You then quote Mat 11: 11:15 and Matt 17:9-13 (both of which speak of Elijah).
As you know, Elijah never died, so incarnation is not an issue, but I am talking about the disciples saying Christ was John the Baptist and Jeremiah (both of whom were dead).
Cause/effect cannot be dismissed from creation or making. When the maker or creator is God Himself, the cause is in timelessness though the effect is in time. Logic, physics, mathematics, geometry, etc. do not apply to the Creator - though they apply quite nicely to the (physical) creation
That's lovely, but the Book of Genesis tells us that God created the light, the universe, the sun and the moon, the earth, etc. (in other words the time as well because we are talking 'days' even if they are not our days).
In that real-time, in the real creation (not before all foundations of the world), God said 'let Us make man!' No need to go into cause/effect and relativistic theories of man; the Bible plainly says man did not exist until some time and was not breathing (alive) until that time when God breathed the breath of life into his lifeless nostrils.
He who lives in eternity knows of Adam from all eternity, but Adam did not exist from all eternity. Therefore knowledge and existence are not one and the same. Adam's soul did not pre-exist his body.
You: You then quote Mat 11: 11:15 and Matt 17:9-13 (both of which speak of Elijah). As you know, Elijah never died, so incarnation is not an issue, but I am talking about the disciples saying Christ was John the Baptist and Jeremiah (both of whom were dead).
We have discussed re-incarnation previously. The resurrection body we shall receive is a re-incarnation, we retain our identity. The two witnesses in Revelation are re-incarnated (then die and are re-animated) and retain their identity. I have no further leaning in the spirit concerning re-incarnation nor am I suggesting that all of us are merely re-incarnations of previously existing identities.
But Christ made it very clear that John the Baptist is the prophesied Elijah who would appear before He comes, and did. This requires spiritual discernment like the body and the blood of Christ we are to eat in John 6 and being born again in John 3.
John the Baptist was not the same, whole identity as Elijah, re-incarnated (John 1:21) as we shall be in our resurrection bodies. He was John the Baptist. Nevertheless, he was also Elijah.
Elijah again appears with Moses on the mount (Matthew 17) in his own, whole identity. Notably, Moses died (Jude) but Elijah did not and neither did Enoch. Some believe the two witnesses in Revelation will be (or were) Moses and Elijah others say Enoch and Elijah because neither died. I have no leaning in the Spirit, but my musing is Enoch and Elijah.
At any rate, the apostles were not expressing a Judaic pagan-influenced belief by answering Jesus question. Nor is Christ's response or lack thereof - nor is His declaration that John the Baptist is Elijah - a Judiac pagan-influenced belief. It is Truth.