Is the doctrine of the Trinity a self-contradiction?

This post is a comment on the following --

... Religious propositions are both unverifiable and unfalsifiable. ...

There is a moral order in the universe, written into its most fundamental laws. That order cannot be the product of vain, capricious, quarrelsome “gods” with no particular interest in Mankind. But it can be the product of a Benevolence that stands above all else, that wants for nothing, and that despite its triune nature suffers no conflict. Indeed, that’s exactly what it is.

The reality of morality is *one* of the ways that we can know that God is. Others have presented these proofs; that's not my purpose here.

The reality of morality shows, via reason alone (without reference to any purported divine revelation):
1) not only that God is;
2) and not only that God is transcendent;
3) and not only that God is personal;
but also, shocking to some, that:
4) God is a multiplicity of persons.

A quick proof of proposition 4) is as follows:

Morality is:
a) interpersonal -- only persons *can* have moral obligations and moral expectations, and only with respect to other persons;
b) relational -- all persons' moral obligations (and expectations) follow from their relationships with/to other persons;

now, because morality is interpersonal and relational, it cannot exist if there are no persons in relationship to one another;
but:
c) Morality is also transcendent -- it is not a created thing; its reality is not contingent upon the existence of human persons.

For instance, if morality were not transcendent, if it were after all a created thing, if its reality were contingent upon the existence of human persons, then knowing what are the moral obligations and expectations between *this* father and his son would tell one nothing about the moral obligations and expectations between *that* father and his son.

Since the reality of morality cannot grounded in human persons, it can be grounded only in divine persons.

So, the real existence of morality shows that there is a *multiplicity* of divine persons. Yet, there is but *one* God; to say that there are two or more Gods is incoherent. Yet again, if there is but one divine person, then morality is not transcendent.

How can this paradox be resolved?

The paradox vanishes IF God is one being and a multiplicity of persons.

This argument does not establish the Christian doctrine of the Trinity, that is, that God is *precisely* three Persons, but it does show that the doctrine is not a self-contradiction. And that is the question of the title.