one of the hardest things to convey to people is what constitutes a plausible definition. so here's  a handout i've been using in one form or another for years. also on the handouts page.

The Task of Definition

There are various sorts of definition, such as stipulative definition, which simply assigns a certain meaning to a word or sign, as in the meanings of mathematical terms.

But we are more concerned with defining terms that are in use in ordinary language, but about the meaning of which we are puzzled or which is controversial. This would include all the major terms in philosophy of art, such as ‘art,’ ‘work of art,’ ‘beauty,’ ‘expression,’ and the like.

The task of definition in such cases is to capture the meaning (as best one can) that is actually associated with the term in everyday usage,  that allows us to use the term successfully in communication. Thus, in part, the task of definition could be conceived to be empirical: we find out, for example, to what sorts of items competent speakers of the language apply the term in question.

One starts with the set of items in question (the things commonly called works of art, for example) and then tries to show what is common and peculiar to them all: in this case what all and only the works the works of art have in common. Then the term is adequately defined.

Another way to state this is that an adequate definition of a term ‘x’ provides necessary and sufficient conditions for the correct application of the term. You could think of necessary conditions for something to count as an x as properties that all x’s have in common; sufficient conditions for something to count as an x are properties that only x’s have in common. Or again, an adequate definition of ‘x’ states the properties that all and only x’s possess.

The way to test or refute a proposed definition, hence, is by counter-example. There are two sorts of counter-example:
(1) an item which the definition counts as an x, but which is not an x.
(2) an item which the definition does not count as an x, but which is an x.

For example, let’s say we define “work of art’ as any object that expresses emotion. Now I’m expressing emotion when I’m yelling at my kids, but that’s not (usually) a work of art. That is, the definition counts yelling as a work of art, but yelling is not a work of art. That is, the definition does not provide sufficient conditions for the correct application of the term.
On the other hand, consider a canvas by Mondrian or a sculpture by Donald Judd: plausibly, these are quite inexpressive or unemotional works. That is, the definition does not count them as works of art, but they are. That is, the definition does not provide necessary conditions for the correct application of the term.

Strictly speaking, a single counter-example of either kind is enough to refute a definition or to show it to be inadequate.