It's my understanding that we use division to classify things in the world so that we can define them, say, with a genus-species tag.

However, in the introductory books I've read, they mention that you want mutual exclusion of the members/species in your classification. I don't see how this is possible if we wanted to create a giant classification for all things. Because how could we have mutual exclusion if we want to be able to define terms like "not happiness" and "anger" in the same giant classification?

If a giant classification like this is not possible, then what's the point in using classification to define things at all if they can't all be related to one another?

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    – J D
    Commented Dec 3, 2019 at 9:26
  • What does it mean : "a giant classification for all things" ? Commented Dec 3, 2019 at 9:26
  • Humans use Categories to organize our understanding of the world we live in. We have Natural Kinds and we have arbitrary classifications. Not every "category" is mutual exclusive: you cited the genus-species where they are related by the inclusion relation. Commented Dec 3, 2019 at 9:28
  • Maybe you arev referring to Diairesis : the Platonic division style of argument. Commented Dec 3, 2019 at 9:37
  • 2
    The type of classification you are referring to is classical categorization. It is only the base classes that need to be mutually exclusive and collectively exhaustive, it does not mean that one can not have overlapping derivative classes analyzable into those base classes. If our base classes are A, B and C then derivative classes A or B, B or C overlap. And categories (properties) themselves are dual to the classes, they supposed to be not non-overlapping but independently assignable.
    – Conifold
    Commented Dec 3, 2019 at 10:52

3 Answers 3


Beware of conflating individual attributes themselves with objects that can have those attributes.

For instance, "happy" and "angry" are two different emotions. Their individual definitions might be mutually exclusive, but that doesn't mean that their existence is mutually exclusive. It is possible for someone to experience both emotions at the same time.

Hello, My name is Iñigo Montoya. You killed my father. Prepare to die. — YouTube

You ask: "how could we have mutual exclusion if we want to be able to define terms like "not happiness" and "anger" in the same giant classification?"

If you want to be able to do that, you can't, at least not in a useful way.

A properly defined classification system requires that all elements directly within a larger class be mutually exclusive and collectively exhaustive (MEACE)

So, if you have a general "emotions" class, then "happy", "sad", "angry", etc. will all be members of that class.

If your system requires a "not happy" classification, then in order to be MEACE, then the "emotions" class can have only two members: "happy" and "not happy", with all the other emotions being members of one of those two classes.

It would work, and it meets the MEACE requirement, but it would be a much less useful system than if it didn't require the "not happy" class.

And, if you wanted it to have a "not angry" class too, you would be out of luck. It's simply not possible to classify emotions that way. Some emotions would have to be in "not angry" and in "*not happy" at the same time, and that's not allowed.

  • Thanks. But what if we wanted to be able to define both "not happy" and "angry". That would mean we would need two separate classifications? Commented Dec 5, 2019 at 21:42

You've hit on an important philosophical issue.

If we define every-thing as a set then 'everything' cannot be a set. Hence fundamental theories must transcend sets and the categories of thought in the manner of Kant or the Perennial philosophy. If we do not do this we cannot have a fundamental theory.

The mystics call this place the 'world of opposites' for just the reason you give in the question. A global category can have no opposite.


Generally speaking, a classification system is an inclusion system. The ideal is that if we have a stream of objects in front of us, we can sort those objects into appropriate buckets based on the characteristics of the objects themselves. There may, of course, be buckets within buckets, but the buckets are meant to be mutually exclusive.

With that in mind, any negation category — like 'not happy' — is a misconstruction. If we make a category for 'happy' with appropriate criteria, then anything that does not fit those criteria is 'not happy' by implication. Such things might fall into some other bucket, or they might fall outside all of our buckets and roll around loose on the table (very annoying, that), but we don't construct a separate category based on the fact that they do not fit in one given category. If we find objects that seem like they should be put in two buckets, or that don't fit into any bucket, that's usually a sign that our categorizations system needs to be redesigned.

So, if we have a category system for emotions — where 'emotions' is an overarching category, different from (say) 'thoughts' or 'perceptions' — then we might add add a bunch of inclusion subcategories within that main category: anger, joy, confusion, fear, greed, etc. We would hope that every emotion we experience would fall neatly into one subcategory or another. If we run across an emotion that seems to fall into two categories, or that doesn't fit well in any of them, then we have to revise our category criteria or create a new category (e.g., as Sartre did when he coined the term 'existential angst').

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