100年后,是时候承认布尔和凯恩斯创立了一种数学上、技术上和逻辑上先进的非精确概率方法

M. E. Brady
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摘要

凯恩斯和布尔对不精确概率理论的贡献不仅仅是“观念”、“建议”或“直觉”。实际上,凯恩斯和布尔在布尔代数和逻辑的基础上推导出了概率的上下边界,并非常详细地解决了问题。他们的工作非常先进,与20世纪80年代中期的工作相比非常有利,当时T. Hailperin在推广布尔斯-凯恩斯方法方面取得了重大进展。不幸的是,这些贡献似乎不为人所知,被忽视了,或者是技术性质的,对当今的研究人员来说太难掌握了。只有埃米尔·博雷尔(Emil Borel)在1924年给出了一个答案,那就是他很难掩盖。
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After 100 Years, the Time Has Come to Acknowledge That Boole and Keynes Founded a Mathematically, Technically, and Logically Advanced Approach to Imprecise Probability
Keynes’s and Boole’s contributions to the theory of imprecise probability are not just “notions” or “suggestions” or “intuitions”. Keynes and Boole actually worked out problems in great detail in which they derive lower and upper probability bounds based on their foundation of Boolean algebra and logic. Their work is very advanced and compares very favorably to work done up to the mid 1980’s, when T. Hailperin made major advances in the generalization of the Boole-Keynes approach.

Unfortunately,it appears that these contributions are not known,have been ignored,or are of a technical nature that is too difficult for present day researchers to master. Only Emil Borel in 1924 gave an answer, which was that it was too difficult for him to cover.
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