Galileo, Ignoramus: Mathematics versus Philosophy in the Scientific Revolution

TL;DR

This paper challenges the traditional view of Galileo as a mathematical pioneer, arguing that his lack of mathematical skill led him to emphasize empirical methods and scientific philosophy, which were less innovative than commonly believed.

Contribution

It offers a revisionist interpretation showing Galileo's mathematical shortcomings shaped his scientific approach and philosophical writings, contrasting with the standard narrative of his pioneering role.

Findings

Galileo lacked advanced mathematical ability.

His emphasis on experiment and empiricism was due to mathematical limitations.

Galileo's scientific philosophy was less original than traditionally thought.

Abstract

I offer a revisionist interpretation of Galileo's role in the history of science. My overarching thesis is that Galileo lacked technical ability in mathematics, and that this can be seen as directly explaining numerous aspects of his life's work. I suggest that it is precisely because he was bad at mathematics that Galileo was keen on experiment and empiricism, and eagerly adopted the telescope. His reliance on these hands-on modes of research was not a pioneering contribution to scientific method, but a last resort of a mind ill equipped to make a contribution on mathematical grounds. Likewise, it is precisely because he was bad at mathematics that Galileo expounded at length about basic principles of scientific method. "Those who can't do, teach." The vision of science articulated by Galileo was less original than is commonly assumed. It had long been taken for granted by mathematicians, who, however, did not stop to pontificate about such things in philosophical prose because they were too busy doing advanced scientific work.