Happily, the ultimate grounds of the doctrine are not to be sought exclusively in these two verses. Rather, the foundations of the doctrine of the Trinity are to be found in the pervasive pattern of divine activity to which the New Testament bears witness. The Father is revealed in Christ through the Spirit. There is the closest of connections between the Father, Son, and Spirit in the New Testament writings. Time after time, passages link these three elements as part of a greater whole. The totality of God's saving presence and power can only, it would seem, be expressed by involving all three elements (for example, see 1 Corinthians 12:4-6; 2 Corinthians 1:21-2; Galatians 4:6; Ephesians 2:20-2; 2 Thessalonians 2:1314; Titus 3:4-6; 1 Peter 1:2).
The same Trinitarian structure can be seen in the Old Testament. Three major "personifications" of God can be discerned within its pages, which naturally lead on to the Christian doctrine of the Trinity. These are:
1. Wisdom This personification of God is especially evident in the Wisdom literature, such as Proverbs, Job, and Ecclesiastes. The attribute of divine wisdom is here treated as if it were a person (hence the idea of "personification"), with an existence apart from, yet dependent upon, God. Wisdom (who is always treated as female, incidentally) is portrayed as active in creation, fashioning the world in her imprint (see Proverbs 1:20-3; 9:1-6; Job 28; Ecclesiastes 24).
2. The Word of God Here, the idea of God's speech or discourse is treated as an entity with an existence independent of God, yet originating with God. The Word of God is portrayed as going forth into the world to confront men and women with the will and purpose of God, bringing guidance, judgment, and salvation (see Psalm 119:89; Psalm 147:15-20; Isaiah 55:10-11).
3. The Spirit of God The Old Testament uses the phrase "the spirit of God" to refer to God's presence and power within creation. The Spirit is portrayed as being present in the expected Messiah (Isaiah 42:1-3), and as being the agent of a new creation which will arise when the old order has finally passed away (Ezekiel 36:26; 37:1-14).These three "hypostatizations" of God (to use a Greek word in place of the English "personification") do not amount to a doctrine of the Trinity in the strict sense of the term. Rather, they point to a pattern of divine activity and presence in and through creation, in which God is both immanent and transcendent. A purely unitarian conception of God proved inadequate to contain this dynamic understanding of God. And it is this pattern of divine activity which is expressed in the doctrine of the Trinity.
The doctrine of the Trinity can be regarded as the outcome of a process of sustained and critical reflection on the pattern of divine activity revealed in Scripture, and continued in Christian experience. This is not to say that Scripture contains a doctrine of the Trinity; rather, Scripture bears witness to a God who demands to be understood in a Trinitarian manner.
Alister E. McGrath, Christian Theology: An Introduction.