Between Kepler and Newton: Hooke's 'principles of congruity and incongruity' and the naturalization of mathematics

• Published in: Annals of science Vol. 76; no. 3-4; pp. 241 - 266
• Main Authors: Gal, Ofer, Hodoba Eric, Cindy
• Format: Journal Article
• Language: English
• Published: England Taylor & Francis 02-10-2019; Taylor & Francis Ltd
• Subjects: Careers; early modern science; Epistemology; History of medicine and histology; History, 17th Century; Hooker; Isaac Newton; Mathematical analysis; Mathematics; Mathematics - history; mathematization; Physics - history; Principles; Robert Hooke; scientific revolution; Vibration; Robert Hooke; mathematization; Isaac Newton; early modern science; scientific revolution
• ISSN: 0003-3790; 1464-505X
• DOI: 10.1080/00033790.2019.1702718

Robert Hooke's development of the theory of matter-as-vibration provides coherence to a career in natural philosophy which is commonly perceived as scattered and haphazard. It also highlights aspects of his work for which he is rarely credited: besides the creative speculative imagination and practical-instrumental ingenuity for which he is known, it displays lucid and consistent theoretical thought and mathematical skills. Most generally and importantly, however, Hooke's 'Principles ... of Congruity and Incongruity of bodies' represent a uniquely powerful approach to the most pressing challenge of the New Science: legitimizing the application of mathematics to the study of nature. This challenge required reshaping the mathematical practices and procedures; an epistemological framework supporting these practices; and a metaphysics which could make sense of this epistemology. Hooke's 'Uniform Geometrical or Mechanical Method' was a bold attempt to answer the three challenges together, by interweaving mathematics through physics into metaphysics and epistemology. Mathematics, in his rendition, was neither an abstract and ideal structure (as it was for Kepler), nor a wholly-flexible, artificial human tool (as it was for Newton). It drew its power from being contingent on the particularities of the material world.