Amplification and Refinement of Bayesian Scientific Methodology

自亚里士多德时代以来，科学推理，即从特定实例到一般规律的过程，一直是哲学关注的问题。然而，直到托马斯·贝叶斯(1763年)，才有任何明确的方法被提出，用概率论来证明从具体到一般规律的推理是正确的。整个贝叶斯科学方法论家族用认知概率的概念来表述科学推理，认为科学假设的先验概率是一个有意义的概念，并利用贝叶斯定理来评估后验概率。希蒙尼教授在1970年提出的贝叶斯主义的一个版本，被称为“温和的个人主义”，建议个人的概率评估应该通过对调查中所有严肃提出的假设持开放态度来“缓和”。在缓和的个人主义的优点中，有可能得出一个强大的科学概括的不可忽略的后验概率。然而，温和的个人主义也有一些需要修改的弱点：值得注意的是，很难证明概率公理的合理性，“认真提出”的含糊不清，以及对“包罗万象”假设的评估的不确定性。在这笔赠款下，希蒙尼教授与两名研究生一起工作，正在扩大和完善他最初的立场，以考虑到这些困难。他希望通过“回火不回火”的方法来消除第一个困难。他认为，通过将概率分析命题与后验原理恰当地结合起来，第二和第三个困难可以得到改善。他和他的学生正在进行一些科学案例研究，目的既是为了说明这种精炼的方法论的力量，也是为了启发式地在归纳推理中制定后验原理。

Scientific inference, the process of going from particular instances to general laws, has been a matter of philosophical concern since the time of Aristotle. Not until Thomas Bayes (1763), however, was there any explicit method presented to use probability theory to justify the inference from particulars to general laws. The entire family of Bayesian scientific methodologies formulates scientific inference in terms of the concept of epistemic probability, considers the prior probability of scientific hypothesis to be a meaningful concept, and makes use of Bayes's theorem for evaluating posterior probabilities. A version of Bayesianism proposed by Professor Shimony in 1970, called "tempered personalism," recommends that personal probability evaluations be "tempered" by openmindedness towards all seriously proposed hypotheses in an investigation. Among the virtues of tempered personalism is the possibility of arriving at a non- negligible posterior probability for a strong scientific generalization. There are, however, some weaknesses in tempered personalism which require modifications: notably, a difficulty in justifying the axioms of probability, the vagueness of "seriously proposed," and uncertainty regarding the evaluation of the "catch- all" hypothesis. Under this grant, Professor Shimony, working with two graduate students, is amplifying and refining his original positions to take account of these difficulties. He expects to remove the first difficulty by a procedure of "tempering without tempering." He believes the second and third difficulties are ameliorated by properly combining analytic propositions of probability with a posteriori principles. He and his students are undertaking a number of scientific case studies for the purpose both of illustrating the power of this refined methodology and for heuristics in formulating the a posteriori principles in inductive inference.