Natural Philosophy Yields Modern Science: Is Mathematics Neither Necessary Nor Sufficient for Science?

Sunday, February 17, 2013
Auditorium/Exhibit Hall C (Hynes Convention Center)
Danielle Mihram , University of Southern California, Los Angeles, CA
G. Arthur Mihram , Princeton, NJ, Princeton, NJ
Background: We seek to understand and elucidate mathematician Quinn’s 2012 conclusion that mathematics is not science:  Validity in mathematics is internal, but in science is external, to one’s application (scientist’s model).  Thus, mathematician Quinn, in our AMS’s Notices of January 2012, notes that mathematics does not qualify as science. Methods: Our Modern Science is the natural philosophy, properly implemented, as described by Cotes in the Preface to Newton’s Mathematical Principles of Natural Philosophy, 1713 ed.  Our historical search here is that of such a natural philosopher (scientist) examining the literature (published conclusions) of the history of science so as to elucidate the role of mathematics therein. Results: First, our ‘data’, the published observations of historians, Butterfield and Sarton, of science, show indeed that our (Modern) Science is indeed natural philosophy, properly conducted: In addition, the scientist, before announcing the model/hypothesis, is behaving counter to the quite strictly conjectural manner employed by other philosophers. Furthermore, Cotes has described the prerequisite for our Modern Science. Conclusions: Second, we provide historical evidence that mathematics is neither: (a) necessary nor (b) sufficient for science: An examination historically of the literatures of mathematics and science reveals: Mathematics is neither necessary (e.g., Darwin) nor sufficient (e.g., Euler; and LT More, Univ. Cincinnati Dean, in his 1915 Limitations of Science) for Modern Science, in contrast with the conclusion which a non‑reflective reader of Newton’s 1713 book’s quite mathematical title often reaches.