If you search on "what the Bible says about astrology", you'll get a flood of evangelical websites with advice like the following:
Astrologers, Satanists, witches, psychics, and all those who are dabbling in magic of some kind - take heed: Man's efforts to predict omens and tell the future through magic are always fruitless. These "gifts" come from Satan, not from your Creator. Dabbling in these will only result in certain spiritual death. God says so. (source)
God command [sic] His people, the nation of Israel not to practice astrology by looking at "signs of the heavens." God calls such "signs" delusions... Studying the stars to attempt to get some message from them is called astrology, and is expressly prohibited in the Bible. Christians should not dabble in astrology, even if they don't really believe it is true. (source)
So historically astrology is rooted in pagan idolatry. The basic concept of astrology - that the movements of heavenly bodies control our lives - is heathen idolatry from the foundation up... The Old Testament clearly says that the future cannot be predicted accurately by the stars. If it could not be done then, it cannot be done now. To place trust in such methods is to learn the ways of the heathen, which is just as wrong now as it was then. (source)
And of all the pagan nations that practiced astrology, none come in for harsher condemnation than Babylon, that great and evil empire whose downfall the Bible's authors celebrated:
Astrology is the "interpretation" of an assumed influence the stars (and planets) exert on human destiny. This is a false belief. The royal astrologers of the Babylonian court were put to shame by God's prophet Daniel (Daniel 1:20) and were powerless to interpret the king's dream (Daniel 2:27). God specifies astrologers as among those who will be burned as stubble in God's judgment (Isaiah 47:13-14). Astrology as a form of divination is expressly forbidden in Scripture (Deuteronomy 18:10-14). (source)
Isaiah 47:13,14 - Babylon originated astrology. God promised to destroy Babylon, then asked what the astrologers, stargazers, and monthly prognosticators would do to stop Him. All these were involved in astrology, but they were powerless against God. (source)
All in all, these Christians couldn't be clearer in their belief that astrology is prohibited by God, no exceptions. Which must make this famous gospel verse very hard for them to explain:
"Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem, saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him." —Matthew 2:1-2
This must be exceedingly awkward for Christians. Astrology is flatly condemned in the Bible as pagan foolishness, sinful idolatry, even the handiwork of demons. Yet according to the Gospel of Matthew, the magi learned of the baby Jesus' existence and nature from a star! Why would demons be interested in helping people find and worship the Son of God? And doesn't this mean that astrology does give true answers at least sometimes, in contradiction to those apologists who claim it never does?
In fact, it gets better: the Greek word translated in Matthew 2:1 as "wise men" is magos - which Strong's Concordance defines as follows:
a) the name given by the Babylonians (Chaldeans), Medes, Persians, and others, to the wise men, teachers, priests, physicians, astrologers, seers, interpreters of dreams, augers, soothsayers, sorcerers etc.
b) the oriental wise men (astrologers) who, having discovered by the rising of a remarkable star that the Messiah had just been born, came to Jerusalem to worship him
c) a false prophet and sorcerer
The very fact that these awkwardly conflicting definitions are cheek-by-jowl shows the problem for Christians. According to Strong's, magi are false prophets, sorcerers - in fact, the term "magi" originated as the name given by the heathen Babylonians to their royal astrologers and soothsayers, whom the Bible explicitly denounces and condemns! And yet somehow, these people were privileged to be among the first humans in the world to know about Jesus' birth. Something really doesn't add up here.
Interestingly, the Jehovah's Witnesses, seemingly alone among Christian sects, have faced up squarely to this problem. Their proposed solution is clever, even if it flies in the face of centuries of Christian doctrine: they believe that the star was an evil sign from Satan, not a herald from God (which is why it led the magi to Herod, Jesus' mortal enemy, according to them). As for how other Christians resolve this problem, or whether it's even occurred to them, I can't say I have any idea.
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