That is the problem with trinitarianism. It morphs into tritheism so easily. God is one is the Shema, It is why the Jewish religion does not support the different persons being God. If you can't understand the spirit unless you hold to a post New Testament Trinitarian formulation then we are in trouble. Especially when the trinitarian formula gets the ever present numerical ordering of the the Trinity.
Kind of interesting in this context because then based upont Trinitarian theory we could say that body, soul and spirit are equally three distinct things instead of being one whole, so in the Trinity the tritheistic view becomes the three are separate persons.
That is why I am a Modalist, there is one God who reveals Himself to man in three ways, The father as the Creator, The son, as Jesus Christ God in human forum, and as the Holy Spirit, God in transcendence active in the lives of the individual people. Never separate (as you look at the full scriptures you see all three modes of God are mentioned in such things as Creation or the incarnation) it is always the same God just different ways for people to understand the one God. God was always trying to reach people were they were so some of the things He inspired were likely meant to help people understand at their place and time. It is up to the people afterwards to grow in their understanding as we learn more about the world around us and thus more about God.