Empress vs. Spider-Man: Margaret Cavendish on pure and applied mathematics

• Published in: Synthese (Dordrecht) Vol. 196; no. 9; pp. 3527 - 3549
• Main Author: Peterman, Alison
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer 01.09.2019; Springer Netherlands; Springer Nature B.V
• Subjects: Applied mathematics; British & Irish literature; Cavendish, Margaret, Duchess of Newcastle-upon-Tyne (1623-1673); Education; English literature; Epistemology; Logic; Mathematicians; Mathematics; Metaphysics; Ontology; Philosophy; Philosophy of Language; Philosophy of Science; S.I. : Use & Abuse of Maths; Truth; Anti-mathematics; Mathematics; Spidermen; Margaret Cavendish; Natural philosophy
• ISSN: 0039-7857; 1573-0964
• DOI: 10.1007/s11229-017-1504-y

The empress of Margaret Cavendish's The Blazing World dismisses pure mathematicians as a waste of her time, and declares of the applied mathematicians that "there [is] neither Truth nor Justice in their Profession". In Cavendish's theoretical work, she defends the Empress' judgments. In this paper, I discuss Cavendish's arguments against pure and applied mathematics. In Sect. 3, I develop an interpretation of some relevant parts of Cavendish's metaphysics and epistemology, focusing on her anti-abstractionism and what I call her 'assimilation' view of knowledge. In Sects. 4 and 5, I use this to develop Cavendish's critiques of pure and applied mathematics, respectively. These critiques center on the claims that mathematics purports to describe non-beings, that nature is infinitely and irreducibly complex, and, perhaps most originally, that mathematical thinking (like other formal methods in philosophy) deforms the subject of representation, not just the object.