Wrong! There is no restriction. A counterfactual statement is simply a conditional statement in which the conditioning clause is actually false. It can be any kind of statement. For example:
"If I were a woman, then I won't be called Bill" is a counterfactual statement, and has nothing to do with a prediction or measurement. All that you need is for the condition/protasis to be *contrary to fact* -- ie, I am actually not a woman.
There can be no counterfactual statement about a measurement after the measurement has been made.
Wrong!
"If I had measured x, I will have obtained y" is a counterfactual statement so long as x was actually not measured. What classifies the statement as "counter-factual" is the fact that the condition/protasis/antecedent is contrary to fact, ie -- I did not measure x. It is obvious therefore that unless a measurement was actually made, you do not have any counterfactual statement, contrary to your claim. In other words, a measurement contrary to the protasis is required, in order to render the statement counterfactual. So you are woefully mistaken, not only can a counterfactual statement be made about a measurement after the measurement has been made, in the above example, it depends on the measurement having been made already.
After a measurement is made, it is factual, not counterfactual.
You are confused. After a measurement, the protasis may be true or false without changing the validity of the statement as whole. If the protasis is true, then the statement as a whole is not counterfactual, otherwise the statement as whole is counterfactual. A counterfactual statement is not the opposite of a factual statement since a counterfactual statement can also be factual.
There is no "if" involved.
Wrong again! You are separating the apodosis from the protasis and that is what is getting you confused. Note a counterfactual statement does not mean the statement is False. It simply means the protasis "If ..." is in fact false. A counterfactual statement can be a factual statement as well. Remember that "counterfactual" is describing the whole statement not parts of it. The truth value of the whole statement is different from the truth value of it's parts.
Let "If X is True, then Y is true" be the root statement under consideration.
The counterfactual statement (in the situation in which X is in fact False) is then:
"If X were True, then Y would be true".
Three different facts are involved:
1) X is True
2) Y is True
3) (X=True) implies (Y=True)
The counterfactual statement only makes claims about statement (3) ie, the relationship between the truth values of X and Y. (3) can be True even if X is false. Just because X is false, does not mean the relationship between the truth value of X and that of Y is not as claimed in statement (3).
Counterfactual definiteness means that the counterfactual statement may be used as if it were factual.
Exactly. But you are confused because you assume that if the counterfactual statement is factual, it means the all parts of it are individually factual. Which is naive and I have been trying to point out to you. Statement (3) above encapsulates a different "fact" from statements (1) and (2). (1) encapsulates the truth value of X, (2) encapsulates the truth value of Y, (3) encapsulates the relationship between the truth values of X and Y. The third fact does not care whether X or Y are true or false. All it cares about is the relationship between their truth values. The counterfactual statement makes that even more apparent by making the claim even when it is a fact that X is false. A counterfactual statement does not mean the whole statement is contrary to fact. It simply means the condition/protasis/antecedent is contrary to fact not the whole statement.
To reject CFD is not to declare a counterfactual statement false, it is to render its truth value null.
This is nonsense. What does it mean to for the truth value of a statement to be null? There is no such thing. A statement is either True or False, there is no middle ground. You are trying to sneak in a third "null" option.
"If Bob had set his detector to A he would have measured X" is a counterfactual statement. To reject CFD is not to declare that it was false pre-measurement, it is to declare that it has no standing post-measurement.
Again this is nonsense. What does it mean for a statement to have "no standing". You are simply inventing on-the-fly ways of describing statements. Apparently you are finding it even more difficult to "reject CFD" or even explain what you mean by "reject CFD" -- which means you at least understand some of what I have been explaining.
I cannot think of any more ways to express it right now. I dislike semantic arguments, so, for the sake of this argument, I will call this concept whatever you wish, like RAPCFD and you can define counterfactual and CFD to your liking, call it BILLCFD Just so long as we are clear on definitions, I don't care what name tag a concept is wearing. I am curious as to why RAPCFD is nonsensical?
I have already explained above. But RAPCFD is nonsensical because if you define CFD such that the statement's truth value changes upon measurement from true to "null" (whatever that means), and the only part of the statement which was actually affected by the measurement was the protasis/antecedent/conditioning clause, then you are saying the relationship between the truth values of the protasis and the apodosis depends on the individual truth value of the protasis. Which is illogical.
You cannot perform such an experiment - that is exactly what makes them counterfactual, by definition. To assume RAPCFD is to say that those counterfactual correlations can be used AS IF they were factual. This is what must be done to obtain the Bell paradox, and then go about resolving it with superluminal action at a distance, non-locality, etc.
But if the QM predictions result in violation then according to the above, they are also not "factual"!? So by rejecting RAPCFD, you are rejecting QM as well. However, as I have explained over and over, the problem with Bell inequalities is not because the correlations are not factual. You still haven't understood the difference between a statement being "True"/"Factual" and a statement being "Actual". That is why I spent a lot of time trying to point to you the error in your view about the meaning of CFD because this misunderstanding is at its root.
What must be done to obtain Bell paradox is to use correlations which although all "factual", cannot all be simultaneously "actual". Just because a statement is factual does not mean it can be used in Bell's inequalities. This is the origin of the violation. The inequalities represent relationships between ACTUAL correlations since they are derived from the perspective of an omniscient being who has knowledge of them without needing any measurements. However, those ACTUAL correlations can never be measured because only pairs can be measured in any actual experiment.
If you take anything at all out of this discussion it should be this:
"Everything that is actual is factual, but not everything that is factual is actual" In this statement lies all of your misunderstanding, that the explanation for the violation of Bell's inequalities. When QM makes predictions about P(a,b), P(b,c), P(a,c), each of those predictions is accurate/factual/True. But only one of those can be actual at a given moment. It is therefore a logical error to take all those terms and use them simultaneously in the same expression which was based on three
actual correlations. QM can not give you three actual correlations because it is impossible to measure them. This is the origin of the violation. It has nothing to do with "realism" or "locality" whatsoever.