Modalism: Strongly refuted by the relationship and distinction between the Father and the Son. Oh, the Father gushes with love over the Son! “This is my Son, whom I love. Listen to him!” The Father sent the Son. The Son glorifies the Father, the Father glorifies the Son. The Son does what he sees the Father doing. The Father works through the Son. The Father bears witness of the Son, and the Son bears witness of the Father.
Arianism: Strongly refuted by the glory of the Son. He is the Yahweh whom Isaiah saw in glory. The Lamb “standing as though it had been slain” is worshipped by the myriads, just as the one sitting on the throne is. He was equal with God, yet condescended to become human, even a human servant, even a human servant who died on a cross! All should honor the Son, just as they honor the Father.
Tritheism: Strongly refuted by the supremacy and oneness of God. He is the Most High. He alone is God. There is none like Yahweh. None before and none after. He knows of none other. He is a jealous God and will not give his glory to another. He does it “for his own sake, COMMA, for his own sake.” All things are from him, and through him, and to him. To him be all the glory, forever. Amen!
The arguments for the Trinity are strong and conclusive. But even if we supposed that the arguments for it are weak, it still wins out against the competing options (tritheism, modalism, Arianism), since the arguments *against* the competing options are strong and conclusive.
In other words, if in the “live pool” of options all your possible interpretations are weak, but one stands out above the others, the strongest is the most rational choice to make.