How probable is an infinite sequence of heads?

Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur (it has no chance of occurring). If the probability is subjective, so is the cert...

Ամբողջական նկարագրություն

Մատենագիտական մանրամասներ
Հիմնական հեղինակ: Williamson, T
Այլ հեղինակներ: The Analysis Trust
Ձևաչափ: Journal article
Լեզու:English
Հրապարակվել է: Oxford University Press 2007
Խորագրեր:
Նկարագրություն
Ամփոփում:Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur (it has no chance of occurring). If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur (it has no weight in your calculations of expected outcomes). And so on for other kinds of probability, such as evidential probability. The formal analogue of this picture is the regularity constraint: a probability distribution over sets of possibilities is regular just in case it assigns probability 0 only to the null set, and therefore probability 1 only to the set of all possibilities.