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Tacking by conjunction, genuine confirmation and convergence to certainty
European Journal for Philosophy of Science ( IF 1.5 ) Pub Date : 2022-07-07 , DOI: 10.1007/s13194-022-00470-0
Gerhard Schurz

Tacking by conjunction is a well-known problem for Bayesian confirmation theory. In the first section, disadvantages of existing Bayesian solution proposals to this problem are pointed out and an alternative solution proposal is presented: that of genuine confirmation (GC). In the second section, the notion of GC is briefly recapitulated and three versions of GC are distinguished: full (qualitative) GC, partial (qualitative) GC and quantitative GC. In the third section, the application of partial GC to pure post-facto speculations is explained. In the fourth section it is demonstrated that full GC is a necessary condition for Bayesian convergence to certainty based on the accumulation of conditionally independent pieces of evidence. It is found that whenever a hypothesis is equivalent to a disjunction of more fine-grained hypotheses conveying different probabilities to the evidence, then conditional independence of the evidence fails. This failure occurs typically for unspecific negations of hypotheses. A refined version of the convergence to certainty theorem that overcomes this difficulty is developed in the final section.



中文翻译:

通过结合、真正的确认和收敛到确定性进行跟踪

联合跟踪是贝叶斯确认理论的一个众所周知的问题。在第一节中,指出了现有贝叶斯解决方案对该问题的缺点,并提出了另一种解决方案:真正确认(GC)。在第二部分中,简要概括了 GC 的概念,并区分了 GC 的三个版本:完全(定性)GC、部分(定性)GC 和定量 GC。在第三部分中,解释了部分 GC 在纯事后推测中的应用。在第四节中,证明了完全 GC 是贝叶斯收敛到确定性的必要条件,基于条件独立证据的积累。研究发现,只要一个假设等同于向证据传达不同概率的更细粒度的假设的析取,那么证据的条件独立性就会失败。这种失败通常发生在对假设的非特定否定时。最后一节提出了克服这个困难的收敛到确定性定理的改进版本。

更新日期:2022-07-08
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