Definitions and Words
We just discussed how concepts are formed. There's a little more to know about the topic. At the point I ended the concept formation discussion, we had completed the process of abstraction. But to retain the concept, it needs to go a little further.
The concept, once formed, needs to be able to be referenced in your mind, or through speech. You have to assign it a symbol which you can later use. The symbol can be in many different forms. We call that symbol a 'word'. You're reading lots of them. Usually words come in the form of an auditory symbol. Read any word out loud, and that's what I mean. It can also be visual. You're reading words on the page in a phonetic alphabet. You could also use sign language. The specific way you do it doesn't matter, just so long as you name the concept.
Only by name the concept can you retain you. You keep track of it that way. The word represents the concept. Without the word, you'd have to continuously reform the concept, instead of just using it.
The other point of giving it a name is that you can refer to the concept in a direct way. By giving it a symbol, you make the concept concrete. You allow it to be wielded with ease. You no longer have to focus on the abstraction of the characteristics of the referents. Instead, you give it a sort of mental form. The concept becomes a kind of thing, which you can discuss in a similar way as you'd describe a real thing. So instead of saying "That car-thing right there (pointing) ran fast", you can say "The car ran fast".
Another useful feature for a concept is a definition. Now usually people think of definitions being tied to words. They are, but it's only indirectly because the word is a pointer to the concept. The definition is really a description of the concept. The definition tries to explain the concept by identifying what referents are a part of the concept. It can do this in a few ways. One is that it identifies the characteristics used to form the concept. You could say that blue is a color, which properly identifies what it is you're abstracting. And then you can say it's the color of the ocean, letting them know which color you're referring to.
A definition usually has a genus and a differentia. The genus identifies the concept by putting it into a slightly more general category. You can put the concept 'car' in to the category of 'motor vehicles'. The concept often shares many of the characteristics of the more general category, so it's a good place to start. A differentia then explains the difference between the concept and the other things in the genus. A car is different from a motorcycle because it has 4 wheels, and usually has a passenger seat or more. It's different from a truck in shape and size.
This process of identifying the concept through a definition implies that context is important. If you're differentiating one concept from all others, it matters which other concepts you've formed. If you only know about cars and motorcycles, it's pretty easy to differentiate them. If you add trucks, it's a little harder. Throw in Sport Utility Vehicles and Jeeps, and you start having bigger problems. Since any level of classification is possible in forming a concept, the definition will have to change accordingly.
A simple example of this is the definition of human. "Rational animal" is often used. The animal part gives us a genus, which allows us to identify a number of characteristics about humans (we're alive, we move around, we eat), and it differentiates us from other animals (we're rational). But what happens if we find another animal that's rational. Say dolphins evolve, or we meet an alien from space. We might have to further qualify the definition.
A definition aims to not only describe a particular concept, but describe it in essential terms. We don't want to know every attribute of human beings. It doesn't matter that we have body hair, we reproduce via male-female sexual intercourse, we wear clothes when it's cold, etc. These things may all be true, and a lot more. But since we're trying to identify the concept, we want to look at the most important attributes in the context of what we're talking about. Usually the important attribute of man is that we are rational. But if you were doing medical research, you might find that in your specific area there were more specific characteristics that were important. You might then describe humans in a different way.
A definition not only identifies the referents of the concept, but it places them into the context of your knowledge. When you have a genus and differentia, you are identifying not only the concept, but how it relates to other concepts.
Important things here. First, a definition is a description of a concept, not a word. A word just symbolizes a concept. The word itself is somewhat arbitrary. There may be some conventions that make some words inappropriate for particular concepts (such as using a base that means something entirely different, and adding a standard suffix). And that means, when discussing the proper definition of a word, you really want to focus on the referents. When people start arguing about definitions, they're usually ignoring the facts of reality that they're supposed to be based on.
Not that you can't argue about what's the best definition for a concept. But if both parties are discussing the same concept, there usually isn't too much of a problem. Practically speaking, if they can convey the concept accurately, the definition is probably fine.
And finally, the definition describes the (contextually) most important attributes, in an attempt to identify the concept properly. Understanding what the context is can help you to understand which is the most important attributes. The importance of these attributes is epistemological, not metaphysical. That means we prioritize them based on our needs in using them for knowledge. Knowledge is the goal, and that means some attributes are going to be more important to focus on.