In the literature, there have been several methods and definitions for working out whether two theories are “equivalent” (essentially the same) or not. In this article, we do something subtler. We provide a means to measure distances (and explore connections) between formal theories. We introduce two natural notions for such distances. The first one is that of axiomatic distance, but we argue that it might be of limited interest. The more interesting and widely applicable notion is that of conceptual distance which measures the minimum number of concepts that distinguish two theories. For instance, we use conceptual distance to show that relativistic and classical kinematics are distinguished by one concept only.

中文翻译：

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形式理论之间的距离

在文献中，有几种方法和定义可以确定两个理论是否“等价”（本质上相同）。在这篇文章中，我们做了一些更微妙的事情。我们提供了一种测量正式理论之间距离（​​并探索联系）的方法。我们为这种距离引入了两个自然概念。第一个是公理距离，但我们认为它的兴趣可能有限。更有趣和更广泛适用的概念是概念距离它衡量区分两种理论的最少概念数量。例如，我们使用概念距离来表明相对论和经典运动学仅通过一个概念来区分。