One of the most interesting things to me, that we discussed in class were Aristotle's 3 laws of logic, or thought. Which is the study of reasoning. The first and most obvious is: identity. This is interpreted as: a subject is equal to the sum of it's predicates; or everything that is, exists/is. If it looks or feels like something, than it is that something.
The second is: non-contradiction. No predicate can be simultaneously attributed and denied to a subject. This is the law saying that nothing can both be and not be, in other words. If a flower is a rose and dead, it has to be that. If something is untrue, it will never be true. And the third is: excluded middle. Of every two contradictorily opposite predicates one must belong to every subject; or in other words, each and everything either is or is not.
Those are the three law's of logic, or thought. Logic was described as the art of non-contradictory identification. These law's lead to two thought categories. One is Induction, and the other is Deduction. Deduction basically says all men are mortal. And induction is like the sun always rises in the morning, therefor you know the sun will rise. I found a picture of the equations to go with Aristotle's laws:
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