I found this to be an interesting article, after reading this scripture:
2 Corinthians 12:2-4 (King James Version)
I knew a man in Christ above fourteen years ago, (whether in the body, I cannot tell; or whether out of the body, I cannot tell: God knoweth;) such an one caught up to the third heaven.
And I knew such a man, (whether in the body, or out of the body, I cannot tell: God knoweth;)
How that he was caught up into paradise, and heard unspeakable words, which it is not lawful for a man to utter.
Does the Bible say how many heavens there are?
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No, the Bible does not tell us how many heavens there are, but I was taught that at that time, the sky (atmosphere) was heaven 1, the stars are in heaven 2 (space), and God lives in heaven 3.
The "third heaven" is a Hebraic way of speaking. The "three heavens" were what we would call the atmosphere (where birds fly), outer space (where the stars are), and heaven per se (where God and the angels and saints live).
I'm not terribly impressed with the theological quality of this article you post. (Not your fault -- it's the writer I'm not crazy about.)
For one thing, John Paul II never said that heaven wasn't a place. The Italian word he used was piu and, as any musician can tell you, piu in Italian means "more". He said that heaven was "more than" [just] "a place", that is, if we think of it as just a place, like Poughkeepsie, NY is a place, then we're trivializing it. Heaven is perfect intimacy with God; there are some people on earth who practically live in that perfect intimacy already, so their heaven has already begun here on earth.
The (first) heaven, where birds fly; the atmosphere.
The (second) heaven; space.
The (third) heaven, the heaven of heavens; where the Throne of God is.
The division of the heavens is recorded in Genesis chapter one, and can be traced through Scripture.
Earth itself is a part of the first heaven, and the Kingdom of Heaven involves a kindom on earth ruled from the Third Heaven. When God’s will is done on earth (first heaven) as it is in (the third) Heaven, that is the Kingdom of Heaven.
This is the work of feminists in the church and it is upsetting to me.