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What Do Mathematicians Want?udProbabilistic Proofs and the Epistemic Goals of Mathematicians

机译:数学家想要什么? ud概率证明与数学家的认识论目标

摘要

Several philosophers have used the framework of means/ends reasoning to explain the methodological choices made by scientists and mathematicians (see, e.g., Goldman 1999, Levi 1962, Maddy 1997). In particular, they have tried to identify the epistemic objectives of scientists and mathematicians that will explain these choices. In this paper, the framework of means/ends reasoning is used to study an important methodological choice made by mathematicians. Namely, mathematicians will only use deductive proofs to establish the truth of mathematical claims. In this paper, I argue that none of the epistemic objectives of mathematicians that are currently on the table provide a satisfactory explanation of this rejection of probabilistic proofs.
机译:几位哲学家已经使用均值/目的推理框架来解释科学家和数学家所做的方法选择(例如,参见Goldman 1999,Levi 1962,Maddy 1997)。特别是,他们试图确定科学家和数学家的认识论目标,以解释这些选择。在本文中,均值/目的推理的框架用于研究数学家做出的重要方法选择。即,数学家将仅使用演绎证明来建立数学主张的真相。在本文中,我认为,目前摆在桌面上的数学家的认识论目标都无法对这种拒绝概率证明的方法提供令人满意的解释。

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    Fallis Don;

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