The conditional in quantum logic
The conditional in quantum logic
复制标题
量子逻辑中的条件
DOI：
10.1007/bf00484952
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发表时间：
1974
期刊：
影响因子：
1.5
通讯作者：
Gary M. Hardegree
中科院分区：
文献类型：
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作者：
Gary M. Hardegree
除了关于“现象学论证”和被称为量子逻辑（QL）的微积分的具体形式结构的物理数学争议之外，还有一个哲学争议，即这种“实验命题的微积分”是否正确地讲是一种逻辑，而不是仅仅类似于所谓的逻辑的简单代数结构。与这个争议直接相关的是逻辑是否是一种逻辑的问题。 与物理几何等同等的经验科学。然而，本文并不关心逻辑（无论是经典逻辑还是量子逻辑）的经验特征的一般问题；相反，它只涉及一个看似决定性的反对意见，反对将 QL 视为逻辑，即 Jauch 和 Piron (1970，p. 176) 提出的反对意见，他们认为，由于 QL 缺乏逻辑的基本特征，即演绎方案，“我们是否可以正确地将一般量子力学的晶格称为逻辑，这是非常值得怀疑的”。他们的论点基于他们认为是晶格的普遍失败。 承认实质蕴涵联结或条件运算的 QL 命题，通过这些运算可以将前件推演方案纳入 QL。 Jauch 和 Piron 的观点也得到了 Greechie 和 Gudder (1971, 1973) 的支持，他们研究了许多结果，表明 QL 中不存在合理的物质条件。 本文的目的是论证，由希尔伯特空间上的投影格表示的正统 QL 实际上承认具有物质条件本质属性的运算。我打算讨论的特定连接词并不是一个新发现，但可以在芬奇（1970）的著作中找到。 Kotas (1967)、Kunsemuller (1964) 和 Mittelstaedt (1970)。 1 相反，本文显然新颖的是这个连接词可以解释为 Stalnaker（反事实）条件的提议，其中邻近度排序
Besides the physicomathematical controversy concerning the'phenomenological justification'and the specific formal structure of the calculus known as quantum logic (QL), there is a philosophical controversy concerning whether this' calculus of experimental propositions' is properly speaking a logic rather than simply an algebraic structure only analogous to logic properly so called.. Directly associated with this controversy is the issue of whether logic is an empirical science on the par with, eg, physical geometry. This article is not concerned, however, with the general question of the empirical character of logic, either classical or quantal; it is rather concerned only with one seemingly decisive objection against regarding QL as logic, namely, the objection advanced by Jauch and Piron (1970, p. 176), who argue that since QL lacks an essential feature of logic-viz., a deduction scheme-it is' very questionable whether we may properly call the lattice of general quantum mechanics a logic.'Their argument is based on what they regard to be the general failure of the lattice of QL propositions to admit a material implication connective or conditional operation by means of which the modus ponens deduction scheme can be incorporated into QL. The view of Jauch and Piron is also supported by Greechie and Gudder (1971, 1973), who examine a number of results which suggest that no reasonable material conditional exists in QL.The purpose of this article is to argue that orthodox QL, which is represented by the lattice of projections on Hilbert space, does in fact admit an operation which possesses the essential properties of a material conditional. The particular connective I intend to discuss is not a new discovery, but can be found in the works of Finch (1970). Kotas (1967), Kunsemuller (1964), and Mittelstaedt (1970). 1 Rather what is apparently new to this article is the proposal that this connective can be interpreted as a Stalnaker (counterfactuaI) conditional, where the nearness ordering