As in Plato’s dialog, Meno, we all have some notions of what certain figures are. For example, we know what a square is. However, some people might be misled by the way one is drawn. A baseball diamond is a square, but it is tilted at 45^o when viewed from home base.

But it is not a simple matter to define things. For example, we know that squares have 4 sides that are equal in length. But is that a good definition of a square? This figure has 4 sides that are the same length, but it isn't a square:

The statement, “a square is a 4-sided figure whose sides have the same length” happens to be a true statement, but it cannot serve as a definition of a square since it is not “reversible.” That is, if the sides of a 4-sided figure have the same length then that figure might not be a square.

A square also has to have its sides perpendicular. In other words, the definition of a square must include all important properties that distinguish a square from other 4-sided figures:

Definition: A square is a 4-sided figure in which all sides are equal and pairs of sides are perpendicular.

We can state 4 properties a good definition must possess:

1. It names the term being defined.

2. It identifies the category to which the term belongs.

3. It states the properties that distinguish the term from others in that category.

4. It is reversible.

In our definition of a square these properties are:

1. Term: square

2. Category: 4-sided figures

3. Properties: equal sides, perpendicular sides

4. Reversible: No other 4-sided figures have those properties.