Understanding if mental illness excuses helps us understand excuses in general. This sounds paradoxical: unless we first fully understand the notion of excuses, we cannot decide whether insanity is an excuse. But if the concept of excuses is already fully understood, how can understanding whether insanity is an excuse throw any further light on it? The answer is that we do not have to fully understand the concept of excuses before we tackle the question of whether insanity excuses. The final meaning of the concept remains open until we have answered this latter question. Take the example of numerical equality: to decide when one class has the same number of members as another, we need to count the members. However, answering the question of whether there are as many even numbers as whole numbers may change the way we think about numerical equality. A more basic way to decide whether two classes are equal in size is to put the members in a one-to-one correspondence: if every member of one class can be related to one (and only one) member of the other class (with no remainder), then the classes are numerically equal. But this can be done for all the even numbers and whole numbers - for any even number, there is a whole number to which it can be placed in oneto-one correspondence with no remainder. Therefore, the two classes are equal in size (both have an infinite number of members)! Having to answer this question requires some prior understanding of numerical equality, but this understanding is not fully settled until we examine this question. Similarly, I hope to show that answering the question of whether insanity is an excuse throws light on the notion of excuses itself.