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text: '[summary: [Cromwell's Rule](https://en.wikipedia.org/wiki/Cromwell%27s_rule) in statistics forbids us to assign probabilities of exactly $0$ or $1$ to any empirical proposition - that is, it is always possible to be mistaken.\n\n- Probabilities of exactly $0$ or $1$ correspond to infinite [1zh log odds], meaning that no finite amount of evidence can ever suffice to reach them, or overturn them. Once you assign probability $0$ or $1,$ you can never change your mind.\n- Sensible [4mr universal priors] never assign probability exactly $0$ or $1$ to any predicted future observation - their hypothesis space is always broad enough to include a scenario where the future is different from the past.]\n\n[Cromwell's Rule](https://en.wikipedia.org/wiki/Cromwell%27s_rule) in statistics argues that no empirical proposition should be assigned a subjective probability of *exactly* $0$ or $1$ - it is always *possible* to be mistaken. (Some argue that this rule should be generalized to logical facts as well.)\n\nA probability of exactly $0$ or $1$ corresponds to infinite [1zh log odds], and would require infinitely [22x strong] evidence to reach starting from any finite [1rm prior]. To put it another way, if you don't start out infinitely certain of a fact before making any observations (before you were born), you won't reach infinite certainty after any finite number of observations involving finite probabilities.\n\nAll sensible [4mr universal priors] seem so far to have the property that they never assign probability exactly $0$ or $1$ to any predicted future observation, since their hypothesis space is always broad enough to include an imaginable state of affairs in which the future is different from the past.\n\nIf you did assign a probability of exactly $0$ or $1,$ you would be unable to [1ly update] no matter how much contrary evidence you observed. [1rb Prior odds] of 0 : 1 (or 1 : 0), times any finite [1rq likelihood ratio], end up yielding 0 : 1 (or 1 : 0).\n\nAs Rafal Smigrodski put it:\n\n> "I am not totally sure I have to be always unsure. Maybe I could be legitimately sure about something. But once I assign a probability of 1 to a proposition, I can never undo it. No matter what I see or learn, I have to reject everything that disagrees with the axiom. I don't like the idea of not being able to change my mind, ever."',
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Summary: '[Cromwell's Rule](https://en.wikipedia.org/wiki/Cromwell%27s_rule) in statistics forbids us to assign probabilities of exactly $0$ or $1$ to any empirical proposition - that is, it is always possible to be mistaken.\n\n- Probabilities of exactly $0$ or $1$ correspond to infinite [1zh log odds], meaning that no finite amount of evidence can ever suffice to reach them, or overturn them. Once you assign probability $0$ or $1,$ you can never change your mind.\n- Sensible [4mr universal priors] never assign probability exactly $0$ or $1$ to any predicted future observation - their hypothesis space is always broad enough to include a scenario where the future is different from the past.'
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