And this was even stranger. The news came from Causation: International Journal Of Science.

It claims to be peer reviewed scientific electronic journal.

The front page boasts exploding graphics with a title *Bell'stheorem …refuted!* in one inch letters .

Inside one finds two (!) peer reviewed papers by Ilija Barukčić:*Bell's theorem. A fallacy of the excludedmiddle* and

*Helicobacter pylori: the cause of human gastric cancer*. Perhaps not surprisingly, the Editorial Board consists of — you guessed: Ilija Barukčić!

But I was curious to see, if indeed, this recent work has resulted in a refutation of Bell theorem (making a lot of my own effort to prove it for myself - succesfully - useless and wrong).

I dug into the first article (which was quite cumbersome — as the text is really overfull of mathematical formulae, repeated endlessly). The conclusions of the author are really bold:

As proofed above, Bell's theorem is fallacious because of specifically logical reasons. The logic of Bell's theorem is not sound. Bell's theorem contradicts classical logic, it is based upon a fallacy. In so far either

Bell's theorem is valid or classical logic is valid but not both. Bell's theorem is not compatible with the law of the excluded middle, it is a fallacy of the excluded middle. Bell has committed the fallacy of the excluded middle, commonly referred to as a false dilemma. This logical fallacy is sometimes known also as a false correlative, an either/or fallacy, a bifurcation or as black and white thinking. Bell's formalisation of local realism, his starting point, is incorrect and is based on a logical contradiction. Bell's theorem, as a false dilemma fallacy, refers to a misuse of the law of the excluded middle. Bell has misapplied the law of excluded middle at an maximum. An extreme simplification, a wishful thinking and a misapplication of the law of the excluded middle is the foundation of Bell's theorem. In so far,**Bell's theorem is the most profound logical fallacy of science.**

Further, Bell's theorem is the definite and best proof known, that correlation analysis contradicts Quantum mechanics and Relativity Theory, that it is a useless and dangerous statistical machinery. Thus, as proofed above, Bell's theorem is refuted definitely, the book on Bell's theorem is completely losed.

Finally I got to the essence of the proof of refutation of Bells theorem. It may be found first on page 18 of the paper. I'll try to repeat here the most important step, taking the liberty of radically simplifying the notation. I ask the Reader to excuse the use of formulae here, but I think it is such a mathematical joke, that should be shared.

The Bell's theorem is given by Barukčić as:

( 1 − ( (1 − (A_{t} ) )· ( 1 − (Not A_{t} )) ) ) ≥( Not A_{t}) + ( Not C_{t} ) · ( ( A_{t} ) − (B_{t} ) ). (1) |

Let's simplify it by denoting the left and right side of equation:

( 1 − ( (1 − ( A_{t} ) )· ( 1 − (Not A_{t} )) ) ) = L (2) |

( Not A_{t}) + ( Not C_{t} ) · ( ( A_{t} ) − (B_{t} ) ) = R (3) |

This really helps, as there are really no operations on *L* and *R* in the `proofs'. Thus what we have is the inequality

L≥ R (4) |

What Barukčić aims at is a proof by *reductio ad absurdum*, i.e., he assumes the theorem to be true, and looks for logical discrepancies. There are four `proofs' and I'll present the first of them, quoting the author as much as it is possible (some substitutions and cuts are put in here, the Reader interested in details can check the original paper).

The term *R* can take the values 0 or 1. In so far, let us assume, that *R* = 0. We

obtain equation *L* ≥ (*R*=0).

It is generally accepted, that a ≥ b means that a = b or a > b, both are equally allowed and

possible, if the inequality is true. In so far, Eq. 1 is true, if L=0.

Eq. 1 is equally true if L > 0. In this case, let us **assume**^{1}, that

L = (R=0),

which satisfies Bell's inequality. On the other hand, Bell is respecting classical logic and thus the law of the excluded middle. The law of excluded middle in classical bivalent logic must yield L=1. Bell's inequality is respecting this law. We obtain

(L=1) = (R=0) (5) |

Bell's inequality leads to a logical contradiction, it not true that 1 = 0. Therefore, our original assumption, that Bell's theorem is correct is false.

This was the first of the four `proofs'. Of course, if one assumes to use equality and to use *R*=0 condition then one gets contradiction. But it is not the Bell theorem that `contradicts classical logic and leads to a logical contradiction' — it is the author himself.

1- Emphasis mine. There is no emphasis on this assumption in the original paper...

This document was translated from L^{A}T_{E}X byH^{E}V^{E}A.