What are the pillars on which the success of modern science rest? Although philosophers have much discussed what is behind science’s success, this paper argues that much of the discussion is misdirected. The extant literature rightly regards the semantic and inferential tools of formal logic and probability theory as pillars of scientific rationality, in the sense that they reveal the justificatory structure of important aspects of scientific practice. As key elements of our rational reconstruction toolbox, they make a fundamental contribution to our understanding of the success of science.

At the same time, any science, however exact, is dominated by approximation, error, and uncertainty, a fact that makes one wonder how science can be so successful. This paper articulates and illustrates general themes—e.g., that truth-preserving arguments often fail to preserve approximate truth—that highlight the need for additional semantic resources. Thus, our proposal is that persistent failures to unravel the reasons behind the success of science in the face of pervasive error and uncertainty should be attributed to an insufficiently rich way of rationally reconstructing scientific and mathematical knowledge. What is missing? This paper claims that there is a third formal method of reasoning that constitutes a distinct pillar on which rests the success of science, namely, perturbation theory. The paper outlines how the representational and inferential tools of perturbation theory differ from those of logic and probability theory, and how they enable us to understand the apparently elusive aspects of the success of science.

However, compared to its peers, perturbative reasoning has not received the attention it deserves. As the paper explains, this partly results from the circumstances in which perturbation theory is taught, and partly from the fact that perturbation theory first appears to be a vaguely related collection of methods offering no systematic semantic insight. In an attempt to show that this first impression is wrong, this paper presents its contribution to the semantic dimension of scientific representation and inference in terms of what I call “semantic layering.”

现代科学成功的支柱是什么？尽管哲学家们对科学成功背后的原因进行了很多讨论，但本文认为大部分讨论都被误导了。现有文献正确地将形式逻辑和概率论的语义和推理工具视为科学理性的支柱，因为它们揭示了科学实践重要方面的正当性结构。作为我们理性重建工具箱的关键要素，它们对我们对科学成功的理解做出了根本性的贡献。

与此同时，任何科学，无论多么精确，都受到近似、错误和不确定性的支配，这一事实让人想知道科学是如何取得如此成功的。这篇论文阐明并说明了一般主题——例如，保持真值的论点通常无法保持近似真值——强调了对额外语义资源的需求。因此，我们的建议是，面对普遍的错误和不确定性，始终未能解开科学成功背后的原因，这应该归因于理性重建科学和数学知识的方式不够丰富。有什么不见了？这篇论文声称，存在第三种形式的推理方法，它构成了科学成功的独特支柱，即扰动理论。

然而，与同行相比，微扰推理并没有得到应有的关注。正如论文所解释的，这部分是由于教授微扰理论的环境，部分是由于微扰理论最初似乎是一组模糊相关的方法，没有提供系统的语义洞察力。为了表明这种第一印象是错误的，本文以我所说的“语义分层”的形式展示了它对科学表示和推理的语义维度的贡献。