- Being purely sure (100% confident) of something (or, likewise, assigning anything zero probability) is claiming that it is indefeasible (completely irrefutable) – literally, nothing whatsoever could possibly refute it, for the simple reason that the lower the probability (or uncertainty), the stronger the evidence must be for that. (That is, for an event with low probability, the probability of the information favoring it must be high, and of course lowering it makes the requirement even higher). In the 0% case the requirement would be infinite and so there is no amount of information that would suffice.
- Claiming indefeasible knowledge equals claiming unconditional belief – the same as saying “I believe no matter what”, for the simple reason that if there is no information that could refute it, then one’s belief is independent of whatever the evidence might say and so even overwhelming evidence to the contrary wouldn’t affect it.
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