>>662477
The dominant opinion in Catholicism is that the doctrine of the Trinity is known only by faith from divine revelation. You cannot reason to it in the same way as the doctrine of God's existence. That said I have heard that St. Bonaventure argued otherwise, but I don't know any more about that.
>>662475
St. Thomas gives a few argument outlines in Summa Theologiae. The easiest to understand is the second, IMO.
>Secondly, [that there is only one God] is proved from the infinity of His perfection. For it was shown above (I:4:2) that God comprehends in Himself the whole perfection of being. If then many gods existed, they would necessarily differ from each other. Something therefore would belong to one which did not belong to another. And if this were a privation, one of them would not be absolutely perfect; but if a perfection, one of them would be without it. So it is impossible for many gods to exist. Hence also the ancient philosophers, constrained as it were by truth, when they asserted an infinite principle, asserted likewise that there was only one such principle.
If there were many "gods" they could not truly be called gods (unequivocally) because they would lack the infinite perfection of God.