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I have the idea that probabilities that are based on historical occurrences are meaningless. My argument:

Suppose the world has existed for n years. And based on our historical records, we found that the probability of event X happening is P. However, it could be the case that all the occurrences are actually rare events when the world keeps going for an infinite amount of time. That means, even if P is 0.99, it could be the case that, the ACTUAL probability of X occurring is 0.00000001, when the world goes on infinitely.

So how is historical probability rationally meaningful?

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    $\begingroup$ If it has rained here in November for as long as records have been kept. It would be useful to think that there is high probability of rain in November, at least for planning $20$ or fewer years into the future. $\endgroup$ Oct 1, 2015 at 4:50

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I have no idea what "actual probability" is. A Coin flip doesn't have a $50$% chance of being heads. If you were to look at all the exact physics and know what was going on you would know whether it would come up heads or tails. This is stupidly complicated so we just call it "random".

This is a very common theme in probability, and a very deep one. We use probability in real life because real life is too complicated to model exactly. It would be impossible to know everything that influences the weather that's why meteorologists pick a few things (pressure, temperature, wind, etc.) and use models and make guesses. "There is a $30$% chance of rain next Thursday" (not here in California of course. We know for a fact that this percentage is exactly $0$).

I mean lets take what you're saying to an extreme. Basically by doing this, you are in fact rejecting all of science. Every time I let go of something, it drops. How can we be sure that this isn't just an extremely unlikely string of flukes? What if the "actual probability" to drop is $.000001$% and we've just been very lucky? Well, the immediate consequence of this line of reasoning is that nothing matters and we can't understand anything and everything is pointless. I don't know about you but that's pretty depressing.

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