Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism, which retains the central advantages of each while avoiding their more serious costs. The key to our approach is using arbitrary reference to explicate how mathematical terms, introduced by abstraction principles like Hume’s, refer. Focusing on numerical terms, we argue that this allows us to treat abstraction principles as implicit definitions serving to determine all (known) properties of the numbers, achieving a key neofregean advantage, while preserving the key structuralist advantage that which objects play the number role doesn’t matter.

中文翻译：

---

结构主义新论†

新弗里格主义和结构主义是最近最有前途的数学哲学方法之一。然而，两者都有严重的成本。我们发展了一种结构主义新逻辑主义的观点，它保留了每一种的核心优势，同时避免了它们更严重的代价。我们方法的关键是使用任意引用来解释由像休谟这样的抽象原则引入的数学术语是如何引用的。专注于数值术语，我们认为这允许我们将抽象原则视为隐式定义，用于确定数字的所有（已知）属性，实现关键的 Neofregean 优势，同时保留关键的结构主义优势，即哪些对象扮演数字角色没关系。