Historical Application To The Sunrise Problem
Laplace used the rule of succession to calculate the probability that the sun will rise tomorrow, given that it has risen every day for the past 5000 years. One obtains a very large factor of approximately 5000 × 365.25, which gives odds of 1826251:1 in favour of the sun rising tomorrow.
However, as the mathematical details below show, the basic assumption for using the rule of succession would be that we have no prior knowledge about the question whether the sun will or will not rise tomorrow, except that it can do either. This is not the case for sunrises.
Laplace knew this well, and himself wrote to conclude the sunrise example: “But this number is far greater for him who, seeing in the totality of phenomena the principle regulating the days and seasons, realises that nothing at the present moment can arrest the course of it.” Yet Laplace was ridiculed for this calculation; his opponents gave no heed to that sentence, or failed to understand its importance.
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