According to Øystein Linnebo's account of abstractionism, abstraction principles, received as Fregean criteria of identity, can be used to reduce facts about singular reference to objects such as directions and numbers to facts that do not involve such objects. In this article, first I show how the resources of Linnebo's metasemantics successfully handle Dummett's challenge against the referentiality of the singular terms formed by abstraction principles. Then, I argue that Linnebo's metasemantic commitments do not provide us with tools for dispelling the threat of a version of referential indeterminacy, according to which nothing in our use of a singular term, even when it is guided by an associated criterion of identity, could determine which particular object it refers to. I end by examining the bearing of the indeterminacy challenge to Linnebo's treatment of Frege's Caesar Problem: in the absence of an argument against the indeterminacy of reference, it is unclear how numerical expressions could qualify as genuine singular terms.

中文翻译：

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Linnebo 通过抽象引用

根据 Øystein Linnebo 对抽象主义的解释，作为弗雷格同一性标准而被接受的抽象原则可用于将关于对象的单一指涉的事实（例如方向和数字）减少到不涉及此类对象的事实。在本文中，我首先展示 Linnebo 的元语义资源如何成功应对 Dummett 对抽象原则形成的单数术语的指称性的挑战。然后，我认为 Linnebo 的元语义承诺并没有为我们提供消除指称不确定性版本威胁的工具，据此，我们对单数术语的使用，即使是在相关的身份标准的指导下，也不能确定它指的是哪个特定对象。