According to Reformed churches, is the trinity a finalized doctrine? From 325 AD at the Council of Nicea up to about the 8th century, councils have been held to determine the correct nature of God. It was eventually decided that the bible reveals a triune god- one god existing as three divine persons. Although shrouded in mystery and containing contradictions that are labeled "beyond our human comprehension", the trinity doctrine has been the most popular Christology for centuries. According to the Westminister Confession of Faith:


  “The whole counsel of God, concerning all things necessary for his own glory, man’s salvation, faith, and life, is either expressly set down in scripture, or by good and necessary consequence may be deduced from scripture: unto which nothing at any time is to be added, whether by new revelations of the Spirit, or traditions of men.”


Suppose I work my way up the ranks to become a respected and exalted member of the church. One day, I have a divine revelation that Wisdom is not merely personified in the bible, but is the fourth person of the Quadrilateral god. Of course, my idea would have many critics. They may say "Proverbs 8:22–30 says Wisdom was brought forth, so it cannot be the eternal god", to which I'd reply "Wisdom is eternally brought-forth through the eternal generation" or something. 

I would show that Wisdom is described as a person that can speak, think, and that Jesus even says she has her own children. I could even quote Theophilus of Antioch to show that I'm not the only one who believes Wisdom is a divine person of God. 

Anyways, my question isn't about whether the Quadinity is true. 

Is the trinity a completed doctrine and too sacred to be reformulated, or do Reformed churches allow alternative ideas to be presented and considered?
Yes and no.  That is, in simple terms:


No, the doctrine of the Trinity is not "finalized" or "completed" – Reformed theologians regularly debate the intricacies of this doctrine
Yes, the doctrine of the Trinity is "finalized" – anyone who rejects the fundamentals of the Trinity would generally not be considered "Reformed."


Your quote of the Westminster Confession of Faith refers to the canon of Scripture, to which nothing may be added, but Reformed thinkers regularly attempt to develop better (and sometimes new) understandings of Christian doctrines, including the doctrine of the Trinity.  But a radically divergent view of God, such as the quadrinity you mention, would be rejected as not Reformed.



All Reformed confessions strongly defend the Trinity.  Here's what one of them says:


  In the unity of the Godhead there be three Persons of one substance, power, and eternity: God the Father, God the Son, and God the Holy Ghost. The Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father;  the Holy Ghost eternally proceeding from the Father and the Son. (Westminster Confession of Faith, II)


Other Reformed confessions go into more detail, but none of them exhaustively describe the doctrine.  Thus, it's possible for two people to say "I affirm Chapter II of the Westminster Standards" but disagree on some aspects of the doctrine of the Trinity.  This actually happens with great regularity.  Here are two examples:


Karl Barth's innovations in the doctrine of the Trinity were a lightning rod in 20th century Reformed theology.  Some Reformed theologians claimed that went too far, but others didn't object.  See my answer to Did Karl Barth confess an orthodox doctrine of the Trinity?
Robert Reymond, in his New Systematic Theology, and Wayne Grudem, in his Systematic Theology, find themselves on opposites sides of an ongoing debate within Reformed circles over subordination of the Son to the Father.  Some admit a "subordination of role," while others do not.


So "no," the doctrine of the Trinity is not finalized; it is something that theologians will likely continue to argue over for a long time to come, because of its central place in Reformed doctrine.

But the importance of the doctrine also means that, "yes," the doctrine of the Trinity is finalized – in Reformed circles, it isn't going anywhere.  Those who reject the basics of the Trinity will generally be considered outside the bounds of Reformed theology, and, if they wish to teach their views, forced to join (or start) another branch.

Of course, "Reformed theology" is just a label, and as such it is applied differently by different people.  As previously mentioned, some consider Barth Reformed, and others don't.  But the Reformed confessions provide helpful guidance in this respect – people who explicitly reject confessional teachings of the Trinity, including someone arguing for a "quadrinity" as you mention, would certainly be outside the bounds of the Reformed confessions, and therefore generally considered outside Reformed theology.