Is the Trinity one thing, or three things? Answer either way, and you will find yourself in trouble.
This is because an answer to such a question is bound to result in misunderstanding because articulating the doctrine of the Trinity in terms of “things” simply is not helpful. We must distinguish further.
For instance, we can say that the Trinity is three things, in that there are three persons. On the other hand, one may point to the single divine nature shared by the persons or that the three persons considered together as a Trinity constitute a single group and therefore respond that the Trinity is one thing. The fact of the matter is, further distinction is needed- “thing” is too broad of a category. When such distinctions are provided and the discussion is narrowed to become more specific, we are able to intelligently articulate what God has revealed.
The classical categorical distinction by which the doctrine of the Trinity was articulated was between the philosophical categories of ‘person’ and ‘essence’. By ‘person’, we refer to the individual. Any individual of a rational nature is a person, such as a man, an angel, or God. On the other hand by essence we mean the nature that exists in persons in abstract, such as human nature, or the divine nature. Thus when we speak of essence we are not speaking of an individual existence, but a common set of characteristics that are the common to many individuals.
We see this understanding of essence vs person articulated by Basil the Great:
“The distinction between οὐσία [essence] and ὑπόστασις [person] is the same as that between the general and the particular ; as, for instance, between the animal and the particular man.” (Letter 236)
These distinctions have allowed classical trinitarianism to be summed up as “one essence, three persons”. Without such distinctions, we will be left either denying the unity of nature shared by the persons, or else deny the distinction of their persons.
It is in part, I believe, because of a lack of proper distinction between these categories that many conceive of the Trinity as being a single person. For when ‘one essence in three persons’ gets confounded with, or traded for ‘one person in three persons’, drastic conceptual differences result.