The author examines the role of critical intellect in creating scientific revolutions, using Galileo as a central example. He contrasts a meticulous, doctrinal criticism that reforms form with a transformative critique that alters scientific substance, and argues that Galileo combined rigorous experimental practice with mathematical reasoning to inaugurate a new scientific approach. The essay situates this intellectual shift among other Renaissance thinkers, compares differing assessments of Galileo's methods, and emphasizes the importance of properly posed problems and methodological clarity for advancing knowledge.