论文标题
弗雷格的类型理论
Frege's theory of types
论文作者
论文摘要
人们通常认为，弗雷格（Frege）在Grundgesetze der Arithmetik中提出的功能级别理论预测了教会简单类型理论的类型的层次结构。这一说法粗略地指出，弗雷格以grundgesetze的说明性语言的意义上以简单类型理论的意义为函数提供了前提。但是，这种观点使很难容纳两个参数的函数名称，并将函数视为不完整的实体。我提出并捍卫了grundgesetze中第一级函数名称的替代解释为简单的类型理论开放术语，而不是函数类型的封闭术语。这种解释提供了弗雷格级别理论的仍然不历史但更忠实的类型理论近似，并且可以自然扩展以适应二级功能。通过两个关键的观察，弗雷格的罗马标记本质上像开放的术语一样，这是可能的，而弗雷格缺乏区分罗马标记和功能名称的明确标准。
It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik anticipates the hierarchy of types that underlies Church's simple theory of types. This claim roughly states that Frege presupposes a type of functions in the sense of simple type theory in the expository language of Grundgesetze. However, this view makes it hard to accommodate function names of two arguments and view functions as incomplete entities. I propose and defend an alternative interpretation of first-level function names in Grundgesetze into simple type-theoretic open terms rather than into closed terms of a function type. This interpretation offers a still unhistorical but more faithful type-theoretic approximation of Frege's theory of levels and can be naturally extended to accommodate second-level functions. It is made possible by two key observations that Frege's Roman markers behave essentially like open terms and that Frege lacks a clear criterion for distinguishing between Roman markers and function names.
