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Aristotle's Accidents
For Aquinas, as for Aristotle and Aristotelians generally, there's a special class of accidents that the substance can't live without. A triangle is by nature a three-sided figure; it's having interior angles that add up to 180 degrees is also an accident. These special accidents are like essences in that the substance cannot live without them. But they are still accidents because they are non-fundamental,. They are caused rather than being fundamental principles that give rise to the substance in the first place.