The Ancient Greeks had a theory, and it changed the whole world. That theory was a unifying principle between like things. Plato called these the forms or ideas. They were supposed to be real, concrete, ideal versions of everyday things which existed in some other realm divorced from the world we live in and only accessible to the philosopher.
Aristotle later improved upon this idea with an approach more grounded in reality. He said that these forms were in the things which instantiated them. So the form of a tree was present in every tree, and this was called its substance or essence. Aristotle also makes a distinction between substantial and accidental differences between things. The substantial differences are those which make things different substances. That is, their forms are different because they are different things. This is the difference between a fish and a mammal.
On the other hand, accidental differences are differences between particulars of the same essence. The difference between two members of the same animal species, like eye color, are accidental.
Later, after Aristotle, many philosophers started to say that these essences weren’t really in the world, but only in our minds (Aristotle thought they were in both the things which instantiate them and in the minds of rational beings). They looked at the differences between things of the same kind and thought that we couldn’t really call all of these differences “accidental.” They found that there was really no such thing as an “essential property,” or a property that something has necessarily.
An example of something that may, at first glance, be thought to be an essential property of man (by this I mean human beings) is reason. It seems like this is something which distinguishes men from everything else, at least in part. But we can imagine that a man may not possess reason, as in the case of severe brain damage. But this is still a man, so how can there really be an essence of men that includes reason? It should be obvious that this can be demonstrated for any supposed “essential property.”
But there are essences. That is, there is a unification between things of the same kind. And this cannot be merely a human convention or a mental construct. This unification affects the way things behave and the way they are. Our ability to predict future events based on what kinds of thing something is is evidence of this. If there were not some unification between all acorn trees that they reproduce using acorns, we could not expect acorns to grow into acorn trees with any sort of regularity. This prediction is only possible because we are supposing there is something like “being an acorn tree” which is actually common to all acorn trees.
What can we say of these properties distinguishing essences which nevertheless seem to be only accidental? The term used to refer to these is “proper accidents.” The first place I encountered this term was Dr. Edward Feser’s Scholastic Metaphysics, and it is perhaps the most interesting idea I have found in Scholasticism. A proper accident is an accident (meaning is can be changed without altering the substance) which is proper to all things with a particular essence. That is, given a particular essence in a thing, that thing will have certain features in the normal course of events.
We can think about the proper accidents of a man to help us understand this. A man, in the normal course of events, has reason, has four limbs, and has eyes. These are due to his being man, so they are some of his proper accidents. But a man without reason is still a man, a man without limbs is still a man, and a man without eyes is still a man. But all of these men have a defect. They lack a perfection of the essence of man. If we contrast this with an accident which is not proper, say, eye color, we can see that a man with blue eyes is no more or less perfect than a man with brown eyes, all else being equal. Thus, a proper accident could also be defined as any property without which a thing will be defective.
Now someone will say to me “would you really say an amputee is defective?” Yes, but defective here is not identical with disposable. None of us has every proper accident in the most perfect way, and thus none of us is perfect. But the more closely we approximate the essence, that is, the more perfectly we have all of our proper accidents, the more perfect we are.
So these proper accidents are what makes men more or less good. The could be thought of as virtues, in the most ancient sense. They are characteristics of a thing which make it a better instance of that kind of thing. If a thing could have all of them perfectly, it would be perfect itself.