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Sounds like an essay question... The main thing to keep in mind about Aristotle is that although he called himself a scientist, he wasn't one by today's standards. He didn't feel the need to test any of his ideas, he just 'reasoned' they were correct. Society at the time accepted this, so his ideas persisted until the scientific revolution. So not only did the fields of science and advanced mathematics not exist during Aristotle's time, he wouldn't have found them necessary anyway. Aristotle based his model of the universe on his observations, but he never tried to find out the fundamental reasons why the world behaved as it did. For instance, he thought that objects fell to the ground when dropped because that was their natural position. It wasn't until Isaac newton proposed the force of gravity that we had a reason 'why'. Aristotle was more interested in finding patterns in the universe and relating them to a grand sense of order and logic, rather than finding satisfactory and simple explanations.

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