We cannot reduce the Enlightenment to a single unifying philosophy or body of thought. But Enlightenment thinkers in intellectual circles in Asia, Europe, and the Americas were inspired by the seventeenth century’s emphasis on using reason to grapple with questions about human nature, the complexities of political power and the social order, and the principles of logic and scientific thinking. Many of the components of Western science that, along with the ideas of the Italian Renaissance, inspired Enlightenment thought were built on scientific traditions developed in the Islamic world, which had absorbed ancient Greek and Indian systems of knowledge. In particular, Al-Andalus, the Muslim-ruled area of Spain and Portugal that rose to power in 711, began wielding significant influence on European intellectual activity in the eleventh and twelfth centuries. By preserving and translating the works of ancient Greek thinkers, such as Aristotle and Plato, that were not available in Europe at the time, Muslim scholars in Spain fueled both the European Renaissance of the twelfth century and the Italian Renaissance of the fourteenth and fifteenth centuries. In addition to preserving seminal Greek texts, Muslim scholars in medieval Al-Andalus, such as the twelfth-century intellectual Averroes, also wrote and translated Arabic philosophical treatises that were widely read by scholars in Christian Europe. Elsewhere in the Muslim world, Arabic, Indian, and Persian treatises on mathematics, medicine, and astronomy had long wielded significant influence on European science and philosophy. The contributions of medieval Persian mathematicians such as Muhammad ibn Musa al-Khwarizmi and Omar Khayyam to the study of algebra, and the pivotal role of sixth-century Indian philosopher Aryabhata in the field of trigonometry, for example, provided scholars of the Scientific Revolution with the intellectual tools to develop novel theories about the cosmos and the nature of planetary motion (Figure 7.4). These advances, however, could not have occurred without the development of the decimal number system in classical India and the innovation of fractions in the Arabic numeral systems of North Africa by the tenth century. Scientists’ ability to calculate advanced mathematical formulas and describe the subtleties of planetary motion not only spurred the Scientific Revolution but also substituted concrete information for superstition and firmly held religious beliefs. The Enlightenment was thus a result of cross-cultural networks of scholarship and knowledge exchange that facilitated the growth of science. Figure 7.4 This page from Muhammad ibn Musa al-Khwarizmi’s algebra treatise, The Compendious Book on Calculation by Completion and Balancing, was first published around 820 and reflects the advanced mathematical scholarship of the Islamic Golden Age. (credit: “The Compendious Book on Calculation by Completion and Balancing” by Muhammad ibn Musa al-Khwarizmi in Oxford University Press/Wikimedia Commons, Public Domain) Among the principles that influenced Enlightenment perceptions of knowledge were the twin concepts of deductive and inductive reasoning. Inherited from the intellectual framework of the Scientific Revolution, these approaches represent different methods of organizing information and developing hypotheses. While inductive reasoning gathers specific examples and observations to arrive at a broad generalization, deductive reasoning, in contrast, begins with a general statement or theory and applies it to specific conclusions. Deductive reasoning had its origins in the fourth century BCE in the teachings of the Greek philosopher Aristotle, but it became a vital component of the Scientific Revolution in the work of French philosopher René Descartes. Descartes combined deductive reasoning with empiricism, the acquisition of knowledge from sensory experiences, to establish the foundations of the scientific method. Inductive reasoning, on the other hand, played an important role in the work of the English natural philosopher Francis Bacon. Bacon asserted that whereas the deductive method began with a proposition and discarded evidence that did not support that premise, inductive reasoning reached a conclusion only after the collection of evidence. According to Bacon, only inductive reasoning enabled researchers to support observations with empirical data rather than conjecture. Ultimately, both inductive and deductive reasoning influenced the intellectual context of the Enlightenment by providing two systematic means of drawing conclusions about the natural world from observations and evidence. Whichever method they adopted, Enlightenment thinkers embraced the scientific method as a means of applying reason and objectivity to the collection and analysis of information.