They also noted that, although one can deduce various laws governing triangles, spheres, circles, and the like, such things do not exists in nature and so are outside of human experience. That is, there can be no triangle in nature found with exactly180 interior degrees, any more than one can find a precisely straight line. In there use of reason, they prefered demonstrative logic , the demonstration of derivations from known principles. The basic operation in demonstrative logic is the syllogism . All categories are defined by their characteristics, some of which are essential and some of which are accidental.
Essential characteristics are such things as bipedal, mammal, and rational.
If so, then socrates has all of the essential characteristics of the category. There is a problem with this. In short, Plato argued that people are born with innate patterns of thought. Although Aristotle tried to demonstarte that the concepts of the universals could be derived from experience, generally speaking, Platonism dominated the Greek and Roman worlds. But the rationalist system could not explain the fall of Rome or the mysteries of the Christian faith and was supplanted by philosophies that could.