The trinitarian symbol is the easiest way to understand what the doctrine of the trinity is (see below). The Father, Spirit and Son are all God, but the Father is not the Son, the Son is not the Spirit, the Spirit is not the Father, etc. Another analogy is water: water can exist as solid, liquid or vapor; it’s the same essence manifesting in different forms.
The mystery of the trinity is really the mystery of unity. Because people have so many barriers between them – physical, psychological and spiritual – we have a difficult time comprehending how three entities can be so unified that they are one. “I don’t mean to push past mystery and try to make light of mystery, but…It’s not a logical inconsistency,” says Ken Wytsma, Pastor of Antioch Church in Bend, OR and Founder of The Justice Conference. “It is perfectly conceivable from a philosophical standpoint.”
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The Trinity on Wikipedia