Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, but unlike later definabilists, Hale seeks to justify full impredicative property comprehension. The most innovative part of his defense, we think, is a “definability constraint” that can serve as an implicit definition of the domain of properties. We make this constraint formally precise and prove that it fails to characterize the domain uniquely. Thus, we conclude, there is no easy road to impredicative definabilism.

中文翻译：

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通往命令式可定义主义的道路并不平坦

鲍勃·黑尔（Bob Hale）捍卫了一种新的性质概念，该概念在两个关键方面基本上属于弗雷格式。首先，像弗雷格一样，黑尔坚持认为每个性质都可以用开放公式来定义。其次，与弗雷格一样，但与后来的可定义论者不同，黑尔试图证明完全的必然性质理解的合理性。我们认为，他的辩护中最具创新性的部分是“可定义性约束”，可以作为属性领域的隐式定义。我们使这个约束在形式上变得精确，并证明它无法唯一地描述该领域。因此，我们得出的结论是，通往命令式可定义主义的道路并不平坦。