Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data.

中文翻译：

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概率模态和无限域

近年来，大量尝试将概率的数学理论应用于自然语言概率谈话的语义。这些类型的“概率”语义通常是由它们解释关于涉及“可能”和“可能”的推理的直觉的能力驱动的——Angelika Kratzer 的规范语义无法通过仅基于世界排序和定性排名的语义来适应这种直觉的提议。然而，Wesley Holliday 和 Thomas Icard 最近的工作被广泛认为削弱了这一动机：他们提出了一种世界排序语义，其产生的逻辑与概率语义基本相同。在本文中，我认为挑战仍然存在：世界秩序语义的捍卫者还没有提供一种合理的语义来捕捉比较可能性的逻辑。Holliday & Icard 的语义只有在模型仅限于 Noetherian 预购时才能产生足够的逻辑。但是我认为诺特限制在涉及无限大的认知可能性域的情况下面临问题。因此，概率语义仍然是对数据的更好解释。