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It is useful to distinguish two kinds of definitions: "center focused definitions" and "boundary focused definitions." A center focused definition is concerned with telling us what the most perfect example of something is. A boundary focused definition is concerned with making clear what does and what does not fall within the category. These two kinds of definitions tend to have different uses.
There is a clear line between Arizona and California. In principle, the line has no width at all. Any object or person, or any event, is either in California or in Arizona or, by straddling the line, is in both. If you commit a crime on one side the Arizona authorities worry about it. If on the other side, the California authorities worry about it. Defining Arizona or California as the territory that lies within its boundary lines is, of course a boundary focused definition.
In archaeology we create a boundary focused definition when we say, for example, that the "Classic" period in Mexican archaeology is that time which extends from AD 300 to AD 900. An event that takes place in 901 is by definition post-Classic. An event in 899 is by definition Classic. Our definition clarifies the boundaries of the period. It is intended to imply nothing else. It is characteristic of a boundary focused definition that something either falls within it or does not. There is no being "more Classic" or "less Classic" with this kind of definition.
If, on the other hand, we speak of the Classic as the period in which Teotihuacan rose to prominence and influenced many other peoples across central Mexico, the definition becomes center focused. Exactly what dates fall into the Classic and what dates do not becomes impossible to say without leaving some ambiguous cases; on the other hand it becomes meaningful to speak of one or another artifact or site as being "more perfectly Classic" than another, or "further from the center of Classic influences," or the like.
Some boundary focused definitions require that several conditions be met for an object to qualify as a member of the category being defined. For example, to qualify as a "resident" for purposes of deciding whether or not non-resident tuition is due, the University of California requires that you (1) be a US citizen and (2) have established residence in California more than one year immediately preceding the residence determination date and (3) be an adult and (4) be financially independent of non-resident parents, as proven by their not taking you as an exemption on federal tax returns. (Click me.) Unless you satisfy all these requirements, you are not defined as a "resident," however vigorously you "reside" here. Each of the rules sets boundaries to residency with the intent that every human can be unambiguously classified as either a resident or a non-resident, and the collective effect is that only those who are residents under each of the separate rules can be classifed as a resident.
Center focused definitions lay out what is central or typical of something, without concern about marginal cases. In archaeology we speak of the "Neolithic" as involving (1) food production rather than foraging, (2) fixed communities, (3) pottery, (4) incipient class differentiation, (5) larger size settlements than those of foraging peoples. These are all relative rather than absolute ideas.
But what if some food is produced and some is foraged? What if the community is fixed for nine months of the year but moves into a seasonal home for the remaining three? What if there is no pottery but there are extremely elaborate gourds and baskets? What if class differentiation is non-existent or highly developed? Our definition of "Neolithic" leaks like a sieve. It would never be useful in court. But it captures a range of features that tend to be highly correlated with each other, and for which, as a cluster, it is convenient to have a label. A center focused definition is intended to describe the "ideal type" of what is defined, a standard against which other examples may be measured. It is not intended to identify precisely what items do and not belong in a class, but to suggest how central they are to it.
Range of Convenience. Because a center focused definition has a center, it also has a periphery: some things are at the "edge" of the category and can be said to fall outside the "range of convenience" of the definition. For example, the fermented products secretly produced in prisons and dormitories may be "beer" in some sense, but for most purposes they fall outside the range of convenience of the term "beer" as it is ordinarily used. Similarly, cadenced speech may or may not qualify as "poetry." Wagering a kiss may or may not count as gambling. Last night's warmed-over pizza may or may not count as "breakfast." Broad paraphrase may or may not count as plagiarism. And so on. All of these strain the range of convenience of definitions.
Most definitions in everyday life are center focused ones, not boundary focused ones. It is hard to get too rigid about the definition of "nerd," for example, or of "party" or of "yellow." It turns out that for certain purposes people actually think a lot more clearly with center focused definitions. Here is an example:
In studying paleontology we talk about the classification of fossils of various extinct "human" and "ape" forms. It is possible to define a "Classic Neanderthal" or a "typical Australopithecus." But when specimens turn up that have a "mix" of characteristics, classifying them becomes very difficult. So too does deciding when a term like "human" can appropriately be applied. When a new form is defined, usually based on very little fossil evidence, we normally must start with a center focused definition. It is difficult to develop clear consensus about the exact boundaries of these forms, and hence to develop agreement about how we would make a boundary focused definition.
Although in such a case learning more about these fossil forms could allow us to move from a center focused to a boundary focused definition, neither type of definition is inherently associated with greater knowledge. They simply have different uses. To count "how many" of something we encounter —how many valuable cars are in the parking lot?— we need to know what is and what is not a countable instance. For this, we need a boundary focused definition. (How expensive must a car be to count as valuable?) But to characterize the nature of something —how good are meals at Café Ventanas?— we often need a center focused definition. (The ice cream is better than the hot dogs, and the sushi are good, but the salads are too expensive.)
In science, creating boundary focused definitions in order to do rigorous research on the concepts is called "operationalization." The word seems normal to me, but I find that people outside of the university stare at me if I use it. People operationalize ideas all the time. They just don't think of it that way.
Passing laws is concerned with making boundary focused definitions out of center focused ones, that is of operationalizing them. We know some people are insane, but what should count as a legitimate "insanity plea"? We know some people are poor, but how "poor" must you be to get food stamps? We know some people are rich, but how much income should flip a person into a higher tax bracket? In creating legal answers to these questions, we must operationalize the terms "insane," "poor," and "rich" so as to place every person either inside the category or outside it.
Similarly in social research we may want to know how well people like a television program, say, or which people like it. When we do our survey, we operationalize "like" (such as "answers with the word 'like' in the telephone survey") so that all cases are unambiguously classified.
In archaeology we may want to know whether "cities" are significantly associated with "river basin adaptations," but to be precise about it we need to operationalize both terms, that is, to create boundary focused definitions of them.
In general, by operationalizing, we convert a center focused definition into a boundary focused one, which allows us to count examples, calculate correlations, and so on.
(Random thought: When that last paragraph is turned into an exam question, it is surprising how many people miss it. I wonder if that'll be true when it appears on this year's exam? Hmmm.)