McCullough-Benner, Colin (Author)
British Journal for the Philosophy of Science
Volume: 71
Issue: 4
Pages: 1331-1358
According to standard accounts of mathematical representations of physical phenomena, positing structure-preserving mappings between a physical target system and the structure(s) picked out by a mathematical theory is essential to such representations. In this paper, I argue that these accounts fail to give a satisfactory explanation of scientific representations that make use of inconsistent mathematical theories and present an alternative, robustly inferential account of mathematical representation that provides not just a better explanation of applications of inconsistent mathematics, but also a compelling explanation of mathematical representations of physical phenomena in general. 1. Inconsistent Mathematics and the Problem of Representation2. The Early Calculus3. Mapping Accounts and the Early Calculus3.1. Partial structures3.2. Inconsistent structures3.3. Related total consistent structures4. A Robustly Inferential Account of the Early Calculus in Applications 4.1. The robustly inferential conception of mathematical representation4.2. The robustly inferential conception and inconsistent mathematics4.3. The robustly inferential conception and mapping accounts5. Beyond Inconsistent Mathematics
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