The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterize the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very natural contexts of application. We introduce in this paper a first-order formal system that captures the notion of grounding and avoids the paradoxes in a novel and non-trivial way. The system we present formally develops Bolzano’s ideas on grounding by employing Hilbert’s ε-terms and an adapted version of Fine’s theory of arbitrary objects.

接地的概念通常被认为是一种客观和解释性的关系。如果一个关系——地面——决定或解释另一个——结果，它就会连接两个关系。在当代关于基础的文献中，很多努力都致力于从逻辑上表征基础的形式方面，但一个主要的难题仍然存在：为普遍和存在公式定义合适的基础原则。事实上，已经提出了一些量化公式的基础原则，但在一些非常自然的应用环境中，所有这些原则都暴露在悖论中。我们在本文中介绍了一个一阶形式系统，它以一种新颖且非平凡的方式捕捉了接地的概念并避免了悖论。我们提出的系统通过采用希尔伯特的理论，正式发展了博尔扎诺的接地思想ε -terms 和 Fine 的任意对象理论的改编版本。