Objection 1. It would seem that joy, sadness, hope and fear are not the four principal passions. For Augustine (De Civ. Dei xiv, 3,[7 sqq.) omits hope and puts desire in its place.
Objection 2. Further, there is a twofold order in the passions of the soul: the order of intention, and the order of execution or generation. The principal passions should therefore be taken, either in the order of intention; and thus joy and sadness, which are the final passions, will be the principal passions; or in the order of execution or generation, and thus love will be the principal passion. Therefore joy and sadness, hope and fear should in no way be called the four principal passions.
Objection 3. Further, just as daring is caused by hope, so fear is caused by despair. Either, therefore, hope and despair should be reckoned as principal passions, since they cause others: or hope and daring, from being akin to one another.
On the contrary, Boethius (De Consol. i) in enumerating the four principal passions, says: "Banish joys: banish fears: Away with hope: away with tears."
I answer that, These four are commonly called the principal passions. Two of them, viz. joy and sadness, are said to be principal because in them all the other passions have their completion and end; wherefore they arise from all the other passions, as is stated in Ethic. ii, 5. Fear and hope are principal passions, not because they complete the others simply, but because they complete them as regards the movement of the appetite towards something: for in respect of good, movement begins in love, goes forward to desire, and ends in hope; while in respect of evil, it begins in hatred, goes on to aversion, and ends in fear. Hence it is customary to distinguish these four passions in relation to the present and the future: for movement regards the future, while rest is in something present: so that joy relates to present good, sadness relates to present evil; hope regards future good, and fear, future evil.
As to the other passions that regard good or evil, present or future, they all culminate in these four. For this reason some have said that these four are the principal passions, because they are general passions; and this is true, provided that by hope and fear we understand the appetite's common tendency to desire or shun something.
Reply to Objection 1. Augustine puts desire or covetousness in place of hope, in so far as they seem to regard the same object, viz. some future good.
Reply to Objection 2. These are called principal passions, in the order of intention and completion. And though fear and hope are not the last passions simply, yet they are the last of those passions that tend towards something as future. Nor can the argument be pressed any further except in the case of anger: yet neither can anger be reckoned a principal passion, because it is an effect of daring, which cannot be a principal passion, as we shall state further on (Reply to Objection 3).
Reply to Objection 3. Despair implies movement away from good; and this is, as it were, accidental: and daring implies movement towards evil; and this too is accidental. Consequently these cannot be principal passions; because that which is accidental cannot be said to be principal. And so neither can anger be called a principal passion, because it arises from daring.
Source: Summa Theologica (New Advent)