Maudlin, Tim (2021) Credence—and Chance—Without Numbers (and with the Euclidean Property). [Preprint]
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Abstract
Accounts of both rational credence and of objective chance have always confronted difficulties associated with events that are assigned “probability zero” by the usual Kolmogorov probability function used to model the situation. One sort of solution recommends extending the number field used to represent credences and chance to the surreals or hyperreals. But the correct solution—the solution that always respects the Euclidean property—is to eliminate numbers from the fundamental representation of credence and chance altogether in favor of a system of relations. This solution also sheds light on other paradoxes, such as the Banach-Tarski paradox and the St. Petersburg paradox.
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| Item Type: | Preprint | ||||||
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| Keywords: | objective chance, credence, Euclidean property, regularity, St. Petersburg paradox, Banach-Tarski paradox | ||||||
| Subjects: | General Issues > Decision Theory Specific Sciences > Mathematics General Issues > Models and Idealization Specific Sciences > Probability/Statistics |
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| Depositing User: | Prof. Tim Maudlin | ||||||
| Date Deposited: | 26 Jun 2021 19:25 | ||||||
| Last Modified: | 26 Jun 2021 19:25 | ||||||
| Item ID: | 19237 | ||||||
| Subjects: | General Issues > Decision Theory Specific Sciences > Mathematics General Issues > Models and Idealization Specific Sciences > Probability/Statistics |
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| Date: | 25 June 2021 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/19237 |
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- Credence—and Chance—Without Numbers (and with the Euclidean Property). (deposited 26 Jun 2021 19:25) [Currently Displayed]
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