The Shared Divine Essence of the Godhead
.... "Well, Satan is referred to as ‘the god of this age’ in Scripture, so why don’t you put him in with your trinity?"
.... Well the Bible does say that there are ‘so-called’ gods and ‘so-called’ lords, and that’s the sort of category that Satan might fit into. And although their point was obviously blasphemous (no matter how you look at it), in strictly doctrinal terms their point is well taken. Why do we only include Father, Son and Holy Ghost as being members of the godhead, when there are other beings referred to as ‘gods’ in the Scriptures? Those so-called ‘gods’ so-called ‘goddesses’?
.... The reason we only include Father, Son and Holy Ghost is because they are shown to be one in essence with each other, and also because all of the purely divine attributes are equally ascribed to each personage.
.... First let’s take a look at the factor of essence. Jesus said very plainly that "I and the Father are one."(John 10:30) and in saying this, He means that He is one in essence with the Father, as can clearly be seen by the context (if you’ll look in verse 33). So the Father and the Son are set forth as being one in essence. Another good place to see this, in the Old Testament, is Isaiah 44:6, or in a prophecy from Zechariah that says:
.... "And I will pour on the house of David and on the inhabitants of Jerusalem the Spirit of grace and supplication; then they will look on Me whom they have pierced; they will mourn for Him as one mourns for his only son, and grieve for Him as one grieves for a firstborn."
.... "And now the Lord GOD, and His Spirit have sent Me."
.... "Nevertheless when one turns to the Lord, the veil is taken away. Now the Lord is the Spirit; and where the Spirit of the Lord is, there is liberty."
(2 Corinthans 3:16-17)