The following article shows the arguments for and against the make-up of the Godhead and this does not deal with the use of the word Trinity, instead we use the word Tri-unity of the Godhead. (The main emphasis of the article looks at the mechanics of the Godhead; this is to be the focus).
There has been a constant argument between those who hold to Tri-Unity, Bi-Unity or Oneness theology, as to how the Godhead is constituted, whether the Father, Son and Holy Spirit constitutes the God, or it is the Son and the Father(the Holy Spirit being simply an impersonal force) or that the Father, the Holy Spirit and Son, are actually Jesus. The accusation constantly being levelled at the Tri-une doctrine is that it is a heresy that originated out of the Roman Catholic Church. It is hoped that this article will address the problem as to what the Bible actually says when dealing in this area.
The Godhead is constructed of three distinct characters yet these are not separate gods but one God. The Bible does not use the word “trinity” but rather “Godhead”. The word “trinity” is seen by the Jews as an anti-Semitic term. So to save any further confusion I will use “Godhead” and how it can easily be shown that the mechanics of the Godhead is made up of the Father, Son & the Holy Spirit.
The case against the mechanics of the Godhead:-
The term Trinity is not biblical or it would be in the scriptures.
None of the writers of the Bible used the term Trinity, “God in three persons”, etc. Therefore the word trinity is a test for error or apostasy.
Matthew 4:4 states “It is written, “'Man shall not live by bread alone, but by every word that comes from the mouth of God.'”. The word “Trinity” never proceeded out of Gods mouth, which proves it is heretical.
The doctrine of "Trinity" is of the Devil.
Jesus never pre-existed he was created through Mary.
Jesus is the Father.
Modalism - Jesus is the only person of the Trinity, but appears in three modes at different times.
The "Holy Trinity" is a blend of recycled paganism from Nimrod's Babylon with Bible titles and unscriptural terms and traditions added, then decreed by Emperor Constantine as the official new religion of the Roman Empire, which was enforced upon all pagans, and apostate Christian’s. After many years of debate, revisions, versions, evolutions, arguing and elimination of dissenters) the doctrine of the Trinity was imposed, in order to unify the nearly collapsed Roman Empire of the 4th century AD. Hence, the “Holy Trinity” is of the whore, Roman Catholicism, and was passed on to her daughters, the Protestant sects.
The Case for the mechanics of the Godhead:-
The Mechanics of the Godhead were taught and defended by the following men who predate the Roman Catholic Church:-
Polycarp (70-155/160). Bishop of Smyrna. Disciple of John the Apostle.
"O Lord God almighty... I bless you and glorify you through the eternal and heavenly high priest Jesus Christ, your beloved Son, through whom be glory to you, with Him and the Holy Spirit, both now and forever" (n. 14, ed. Funk; PG 5.1040).
Justin Martyr (100?-165?). He was a Christian apologist and martyr.
"For, in the name of God, the Father and Lord of the universe, and of our Savior Jesus Christ, and of the Holy Spirit, they then receive the washing with water" (First Apol., LXI).
Irenaeus (115-190). As a boy he listened to Polycarp, the disciple of John. He became Bishop of Lyons.
"The Church, though dispersed throughout the whole world, even to the ends of the earth, has received from the apostles and their disciples this faith: ...one God, the Father Almighty, Maker of heaven, and earth, and the sea, and all things that are in them; and in one Christ Jesus, the Son of God, who became incarnate for our salvation; and in the Holy Spirit, who proclaimed through the prophets the dispensations of God, and the advents, and the birth from a virgin, and the passion, and the resurrection from the dead, and the ascension into heaven in the flesh of the beloved Christ Jesus, our Lord, and His manifestation from heaven in the glory of the Father ‘to gather all things in one,' and to raise up anew all flesh of the whole human race, in order that to Christ Jesus, our Lord, and God, and Savior, and King, according to the will of the invisible Father, ‘every knee should bow, of things in heaven, and things in earth, and things under the earth, and that every tongue should confess; to him, and that He should execute just judgment towards all...'" (Against Heresies X.l)
Tertullian (160-215). African apologist and theologian. He wrote much in defense of Christianity.
"We define that there are two, the Father and the Son, and three with the Holy Spirit, and this number is made by the pattern of salvation... [which] brings about unity in trinity, interrelating the three, the Father, the Son, and the Holy Spirit. They are three, not in dignity, but in degree, not in substance but in form, not in power but in kind. They are of one substance and power, because there is one God from whom these degrees, forms and kinds devolve in the name of Father, Son and Holy Spirit." (Adv. Prax. 23; PL 2.156-7).
The Scriptural argument for Mechanics of the Godhead:-
The word "Godhead" occurs three times in the scriptures (Acts 17:29, Rom. 1:20, Col 2:9) of which there are three different Greek words translated Godhead in these occurrences,
Theios - qei'oß (Acts 17:29), Theiotēs - qeiovthß (Romans: 1:20) and Theotēs - qeovthß (Colossian 2:29).
According to Thayer's Greek-English Lexicon , the Greek word Theios describes a general name of deities or divinities as used by the Greeks spoken of the only and true God, while this word along with Theiotēs may also be translated, "divinity, divine nature"
A distinction may be made between the two words ‘Theios/Theiotēs’ which reflect the attributes of God, His Divine nature and properties and ‘Theotēs’ that indicates the divine essence of the Godhood and very the personality and state of being God 
Thayer thus concludes that the Godhead may be seen as encompassing, divinity, divine nature, and the essence of God Himself. He also highlights that the Greek term for "God" is the word ‘Theos’ which means "divine, supreme divinity, deity". The word Theos is not a title, but a Greek word that describes who Jesus is.
John 20:27-28 Then He said to Thomas, “Reach your finger here, and look at My hands; and reach your hand here, and put it into My side. Do not be unbelieving, but believing.” And Thomas answered and said to Him, “My Lord and my God (Theos)!”
Romans 9:5 Christ came, who is over all, the eternally blessed God (Theos). Amen.
Jesus Himself emphasises this point while speaking to the religious leader of His day:
John 8:56-59 Your father Abraham rejoiced to see My day, and he saw it and was glad.” Then the Jews said to Him, “You are not yet fifty years old, and have You seen Abraham?” Jesus said to them, “Most assuredly, I say to you, before Abraham was, I AM.” Then they took up stones to throw at Him; but Jesus hid Himself and went out of the temple, going through the midst of them, and so passed by.
Jesus Himself here professes to have pre existed before Abraham, and He even applies one of the very names of God to Himself – ‘I AM’ (Exodus 2:12-14). There can be no mistaking this – that is surely why the Jews picked up stones. They were going to stone Him for blasphemy! It is further interesting to carefully note the response of the guards who came to seize Jesus when He proclaimed who He was once again, shortly before His crucifixion:
John 18:4-6 therefore, knowing all things that would come upon Him, went forward and said to them, “Whom are you seeking?” They answered Him, “Jesus of Nazareth.” Jesus said to them, “I am He.” And Judas, who betrayed Him, also stood with them. Now when He said to them, “I am He,” they drew back and fell to the ground.
Note: Italicised words do note appear within the original Greek texts.
The Godhead consists of three entities.
The term God (divine) is applied to the Father (Romans 1:7), the Son (Hebrews 1:8), and the Holy Spirit (Acts 5:3,4). While three entities comprise the Godhead (state of being God), they are one in nature, purpose, and thinking (John 14:8-11). The scriptures never refer to the Father, Son, and Holy Spirit (Godhead) as ‘gods’. When "gods" is used, it refers to idols or pagan pantheons.
Moreover, it is significant that the Hebrew adjective of singularity (one) is used with the plural noun God (Elohim). "Hear, O Israel: the Lord our God is one Lord" (Deuteronomy 6: 4). Notwithstanding, the scriptures clearly present three separate and distinct entities or personalities: 2 Corinthians 13:14, Ephesians 4:4-6, Matthew 3:13-17.
The Apostle John describes Jesus as being the ‘Word’ (Greek – Logos λόγος). Both John 1:2 and 1 John 4:14 state that this Logos (Word) pre-existed and was sent by His Father. John 1:14 describes how the Logos becoming flesh and manifesting as the only begotten (monogenēs) son of the Father.
John 1:14 And the Word became flesh and dwelt among us, and we beheld His glory, the glory as of the only begotten of the Father, full of grace and truth.
Psalm 2 is widely considered a Messianic psalm prophetically describing the Lord's "Anointed One" (verse 2). It contains in verse 7 the divine decree: "You are my son, today I have become your Father." Verse 12 contains the words "Kiss the son". This psalm denotes a Father—Son relationship between God and the Messiah, who as the son would be the heir (verse 8). Isaiah 9, also considered a Messianic prophecy, describes the coming Messiah as "Mighty God" (verse 6).
Isaiah 9:6 For unto us a Child is born, Unto us a Son is given; And the government will be upon His shoulder. And His name will be called Wonderful, Counselor, Mighty God, Everlasting Father, Prince of Peace.
Psalm 110 describes the LORD (understood as God the Father) sharing his eternal glory with the psalmist's Lord (understood to be the Son, the Messiah).”
Psalm 110:1-2 The LORD said to my Lord, “Sit at My right hand, Till I make Your enemies Your footstool.” The LORD shall send the rod of Your strength out of Zion. Rule in the midst of Your enemies!
Jesus is the Incarnation of God according to Hebrews 2:5-18 while John 1:14 declares that Jesus has not been created. Matthew 1:20-23 describes how the Angel of the Lord appeared to Joseph in a dream and that through the birth of Jesus the Messianic prophecy of Isaiah 7:14 would be fulfilled: Jesus would be given the name Immanuel (Hebrew עִמָּנוּאֵל ) translated God with us. This meant that Jesus was God fully united to man.
Isaiah 7:14 Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel.
In John 1:3, John an Apostle of Jesus confirms Jesus’s divinity by stating that:
John 1:3 All things were made through Him, and without Him nothing was made that was made.
The same confirmation can be found in Colossians 1:16 and Hebrews 1:1 &10. Paul, in the book of Romans 10:9-13, testifies that Jesus is the same Lord that Isaiah 44:24 talks about. Psalm 2:7 again shows Father God’s confirmation of His Sons existence in heaven before He took human form. John also records that Jesus was worshiped by Thomas an Apostle of Jesus (John 20:28). In Colossians 1:13–19 Jesus is the Direct Image of God, when the people looked upon him they knew God took human form. (Matthew 9:18, Matthew 14:33, Matthew 15:25, Matthew 28:9, Matthew 28:17 and 1 Timothy 3:16 all say that God was manifested in the flesh).
The Godhead can be seen in Jesus relationship with his father in Matthew 11:25. This scripture is very unique as it shows the exclusive bond that Jesus has with His Father, this is why if we are to know Father God we must know the Son. Thus in John 14:6 Jesus and the Father are both Theos (God).
The Bible also teaches God is ONE God, but that He eternally self-exists in nature as Father, Son, and Holy Spirit, according to the Scriptures (Matt. 3:16, 17; 28:19; Philippians 2:11; John 1:1; 2 Peter 1:1 [in Greek and more accurate translations], Acts 5:3,4).
Let us look at John 1:18 and what it means within the context of a holistic view of the Bible.
John 1:18 No one has seen God at any time. The only begotten Son, who is in the bosom of the Father, He has declared Him.
The prophet Micah tells us that:
Micah 5:2 “ But you, Bethlehem Ephrathah, Though you are little among the thousands of Judah, Yet out of you shall come forth to Me The One to be Ruler in Israel, Whose goings forth are from of old, From everlasting.”
Not only can we understand that the coming Messiah would be born in Bethlehem, but that His going forth is from everlasting! His very being is one from eternity. It is for this reason that many scholars conclude that it was the Messiah himself (who is the image of the invisible God) – God, who manifested Himself to Abraham along with two other angels (Genesis 18), To Jacob as he wrestled (Genesis 32), to Moses in the burning bush (Exodus 3) and in communion along with the 70 elders of Israel (Exodus 24)
Exodus 24:9-11 Then Moses went up, also Aaron, Nadab, and Abihu, and seventy of the elders of Israel, and they saw the God of Israel. And there was under His feet as it were a paved work of sapphire stone, and it was like the very heavens in its clarity. But on the nobles of the children of Israel He did not lay His hand. So they saw God, and they ate and drank.
We could also consider Joshua who saw and worshipped the Commander and Chief of the Lords Army (Joshua 5:13-15), and Samson’s parents (Judges 13). We could go on and on…
Therefore, John 1:18 cannot mean God was never seen, but the main point that is overlooked is the fact that this passage does not say "no one has seen God in human flesh at any time." The first premise of the anti-triune argument is based on a misinterpretation of the verse and an addition to the verse, i.e., the idea that the passage refers to "God in human flesh." Jesus is revealed as God manifested in the flesh in John 1:1, 14 and 1 Timothy 3:16. John 1:18 simply means no one has seen God in the totality of His being as a Spirit, or His "face".
 Ben Rast puts it this way
There is only one God
The Father is God
Jesus is God
The Holy Spirit is God
While God the Father is only known as the Father in the New Testament, Christians, Jews, Muslims, and pseudo-Christian cults understand that the Father in the New Testament is the Yahweh of the Old Testament, though some disagree with the characterization of “Father”. However, it is important to establish that the Father of the New Testament is the true God referred to in the Old Testament, known often as Yahweh, or “Jehovah”.
Jesus as we have seen accepted worship. This is not adoration of a mere prophet, but praise and worship due only to God. Jesus was either God or He was crazy, and there is ample evidence against the latter and in support of the former. Further evidence comes from the fact that Jesus has many of the attributes of God:
Creator (John 1:3, 1 Corinthians 8:6; Colossians 1:16-17; Hebrews 1:2; Revelation 3:14)
Unchanging (Hebrews 1:10-12; 13:8)
Eternal (John 1:1; 8:58; 17:5; Colossians. 1:17; Hebrews 1:2)
Omniscient (John 16:30)
Omnipresent (Matthew 18:20; 28:20; John 3:13; Ephesians 1:23; 4:10; Colossians 3:11)
It is clear from the Scriptural evidence above that Jesus is God. He is the LORD (Jehovah/Yahweh) of the Old Testament, and therefore is the one true Elohim or Theos. He shares this role as God with the Father. As we are about to see, He also shares this role with the Holy Spirit.
The Godhead can also be seen in the following scriptures, John 3:17, 35; 5:22-23, 31-32; 8:16-18; 11:41-42; 12:28; 14:31; 17:1-26; Romans 1:7; 1 Corinthians 1:3; 15:24-28; 2 Corinthians 1:2; Galatians 1:3; 4:4; Ephesians 1:2; 6:23; Philippians 1:2; 1 Thessalonians 1:1; 2 Thessalonians 1:1-2; 1 Timothy 1:1-2; 2 Timothy 1:2; Titus 1:4; Philemon 3; James 1:1; 2 Peter 1:2; 1 John 4:10; 2 John 3
This can even be explained through the ontological views of God (the study of natural elements to explain the Godhead):
 This can be defined as:
Marriage: two distinct individuals, are joined as one.
Class of being: deity, Mankind: Singular word for a class of being composed of many individuals.
Family: Singular word comprised of many members.
Organization: Singular word for a group of individuals functioning together for a common goal or purpose.
Church/Body: Singular word with Christ as the head and individual Christians as the body.
Unity: Three can be one in unity and purpose.
Witnesses in Heaven to the Godhead
1 John 5:7–9 For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one. And there are three that bear witness in earth, the Spirit, and the water, and the blood: and these three agree in one. If we receive the witness of men, the witness of God is greater: for this is the witness of God which he hath testified of his Son.
Acts 2:32-33 This Jesus God has raised up, of which we are all witnesses. Therefore being exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, He poured out this which you now see and hear.
John 17:20-22 “I do not pray for these alone, but also for those who will believe in Me through their word; that they all may be one, as You, Father, are in Me, and I in You; that they also may be one in Us, that the world may believe that You sent Me. And the glory which You gave Me I have given them, that they may be one just as We are one:
The testimony of Jesus Divinity:
Matthew 3:16–17 "As soon as Jesus Christ was baptized, he went up out of the water. At that moment heaven was opened, and he saw the Spirit of God descending like a dove and landing on him. And a voice from heaven said, 'This is my Son,( Greek: υἱός, huios) whom I love; with him I am well pleased.'"
The Son pleased the Father being the firstborn Son of God, God is known through the Son. The Son is the eternal object of the Father's love, John 17:24, and the sole Revealer of the Father's character, John 1:14; Hebrews 1:3. The words, 'Father' and 'Son,' are never in the NT so used as to suggest that the Father existed before the Son; the Prologue to the Gospel according to John distinctly asserts that the Word existed 'in the beginning,' and that this Word is the Son, Who 'became flesh and dwelt among us '.
Mark 1:10–11 And straightway coming up out of the water, he saw the heavens opened, and the Spirit like a dove descending upon him: And there came a voice from heaven, [saying], Thou art my beloved Son,( Greek: υἱός, huios) in whom I am well pleased.
Luke 3:22 And the Holy Ghost descended in a bodily shape like a dove upon him, and a voice came from heaven, which said, Thou art my beloved Son; (Greek: υἱός, huios) in thee I am well pleased.
John 1:32 - 34 And John bare record, saying, I saw the Spirit descending from heaven like a dove, and it abode upon him. And I knew him not: but he that sent me to baptize with water, the same said unto me, Upon whom thou shalt see the Spirit descending, and remaining on Him, the same is he which baptizeth with the Holy Ghost. And I saw, and bare record that this is the Son (huios) of God (theos).
Huios Theos: The title Son of God is not of office, but it is what is used to describe his nature and divinity and this title is used to describe the relationship between the father and the son. It is who he is, his proper and true divinity. Nathaniel shows at his first meeting with Philip and called Him (Jesus) the Son of God (John 1:49)
Luke 1:35: "The angel answered and said to her, 'The Holy Spirit will come upon you, and the power of the Most High will overshadow you; and for that reason the holy Child shall be called the Son (huios) of God (theos).'"
Thus we can see from the Greek wording of these scriptures that the divinity of God (theos) is applied to the Son (huios), thus the term Son of God actually denotes God the Son.
The Hebrew name for God is Elohim (a plural form) and Jehovah this shows His power and pre-eminence, God is self-existing,  the Divine attributes are likewise indicated or definitely predicated of Christ, e.g., Matthew 20:18, 19; John 1:1-3; 1:18; 5:22-29; 8:58; 14:6; 17:22-24; 20:28; Romans 1:4; 9:5; Philippians 3:21; Colossians 1:15; 2:3; Titus 2:13; Hebrews 1:3; 13:8; 1 John 5:20; Revelation 22:12,13.
Matthew 28:19: "Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit"
Let us again remember:
1 John 5:7 For there are three that bear record in heaven, the Father, the Word, (logos) and the Holy Ghost: and these three are one.
The Testimony of the Holy Spirit:
The fact that the Holy Spirit is God is clearly seen in many Scriptures, including Acts 5:3-4. In this verse Peter confronts Ananias as to why he lied to the Holy Spirit and tells him that he had “not lied to men but to God.” It is a clear declaration that lying to the Holy Spirit is lying to God. We can also know that the Holy Spirit is God because He possesses the characteristics of God. For example, His omnipresence
Psalm 139:7-8 Where can I go from Your Spirit? Or where can I flee from Your presence? If I ascend into heaven, You are there; If I make my bed in hell, behold, You are there.
Then in 1 Corinthians 2:10-11, we see the characteristic of omniscience in the Holy Spirit. “But God has revealed it to us by his Spirit. The Spirit searches all things, even the deep things of God. For who among men knows the thoughts of a man except the man’s spirit within him? In the same way no one knows the thoughts of God except the Spirit of God.”. It is this Spirit and God who raised Jesus from the dead (Romans 8:11).
We can know that the Holy Spirit is indeed a divine person because He possesses a mind, emotions, and a will. The Holy Spirit thinks and knows (1 Corinthians 2:10). The Holy Spirit can be grieved (Ephesians 4:30). The Spirit intercedes for us (Romans 8:26-27). He makes decisions according to His will (1 Corinthians 12:7-11). The Holy Spirit is God, the third Person of the Trinity. As God, the Holy Spirit can truly function as the Comforter and Counselor that Jesus promised He would be (John 14:16, 26, 15:26).
The Holy Spirit makes choices collectively not individually according to His will at the same time as the Father and the Son, John 14:16, 26, 15:26 The Holy Spirit does do the work of a counsellor and will provide comforter (Greek - paraklētos). This does not mean the Spirit will coddle you for your emotional well being but according to vines dictionary it this comforter is:
Called to one's side, esp. called to one's aid one who pleads another's cause before a judge, a pleader, counsel for defence, legal assistant, an advocate
1) one who pleads another's cause with one, an intercessor
2) of Christ in his exaltation at God's right hand, pleading with God the Father for the pardon of our sins
3) in the widest sense, a helper, one who succours, aider, assistant
4) of the Holy Spirit destined to take the place of Christ with the apostles (after his ascension to the Father), to lead them to a deeper knowledge of the gospel truth, and give them divine strength needed to enable them to undergo trials and persecutions on behalf of the divine kingdom.
"Modalism is a second and third century heresy that denies the doctrine of the tri-unity of the Godhead, teaching there is only one Person in the Godhead. While the Tri-unity doctrine teaches three distinct Persons, Modalism maintains that one Person (usually the Father) has manifested Himself at different times under different names (Jesus/Spirit) or modes. Thus, Father, Son, and Holy Ghost are three names for the same Person. Originally taught in various forms by Noetus, Praxeas and Sabellius. Modified forms of this doctrine can be found in the teachings of William Branham, some Apostolic churches and the United Pentecostal Church." .
 From Notes on Thessalonians, by Hogg and Vine (1996) pp. 46, 47.
 From Notes by Vines dictionary Strong’s definition, Strong's Number: g2316
By Miguel Hayworth – 23/11/2010