“How many persons are there in the Godhead? There are three persons in the Godhead; the Father, the Son, and the Holy Ghost; and these three are one God, the same in substance, equal in power and glory.”
While “Trinity” is not a biblical word, it is the word that theologians have agreed upon to voice the understanding of God put forth in Scripture and summarized in WSC #6. The idea is that there is one God who exists in three persons. The three persons, Father, Son, and Holy Ghost are all equally God and are one God.
Throughout history, there have been multiple attempts to illustrate or design an analogy to help explain the Trinity. Some have, and still do, explain the Trinity using the analogy of water and its three states or modes, solid (ice), liquid, and gas (steam). However, this analogy fails because God does not exist as one substance that is in different modes at different times. God exists at all times as one God in three persons. The water analogy illustrates the heresy known as modalism.
Others have tried to use the analogy of Neapolitan ice cream. The problem here is that the three flavors do not actually share the same substance and the only “oneness” they have is based on proximity. Ultimately, Neapolitan ice cream beautifully illustrates tri-theism, three gods, but fails to properly explain Trinitarian monotheism.
In the end, there has never been an analogy for the Trinity that does not break down in some major way, so if you here the words, “The Trinity is like…” it is probably a good idea to listen with guarded ears.
Based on the biblical teaching the most that can really be said (without getting into longer more technical formulations) is that which has been handed down for generations in the Westminster Shorter Catechism. “There are three persons in the Godhead; the Father, the Son, and the Holy Ghost; and these three are one God, the same in substance, equal in power and glory.”
The Larger Catechism does take one more step saying the three persons can be distinguished by their personal properties, which it then explains in the next question. “What are the personal properties of the three persons in the Godhead? It is proper to the Father to beget the Son, and to the Son to be begotten of the Father, and to the Holy Ghost to proceed from the Father and the Son from all eternity.”
The doctrine of the Trinity is precious to the church; we would do good to master the simple formulation found in Westminster Shorter Catechism #6.

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