Aristotle's teachings, for two millenia, had been the mainstay for scientific knowledge in the West. He based his arguments on deductive reasoning, where the primal causes of things ("axioms") once determined, would describe all other observed phenomena.  Although this reasoning worked well for some branches of mathematics, and the reasoning was sound by rules of logic, in other branches of science it led erroneous conclusions. However, to question such conclusions was, as the centuries rolled forward, to criticize a Great Ancient -- Indeed, Galileo Galilei (1564-1642) found himself in trouble with the Church because he questioned the cosmology established and upheld by the Church since ancient times.  By the Late Renaissance, Galileo, among others, began to argue by way of inductive reasoning, where observed phenomena would lead to axioms -- the precise inverse of deduction.  Furthermore, by his measuring observed phenomena, or gathering data, he was able to uphold his arguments.  By quantifying mathematically natural observations, he established the process known as the Scientific Method, upon which the modern world has been benefiting since.  Both Rene Descartes (1596-1650) and Isaac Newton (1642-1727) adapted inductive reasoning in their works, which not only revolutionized the study of philosophy, but developed new branches of mathematics. See more at the links: