Thank you for the theological question on the Trinity, “How do I explain to a young believer that the Holy Trinity is one God in three persons and not the worship of three different gods?”
Here are some thoughts for one consideration in explaining the Godhead:
A. I would explain that the term, trinity, is not found in the Bible. It is a theological term that the early Church Fathers used to God.
B. I would explain that the term, God, in Hebrew is Elohim. The form of Elohim is plural, which indicates more than one. The number within the Godhead is not known in Genesis 1:1.
C. I would explain that in Genesis 1:2 there is the statement that the Spirit of God was present at the recreation of the Earth. The word, spirit, can be interpreted as an impersonal force or as a being. It is important to show that the Spirit of God is more than an impersonal force, but a being. One may use Ephesians 4:30 as an example that believers are not to grieve the Holy Spirit. One can’t grieve a force but only a being.
D. I would explain that YHWH is the third person of the Godhead. Jesus states that no one has ever seen God (Jn. 6:46), that is God the Father since God is spirit (Jn. 4:24). Jesus states that he is the one who reflects the character of God. Thomas asked Jesus to show him the Father. Jesus reply that he who has seen him has seen the Father.
One may further use the example that YHWH came and spoke to Abraham. In John 8, Jesus says this, “56 Your father Abraham rejoiced at the thought of seeing my day; he saw it and was glad.” Abraham saw YHWH which Jesus said that he saw him. This equates that YHWH is God incarnated as the God-Man.
Have him/her read the Gospel of John and highlight how Jesus relates himself and the Spirit to God the Father. Believers are to be baptized in the name of the Father, and of the Son, and of the Holy Spirit.
It is important not to overwhelm a believer who theological terms, but keeping it as simple as possible. I would emphasis that we pray to God the Father through the Holy Spirit in the name of Jesus Christ. For further reading or thought, one may read Romans 8 and Galatians 5.
One can’t fully explain the Godhead since it is a mystery to us. It is important to emphasize that there two extremes to avoid. One being there are three separate Gods. There is only one God. The other extreme is that there is one God playing three roles as an actor playing differing role.
SUMMARY: Avoid using the term, trinity, rather use the phrase, plurality of the Godhead, for the time being.
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