What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of definitions. Specifically, I pursue this issue via an examination of Frege’s views about the scientific unification of logic and arithmetic. In my view, what interpreters have failed to appreciate is that logicism is a project of unification, not reduction. For Frege, unification involves two separate steps: (1) an account of the content expressed by arithmetical claims and (2) the justification of that content. The distinction between these steps allows us to see that there are two notions of definition at play in Frege’s logicist work, viz., one concerned with conceptual analysis, the other concerned with the construction of gap-free proof. I then use this discussion to explain how Frege employs his definitions to defend an epistemological thesis about arithmetic, and to clarify Grundlagen’s fruitfulness condition of definitions, and thereby address two interpretive puzzles from the recent literature.

中文翻译：

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弗雷格的统一

是什么使某些定义富有成效？定义如何发挥解释作用？本文的目的是通过对弗雷格对定义的处理的调查来检验这些问题。具体来说，我通过考察弗雷格关于逻辑和算术科学统一的观点来探讨这个问题。在我看来，解释者没有意识到逻辑主义是一个统一的项目，而不是简化的项目。对于弗雷格来说，统一包括两个独立的步骤：（1）对算术声明所表达的内容的说明；（2）对该内容的证明。这些步骤之间的区别使我们能够看到，在弗雷格的逻辑主义著作中，有两种定义概念在起作用，即，一种与概念分析有关，另一种与无间隙证明的构造有关。