This missing the important point - why should we believe that the future is somehow modeled on the past.

I did not exactly miss that point, I

*dis*missed it. And I didn't dismiss it because I don't agree with it. I am just saying that that idea doesn't help you answer the original question of probability:

You can speculate about the unexpected, but if you descend along that path, it make no sense (and is not possible) to define a quantitative probability. You have no set of data to make any estimates, nor would you accept any analysis based on previously established relationships because they may be obsolete in face of the unexpected event. Hence, the problem (asking about the probability of the unexpected) is ill-posed.

So the earth rotated in the past, why cant it just stop tomorrow? Why is inductive argument rational?

The Earth might stop. That's not the point. The task was to assign a probability to that event. I have been trying to explain in my previous (and this post) why that doesn't make sense, .....

*unless* we are talking about events that will indeed by describable by prior experience, data, and the established laws of physics. If you were to ask, for example, what would be the probability for an asteroid to hit the Earth and make it rotate in such a way that the sun becomes geostationary... I am sure you can come up with an answer. But that's not what you guys were discussing. In fact the whole discussion has been avoiding the main question so far: What is the probability?

Why is induction rational? Because logic and rationality, as we know it and use it, depends on induction. If the addition of two integers as in "1+1" is an integer "2" today, and an integer "3" tomorrow, our way to look at logic becomes pretty much useless. Mathematics may be able to describe chaos to some extend, but when the laws of math themselves became chaotic we'd be dealing with more trouble that not seeing the sun.

Is that impossible? Nothing is impossible (what an unfalsifyable, utterly irrelevant statement). But can you tell me the probability of that happening?

You can philosophize over a complete break-down of science, but the qualitative statement "it's possible" is in no way helping to determine a quantitative probability to that event. That was the question, and that's my point.

What's the answer?