performed also have outcomes. The act of measurement merely reveals a property which was already there. Wikipedia has an article on the topic. It cites numerous published papers by respected scientists and academics, and I think it shows that the “Bell community” is a community - people are using those two words in a consistent way, independently of what they think of the theorem; independently of their view on quantum foundations and interpretations. https://en.m.wikipedia.org/wiki/Counterfactual_definiteness

[gill1109]

2. Let the three mathematical relations between Bell's equations (14) and (15) be, respectively: (14a), (14b), (14c).

3. Then Bell's error is his move from (14a) to (14b).

The contradiction is present even on the left-hand side of 14a.

P(a,b) - P(a,c) = "The correlation obtained if Alice and Bob measure at settings (a,b)" - "The correlation obtained if Alice and Bob measure at settings (a,c)"

The two terms contain contradictory premises. If Alice and Bob measured at (a,b) then they did not measure at (a,c). P(a,c) is counterfactual to P(a,b). The antecedents are contradictory therefore the combination of terms does not make physical sense since there is no universe in which True is False.

Sorry, this is nonsense.

Suppose last year, a loaf of bread cost 75 cent. This year it costs 90 cents. I say: a loaf of bread has got 15 cents more expensive. Michel says you can’t sell the same loaf of bread at two different times a year apart. The antecedents are contradictory. The combination of terms does not make physical sense because there is no universe in which True is False. I say b******t man, bread has got more expensive while my pension is going down and taxation is going up.

Comparing those two correlations does not presuppose that Alice and Bob did two measurements at the same time. Comparing them was done by Bell in order to show that certain physical assumptions had observable consequences. So one can check those physical assumptions by finding out if their necessary consequence was true or false.

In this case, Bell asked whether functions A and B, and a probability distribution of the underlying microscopic state lambda of all the particles making up the detectors, the source, and the transmission lines between them, could exist such that ... . He showed that those assumptions would entail consequences for the possible observed correlations. He showed that according to QM it might be possible to “escape” those consequences.

[minkwe]

https://arxiv.org/pdf/1207.5103.pdf "Statistics, Causality and Bell's theorem", you reveal this deficiency very cleary:

In a nut-shell, the inequality is an empirically verifiable consequence of the idea that the outcome of one measurement on one system cannot depend on which measurement is performed on the other. This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

5) You admit in your paper that Bell's inequalities are formulated using outcomes of measurements that are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

[FrediFizzx]

https://arxiv.org/pdf/1207.5103.pdf "Statistics, Causality and Bell's theorem", you reveal this deficiency very cleary:

In a nut-shell, the inequality is an empirically verifiable consequence of the idea that the outcome of one measurement on one system cannot depend on which measurement is performed on the other. This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

5) You admit in your paper that Bell's inequalities are formulated using outcomes of measurements that are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

You're mistaken if you think you are going to get a straight answer from Blah! Blah! Blah! Gill. He is just going to bore us to death until you give up or it's forgotten.
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[gill1109]

https://arxiv.org/pdf/1207.5103.pdf "Statistics, Causality and Bell's theorem", you reveal this deficiency very cleary:

In a nut-shell, the inequality is an empirically verifiable consequence of the idea that the outcome of one measurement on one system cannot depend on which measurement is performed on the other. This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

5) You admit in your paper that Bell's inequalities are formulated using outcomes of measurements that are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

No, I can’t. One does not “perform” a term of an expression.

The derivation of that inequality is done under some assumptions, of existence of a variable called lambda, and of functions called A and B, and it involves the expressions A(a, lambda) = - B(a, lambda), A(b, lambda) = -B(b, lambda), A(c, lambda) = -B(c, lambda).

These represent the outcomes which would have been observed, had Alice used settings a, b or c; and the negatives of the outcomes Bob would have observed, had Bob used settings a, b, or c. The derivation of the inequality you mention does not assume that Alice or Bob actually do anything at all. It does assume determinism, and locality. It assumes that some deterministic evolution of the entire physical system under study takes place, such that a measurement outcome is a deterministic function of the state of the entire system being studied. Part of the description of the state is the list of positions and momenta of all the particles involved at some initial time point prior to the choice of settings by Alice and Bob. Then they each press a button selecting a setting. Then a short time later pieces of paper are printed with “+1” or “-1” written on them.

People in the philosophy of science, perhaps starting with Henry Stapp in 1971, have been using the word “counterfactual definiteness” to describe this state of affairs. As everyone knows, and as EPR in particular discussed, quantum physics does not describe in a fine-grained way “what would happen if” you chose to measure the position, or the momentum, of some particle. It denies that a particle “has position” or “has momentum”.

It seems that people nowadays have become so used to the (in the 1920s) new dogmas of quantum mechanics that they have totally forgotten that physics had been dominated for several hundred years by the dogmas of Newtonian mechanics. That science had been incredibly successful and led to the machines and engineering feats of the 19th century, it led to the idea that physics was essentially finished. There were just a few small anomalies or puzzles left to be sorted out.

The optimism was shattered on the one hand by the horrors of the First World War, and on the other hand by the new physics of Schrödinger, Heisenberg, Bohr and Einstein.

[FrediFizzx]

https://arxiv.org/pdf/1207.5103.pdf "Statistics, Causality and Bell's theorem", you reveal this deficiency very cleary:

In a nut-shell, the inequality is an empirically verifiable consequence of the idea that the outcome of one measurement on one system cannot depend on which measurement is performed on the other. This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

5) You admit in your paper that Bell's inequalities are formulated using outcomes of measurements that are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

No, I can’t. One does not “perform” a term of an expression. ...

OMG! Blah! Blah! Blah! If one of the terms is performed the other two aren't performed.
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[FrediFizzx]

You admit in your paper that Bell's inequalities are formulated using outcomes of measurements that are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

No, I can’t. One does not “perform” a term of an expression.

OMG! Blah! Blah! Blah! If one of the terms is performed the other two aren't performed.

One does not “perform” a correlation. You can compute one if you have a theory which tells you what it should be; you can measure one, if you can perform a suitable experiment. Either way, assumptions/context are necessary.

In present day Bell-CHSH experiments, four correlations are calculated from one long experimental run. In each “trial” in the run of, say, N trials, Alice and Bob each choose, by tossing a fair coin, between one of two settings, and each gets to observe a binary measurement outcome. They end up with an Nx4 spread sheet with columns named, say, A, B, X and Y. The A and B columns contain labels ‘1’ and ‘2’ in completely random order. The X and Y columns are filled with +/-1’s.

[FrediFizzx]

You admit in your paper that Bell's inequalities are formulated using outcomes of measurements that are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

No, I can’t. One does not “perform” a term of an expression.

OMG! Blah! Blah! Blah! If one of the terms is performed the other two aren't performed.

One does not “perform” a correlation. ...

So, you are sticking to that boring stupid nonsense? Blah! Blah! Blah! You know what Michel means.
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[gill1109]

You admit in your paper that Bell's inequalities are formulated using outcomes of measurements that are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

Let me try again.

In Bell’s derivation of , Bell is assuming a deterministic local hidden variables theory, according to which P(a, b) is the integral over lambda of A(a, lambda) times B(b, lambda) with respect to a probability measure rho over values of lambda. In that integral expression, A(a, lambda) is generally called (by scholars in the foundations of quantum physics) a counterfactual variable, since it represents the outcome which Alice would observe if she were to use setting a, when the initial micro state of the joint system of detectors and source and transmission lines is given by the element lambda of some huge space Lambda. Similarly for B(b, lambda) and for the ingredients in the other two theoretical correlations. Notice that lambda is the assumed fine-grained specification of relevant parts of a huge physical system at some initial time point before anything happens at all. “A” is some function. “a” is a possible setting which later could be introduced at one end of that system, from outside.

“Counterfactual definiteness” used to be more or less just a fancy name for “determinism”. Later, with the transition from Bell 1964 to CHSH 1969, people understood that stochastic hidden variable models would allow more generality and moreover would allow experimental verification. That means that local randomness is allowed - randomness inside microscopic subsystems, independently at different locations in space. One arrives at a model of physical space as a stochastic cellular automaton. Think of Conway’s game of Life with rules extended to allow local independent coin toss decisions. You can imagine all possible needed coin tosses being performed in advance. A stochastic model becomes a deterministic model. Remember, in Kolmogorov probability, a real-valued random variable is represented by a deterministic function X from a space Omega to the real numbers. Probability is spread over Omega.

[FrediFizzx]

You admit in your paper that Bell's inequalities are formulated using outcomes of measurements that are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

Let me try again. ... (boring known stuff snipped out)

You still didn't answer the question though it seems that you are saying all the term are not performed. Sounds like nonsense to me.
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[minkwe]

You admit in your paper that Bell's inequalities are formulated using outcomes of measurements that are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

Let me try again. ... (boring known stuff snipped out)

You still didn't answer the question though it seems that you are saying all the terms are not performed. Sounds like nonsense to me.
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It is nonsense indeed. Looks like Richard doesn't want to answer. He prefers to talk about the First World War, and 10 other off-topics instead. So I won't bother responding to those posts until he answers this question, the answer to which he knows well, having implied it in his papers. But let me make it even more difficult to dodge. Here is Bell's equation 14b in full.



Richard says in his paper:

its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

Clearly, Richard is saying here that there are outcomes of measurements not actually performed which are assumed to exist alongside outcomes of measurements actually performed.

In response to earlier questioning, he clarified that by "exist", he wasn't talking about the real-world, just "exist" in a mathematical sense. So my question to Richard remains. He needs to point out which terms represent outcomes from performed measurements and which represent outcomes from non-performed measurements in Bell's 14a.

[minkwe]

While waiting for Richard to finally answer the question. Here is an interesting article on the subject for the other interested parties to check out:

https://arxiv.org/pdf/1605.04889.pdf

Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that is not only commensurate with classical physics (as for example Einstein’s special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell’s choice of mathematical functions and independent variables implicitly includes counterfactual definiteness and reduces the generality of the physics of Bell-type theories so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.

[gill1109]

Clearly, Richard is saying here that there are outcomes of measurements not actually performed which are assumed to exist alongside outcomes of measurements actually performed. In response to earlier questioning, he clarified that by "exist", he wasn't talking about the real-world, just "exist" in a mathematical sense. So my question to Richard remains. He needs to point out which terms represent outcomes from performed measurements and which represent outcomes from non-performed measurements in Bell's 14a.

I think I already answered this. I wrote: The derivation of that inequality is done under some assumptions: of existence of a variable called lambda, and of functions called A and B, and it involves the expressions A(a, lambda) = - B(a, lambda), A(b, lambda) = -B(b, lambda), A(c, lambda) = -B(c, lambda). These represent the outcomes which would have been observed, had Alice used settings a, b or c; and the negatives of the outcomes Bob would have observed, had Bob used settings a, b, or c. The derivation of the inequality you mention does not assume that Alice or Bob actually do anything at all. It does assume determinism, and locality. It assumes that some deterministic evolution of the entire physical system under study takes place, such that a measurement outcome is a deterministic function of the state of the entire system being studied, together with the locally introduced setting. Part of the description of the state is the list of positions and momenta of all the particles involved at some initial time point prior to the choice of settings by Alice and Bob. Then they each press a button selecting a setting. Then a short time later pieces of paper are printed with “+1” or “-1” written on them.

Transitioning and generalising to the CHSH situation, according to the model, if Alice actually does choose to use setting “a”, she’ll get to see the outcome A(a, lambda), whereas if she had used a’, she would have seen A(a’, lambda). Similarly for Bob. If he tosses a coin to use setting b or b’, he’ll get to see B(b, lambda) or B(b’, lambda). (We no longer assume perfect anticorrelation at equal settings, so no relationship between the functions A and B is assumed). But anyway, alongside of the actually observed outcomes belonging to the actually chosen settings, there are also defined the counterfactual outcomes which would have been observed, had the other setting been chosen.

You are free to find these assumptions stupid. Anyway, it turns out that they conflict with quantum mechanics, so if you believe quantum mechanics, and the experiments which confirm it, you had better abandon them.

I don’t see what the problem is. Bell makes some assumptions which you don’t like, and under those assumptions, derives consequences which are contradicted by experiment. Niels Bohr would have been bored. David Bohm was delighted. But Einstein would have been deeply disturbed.

Regarding the paper by Karl Hess, Hans de Raedt and Kristen Michielsen https://arxiv.org/abs/1605.04889
Counterfactual Definiteness and Bell's Inequality;
Abstract: Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that is not only commensurate with classical physics (as for example Einstein's special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell's choice of mathematical functions and independent variables implicitly includes counterfactual definiteness and reduces the generality of the physics of Bell-type theories so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.

Unfortunately these folk don’t understand much. They think that there are big problems concerning time in Bell experiments. However they are wrong. We could start a new topic and I would be happy to point out the misunderstandings and self-contradictions in this paper which I see rather easily. It seems that they want to assume dependence between the experimenters’ setting choices and the microvariables describing the physical system of source and detectors. Indeed, Bell’s theorem assumes that settings can be chosen freely. These folk apparently believe in superdeterminism. Bell’s theorem is correct, as a mathematical theorem; they avoid its consequences by violating “no-conspiracy”. They *do* believe in local realism, in determinism.

The paper was originally submitted by Karl Hess to the journal PNAS. He’s a member of the US Academy of Sciences, and hence has the prerogative of getting things published there, despite negative referee reports. But the paper finally appeared elsewhere. It has by now been cited 11 times, mainly by the authors themselves. It seems that not many people understand (or agree with) what the authors are saying. Perhaps Michel would like to expound their point of view in a new thread.

[minkwe]

I think I already answered this. I wrote: The derivation of that inequality is done under some assumptions: of existence of a variable called lambda, and of functions called A and B, and it involves the expressions A(a, lambda) = - B(a, lambda), A(b, lambda) = -B(b, lambda), A(c, lambda) = -B(c, lambda). These represent the outcomes which would have been observed, had Alice used settings a, b or c; and the negatives of the outcomes Bob would have observed, had Bob used settings a, b, or c. The derivation of the inequality you mention does not assume that Alice or Bob actually do anything at all.

Richard, you are trying very hard but failing still. For some reason, you are avoiding your own statements in your paper. You mentioned something existing alongside something else. The two things you claimed existed alongside each other were

1) outcomes of measurements that are not actually performed
2) outcomes of those actually performed

Yet despite repeated questioning, you are unable to explain what you meant by that, which means either you don't understand Counterfactual Definiteness or you are more focused on trying to avoid a perceived trap than answering honestly.

More evidence from your paper that you are dodging and trying to run away from your own paper:

Under realism we can imagine, for each run, alongside of the outcomes of the actually measured pair of variables, also the outcomes of the not measured pair. Under locality, the outcomes in Alice’s wing cannot depend on the choice of which variable is measured in Bob’s wing. Thus, for each run there is a suite of potential outcomes A, A', B and B', but only one of A and A', and only one of B and B' actually gets to be observed. By freedom, the choices are statistically independent of the actual values of the four. I will assume furthermore that the suite of counterfactual outcomes in the j-th run does not actually depend on which particular variables were observed in previous runs.
...

We must first agree that though, say, only A and B are actually measured in one particular run, still, in a mathematical sense, A' and B' also exist (or at least may be constructed) alongside of the other two; and moreover, they may be thought to be located in space and time just where one would imagine.

[minkwe]

The paper was originally submitted by Karl Hess to the journal PNAS. He’s a member of the US Academy of Sciences, and hence has the prerogative of getting things published there, despite negative referee reports. But the paper finally appeared elsewhere. It has by now been cited 11 times, mainly by the authors themselves. It seems that not many people understand (or agree with) what the authors are saying.

It sounds like you are gloating about some "accomplishment". I already know what you did so stay on topic.

[gill1109]

I think I already answered this. I wrote: The derivation of that inequality is done under some assumptions: of existence of a variable called lambda, and of functions called A and B, and it involves the expressions A(a, lambda) = - B(a, lambda), A(b, lambda) = -B(b, lambda), A(c, lambda) = -B(c, lambda). These represent the outcomes which would have been observed, had Alice used settings a, b or c; and the negatives of the outcomes Bob would have observed, had Bob used settings a, b, or c. The derivation of the inequality you mention does not assume that Alice or Bob actually do anything at all.

Richard, you are trying very hard but failing still. For some reason, you are avoiding your own statements in your paper. You mentioned something existing alongside something else. The two things you claimed existed alongside each other were

1) outcomes of measurements that are not actually performed
2) outcomes of those actually performed

Yet despite repeated questioning, you are unable to explain what you meant by that, which means either you don't understand Counterfactual Definiteness or you are more focused on trying to avoid a perceived trap than answering honestly.

More evidence from your paper that you are dodging and trying to run away from your own paper:

Under realism we can imagine, for each run, alongside of the outcomes of the actually measured pair of variables, also the outcomes of the not measured pair. Under locality, the outcomes in Alice’s wing cannot depend on the choice of which variable is measured in Bob’s wing. Thus, for each run there is a suite of potential outcomes A, A', B and B', but only one of A and A', and only one of B and B' actually gets to be observed. By freedom, the choices are statistically independent of the actual values of the four. I will assume furthermore that the suite of counterfactual outcomes in the j-th run does not actually depend on which particular variables were observed in previous runs.
...

We must first agree that though, say, only A and B are actually measured in one particular run, still, in a mathematical sense, A' and B' also exist (or at least may be constructed) alongside of the other two; and moreover, they may be thought to be located in space and time just where one would imagine.

Michel, suppose Alice actually chooses to insert setting a, and Bob b. They do this by the tosses of two coins. They could have chosen a’ and b’. Then A(a, lambda) and B(b, lambda) are the outcomes they actually observe. A(a’, lambda) and B(b’, lambda) are the outcomes they would have observed, had their coin tosses fallen differently.

What is the problem here?

Even Hess, de Raedt and Michielsen all believe in counterfactual definiteness, because they believe in determinism. They understand Bell’s proof, very well. They escape from it by supposing some kind of superdeterminism. They think the outcomes of the measurements are also determined by the exact times at which they are actually performed, over which Alice and Bob have no control. So apparently the quantum correlations are determined by correlations in microscopic delays or inaccuracies in the exact times at which Alice and Bob press those buttons on their devices. Unbeknown to them, they not only set a switch depending on the outcome, H or T, of a coin toss, but the correlations between the trembling in their trembling fingers introduces further correlations between the measurement outcomes, which thereby violate the Bell (Vorobev, Bass, Boole... limits).

They don’t actually have any physical theory of why these micro inaccuracies in time are so strongly correlated. But yes, mathematically that is a way out. I personally don’t find it physically very interesting or fruitful. But I’m a mathematician, not a physicist.

What I can say is that I haven’t noticed any important physics research groups following up on these ideas, either with experiment or actual theory.

But who knows. Maybe this is just the silence before the storm. Somewhere, some young genius has read that paper by Hess et al., and is figuring out how to restore determinism and locality to physics.

[FrediFizzx]

I think I already answered this. I wrote: The derivation of that inequality is done under some assumptions: of existence of a variable called lambda, and of functions called A and B, and it involves the expressions A(a, lambda) = - B(a, lambda), A(b, lambda) = -B(b, lambda), A(c, lambda) = -B(c, lambda). These represent the outcomes which would have been observed, had Alice used settings a, b or c; and the negatives of the outcomes Bob would have observed, had Bob used settings a, b, or c. The derivation of the inequality you mention does not assume that Alice or Bob actually do anything at all.

Richard, you are trying very hard but failing still. For some reason, you are avoiding your own statements in your paper. You mentioned something existing alongside something else. The two things you claimed existed alongside each other were

1) outcomes of measurements that are not actually performed
2) outcomes of those actually performed

Yet despite repeated questioning, you are unable to explain what you meant by that, which means either you don't understand Counterfactual Definiteness or you are more focused on trying to avoid a perceived trap than answering honestly. ...

Yeah, ya get Bell fans to about this point in the debate and then they start choking on their own nonsense. Doubtful that you will ever get a straigt answer from them.
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[FrediFizzx]

While waiting for Richard to finally answer the question. Here is an interesting article on the subject for the other interested parties to check out:

https://arxiv.org/pdf/1605.04889.pdf

Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that is not only commensurate with classical physics (as for example Einstein’s special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell’s choice of mathematical functions and independent variables implicitly includes counterfactual definiteness and reduces the generality of the physics of Bell-type theories so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.

That is what we have been saying all along. It is impossible for there to be conterfactual outcomes of the other two setting pairs because they can't happen at the same time. The Bell fans only response is that they don't have to happen at the same time. Completely laughable.
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[gill1109]

I think I already answered this. I wrote: The derivation of that inequality is done under some assumptions: of existence of a variable called lambda, and of functions called A and B, and it involves the expressions A(a, lambda) = - B(a, lambda), A(b, lambda) = -B(b, lambda), A(c, lambda) = -B(c, lambda). These represent the outcomes which would have been observed, had Alice used settings a, b or c; and the negatives of the outcomes Bob would have observed, had Bob used settings a, b, or c. The derivation of the inequality you mention does not assume that Alice or Bob actually do anything at all.

Richard, you are trying very hard but failing still. For some reason, you are avoiding your own statements in your paper. You mentioned something existing alongside something else. The two things you claimed existed alongside each other were

1) outcomes of measurements that are not actually performed
2) outcomes of those actually performed

Yet despite repeated questioning, you are unable to explain what you meant by that, which means either you don't understand Counterfactual Definiteness or you are more focused on trying to avoid a perceived trap than answering honestly. ...

Yeah, ya get Bell fans to about this point in the debate and then they start choking on their own nonsense. Doubtful that you will ever get a straight answer from them.
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Fred, I wrote:

Michel, suppose Alice actually chooses to insert setting a, and Bob b. They do this by the tosses of two coins. They could have chosen a’ and b’. Then A(a, lambda) and B(b, lambda) are the outcomes they actually observe. A(a’, lambda) and B(b’, lambda) are the outcomes they would have observed, had their coin tosses fallen differently.

I think that that was a very straight answer to Michel. Anyway, why don’t you wait to hear whether or not he is satisfied?

Fred also wrote

That is what we have been saying all along. It is impossible for there to be conterfactual outcomes of the other two setting pairs because they can't happen at the same time. The Bell fans only response is that they don't have to happen at the same time.

If you have a local hidden variables model, and Alice chooses setting a, but not a’, then according to that model she observes A(a, lambda). She doesn’t observe A(a’, lambda). But both functions of lambda do exist. Both of those two numbers exist. “A” is a function. “lambda” is an element of some set. “a” and “a’” are elements of another set. “A(a, lambda)” and “A(a’, lambda)” are elements of the set {-1, +1}.