Galileo's Reconciliation of Mathematics and the Investigation of Nature
Modern science uses mathematics to describe nature. However, in the early modern period (roughly, the sixteenth to eighteenth centuries), natural philosophers rarely used mathematics to gain knowledge about nature because of two problems. The Ontological Problem is that mathematics seems inappropriate for gaining knowledge of nature because nature does not seem to exhibit essential mathematical properties. The Practical Problem is that, even if nature does have mathematical properties, mathematical calculations give predictions that do not exactly match what we observe, making them inappropriate for gaining knowledge of nature. Galileo, in the Dialogue on the Two Chief World Systems and the Discourses Concerning Two New Sciences, argued for the use of mathematics in the investigation of nature. He responded to the problems by valuing reason over observation and developing an error theory. He showed that mathematics could generate knowledge about the natural world, and that discrepancies between mathematical calculations and observations could be overcome. This essay describes why the Ontological and Practical problems presented barriers to the use of mathematics to gain knowledge of nature, and Galileo’s solutions.