# Absolute certainty

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Revision as of 02:33, 20 December 2010 by Vladimir Nesov (talk | contribs) (added "Probing the Improbable" FHI paper)

Possessing **absolute certainty** in a fact, or Bayesian probability of 1, isn't a good idea. Losing an epistemic bet made with absolute certainty corresponds to receiving infinite negative payoff, according to the logarithmic proper scoring rule.

The same principle applies to mathematical truths. Not possessing absolute certainty in math doesn't make the math itself uncertain, the same way that an uncertain map doesn't cause the territory to blur out. The world, and the math, are precise, while knowledge about them is incomplete.

The impossibility of justified absolute certainty is sometimes used as a rationalization for the fallacy of gray.

## Blog posts

- Infinite Certainty
- 0 And 1 Are Not Probabilities
- How to Convince Me That 2 + 2 = 3
- Confidence levels inside and outside an argument by Yvain

## References

- Toby Ord, Rafaela Hillerbrand, Anders Sandberg (2008).
*Probing the Improbable: Methodological Challenges for Risks with Low Probabilities and High Stakes*. http://arxiv.org/abs/0810.5515.