The New Testament does not contain a doctrine or theology of the Trinity, but it is thoroughly Trinitarian. The epistle for Trinity Sunday provides a sample of Paul’s Trinitarian thought.
Therefore, since we have been justified by faith, we have peace with God through our Lord Jesus Christ. Through him we have also obtained access by faith into this grace in which we stand, and we boast in hope of the glory of God. Not only that, but we boast in our trials, knowing that trials produces perseverance, and perseverance produces evidence [of our faith and/and or God’s grace], and this evidence produces hope, and of this hope we are not ashamed, because God’s love has been poured into our hearts through the Holy Spirit who has been given to us. (Romans 5:1-5) (Author’s translation)
Paul does not appear to have any interest in giving us a philosophical treatise describing the inner nature of God in the heavenly realms. Rather, he gives us the story of salvation in Trinitarian language.
Boasting and shame are themes in Paul’s letter to the Romans. Instead of boasting in the Law, Paul boasts in the hope of the glory of God (an eschatological hope based on God’s mighty acts of salvation in Christ). He also boasts in the suffering that faithfulness to Christ produces because this, too, produces hope. Paul’s two boasts, then, reflect the power of the resurrection and the humility of the cross. Of these, Paul is not ashamed. At the beginning of the letter, Paul stated emphatically that he is not ashamed of the gospel of God (Romans 1:16). Now Paul tells us why he is able to stand against the social pressures of the prevailing worldview: God has poured his love into our hearts by means of the Holy Spirit.
I am happy to affirm the historic creeds of the church with reference to the Holy Trinity, as long as we recall that the creeds are the end of a long process of reflection on the Biblical text rather than the starting point for pointless philosophical speculation.