More Logic
written August 14, 2016
Consider a number of entities.
Each entity can be associated with the X or Y trait, or rarely, both or neither. Each entity can also be associated with a number of integers.
Here are some entities:
 Alpha has X and 1, 3, and 5.
 Beta has Y and 2, 4, 6, and 8.
 Gamma has X and 1, 5, and 6.
 Delta has Y and 1, 5, and 9.
 Epsilon has X and Y and 1, 2, 5, 6, and 9.
 Zeta has neither X nor Y, and 1, 4, 7, and 8.
Assume that most entities look like Alpha and Beta. We can form two classes from these entities, A and B. A has X and odd numbers, while B has Y and even numbers. Alpha and Beta are easy to categorize into classes A and B. We can also see from Alpha and Beta (and the unknown examples like them) that A and B are likely mutually exclusive. However, to categorize the other four entities is tricky.

Gamma has X and two odd numbers, but one even number. We can still say that Gamma is an A because it has X and is mostly odd. We can flex the definitions by saying that A just has an affinity for odd numbers, and B for even.

Delta has Y, but only odd numbers no evens. Is Delta an A or a B? It can be an A because it has X, but it can also be a B since it has only even numbers. Maybe it's both at the same time?

Epsilon has both X and Y, and a plethora of numbers. Epsilon is quite clearly both A and B simultantiously.

Zeta has neither trait, and a mix of numbers. Is Zeta neither A nor B? Or is Zeta both A and B?
As you can see, problems arise.
Maybe A and B aren't just labels, but two ends of a spectrum? We can create a spectrum of A to B and put every entity in a place on it.
Maybe A and B are two axes of a chart, and entities have differing amounts of Aness and Bness?
Maybe we should create a third class, C, for anything that doesn't fit neatly into A or B?
Maybe we should restrict the definition of A and B to the presence of X and Y, and ignore the integers? Or maybe restirct the definition to the integers and ignore X and Y?
Or maybe, just maybe, we can agree that the class definitions of A and B don't work, and there's no way we can make them work, and we should just judge entites for their traits and integers on their own?
Nah, that's a silly idea.