What is the Trinity?
According to the Catechism of the Catholic Church,
253 The Trinity is One. We do not confess three Gods, but one God in three persons, the "consubstantial Trinity". The divine persons do not share the one divinity among themselves but each of them is God whole and entire: "The Father is that which the Son is, the Son that which the Father is, the Father and the Son that which the Holy Spirit is, i.e. by nature one God." In the words of the Fourth Lateran Council (1215), "Each of the persons is that supreme reality, viz., the divine substance, essence or nature."
254 The divine persons are really distinct from one another. "God is one but not solitary." "Father", "Son", "Holy Spirit" are not simply names designating modalities of the divine being, for they are really distinct from one another: "He is not the Father who is the Son, nor is the Son he who is the Father, nor is the Holy Spirit he who is the Father or the Son." They are distinct from one another in their relations of origin: "It is the Father who generates, the Son who is begotten, and the Holy Spirit who proceeds." The divine Unity is Triune.
255 The divine persons are relative to one another. Because it does not divide the divine unity, the real distinction of the persons from one another resides solely in the relationships which relate them to one another: "In the relational names of the persons the Father is related to the Son, the Son to the Father, and the Holy Spirit to both. While they are called three persons in view of their relations, we believe in one nature or substance." Indeed "everything (in them) is one where there is no opposition of relationship." "Because of that unity the Father is wholly in the Son and wholly in the Holy Spirit; the Son is wholly in the Father and wholly in the Holy Spirit; the Holy Spirit is wholly in the Father and wholly in the Son."
I am expected to show that there is one God in three persons in scripture. For the sake of argument and historical heresies, I will cite a few sources showing that God is one and the Father is God but not elaborate as historically these statements aren't disputed but rather that the Son and Holy Spirit are likewise God. As for the Son, I must show that He is God but not the Father nor the Spirit; and for the Spirit likewise that He is God but not the Father nor the Son. If my opponent agrees that there is no disagreement with God being One and the Father being God, I believe it right to not waste time debating something we agree on. If my opponent however disagrees that God is One and/or the Father being God I shall nonetheless cite a few passages for him to contest.
One God
Isaiah 45:5 I am the LORD, there is no other, there is no God besides me.
Deuteronomy 6:4 Hear, O Israel! The LORD is our God, the LORD alone!
Exodus 20:3 You shall not have other gods beside me.
The Father
1 Corinthians 8:6 yet for us there is one God, the Father, from whom all things are and for whom we exist...
Ephesians 4:6 one God and Father of all, who is over all and through all and in all.
Isaiah 64:7 Yet, LORD, you are our father...
The Son
Again, here I must show three things: that the Son is God, the Son is not the Father, the Son is not the Holy Spirit
John 1-1;14 In the beginning was the Word, and the Word was with God, and the Word was God.; And the Word became flesh and made his dwelling among us, and we saw his glory, the glory as of the Father’s only Son, full of grace and truth.
Here in John 1:1 we seem to have a contradiction of phrases. "The Word was with God" shows that the Word and God are distinct from one another. However, "the Word was God" states that the Word and God aren't distinct. In Trinitarian theology, this is easily understood. The Word, which we are told became flesh and is the only Son of the Father in John 1:14, is said to be with God showing a distinction of personhood. He is at the same time said to be God confirming the divinity of the Son with the Father. In this sense, there is no contradiction with the text.
Luke 3:22 and the holy Spirit descended upon him in bodily form like a dove. And a voice came from heaven, “You are my beloved Son; with you I am well pleased.”
Here we see all three persons of the Trinity mentioned. Jesus is identified as the Son by the Father. Unless God is a deceiver, the Father distinguishes Himself from the Son. The text also distinguishes the Spirit and Jesus as the Spirit is He who descends upon Jesus.
Acts 3:15 The author of life you put to death, but God raised him from the dead; of this we are witnesses.
In Acts, Jesus is referred to as the author of life. In what way is Jesus the author of life if He did not create it?
John 1:3-4 All things came to be through him, and without him nothing came to be. What came to be through him was life, and this life was the light of the human race;
It is in this way that Jesus, the Son of the Father, the Word, is the author of life. He is identified as Creator of all things including life.
Matthew 4:7 Jesus answered him, “Again it is written, ‘You shall not put the Lord, your God, to the test.’”
Luke 4:12 Jesus said to him in reply, “It also says, ‘You shall not put the Lord, your God, to the test.’”
Here Jesus tells Satan that he is not supposed to put God to the test, yet Satan is testing Jesus.
Isaiah 41:4 Who has called forth the generations from the beginning? I, the LORD, am the first, and at the last I am he.
Isaiah 44:6 Thus says the LORD, Israel’s king, its redeemer, the LORD of hosts: I am the first, I am the last; there is no God but me.
Isaiah 46:12 Listen to me, Jacob, Israel, whom I called! I, it is I who am the first and am I the last.
Revelation 1:8 “I am the Alpha and the Omega,” says the Lord God, “the one who is and who was and who is to come, the almighty.”
In these four citations we see that it clearly states God as the first and the last, the Alpha and the Omega. Alpha and Omega are the first and last letters of the Greek alphabet. Alpha and Omega = First and Last.
Revelation 2:8 ...“‘The first and the last, who once died but came to life, says this:
God died and came back to life? More than one person has died and come back to life but when did God die let alone come back to life?
Revelation 1:17-18 When I caught sight of him, I fell down at his feet as though dead. He touched me with his right hand and said, “Do not be afraid. I am the first and the last, the one who lives. Once I was dead, but now I am alive forever and ever.
Is God truly claiming that He died and is now alive? How does this make sense? When did God die?
Revelation 22:12-13 “Behold, I am coming soon. I bring with me the recompense I will give to each according to his deeds. I am the Alpha and the Omega, the first and the last, the beginning and the end.”
Here God is claiming that He is coming soon. He is using the same titles that we saw earlier.
Revelation 22:16 “I, Jesus...
Revelation 22:20 The one who gives this testimony says, “Yes, I am coming soon.” Amen! Come, Lord Jesus!
Here in the final passages of Revelation, not only does Jesus show Himself to be the one talking but the author also reveals that the one who is coming, the Alpha and Omega, the first and the last, is also Jesus. Not only does God identify Himself by these titles but Jesus as well. It seems as if Jesus and the author are positing the divinity of Christ. By claiming divine titles, He claims himself to be God.
The Spirit
First is to distinguish the Spirit from the Father and the Son. Being that the Spirit is labeled 'of God' and 'of Christ' or some other similar manner, the idea that it is possessed indicates that it is not the possessor. The relation of possessor/possessed identifies two distinct persons.
Acts 5:3-4 But Peter said, “Ananias, why has Satan filled your heart so that you lied to the holy Spirit and retained part of the price of the land? While it remained unsold, did it not remain yours? And when it was sold, was it not still under your control? Why did you contrive this deed? You have lied not to human beings, but to God.”
Here, Peter claims that Ananias lied to the Spirit and later claims that as lying to God.
1 Corinthians 2:12 We have not received the spirit of the world but the Spirit that is from God, so that we may understand the things freely given us by God.
Galatians 4:6 As proof that you are children, God sent the spirit of his Son into our hearts, crying out, “Abba, Father!”
Paul states that we received the Spirit that is from God and in Galatians God sent the Spirit of His Son. Here the Spirit of God and of Christ are the same spirit. But the Father is not sending Himself nor is He sending the Son. The Spirit is He who is being sent.
1 Corinthians 2:11 Among human beings, who knows what pertains to a person except the spirit of the person that is within? Similarly, no one knows what pertains to God except the Spirit of God.
Here, Paul claims that the Spirit of God is within God and knows what pertains to God. If this is true, just as much as your spirit is yours and is you the Spirit of God is God's and is God.
1 Corinthians 3:16-17 Do you not know that you are the temple of God, and that the Spirit of God dwells in you? If anyone destroys God’s temple, God will destroy that person; for the temple of God, which you are, is holy.
1 Corinthians 6:19-20 Do you not know that your body is a temple of the holy Spirit within you, whom you have from God, and that you are not your own? For you have been purchased at a price. Therefore, glorify God in your body.
In these two verses we see a parallel. Our bodies our called the temple of God in one verse and of the Spirit in the other verse. In the second verse we are called to glorify God that's in our body. This ties into the previous passage on the Spirit's identity. As much as our spirit is us, the Spirit of God is God. Here the divinity of the Spirit is explicitly stated.
I would like to quote and explain one final passage:
Matthew 28:19 Go, therefore, and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the holy Spirit,
Here we see the three persons of the Trinity mentioned, the Father, the Son, and the Holy Spirit. However, they are said to have one name. If these are three separate beings, in what way do they have one name? In Trinitarian theology this is simple, the three persons are distinguished from each other, but their one name is 'God' representing their one being. If not God, what name do they share?
I am intentionally keeping this short. There are dozens and dozens of passages that I can use but for the sake of debate I will not write a book that's worth 2000 years of Church history. God bless!