The water, ice, and steam analogy is wrong for most purposes. The only thing it is good for is the logical point that “one and three” is not automatically contradictory if “one” and “three” reckon according to different rationales. But as an account of how the persons in the Trinity are actually distinct it is totally wrong. There are not three forms of of God, because God’s form is the same as his being.
An argument from silence is not an argument, and I do not consider myself in a position to say what Jesus should or should not have said to instruct the Pharisees. Apart from that, I totally agree that they would not have known what a “person” was, because it is a uniquely Christian idea originating in the Church rather than in Israel or even in Greece. But you don’t need to understand the definition of “person” to accept the doctrine of the Trinity by faith. The specification of “substance” and “person” is a developed, formal articulation of a doctrine taught in scripture materially, not formally.
Let me explain what I mean by “material” and “formal.” Material doctrine is the raw data of scripture taken in itself without significant interpretation. Formal doctrine is the expression of scriptural teaching as understood by the Church. A formal understanding of the Trinity is not necessary to believe in it materially, to be a Christian, and to be saved. Material doctrine is sufficient for that. The formal doctrine is a further development, implicit in the material doctrine, that Christians attain to as they grow to maturity.
What Christ does teach to the Pharisees are three doctrines that taken together materially constitute the doctrine that is nowadays known formally as the doctrine of the Trinity:
- Oneness of God: God is one and his nature is expressed in the name I AM.
- Distinction of Father, Son, and Holy Spirit: the three persons are not interchangeable, and they relate to each other as individuals, speak to each other, have personal names, etc.
- Equality of persons: all are the One God in the same sense and with no difference in degree; this does not exclude a subordination of Jesus as a man; although as God, “in the form of God,” he is equal to the Father he “becomes obedient” in taking on flesh and dying, notwithstanding his inherent equality. (Phil 2)
Of course, we don’t just look to what Jesus said to the Pharisees to establish these doctrines, and so I would reject any artificial attempt to make his teaching to the Pharisees a sole standard for determining what he taught about himself and his Father. Yet to limit ourselves for the sake of discussion to just the discourses with Pharisees, all three doctrines can be found there. In fact, you can find the Pharisees being offended by each of the second two and the third in particular. I suspect you already know the arguments for the first part of the doctrine, and you ask questions about the second lower down, so for now I will just discuss the equality of the Father and Son.
The clearest evidence of the equality of persons - which oddly enough the Greek Fathers who framed to doctrine in the first place did not know enough Hebrew to catch on to - is that Jesus teaches that the Father and the son are both Yahweh. Most famous are the I AM statements in John. I know Mormons accept this, but what did the Pharisees think? It must be emphasized that the Pharisees knew of no higher God than Yahweh. There is no separate, higher being called Elohim for them, because they think Elohim and Yahweh are identical. One very representative example of Rabbinical thinking about Yahweh’s identity comes up in the Letter to the Hebrews, when Paul explains that the reason God swore to Abraham by his own name is that there was none higher to swear by. (Heb 6:13) Since Yahweh is the covenant name that God uses in making all his oaths and promises, this means Yahweh is the Most High God, the same as Elohim, El Elyon, El Shadday, etc. To be Yahweh is to be subordinate to no one; the form of all Old Testament covenant oaths is designed to make exactly that point, and Pharisees schooled in the same milieu as Paul understood it in that way.
That the Father is Yahweh is abundantly proven in Scripture, but Jesus teaches it to the Pharisees in particular Matt 22:44, when he interprets Psalm 110 as a discourse of the Father to the Son: “The Lord (
Yahweh) said unto my Lord (
Adonay), Sit thou at my right hand, until I make thine enemies thy footstool.” Everybody knows whose right hands Jesus sits on, and here we are told it is Yahweh.
In working to a material account of the Trinity, we should note that there is a convergence in the doctrine of the Father and Son’s personal equality and the unity of God, because the divine name Yahweh is the locus of both teachings. The name, which simply means “I AM” makes reference to being, and identifies God precisely as he is in the order of being. The same name represents his unqualified sovereignty with none higher than him, not just from our perspective, but from his, since he has no one higher to swear by.