According to Aristotle, definition is a two-step process. To define any kind of thing, you must first establish what this thing or phenomenon has in common with other things, that is, you have to determine to which class of things it belongs. Secondly, you must determine what makes this thing different from others in the same class. This is also known as definition by genus and difference. Thus, he famously claimed that "man" belongs to the class of living things or "animals", but is different from other animals in being rational. This also has to do with the "essence" or nature of thing.
Ludwig Wittgestein suggested that this way of defining or classifying things does not always work . In fact, it fails in some very interesting cases. Thus language is a rather complex phenomenon, or perhaps a complex of phenomena that are rather disparate from one another and cannot be properly understood, by simply relying on the traditional Aristotelian notion of definition. "Instead of producing something common to all that we call language, I am saying that these phenomena have no one thing in common which makes us use the same word for all, - but that they are related to one another in many different ways. And it is because of this relationship, or these relationships, that we call them all 'language'".
He further suggested that "language" was similar to "games" in this regard. There are many different kinds of games, ranging from board-games, card-games, ball-games, games people play, to electronic games, which he claimed have nothing in common, except similarities and relationships. In fact, what we see is "a complicated network of similarities overlapping and criss-crossing," not one property they all share. Therefore, he could not conceive of a "better expression to characterize these similarities than 'family resemblances'; for the various resemblances between members of a family: build, features, color of eyes, gait, temperament, etc. etc. overlap and criss-cross in the same way." Furthermore: "'games' form a family. And for instance the kinds of number form a family in the same way." Often, when we give a name to things, we do so in order to point out that it has "an indirect relationship to other things we call the same name." In this way, we extend our concepts "as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres". (See Ludwig Wittgenstein, Philosophical Investigations (65, 66, and 67).
Leaving open the question whether this is true of language, it certainly describes the way he investigated the philosophical phenomena that interested him.
I also think that it is highly suggestive for the methodology of note-taking. To try and force one's notes into a rigid hierarchy of categories and definition too early can be counter productive. It will stand in the way of seeing indirect relationships to other things. We should develop the concepts and theories based on the notes "as in spinning a thread we twist fibre on fibre." Furthermore, the strength of the thread" will not not necessarily "reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres". This is one of the reason why I like the wiki approach to note-taking as exemplified to my mind best in Connectedtext.
I still think that in the end, that is in publication (which is the end of all ends, isn't it?) "a complicated network of similarities overlapping and criss-crossing" is not enough. You need to present a thesis or two and defend them, as Wittgenstein ultimately did too.