This is great !! A juicy bit for everyone !! ...
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Methodology of Science:
Basically, there are two different methodologies to study Nature, both inherited from different ways of thinking in ancient Greece:
The mathematical deductive method: This is the method thought by Pythagoras and Plato. The pure relations of numbers in Arithmetic and Geometry are the immutable reality behind changing appearances in the world of the senses. We cannot reach the truth through observation with the senses, but only through pure reason ...
The empirical inductive method: This is the method thought by Anaxagoras of how to know Nature. Aristotle uses both inductive and deductive methods, and he says that “the mathematical method is not the method of the physicists, because Nature, perhaps all, involves matter” (Meta- physics, book II). Matter and not numbers or mathematics. Nature should be known through observations and extrapolations of them."
Hehe ... hehe ....
Cheers