Aristotle next points out that emotional skills are not naturally instilled in us. The reason, he says, is that natural inclinations cannot be trained, whereas emotions can. Aristotle gives the following (amusing) example. Stones like to fall to the earth, and that's something they do naturally. Consequently, I could never train a stone to fall upwards, even if I spent half my life throwing the stone up in the air over and over again. The stone would never develop the habit of flying upwards, for it goes down naturally.
Emotional skills, on the other hand, can be trained, so they must not be natural proclivities in us. This is not to say that emotional skills are contrary to our nature. No, says Aristotle, we are naturally set up to develop these skills. But the point is that we won't develop these skills naturally. Rather, we need to develop them through training, namely by developing the right habits.
Also, says Aristotle, natural proclivities are first potential and then actual, whereas emotional skills are first actual then potential. The idea here is that natural proclivities are already built-in, and so we can exercise them whenever we want because we already have them. Emotional skills, by contrast, are not built-in. Rather, they need to be developed first. And the only way to develop them is to start doing them: to practice them.
With emotional skills then, we have to start doing them first, and only after doing them for a while can we develop the skill to do them well. For instance, people become good builders by building, and they become good piano players by playing. The same goes for emotional skills: we develop them by practice. They are not built-in in the way that natural proclivities are.
(One might object: some emotions are natural proclivities. Take anger, jealousy, and so on --- surely these are natural responses to certain situations. I suppose, though, that Aristotle could say that although these may appear to us as 'natural responses', they are in fact trained responses; it's just that we have been trained in these ways from a very young age.)
Three invariance arguments
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Suppose we have two infinite collections of items *L**n* and *R**n* indexed
by integers *n*, and suppose we have a total preorder ≤ on all the items.
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