A definition is a proposition that tries to make a thing's nature clear to us. The terms of this proposition must be transposable without requiring a change in either quality or quantity. In definitions, in other words, extension and comprehension must be equivalent in the subject and attribute, as in: “Every man is a two-handed mammal = every two-handed mammal is a man.”

It's often said that there are two kinds of definitions – of things and of words.

Definitions of things reveal their nature, while those of words reveal their meanings. The Port-Royal logicians insisted that the difference between these two kinds of definitions is so great that each follows its own laws. Where definitions of words are arbitrary and nominal in the sense that a word might be given any definition whatever, definitions of things try to explicate the nature of real objects and thus can't be arbitrary. Definitions of words are incontestable, whereas definitions of things can be false and subject to debate.

But is this distinction valid? It doesn't seem so to us. Whenever we define something, whether it be a thing or a word, we're expressing its idea in terms of a proposition. Here's a definition: “Geometry is the science of sizes.” Now, how could we accept that this definition, as a definition of things, is so different from what it would become if we substituted some other word for “geometry”?