Objection 1. It would seem that there are not four cardinal virtues. For prudence is the directing principle of the other moral virtues, as is clear from what has been said above (Question 58, Article 4). But that which directs other things ranks before them. Therefore prudence alone is a principal virtue.
Objection 2. Further, the principal virtues are, in a way, moral virtues. Now we are directed to moral works both by the practical reason, and by a right appetite, as stated in Ethic. vi, 2. Therefore there are only two cardinal virtues.
Objection 3. Further, even among the other virtues one ranks higher than another. But in order that a virtue be principal, it needs not to rank above all the others, but above some. Therefore it seems that there are many more principal virtues.
On the contrary, Gregory says (Moral. ii): "The entire structure of good works is built on four virtues."
I answer that, Things may be numbered either in respect of their formal principles, or according to the subjects in which they are: and either way we find that there are four cardinal virtues.
For the formal principle of the virtue of which we speak now is good as defined by reason; which good is considered in two ways. First, as existing in the very act of reason: and thus we have one principal virtue, called "Prudence." Secondly, according as the reason puts its order into something else; either into operations, and then we have "Justice"; or into passions, and then we need two virtues. For the need of putting the order of reason into the passions is due to their thwarting reason: and this occurs in two ways. First, by the passions inciting to something against reason, and then the passions need a curb, which we call "Temperance." Secondly, by the passions withdrawing us from following the dictate of reason, e.g. through fear of danger or toil: and then man needs to be strengthened for that which reason dictates, lest he turn back; and to this end there is "Fortitude."
In like manner, we find the same number if we consider the subjects of virtue. For there are four subjects of the virtue we speak of now: viz. the power which is rational in its essence, and this is perfected by "Prudence"; and that which is rational by participation, and is threefold, the will, subject of "Justice," the concupiscible faculty, subject of "Temperance," and the irascible faculty, subject of "Fortitude."
Reply to Objection 1. Prudence is the principal of all the virtues simply. The others are principal, each in its own genus.
Reply to Objection 2. That part of the soul which is rational by participation is threefold, as stated above.
Reply to Objection 3. All the other virtues among which one ranks before another, are reducible to the above four, both as to the subject and as to the formal principle.
Source: Summa Theologica (New Advent)