Credence—and Chance—Without Numbers (and with the Euclidean Property)

null, Tim Maudlin (New York University)

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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 chances 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.