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Abhishek
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Wed Jan 09, 2019 11:28 am
In order to build their mathematical knowledge they came to conclusions by reasoning deductively from what appeared to be self-evident.
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Abhishek
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Wed Jan 09, 2019 11:29 am
This approach proved to be powerful and its success in mathematics encouraged its application in many other disciplines.
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Abhishek
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Wed Jan 09, 2019 11:29 am
The Greeks eventually came to believe that the only acceptable way of obtaining knowledge was the use of deduction.
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Abhishek
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Wed Jan 09, 2019 11:29 am
ARISTOTELIAN LOGIC
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Abhishek
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Wed Jan 09, 2019 11:29 am
Aristotle was the first philosopher who developed a systematic study of logic.
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Abhishek
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Wed Jan 09, 2019 11:30 am
His framework would become an authority in deductive reasoning for over two thousand years.
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Abhishek
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Wed Jan 09, 2019 11:30 am
Although he repeatedly admitted the importance of induction, he prioritized the use of deduction to build knowledge.
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Abhishek
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Wed Jan 09, 2019 11:30 am
The doctrine of syllogism is his most influential contribution to logic.
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Abhishek
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Wed Jan 09, 2019 11:30 am
He defined the syllogism as a “discourse in which certain things having been stated, something else follows of necesity from their being so”.
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Abhishek
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Wed Jan 09, 2019 11:31 am
A well known example is:
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Abhishek
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Wed Jan 09, 2019 11:31 am
LEGACY
Aristotle’s contribution in logic and science became an authority and remained unchallenged as late as the modern age.
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Abhishek
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Wed Jan 09, 2019 11:31 am
It took many centuries to notice the flaws of Aristotle’s approach to science.
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Abhishek
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Wed Jan 09, 2019 11:31 am
Platonic influence also contributed to undervalue inference and experimentation:
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Abhishek
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Wed Jan 09, 2019 11:31 am
Plato’s philosophy considered the world to be only an imperfect representation of the ideal truth sitting in the world of ideas.
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Abhishek
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Wed Jan 09, 2019 11:32 am
By discovering mathematical theorems, the Greeks came across the art of deductive reasoning.
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Abhishek
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Wed Jan 09, 2019 11:32 am
In order to build their mathematical knowledge they came to conclusions by reasoning deductively from what appeared to be self-evident.
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Abhishek
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Wed Jan 09, 2019 11:32 am
This approach proved to be powerful and its success in mathematics encouraged its application in many other disciplines.
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Abhishek
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Wed Jan 09, 2019 11:32 am
The Greeks eventually came to believe that the only acceptable way of obtaining knowledge was the use of deduction.
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Abhishek
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Wed Jan 09, 2019 11:33 am
Deduction did not work for some kind of knowledge.
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Abhishek
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Wed Jan 09, 2019 11:33 am
“What is the distance from Athens to Chios?”
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Abhishek
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Wed Jan 09, 2019 11:33 am
In this case, the answer cannot be derived from abstract principles; we have to actually measure it.
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Abhishek
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Wed Jan 09, 2019 11:33 am
The Greeks, when necessary, looked at nature to get the answers they were looking for, but they still considered that the highest type of knowledge was the one derived directly from the intellect. It is interesting to note that when observations were taken in consideration,
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Abhishek
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Wed Jan 09, 2019 11:33 am
it tended to be subordinated to the theoretical knowledge.
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Abhishek
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Wed Jan 09, 2019 11:33 am
An example of this could be one of the surviving works of Archimedes,
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Abhishek
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Wed Jan 09, 2019 11:34 am
The Method, which explains how mechanical experiments can help the understanding of geometry.
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