gill1109 wrote:Certainly, the distinction between statistical independence, mathematical independence, and physical independence has confused readers and critics of Bell for all these long years, and still does. There are very interesting “metaphysical” analyses of when one kind of independence might imply another in recent works on Causality. I think of Judea Pearl’s “modern classic” (2nd edition) and of the new book on machine learning and causality by Jonas Peters et al, you can find a legal and free pdf on internet if you follow the links carefully. Both books even use the Bell-CHSH business as an example. They are both based on the modern theory of “graphical models” aka “Bayes nets”, a wonderful integration of computing, graphics, probability theory, and statistics. Lots and lots of money being made with them, too. I’ll try to add some links and exact references later.

I think these two books are pretty much essential reading for those interested in causality nowadays. Each includes the Bell-CHSH EPRB example as a short and elementary application of a much broader theory! Both have extensive discussions about causality in physics and about different kinds of independence and the relations between them.

Judea Pearl (2009) "Causality : Models, Reasoning, and Inference", *2nd edition*

http://bayes.cs.ucla.edu/BOOK-2K/

Ebook and paper both for sale, both worth every penny.

1st edition was (2000)

Jonas Peters, Dominik Janzing, and Bernhard Schölkopf (2017), "Elements of Causal Inference - Foundations and Learning Algorithms".

https://mitpress.mit.edu/books/elements-causal-inference

Open access free pdf available. Paper version is worth every penny.

Judea Pearl's son Daniel was the journalist of the Wall Street Journal captured and murdered by the Taliban in 2002.

https://en.wikipedia.org/wiki/Daniel_Pearl

Jonas Peters works in algebraic statistics as well as in causality and in machine learning

http://web.math.ku.dk/~peters/

For completeness, I'd like to mention some "unconventional" books on the foundations of logic and mathematics and hence also about causality. The first is by the well-known Bell-denier Ilija Barukčić

Theoriae causalitatis principia mathematica

Ilija Barukčić

https://books.google.nl/books/about/Theoriae_causalitatis_principia_mathemat.html?id=z28lDwAAQBAJ

Prolegomena to the Complete Physical and Mathematical Theory of Rational Human Intelligence

Leo Depuydt

https://www.amazon.com/Prolegomena-Complete-Physical-Mathematical-Intelligence/dp/1618961012

A Logic of Exceptions

Thomas Colignatus / Thomas Cool

http://thomascool.eu/Papers/ALOE/Index.html

http://thomascool.eu/