Ockham's Razor: A New Justification

奥卡姆剃刀：新的理由

• 批准号: 0750681
• 负责人: Kevin Kelly
• 金额: $ 10.35万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-03-15 至 2011-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0750681&HistoricalAwards=false
• 关键词: Ockham; Razor; New; Justification

When faced with a choice among alternative theories compatible with current experience, scientists, standard statistical techniques, and the most recent data-mining software all tend to side with the simplest theory, where simplicity has something to do with minimizing independent entities, principles, causes, or equational coefficients. This systematic bias toward simplicity has a name: Ockham's razor.There are numerous explanations of the appeal of simple theories: they are pretty, unified, symmetrical, explanatory, severely testable, reduce the variance of empirical estimates, and are more probable with respect to of-the-shelf prior probability measures. What has proven much harder to explain is how favoring simple theories advances the search for a correct theory, compatible with all future observations. Of course, if the totality experience were as simple as possible in light of current experience, Ockham's razor would point at an empirically adequate theory, but that is a circular appeal to Ockham's razor: What competent shaman's oracle fails to insist upon its own reliability? Indeed, every standard account of simplicity either fails to address the preceding, obvious, concern or does so via a direct or tacit appeal to circularity.This proposal concerns a new, non-circular justification, according to which Ockham's razor does not point at or indicate an empirically adequate theory but, rather, keeps inquiry on the straightest possible route to such a theory. 'Straightness' of convergence is measured according to diachronic cognitive costs prior to convergence to the true theory, such as the number of times the empirical method reverses its opinion as the data accumulate, the lateness of occurrence of these reversals of opinion, and the total number of times a false theory is produced.Some rigorous optimality theorems of the sort just described have already been established. The proposal is to generalize these results in various essential dimensions, to study more deeply their concrete consequences for practice, both contemporary and historical, and to perform diagnostic computer simulations to study the convergent efficiency of standard statistical and machine learning strategies for model selection. The proposed work, therefore, involves a balanced mix of conceptual refinement, mathematics, methodology, and simulation studies based on computer-generated random data.The intellectual merit of developing a new, truth-directed explanation for one of the outstanding mysteries concerning scientific method is evident. No question could be more generally or deeply relevant to the mission of the National Science Foundation. Regarding broader impact, Ockham's razor is as much a puzzle for scientists, science students, and the broader public as it is for the philosophy of science. The proposed explanation is simple and inspiring enough, in its outlines, to serve as a standard, textbook explanation of the role of simplicity in science.

当科学家、标准统计技术和最新的数据挖掘软件面临与当前经验兼容的替代理论的选择时，它们都倾向于支持最简单的理论，其中简单性与最小化独立实体、原则、原因或方程系数有关。这种对简单性的系统性偏好有一个名字：奥卡姆剃刀，简单理论的吸引力有很多解释：它们漂亮、统一、对称、解释性强、可严格检验、减少经验估计的方差，而且相对于现成的先验概率测度来说更有可能。事实证明，更难解释的是，支持简单理论如何促进对与所有未来观察兼容的正确理论的探索。当然，如果总体性经验在当前经验的光照下尽可能简单，奥卡姆剃刀将指向一个经验上充分的理论，但这是对奥卡姆剃刀的循环呼吁：有能力的萨满神谕不能坚持自己的可靠性吗？事实上，每一个关于简单性的标准解释要么没有解决前面的、显而易见的问题，要么通过直接或默许的循环来解决问题。这个提议涉及一个新的、非循环的论证，根据这个论证，奥卡姆剃刀并不指向或表明一个经验上充分的理论，而是继续探索通向这样一个理论的最直接的可能途径。收敛的“直线性”是根据在收敛到正确理论之前的历时认知成本来衡量的，例如随着数据的积累，经验方法推翻其观点的次数，这些观点的逆转发生的晚，以及产生错误理论的总次数。我们的建议是在各种基本维度上概括这些结果，更深入地研究它们对当代和历史实践的具体影响，并进行诊断计算机模拟，以研究标准统计和机器学习策略在模型选择中的收敛效率。因此，拟议中的工作涉及概念提炼、数学、方法论和基于计算机生成的随机数据的模拟研究的平衡组合，为科学方法的一个突出谜团开发一个新的、以真理为导向的解释的智力价值是显而易见的。没有什么问题比这更普遍或更深刻地关系到国家科学基金会的使命了。关于更广泛的影响，奥卡姆剃刀对科学家、理科学生和更广泛的公众来说是一个难题，就像它对科学哲学一样。所提出的解释是简单和鼓舞人心的，在其大纲中，作为一个标准，教科书解释的简单性在科学中的作用。