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djcb comments on Attempts to work around Goedel's theorem by using randomness - Less Wrong
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Well, not if you want to proof mathematical theorems.
Still, in some cases it can be useful to trait absolute certainty for only a probabilistic certainty (think bloom filters); and for some game-theoretical strategies it can be beneficial to add actual randomness.
Indeed. For me, cryptographic hashing is the most salient example of this. Software like git builds entire castles on the probabilistic certainty that SHA-1 hash collisions never happen.