It is not necessary to know the exact bias to enact the following reasoning:
"Coins can be rigged to display one face more than the other. If this coin is rigged in this way, then the face I have seen is more likely than the other to be the favored side. If the coin is not rigged in this way, it is probably fair, in which case the side I saw last time is equally likely to come up next by chance. It is therefore a better bet to expect a repeat."
Key phrase: judgment under uncertainty.
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Your definition of "know" is wrong.
Very well, I could have phrased it in a better way. Let me try again; and let's hope I am not mistaken.
Considering that even if there is such a thing as an objective probability, it can be shown that such information is impossible to acquire (impossible to falsify); how could it be anything but religion to believe in such a thing?