Dear Rey:

From my point of view, there is a clear separation between classes (a.k.a concepts) and instances (a.k.a individual). A class represents a set of objects (abstracts or not), meanwhile, an instance represents just one occurrence of a class. For example, Country is a class of objects, and Cuba is just an instance of the Country class. The subsumption relationship in a set of classes is based on the Category theory. In some cases, a.k.a subsumptive containment hierarchy [1]. Maybe, if you could provide an example of your context, we can share some other ideas.

Best regards.

[1] https://en.wikipedia.org/wiki/Hierarchy#Subsumptive_containment_hierarchy

Thak you Yusniel for your contribution. In fact I am looking for a way of formalizing, or make "calculable" the determination of what is an instance. I'll try to explain: when one says the people living in Greenland is a subset of men, it is clear because we know, they have, they have the same properties of the men set. When one say "John is an instance of set of men", it is supposed that one KNOWS that John has the properties of men. But: why is John an instance and not a subclass? John is a set of, say, organs. They problem is that these organs don't have the human properties (some of them, yes, but not the system of them).

Then, what is the formal step when one thing can not be considered a subset of higher category? Here is where I one to find and formal expression of that, different from knowing by experience or by comparing properties. Probably it is an intuitive by nature knowledge (like defining what is a set), but I was thinking that the concept of level of analyzing can be an approach to the problem. In that case, the minimal level of analyzing of any concept is the instance of that concept. Or, might be, considering the dialectical law of quantitative accumulation, leading to qualitative "jumps", but using that idea in the contrary direction...

Just thinking....

Best regards,

Rey.

Would the empty set or the 'impossible' concept be a counter example.... or, famously, the class of unicorns?

We tend to identify patterns (either consciously or subconsciously) across objects. Leaves on a tree are green, but so is grass; rocks are hard, and so is concrete. We find some of these identified patterns more useful than others. For example, 'green' is a more useful identified pattern than 'green or concrete'. These useful patterns are almost always coarse-grained abstractions. "The green grass" makes no mention of the grass being cylindrical, for instance. Even our use of extensive collections of patterns, e.g. green, cylindrical, sharp, etc., won't necessarily uniquely identify a given object, e.g. a blade of grass. And if it did, that would be such a lengthy, cumbersome, list to make, it'd be nearly useless.

Fortunately, we don't have to make such lengthy lists of patterns. We instead draw a distinction between classes (useful, coarse-grained, identified, patterns) and instances (focal points of pattern collections). Consequently, as a rule of thumb: classes repeat; instances don't. In a given classroom, there are often several humans but only one Human, i.e. there are several instances of Human, but only one class Human.

All that said, Rey Segundo Guerrero-Proenza you suggest there's equivocation in saying "John" is an instance since - because John has organs - it seems just as clear he's a set of some sort, namely, of organs. True, the instance of John has organs, and they might form a set, and indeed, all of John's parts might form a set. But this doesn't mean the instance "John" is identical to the "complete set of John parts". If that were true, then since sets are extensional, if John lost a cell part he'd no longer exist.