It is being claimed that three persons have omniscience: the Father (Psalm 147:5), the Son (John 16:30), and the Holy Spirit (1 Corinthians 2:10). And by this reasoning, it is then imagined that all three are persons of the one God, forming what is often called the trinity.
{Psalms 147:5 - Great is our Lord, and of great power: his understanding is infinite.
The phrase, "Our Lord," is referring to "Jehovah" of verses 1 and 2; in the King James Version we find that God's Holy Name has been changed to "the LORD" in verses 1 and 2.
The word translated as "infinite" above is Strong's #369. Brown-Driver-Brigg's definition of this word is: "1) nothing, not, nought; 1a) nothing, nought (noun); 1b) not (negative); 1c) to have not (of possession); 1d) without (adverb): 1e) for lack of (without a preposition)." Strong himself defines the word as meaning "As if from a primitive root meaning to be nothing or not exist; a non-entity; generally used as a negative particle: - else, except, fail [father-] less, be gone, in [-curable], neither, never, no (where), none, nor (any, thing), not, nothing, to nought, past, un [-searchable], well-nigh, without." As a negative, it appears to be not putting a limit on Jehovah's understanding.
Jehovah's understanding is definitely not limited. Jehovah certainly posseses all knowledge of all his creation, and that knowledge never ends. But as related to the verse, God understands each of us where man may not understand. He understands each of us better than we understand ourselves. His understanding is not limited as is man's.
{John 16:30} Now we know that you know all, and do not need for anyone to question you. By this we believe that you came forth from God."
1 John 2:20 - But ye have an unction from the Holy One, and ye know all things.
"God" in John 16:30 refers to only one person, not three persons. That one person is the God and Father of Jesus. (John 16:28) Thus, we certainly have no reason to think that disciples were calling Jesus God or a person of God by their response. Indeed, Jesus had taught them that he had come forth from God, and that Jesus' teachings were from God (John 6:46; 7:17; 8:40,42; 13:3; 16:27,30) and thus, according to scriptures, his power and might -- including his ability to know the thoughts of men -- is because God had anointed Jesus with the Holy Spirit and power, for God was with him. -- Isaiah 11:2-3; 61:1; Acts 10:38.
The word "all" is translated from a form of the word often transliterated as "pas." (Strong's 3956) A study of its usage in the Bible reveals that all forms of the Greek word "pas" rarely are speaking of absolutely everything in the entire universe. The context most often shows what is included in the usage of pas, although not always. Common evidence should also be applied to determine what is or what is not being included, as Paul wrote of in 1 Corinthians 15:27.
A form of the same phrase rendered "know all" that the disciples used in John 16:30 is also in used in 1 John 2:20, where it is applied the anointed sons of God. The King James Version (and many other translations) adds the word "things" after "all" in 1 John 2:20. There is actually corresponding word in the Greek that means "things." Nevertheless, John was not saying those anointed ones knew absolutely everything in the universe. Obviously, in 1 John 2:20 the "all" is referring to the knowledge and understanding about Jesus and his God. Likewise, in John 16:30, the "all" should be understood as referring to "all" pertaining to what Jesus was speaking about in context. Jesus, however, shows that he does not know absolutely everything that his God and Father knows. (Mark 13:32) Likewise, in Revelation 1:1, if Jesus knew absolutely everything in the universe and time, there would not have been any need for him to receive the revelation from his God.
Related info on other sites:
Anaylsis of John 16:30 (Oddly this analysis adds the word "things' to "all." The word "things" is not inherit in the form Panta)
Analysis of 1 John 2:20
Analysis of Strong's #3956
1 Corinthians 2:10 - But to us, God revealed them through the spirit. For the spirit searches all things, yes, the deep things of God.
Again, "God" here is presented as being only one person, not more than one person. "The spirit" spoken of here "searches", more correctly "examines", seeking to know the deep things of God. Obviously, "the spirit" spoken of here is not an omniscient person, for why would an omniscient being need to search, or examine, the deep things of God?
Paul is obviously referring to the spirit within "us" -- the apostles especially. God has revealed his truths by means of his holy spirit through the apostles. The one person who is the God of Abraham, Isaac, and Jacob (Acts 3:13-26; Acts 17:29-31; 1 Corinthians 8:6; Hebrews 1:1,2), by means of His Holy Spirit, especially led the apostles into all the truths concerning Christ and what he said, and thereby the faith was delivered to the saints in the first century. (John 14:26; 16:4-13; Galatians 1:12; Ephesians 3:5; 2 Timothy 2:2; Jude 1:3) The truths revealed to the apostles and made available to us are recorded in the Bible itself. (Ephesians 3:3-12; Colossians 1:25,26; 1 John 4:6) Of course, without the holy spirit, these things that are recorded will still be a mystery to us. -- Mark 4:11; 1 Corinthians 2:7-10.
What we do not find in Psalm 147:5, John 16:30 and 1 Corinthians 2:10 is any thought that the God of Abraham, Isaac and Jacob is more then one person, nor do we find any thought that Jesus is the God of Abraham, Isaac and Jacob. Such ideas have to formulated with assumptions beyond what is written, and then those assumptions have to added to and read into the scriptures.