What is the biblical/logical basis for rejecting the "physical" interpretation of Christ's being the Only Begotten Son?

What does 'begotten' mean in the context of John 3:16 and 4:9? According to the dictionary we have only two meanings:

• A. Procreate or generate offspring.
• B. Cause to be produced.

We have a logical issue in relation to Jesus' eternal nature. If A, then he is not eternally existing, and did not exist before bring born to Mary and God. If B, he is a caused entity and therefore did not exist before being caused to exist by God, and hence not eternally existing again.

Better minds may have an answer to this conundrum. We have the same logical issue if we take the Greek text of John 3:16 and 4:9 (as others have shown above) to mean 'only Child' or 'only Son' and look at the definitions of Child or Son.

Of course we could avoid the question by saying our languages are incapable of explaining Jesus' nature, but it seems such a crucial matter of faith ought to be explainable in words and not be so semantically and logically difficult.

The Bible clearly says that Jesus is God's only begotten son. You've quoted some of the main passages in your question. However you should note that more modern translations render "only begotten" as "one and only", so not too much evidence should be placed on the 'begotten' aspect. It is of course true that all Christians are adopted sons of God.

So the real question is about Lucifer being a son of God. That's essentially a Mormon belief, and it's sole justification is from the Mormon scriptures. There is nothing in the Bible to support it.

The question seems to hinge on the source of Jesus' begotten-ness. Is he the only son of God who was begotten by Mary, or is he the only son of God, who was begotten by God himself?

As Caleb points out, the Greek word in question is μονογενῆ, which is a compound word from μόνος (only) and γένος (child), and modern translations do not use the word 'begotten'.

This is already a problem for the LDS interpretation, I think. It relyies on a distinction between the source of Jesus' sonship (God) and his begotten-ness (Mary), when the Greek does not really allow for that distinction.

But let's press on. We still need to ask: what is the source of Jesus' uniqueness, his one-and-only-ness? Consider John 1:14 NIV:

The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth.

This is a pretty straightforward rendering of the Greek (μονογενοῦς παρὰ πατρός, literally "only son from the father"). It seems clear to me from this verse that Jesus' uniqueness comes from his relationship to the Father.

But the most convincing argument, to me, is what is not said. Mary is not mentioned by John until chapter 2, and is not mentioned in the surrounding context of any of John's only-son passages - which seem to emphasize (1:14 in particular) Jesus' divinity rather than his humanity.

The LDS belief goes beyond just Christ and Lucifer being brothers; they believe that all of us are spiritually siblings of Christ too. Their doctrine isn't restricted to the Bible, but there is a supporting passage:

Romans 8:16 (KJV)

¹⁶ The Spirit itself beareth witness with our spirit, that we are the children of God

If Christ is the only son of God, then how are we also children of God?

a_hardin quoted Colossians 1:15-17 to show that Christ was created differently than Lucifer and we were, however a passage in Revelations seems to say otherwise:

Revelation 3:14 (ESV)
¹⁴ "And to the angel of the church in Laodicea write: 'The words of the Amen, the faithful and true witness, the beginning of God’s creation.

I guess this is why the Nicene Creed says that Jesus "was begotten not made." If Jesus was made, then there is the possibility that God could make other sons.

To hold that Jesus was made in the same sense that Lucifer was made can thus be safely at least declared "non-orthodox" and out of keeping with orthodox Christianity, at least as it has been defined since 325 AD.

A Mormon, of course, will object that the Nicene Creed wasn't given by revelation. That may be true, but it still puts them at odds with 1700 years of Christian scholarship, and so in my mind, at least raises the bar / puts the ball in their court to prove otherwise.

Ask: Who made Lucifer

Let's digress for a second and ask who made Lucifer.

As John 1:3 reminds us, there was nothing made that Jesus did not make. Thus, the question is "Is Lucifer a created being?" If the answer to that question is yes, then Jesus (via 1:14) made Satan and not God. As such, John 1:3 must be wrong or they are.

If Jesus made Satan, Jesus is Satan's father - not his brother.

God would at best be his grandfather, although as stated above, orthodox Christianity states Jesus was begotten not made. In any event, Jesus and Satan can't both have been made by God, since all things that were made were made by Jesus.

If they say 'No, Lucifer was not a created being," then ask them how Satan is not co-equal to God. If they assert that he is, they are Gnostics, as evidenced by their dualism. Paul clearly calls Gnostics heretics. I think you are on safe ground then calling them the same.

If you listen to LDS teachers or read their doctrines you will see the very conscientiously worded phrase "the only God and his Son" rather than "God and his only Son." It's the same set of words but the dots are connected differently.

The difference seems to hang on the word "only". What does it connect to?

It appears that the operative phrase in John 3:16 is τὸν υἱὸν τὸν μονογενῆ (ton huion ton monogenē). Perhpas somebody with some real Greek knowledge could expound on this specific verse, but the the "only" bit seems to really indicate that he was an only son Son, not just by that method. In fact many translations¹ don't even addd the word "begotten" although the original word is a compound that includes something about being a child, presumably in order to clarify in modern language what the adjective only is modifying. The meaning of the phrase in "King James English" which is retained in many English translations does not help us understand exactly what the verse is emphasizing. (See this answer for another example.)

John 3:16 (ESV)
For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.

Some English translations go so far as to add extra emphasis to the fact that he is an only son by stating that bit twice without using the word 'begat'.

So it looks like we need to look farther than just this verse. So let's follow that word to some other usages in the Bible. In the following verses (and also Luke 9:38):

Luke 7:12a (ESV)
As he drew near to the gate of the town, behold, a man who had died was being carried out, the only son of his mother, and she was a widow, ...

Luke 8:42a (ESV)
for he had an only daughter, about twelve years of age, and she was dying.

... the context is quite clearly that of an only child, not an only child "that had a physical birth" rather than some other means. The word is also used by the same author earlier in John to refer, not to a child at all, but just to emphasis the "only" bit. In fact is used used of God himself:

John 1:18 (ESV)
No one has ever seen God; the only God, who is at the Father's side, he has made him known.

Another way to approach this issue is to show the other aspects of the relationship between Jesus and God. In John just a few chapters later we find Jesus making this statement:

John 10:30 (ESV)
I and the Father are one.

This (and a myriad of other verses indicating this unity of identity (see proof texts for Jesus being God)) lead us to a special understanding of who Jesus was in relation to God. We also find that this relationship between the three persons of the trinity is exclusive of other persons. When it comes to Lucifer, we find no similar references of a unity relationship with the father. In fact he is referenced as an angel, a created being.

¹ ESV, HCSB, NIV, NLT, ISV, GW, BBE, WEB, and others...