A term for a concept formed through abstraction and from categorization?

Question

For e.g, lets say you take the number 1, 2, 3, 4... etc. From these list of numbers, you can abstract from these ideas the concept of a number. You can't do this if you only know of the number 1, if so, it would be the number, rather than a number, but I digress.

Lets now say you want to define specific types of numbers, like integers, decimals, or primes. This is abstraction though categorization. As you already had the concept of a number, you aren't making an entirely new concept, in and within itself, but categorizing a concept and defining new concepts for those categories, which is part of the main concept.

Furthermore, in the former case, when the concept is formed, you expand your scope, in the former, you are narrowing it down to greater precision. So the two ways in which concepts can be formed should, I feel, be given precise terms.

Answer 1

I think you want generalization (1, 2, 3 are numbers), specialization (a number is 1), and possibly subcategorization (numbers are odd, even, prime).

Answer 2

This sounds like a question a developer would ask, and I'll posit that classification is perhaps the word.

For instance, in object-oriented programming (OOP), objects from the outside world, such as cars and trucks, can be represented in code; we call these Classes. For instance, we can have a Car class, and a Motorcycle class, both of which might extend from a parent class of Automobile that happens to contain a numberOfWheels property, and say, color or anything else that's common between the two.

This is very similar to your numbers example. In OOP, we'd have a Double class (like a decimal), an Integer class, an so on, that extends from a Number class, which in turn extends from the God-tier object - the most generic of all - Object:

But don't take my word for it:

• Double: https://docs.oracle.com/javase/7/docs/api/java/lang/Double.html
• Object: https://docs.oracle.com/javase/7/docs/api/java/lang/Object.html