Roughly speaking, in a book like this, there are two types of "definition". A relatively simple type of definition is used to specify the meaning a new word or phrase, by describing it with familiar words and phrases. A much more complicated type, some times called "working definition", is used to specify the meaning a word or phrase which is already familiar to the readers.

Working definition is needed when a word will be used with a specific meaning, which may either be one of several common usages of the word, or be different from all of them. An author introduces a working definition to clarify the meaning of the word in his writing, so as to avoid misunderstandings, as well as to indicate what he thinks what it should mean, despite of the current common usage.

A classic treatment to this topic was given by Rudolf Carnap. In Carnap (1950), he explained what he think the word "probability" should mean. Beside proposing a definition, he also discussed the "meta-problem" of "transformation of an inexact, prescientific concept, the explicandum, into a new exact concept, the explicatum." He proposed four requirements: similarity, exactness, fruitfulness, and simplicity, with the following explanation:

If a concept is given as explicandum, the task consists in finding another concept as its explicatum which fulfills the following requirements to a sufficient degree.

1. The explicatum is to be similar to the explicandum in such a way that, in most cases in which the explicandum has so far been used, the explicatum can be used; however, close similarity is not required, and considerable differences are permitted.

2. The characterization of the explicatum, that is, the rules of its use (for instance, in the form of a definition), is to be given in an exact form, so as to introduce the explicatum into a well-connected system of scientific concepts.

3. The explicatum is to be a fruitful concept, that is, useful for the formulation of many universal statements (empirical laws in the case of a nonlogical concept, logical theorems in the case of a logical concept).

4. The explicatum should be as simple as possible; this means as simple as the more important requirements (1), (2), and (3) permits.

I have been following the same requirements when given working definitions. Obviously, very often a compromise is needed when the requirements conflict. For example, words in natural language usually hard to define, so a relatively more exact and simple definition is often less similar to the original word. On the other hand, to use a word in a theory in the same way as it is used in everyday life would make the theory too uncertain to be fruitful. Therefore, to stress one requirement too much is not a good idea.