In Summa Theologica II-I Q87 A1 corp. Aquinas says the following:

Now it is evident that all things contained in an order, are, in a manner, one, in relation to the principle of that order. Consequently, whatever rises up against an order, is put down by that order or by the principle thereof. And because sin is an inordinate act, it is evident that whoever sins, commits an offense against an order: wherefore he is put down, in consequence, by that same order, which repression is punishment.

The idea is that when one is directed (or “ordered”) toward an end, one is also directed away from contrary ends. Thus insofar as a part moves contrary to the ends of the whole (or “rises up against the order”, an “inordinate act”), it will be counteracted (“put down”) because of the directedness of the whole towards its ends (“by that order or principle thereof”). This will apply to substantial activities which, as we’ll see in a later post, gives us the correct analysis of common goods and human communities in general.

What’s particularly interesting is that from this simple fact we can derive the three, otherwise intuitive, criteria for just punishment:

1. Guilt: we should only punish those who go contrary to the good of a community, since the order of the whole will only counteract those parts which move contrary to it.
2. Proportion: punishment should be proportioned to crimes, since the order of the whole need only to counteract enough to restore itself from the part’s deviation.
3. Equity: punishments are alike to the extent that their crimes are alike, since the reason for the counteraction is the deviation itself and not some irrelevant factor.