In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed “spin- 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”.

中文翻译：

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Pitowsky 的 Kolmogorovian 模型和超决定论

为了证明局部隐藏变量在数学上是可能的，Pitowsky 构建了“自旋函数”和后来的“Kolmogorovian 模型”，它采用了非标准的概率概念。我们描述了 Pitowsky 的分析并争论（事后的好处）他的隐藏变量概念实际上只是超决定论（因此与物理无关）。Pitowsky 的第一个构造使用了连续统假设。Farah 和 Magidor 认为这表明在某个阶段物理学可能会支持或反对采用集合论的特定新公理。我们宁愿争辩说它支持相反的观点，即普遍的直觉“如果你需要一个不可测量的函数，它在物理上是无关紧要的”。