Pitowsky’s Kolmogorovian Models and Super-determinism

Abstract

In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed “spin-https://static-content.springer.com/image/art%3A10.1007%2Fs10701-016-0049-0/MediaObjects/10701_2016_49_IEq1_HTML.gif functions” and later “Kolmogorovian models”, which employs a nonstandard notion of probability. We describe Pitowsky’s analysis and argue (with the benefit of hindsight) that his notion of hidden variables is in fact just super-determinism (and accordingly physically not relevant). Pitowsky’s first construction uses the Continuum Hypothesis. Farah and Magidor took this as an indication that at some stage physics might give arguments for or against adopting specific new axioms of set theory. We would rather argue that it supports the opposing view, i.e., the widespread intuition “if you need a non-measurable function, it is physically irrelevant”.