Does the Fact That Worship is Given to Jesus Prove That He is God?
No.
The "worship" given to Jesus means no more than the "worship" given to king David as God's representative. "And all the congregation blessed the LORD God of their fathers, and bowed down their heads, and worshipped the LORD, and the king." -- 1 Chronicles 29:20, KJV
The "worship" given to king David did not prove that he was God.
But like David, as God's representative, Jesus is given deference and respect, "worship" in that form as God's resurrected Son and heavenly King, but not as God.
The Meaning of the Greek and Hebrew Words 'Proskuneo' and 'Shachah'
The act described by proskuneo (or shachah) was of bowing or kneeling, and it generally indicated an act of respect and a display of one's willingness to submit to or serve another person who occupied a superior position, regardless of his nature (somewhat similar to a salute in the military today).
The Hebrew word most often translated "worship" is shachah, and it is usually rendered as proskuneo in the Greek Septuagint version of the Old Testament. Unger and White say of this word: "Shachah ... 'to worship, prostrate oneself, bow down.'" And, "The act of bowing down in homage done before a superior [in rank] or a ruler. Thus David 'bowed' himself [shachah] before Saul (1 Sam. 24:8). Sometimes it is a social or economic superior to whom one bows, as when Ruth 'bowed' [shachah] to the ground before Boaz (Ruth 2:10)." - Nelson's Expository Dictionary of the Old Testament, 1980, Thomas Nelson Publ., p. 482.
Even the extremely trinitarian W. E. Vine writes in his An Expository Dictionary of New Testament Words, p. 1247:
"PROSKUNEO ... to make obeisance, do reverence to (from pros, towards, and kuneo, to kiss), is the most frequent word rendered 'to worship'. It is used for an act of homage or reverence (a) to God ...; (b) to Christ ...; (c) to a MAN, Matt. 18:26." ("Obeisance," of course, shows "respect, submission, or reverence" - Webster's New Collegiate Dictionary, 1961.)
It was done, of course, in its very highest sense to God alone, but it was also done, in a lower sense of the same word, to kings, angels, prophets, etc. That is why proskuneo is translated "prostrated himself before" at Matt. 18:26 NASB, even though the KJV uses "worship" there. Notice how other trinitarian translations render that verse (RSV and NIV for example) where a servant "worships" [proskuneo] his master. And that is why, in the account of the man blind from birth whom Jesus healed, we see that man giving proskuneo to Jesus at John 9:38. The ASV, in a footnote for John 9:38, says,
"The Greek word [proskuneo] denotes an act of reverence, whether paid to a creature, as here [Jesus], or to the Creator."
For more, see:
Is It Proper to Worship Jesus? "Worship" (Proskuneo /Shachah) (Defend Jehovah's Witnesses)
"Worship" (Proskuneo /Shachah) Different Levels of Meaning in Scripture (Examining the Trinity)
The Bible’s Viewpoint - Is It Proper to Worship Jesus? (g00 4/8 pp. 26-27; Watchtower Online Library)
Obeisance to the Glorified Jesus Christ (Insight-2 pp. 523-524; Watchtower Online Library)
Worship - Links to Information (Defend Jehovah's Witnesses)
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