1. Descartes and the Enlightenment Ms. Berolini and Ms. Garrity

2. Objectives 1. Students will be able to identify key Enlightenment thinkers and philosophers that relate to Descartes. 2. Students will be able to apply the mathematical concepts learned in this unit in a new context. 3. Students will be able to connect Descartes’ ideas to those of later thinkers and to the present day.

3. Guiding Question  Why is Descartes important to both math and philosophy?

4. Descartes’ Impact  Descartes’ thought helped lead to the Enlightenment  Descartes’ determination to uncover many “clear and distinct” ideas about the natural world inspired many future thinkers to do the same  His rejection of the ideas of the past also led other thinkers to reject the thought of the medieval period and create their own ideas  His secular approach to math and science was also influential to many later Enlightenment thinkers who placed emphasis on human reason over divine revelation

5. Specific Figures he Influenced  Blaise Pascal  Baruch Spinoza  John Locke  Pierre Bayle  Bernard Le Bovier de Fontenelle

6. Blaise Pascal  1623-1662  Like Descartes he wanted to uncover new truths about the human experience  Rejects how Descartes employs God in his work solely to advance his argument  Reaction against Descartes’ emphasis on human reason over divine revelation, Pascal believes humans should aspire to achieve a balance between the two  Proposes the “wager” concept arguing that it is makes more sense to live one’s life believing that God exists than to live one’s life believing that there is no God

7. Baruch Spinoza  1632-1677  Followed Descartes rationalism and believed truth could only be grasped through reason  Inspired by Descartes to uncover his own ideas:  Wrote Theological-Political Treatise arguing the importance of free thought and denouncing the extensive influence of church leaders who limit free thought  Spinoza radicalized Descartes’ ideas  Only one substance exists: God  Denounced the mind/body dualism of Descartes

8. John Locke  1632-1704  Influenced by the Cartesian tradition of original thought  Follows the secular tradition of Descartes  aims to base government on a social contract between individuals in which all citizens give up their right to a govern themselves to a government that will protect these rights  Departure from idea of a religious covenant  Reaction against Descartes’ rationalism  Promotes empiricism and believes that knowledge comes from experience  Tabula rasa : humans have no innate ideas

9. Pierre Bayle  1647-1706  Studied the work of Descartes  His Historical and Critical Dictionary summarized the inaccuracies and misunderstandings of past and present thinkers of all religions  Followed Descartes’ method of employing skepticism and relying on reason  Emphasized relying on rational thought over faith  Proponent of religious toleration

10. Bernard Le Bovier de Fontenelle  1657-1767  French author who wrote about philosophy and upheld Descartes’ ideas  His Conversations on the Plurality of Worlds, aimed to make philosophy applicable to all and reiterated Descartes’ ideas about physics  In his Quarrel of the Ancients and the Moderns he identified modern thought as superior to ancient thought  In The History of Oracles he identified the ancient oracles as mere superstition and and later applied notions of superstition to Christian miracles as well

11. Sir Isaac Newton  1643-1727  Physicist, mathematician, astronomer, natural philosopher, alchemist and theologian  “Principia Mathematica" (1687)  Infinitesimal calculus  Built on the work of many mathematicians before him, such as Descartes  Allowed mathematicians and engineers to understand motion  Differential & Integral calculus, Fundamental Theorem of Calculus  Used Coordinate Geometry to derive solutions (also expanding on Descartes’ work)  “Newton’s Method” for finding zeros of a function

12. Gottfried Wilhelm Leibniz  (1646-1716)  Philosopher, politician, mathematician  Considered, with Descartes, one of the greatest rationalists of the 17 th Century  Independently (from Newton) develop Infinitesimal calculus  Publish mathematical findings first  Connect the concept of a function with geometrical curves  Solving equations using matrices  Practical counting machine  Able to calculate zeros

13. Questions?