Yet we wouldn’t accept such a definition even if it itemized every possible exception. Why? Because, from a different point of view, this definition is inadequate: not because it fails to bring the meaning of the definition closer to the actual meaning of courage, but because all it does is try to save the original definition by tacking on ad hoc exceptions. That is, we reject it because it fails to be a good, well-formed definition. A good definition is simple and provides a principle that would exclude all possible exceptions without having to enumerate them one by one.

What do we do? We come up with a new definition that once again is simple (without adding exceptions). We could try, “Courage is the ability to act while confronting a great fear.” Adding “confronting” would seem to disqualify tying one’s shoelaces and even shouting profanities since one could shout profanities while running away.

Yet adding an ad hoc exception may sometimes be just what is called for. Suppose I define courage as “the ability to act while confronting a danger to oneself.” “Confronting” is retained, so this would (normally) exclude running away. Yet one could also act out of anger, so that courage may not be the principal trait exhibited. We could add the ad hoc hypothesis “except when motivated principally by anger.” This would be desirable in this case, for the phenomenon turned out to be composite — actions that may arise from separate causes (courage and anger).

It’s important to see that this process — like that whereby a poem is written — rests on two requirements that have to be met. A good definition or poem must be one (a) whose expressed meaning matches the actual meaning that was grasped in a pre-articulated way and (b) which satisfies some criterion of form (embodies an explanatory principle or satisfies poetic form).

Now compare this with a scientific example: Johannes Kepler’s discovery that the orbit of Mars is an ellipse.

In this case, the actual meaning of courage (what a definition is designed to define) corresponds with the actual observations that Kepler sought to explain — that is, the data regarding the orbit of Mars. In the case of definition, we compare the literal meaning of a proposed definition with the actual meaning we want to define. In Kepler’s case, he needed to compare the predicted observations from a proposed explanatory hypothesis with the actual observations he wanted to explain.

Early on, Kepler determined that the orbit of Mars was not a circle (the default perfect shape of the planetary spheres, an idea inherited from the Greeks). There is a very simple equation for a circle, but the first noncircular shape Kepler entertained as a replacement was an oval. Despite our use of the word “oval” as sometimes synonymous with ellipse, Kepler understood it as egg-shaped (in the asymmetrical chicken-egg way). Maybe he thought the orbit had to be lopsided (rather than symmetrical) because he knew the Sun was not at the center of the oval. Unfortunately, there is no simple equation for such an oval (although there is one for an ellipse).