Article ID: CBB210493760

Representing the World with Inconsistent Mathematics (2020)


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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Authors & Contributors
Nescolarde-Selva, Josue Antonio
Eric, Cindy Hodoba
Usó-Doménech, J. L.
Gash, Hugh
Serfati, Michel
Schlote, Karl-Heinz
Foundations of Science
Studies in History and Philosophy of Science
Science and Education
Bruniana & Campanelliana: Ricerche Filosofiche e Materiali Storico-testuali
Annals of Science: The History of Science and Technology
Verlag Harri Deutsch
Princeton University Press
Harrassowitz in Kommission
Mathematics and its relationship to nature
Mathematics and its relationship to science
Philosophy of mathematics
Philosophy of science
Symbolism; symbolic representation
Newton, Isaac
Leibniz, Gottfried Wilhelm von
Kant, Immanuel
Wigner, Eugene Paul
Spinoza, Baruch
Locke, John
Time Periods
18th century
17th century
20th century, late
Early modern
21st century

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