What sets 539 apart from other dates agreed on by mainstream historians?
539 is an absolute date. 539 is also a date where sacred and secular historical events coincide. Other dates, like the 586 date for the fall of babylon does not fall into that category.
I take it that you mean by 'absolute' the meaning 'Not to be doubted or questioned' (which is how my dictionary defines it). By itself that doesn't explain anything about why 539 would be an undoubtable or unquestionable date. By calling it absolute I think it should be obvious and completely clear why this date is undoubtable or unquestionable. It is also interesting that the Watchtower society stopped using the term 'absolute date' in 1971. But we'll get back to that later.
So far you have provided two reasons:
1) the Nabonidus chronicle;
2) secular historians, of which you mentioned Diodorus, Africanus, and Eusebius.
You statement that '539 is also a date where sacred and secular historical events coincide' is not relevant to this question since the arrival at is only 'absolute' in secular sense and not in sacred sense. There's nothing in the sacred history that by itself gives us an 'absolute' reference. The sacred history refers to a secular person, in this case Cyrus. The timeframe within secular history for this person is subsequently derived from secular data alone. Once this datum has been established it is assumed to be valid as well in the sacred history, and by some called 'absolute'.
But it is very important to understand that the fact that 539 may be called 'absolute' IS COMPLETELY BASED ON SECULAR DATA. Therefore your statement "It is the Bible or historians" leaves a lot to be wished for. Your 'Bible' by itself doesn't carry a single absolute datum. Events from its history can at best be called 'absolute' due to SECULAR DATA. So a more accurate description of your choice would be 'it is historians or historians'. But I digress.
Do you know how 539 BCE is calculated? You mentioned the Nabonidus chronicle. Exactly HOW does the Nabonidus chronicle point to this year?The date is calculated by astronomical observations.
The quoted translation (of ANET) by itself is interesting. It mentions the Babylonian months of 'Tashritu' and the month 'Arahshamnu'. The part you quote however, doesn't contain any reference to years, but only to months. The number 539 is not mentioned anywhere, which is logical since it refers to a calendar that was invented ages after that point in time. So there needs to be some kind of reference on this Nabonidus chronicle that refers to something astronomical. Well, I can be short about that:
there isn't.
The part that describes the year for the month of 'Tashritu' is damaged and illegible. If 539 is correct there should have been a reference to the seventeenth (17th) year of Nabonidus. But let's assume that this text was indeed legible, what would the Nabonidus chronicle by itself tell us? It tells that Babylon was captured on the 16th day of Tashritu in the 17th year of Nabonidus. Period. There are no astronomical observations on the Nabonidus chronicle.
However, it is very important that The Watchtower has told its audience from 1952 onwards the following:
This date is made Absolute by reason of archeaological discovery and deciphering of the famous Nabunaid Chronicle, which itself gives a date for the fall of Babylon
The Watchtower February 1, 1952, p. 94.
That the above statement is misleading, not to say untrue, was acknowledged some twenty years later when the Watchtower conceded that the Nabonidus chronicle by itself could not be used to derive 539. You can find it in The Watchtower of May 15th, 1971 on page 316. The Society from that point on didn't call 539 an 'absolute date' anymore, but instead used the term 'pivotal date'.
Therefore YoYo, I must ask you again, how does the Nabonidus chronicle point to 539? I gave you some clues above unless you want to challenge them of course. My next question for you therefore is:
5) Where can we find the 'astronomical observations' you mentioned in your answer?
If you've answered that one, I'll come back to the answers you gave on my questions 3) and 4).
Now I should address the historians you mentioned. I had a hunch which ones you'd be referring to and I was correct in my hunch. This gives way to my next question.
6) How can Eusebius, Africanus and Diodorus (or their works) be used to derive 539?
After being asked by me, you brought these up as credible historians. So you should know about their work and how it can be used to prove the correctness of 539. If you indeed looked up the Watchtower of May 15th, 1971, you will find a clue there. It's called olympiads. But be careful... if you just parrot the WT you may find yourself in trouble real soon now. I also advise you NOT to mention Ptolemy's Canon. If you intend to do so, you'd better be aware of what the WT says about it in other places, such as when they discuss Artaxerxes. But again I digress.
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Every absurdity has a champion to defend it.