This is a very short course in logic for those who like to use the Socratic method in leading believers to see the falsity of theism. Even such a small course as this will prove helpful, for it is the very basis, the foundation of, logical discourse.

In your questioning of theists in order to lead them to the realization that theism has no basis in reality always remember, and when possible, utilize the three laws of logic, in establishing the truth or falsity of a thing.

What are the three laws of logic ? They are as follows.

(1) The Law of Identity, which states that something is itself, and not something else. The term being used corresponds and coincides with the thing being described.

(2) The Law of Non-contradiction. This law develops more fully the first law, in that it teaches that the thing being described in the first law cannot be both itself and not itself at the same time and in the same sense.

(3) The Law of the Excluded Middle. This final law says that a thing must be either true or false, it cannot be both. In other words, there is no middle ground. In other words, as an example, a woman cannot be a little pregnant.

Christians have tried to sneak in a fourth law, called the Law of Sufficient Cause. This is not one of the true laws of logic, there are only three, the three enumerated above. The purpose of this spurious fourth law is meant only to justify the existence of God as the sufficient cause of the universe.

So, there you have it. In using your Socratic questioning it would be only helpful to remember these three laws in establishing the truth or falsity of a thing.

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I understand that, and it is not incompatible with what I am saying.

that is not incompatible with what I am saying.

Why do you think that?  If there's a hidden "rule" then the hidden rule gives you a hidden variable. 

An explanation of Bell's theorem.

I've read that article 3 times just to be sure, and I could find nothing to contradict what I've been saying. There is a link within that attempts to challenge the specific details of Bohr's model, but does not challenge the idea of non-local hidden variables, which I have said before might be impossible to challenge--it might be metaphysical. Your site attempts to refute cellular automata by calling it a local variable (from that the cells only affect their nearest neighbors), but it is the rule which is not dependent on any state of cells that makes it deterministic, which is non-local. You cannot tell what the rule is from observing the cells, thus observation appears indeterministic.

I do not hold that there must be non-local hidden variables, but that science so far cannot disprove the possibility.

It is not likely that Leibniz could have conceived of your example at the time he wrote.

Bell's inequality is just a logical fact.  It says that if you have a collection of objects which can either have or not have properties A,B, C, then

number (A and not B) + number(B and not C) >= number(A and not C). 

In the case of two spin 1/2 particles going off in opposite directions, with total spin of zero, you can take the properties to be "particle 1 has spin up in direction A", "particle 1 has spin up in direction B", etc. 

Experiments have been done which show that Bell's inequality is violated with entangled particles, meaning they do NOT have a definite spin before they are measured. 

A particle can have a property without that property being measurable.  This is true in standard quantum mechanics as well.  A particle could have a definite spin in direction A, and you can't determine what direction A is, unless you already know direction A so you can measure the spin in that direction. 

So how does the "cellular automata" idea manage to account for the experimental contradictions to Bell's inequality? 

From a bit of looking, it seems that Plamen Petrov, a proponent of the "cellular automata" idea, constructed a toy system that is super-deterministic and appears to violate Bell's inequality, because the observer's choices are also determined. 

Bell's theorem assumes that the observer has a choice of which direction to measure the particle spin. 

But if the direction the observer chooses to measure the particle spins is correlated somehow with the actual particle spins - you might be able to generate an apparent violation of Bell's inequality. 

However, Bell argued that super-determinism is implausible because

Even if the measurements performed are chosen by deterministic random number generators, the choices can be assumed to be "effectively free for the purpose at hand," because the machine's choice is altered by a large number of very small effects. It is unlikely for the hidden variable to be sensitive to all of the same small influences that the random number generator was.

That seems sensible to me. 

I am proposing Wolfram's idea of cellular automata (and Dan Dennett's) due to the metaphysical possibility of a nonlocal hidden variable, which is palpable from a philosophical perspective, if not scientific, and I admit that it might not be scientifically compatible. But let's look at the argument presented above: it's infinitely regressive. For if a measured electron is deterministic because the observer lacks a choice, then it could be also said that all the small effects are deterministic because their observers lack a choice, and so forth.
And we must be mindful, for the purposes of clarity, that QM does not prove human free will, neither does it seem to have much apoarent effect on the macro world. Classical physics, though ultimately incorrect, is still reliable for measuring all macro interactions, despite the "randomness" of QM.

metaphysical possibility of a nonlocal hidden variable

QM already has a sort of nonlocal hidden variable - the entangled state. 

if a measured electron is deterministic because the observer lacks a choice

That's not what I said.  I said you can produce a toy model that violates the Bell inequality if the observer doesn't have a free choice of what measurement to make.  But as Bell said, that seems an implausible way for reality to work. 

How would you generate the observed experimental results that violate the Bell inequality, without quantum randomness OR free choice by the observer? 

palpable from a philosophical perspective, if not scientific

Many quantum states can't be completely known, anyway. 

Your idea about a deterministically evolving reality ("cellular automata") does seem to involve local hidden variables.  Which are disproved by the experiments showing violations of Bell's inequality. 

I don't see how cellular automata requires any local variables for the reasons stated above, but more importantly, free will isn't necessary for action. Calling it an unrealistic toy model is... well... not a serious argument at all.

Again, how would you generate the observed experimental results that violate the Bell inequality, without quantum randomness and WITH free choice by the observer?

Calling it an unrealistic toy model is... well... not a serious argument at all.

I said that Plamen Petrov came up with a toy model that violates the Bell inequality because of "superdeterminism" - the choice of measurement is determined as well.  Take a look at the discussion I linked to, above, for more on that. 

Are you asking without randomness OR free choice, or without randomness and WITH free choice? Since I've answered the former, I will now answer the latter. Wolfram's cellular automata allows either no randomness and free choice, or both randomness and free choice. On the surface of it if we examine the various states of the cells, there appears to be patterns which could not be determined, hence it becomes conceivable that the world is as scientists describe. But at the root of the structure is a rule that determines everything else. The mathematical rule could be said to be the metaphysical nature of the universe, contained in all things.

Now, I do not necessarily subscribe to metaphysics, I only make the following point: quantum randomness does not at all demonstrate that a past recorded value could have been any other value--in fact, why don't we shift to Plamen Petrov's argument since that seems easier, now, to defend...

Trying to make this concrete:

Suppose you have these two spin 1/2 particles flying apart, with total spin zero, and according to QM, each one has indefinite spin. 

You don't like quantum randomness - so would you like each particle to have a definite spin when they separate?

This isn't what happens, as has been shown in experiments.

If each particle has a definite spin, the results of measurements on the particles would have to obey Bell's inequality. 

However, experimentally, Bell's inequality has been found to be violated.  This means that the particles do NOT have a definite spin when they separate.

They do not even have a "metaphysically definite" spin or a "philosophically definite" spin, in your lingo. 

This problem can be avoided if you assume the experimenter's measurement choices are determined.  However, it seems implausible that the experimenter's measurement choices are determined in such a way that Bell's inequality is only apparently violated. 

SO, what do you suggest as an alternative to quantum randomness, in this situation?  If the experimenter can make measurement choices? 

why don't we shift to Plamen Petrov's argument

That was only with a toy model. 



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