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Rene Descartes: Deductive Reasoning
It has been said that both modern philosophy and modern mathematics began with the
work of Rene Descartes (1596 – 1650). His analytic method of thinking focused attention on the
problem of how we know which has occupied philosophers ever since. Descartes became
dissatisfied with the unsystematic methods utilized by the previous authorities in science, since
he concluded they had not "produced anything which was not in dispute and consequently
doubtful." The only exception to this was in the field of mathematics which he believed was built
on a “solid foundation.” Descartes would use Euclid’s geometric proofs as the basis for his own
deductive truths. Medieval science, on the other hand, was largely based on authorities from the
past rather than observations in the present, therefore Descartes decided to conduct a personal
plan of investigation. After consideration of all the previous methods of inquiry, Descartes
decided that there must be a better way; and in his Discourse on Method he wrote, “I eventually
reached the decision to study my own self, and choose the right path.”
Descartes aspired to rebuild a new system of truth based upon an unquestionable first
principle. The first principle that he finally felt was self-evident was summarized in the
statement, “I think, therefore I am.” Descartes believed that he could then use his new method of
reasoning to build on such a first principle, ultimately leading to the unification of all knowledge.
In short, his method required (1) accepting as "truth" only clear, distinct ideas that could
not be doubted, (2) breaking a problem down into parts, (3) deducing one conclusion from
another, and (4) conducting a systematic synthesis of all things. Descartes based his entire
philosophical approach to science on this deductive method of reasoning.
The Reasoning
Deductive reasoning works from the more general to the more specific. Sometimes this is
informally called a "top-down" approach. First, a general theory about a specific topic is
developed. Then, the theory is narrowed down into more specific hypotheses that can be tested.
After that, the hypothesis is narrowed down even further for data collecting based off
of observations that address the hypotheses. This ultimately tests the hypotheses with specific
data leading to a confirmation (or not) of the original theory.
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Directions: Since Descartes was a fan of Euclid, let’s practice your skills from geometry this
year to practice deductive reasoning to prove Proposition 5! Conduct the proof on a
separate sheet of paper.
You are allowed to use the following:
 Postulates (on the table)
 Common Notions (on the table)
 Proposition 1 (On a given finite straight line to construct an equilateral triangle)
Proposition 2 (To place at a given point [as an extremity] a straight line equal to a
given straight line)
 Proposition 3 (Given two unequal straight lines, to cut off from the greater a straight
line equal to the less)
 Proposition 4 (Side Angle Side)
Reflection: How does proving a geometric proof use deductive reasoning?
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Why is this type of reasoning useful?
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