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...
| मुख्य लेखक: | |
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| अन्य लेखक: | |
| स्वरूप: | Journal article |
| भाषा: | English |
| प्रकाशित: |
Oxford University Press
2007
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| विषय: |
| _version_ | 1826304849462951936 |
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| author | Williamson, T |
| author2 | The Analysis Trust |
| author_facet | The Analysis Trust Williamson, T |
| author_sort | Williamson, T |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T06:23:59Z |
| format | Journal article |
| id | oxford-uuid:f3a2b59a-409d-41cf-9b15-b5f86d0fd3d9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:23:59Z |
| publishDate | 2007 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:f3a2b59a-409d-41cf-9b15-b5f86d0fd3d92022-03-27T12:13:39ZHow probable is an infinite sequence of heads?Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f3a2b59a-409d-41cf-9b15-b5f86d0fd3d9PhilosophyEnglishOxford University Research Archive - ValetOxford University Press2007Williamson, TThe Analysis TrustIsn'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. |
| spellingShingle | Philosophy Williamson, T How probable is an infinite sequence of heads? |
| title | How probable is an infinite sequence of heads? |
| title_full | How probable is an infinite sequence of heads? |
| title_fullStr | How probable is an infinite sequence of heads? |
| title_full_unstemmed | How probable is an infinite sequence of heads? |
| title_short | How probable is an infinite sequence of heads? |
| title_sort | how probable is an infinite sequence of heads |
| topic | Philosophy |
| work_keys_str_mv | AT williamsont howprobableisaninfinitesequenceofheads |