Title: Roots and (re)sources of value (in)definiteness versus contextuality. A contribution to the Pitowsky Volume in memory of Itamar Pitowsky (1950--2010) Show Chinese title

Title: 价值（不）确定性与情境性的根源与（再）来源。 向皮陶斯基文集的贡献，以纪念伊塔马尔·皮陶斯基（1950–2010）

Abstract: In Itamar Pitowsky's reading of the Gleason and the Kochen-Specker theorems, in particular, his Logical Indeterminacy Principle, the emphasis is on the value indefiniteness of observables which are not within the preparation context. This is in stark contrast to the prevalent term {\em contextuality} used by many researchers in informal, heuristic yet omni-realistic and potentially misleading ways. This paper discusses both concepts and argues in favor of value indefiniteness in all but a continuum of contexts intertwining in the vector representing a single pure (prepared) state. Even more restrictively, and inspired by operationalism but not justified by Pitowsky's Logical Indeterminacy Principle or similar, one could identify with a "quantum state" a single quantum context -- aka the respective maximal observable, or, in terms of its spectral decomposition, the associated orthonormal basis - from the continuum of intertwining context, as per the associated maximal observable actually or implicitly measured. Show Chinese abstract

Abstract: 在伊塔马尔·皮陶斯基对格里马尔迪定理和科亨-斯派克特定理的解读中，特别是他的逻辑不确定性原理，重点在于那些不在制备上下文中的可观测量的值不定性。 这与许多研究人员在非正式、启发式但过于现实主义且可能具有误导性的背景下广泛使用的普遍术语 {\em 上下文性} 形成了鲜明对比。 本文讨论了这两个概念，并支持在一个纯（制备）态所表示的单一向量中交织的几乎所有连续上下文中值不定性。更进一步地，受到操作主义的启发，但并未由皮陶斯基的逻辑不确定性原理或类似的理论证明，可以从交织上下文的连续统中识别出一个“量子态”——即相应的最大可观测量，或者根据其谱分解，与之相关的正交基——这是通过实际或隐含测量的最大可观测量来确定的。