Semantic layering and the success of mathematical sciences

What are the pillars on which success of modern science rest? Although philosophers have much discussed what is behind science’s success, this paper argues that discussion misdirected. The extant literature rightly regards semantic and inferential tools formal logic probability theory as scientific rationality, in sense they reveal justificatory structure important aspects practice. As key elements our rational reconstruction toolbox, make a fundamental contribution to understanding science. At same time, any science, however exact, dominated by approximation, error, uncertainty, fact makes one wonder how can be so successful. This articulates illustrates general themes—e.g., truth-preserving arguments often fail preserve approximate truth—that highlight need for additional resources. Thus, proposal persistent failures unravel reasons face pervasive error uncertainty should attributed an insufficiently rich way rationally reconstructing mathematical knowledge. missing? claims there third method reasoning constitutes distinct pillar rests namely, perturbation theory. outlines representational differ from those theory, enable us understand apparently elusive However, compared its peers, perturbative has not received attention it deserves. explains, partly results circumstances taught, first appears vaguely related collection methods offering no systematic insight. In attempt show impression wrong, presents dimension representation inference terms I call “semantic layering.”