Descartes and
the
Enlightenment
Ms. Berolini and Ms. Garrity
Objectives
1.
2.
3.
Students will be able to identify key
Enlightenment thinkers and philosophers
that relate to Descartes.
Students will be able to apply the
mathematical concepts learned in this
unit in a new context.
Students will be able to connect
Descartes’ ideas to those of later thinkers
and to the present day.
Guiding Question
 Why
is Descartes important to both math
and philosophy?
Descartes’ Impact
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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
Specific Figures he Influenced
 Blaise
Pascal
 Baruch Spinoza
 John Locke
 Pierre Bayle
 Bernard Le Bovier de Fontenelle
Blaise Pascal
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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
Baruch Spinoza
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1632-1677
Followed Descartes rationalism and believed truth
could only be grasped through reason
Inspired by Descartes to uncover his own ideas:
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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

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Only one substance exists: God
Denounced the mind/body dualism of Descartes
John Locke
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1632-1704
Influenced by the Cartesian tradition of
original thought
Follows the secular tradition of Descartes
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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
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Promotes empiricism and believes that
knowledge comes from experience
Tabula rasa: humans have no innate ideas
Pierre Bayle
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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
Bernard Le Bovier de
Fontenelle
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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
Sir Isaac Newton
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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
Gottfried Wilhelm Leibniz
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(1646-1716)
Philosopher, politician, mathematician
Considered, with Descartes, one of the greatest
rationalists of the 17th 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
Questions?