As many of you may know, Thomas Aquinas ("the Angelic Doctor") was a devout Medieval philosopher-theologian, who
effected an influential Trinitarian synthesis by combining thoughts from Scripture with ancient Greek thought. Hence, what Thomas has to say about the demonstrability of the Trinity doctrine is noteworthy. The following quotes can be found in
Edmund J. Fortman's The Triune God: A Historical Study of the Doctrine of the Trinity. See pp. 204-205.
"that God is triune is uniquely an object of belief,
and one cannot prove it in any demonstrative way. Some
reasons can be advanced but they are not
necessitating, and they have probability only for the
believer" (In Boeth de Trin 1.4).
"we can only know what belongs to the unity of the
essence, but not what belongs to the distinction of
the persons" (Summa Theologiae 1a.32.1).
Thomas contends that the Trinity is not irrational, but
transrational: it is a divine mystery that surpasses
all human understanding.
The Doctor has subsequently been criticized for making an
unnecessary distinction between God de Uno
and God de Trino. Observe how Thomas professes that
while the one essence of Deity can be known by means of natural reason, the personal distinctions of the Godhead cannot be known via ratio.