What is absolutely unrestricted quantification? We distinguish two theoretical roles and identify two conceptions of absolute generality: maximally strong generality and maximally inclusive generality. We also distinguish two corresponding kinds of absolute domain. A maximally strong domain contains every potential counterexample to a generalisation. A maximally inclusive domain is such that no domain extends it. We argue that both conceptions of absolute generality are legitimate and investigate the relations between them. Although these conceptions coincide in standard settings, we show how they diverge under more complex assumptions about the structure of meaningful predication, such as cumulative type theory. We conclude by arguing that maximally strong generality is the more theoretically valuable conception.

什么是绝对无限制量化？我们区分了两个理论角色，并确定了绝对普遍性的两个概念：最大强普遍性和最大包容性普遍性。我们还区分了两种相应的绝对域。最大强域包含泛化的每个潜在反例。最大包容域是指没有域扩展它。我们认为这两种绝对普遍性的概念都是合理的，并研究了它们之间的关系。尽管这些概念在标准设置中是一致的，但我们展示了它们如何在关于有意义的谓词结构的更复杂假设下发生分歧，例如累积类型理论。最后，我们认为最大强普遍性是更具理论价值的概念。