Ockham's Razor: A New Justification

当面对与当前经验相容的可选理论时，科学家、标准统计技术和最新的数据挖掘软件都倾向于站在最简单的理论一边，其中的简单性与最小化独立实体、原则、原因或等式系数有关。这种对简单的系统性偏见有一个名字：奥卡姆剃刀。对于简单理论的吸引力，有许多解释：它们是漂亮的、统一的、对称的、解释性的、严格可测试的、减少了经验估计的差异，并且相对于现成的先验概率测量更有可能。事实证明，更难以解释的是，对简单理论的偏爱如何推动了对与未来所有观测相一致的正确理论的探索。当然，如果整体经验在当前的经验下尽可能简单，奥卡姆剃刀会指向一个经验充足的理论，但这是对奥卡姆剃刀的循环呼吁：哪个称职的萨满的神谕不坚持自己的可靠性？事实上，每一个关于简单性的标准描述，要么无法解决前面显而易见的问题，要么通过直接或默许的循环性来解决问题。这一提议涉及一种新的、非循环的论证，根据这种论证，奥卡姆剃刀并没有指向或表明一种经验上充分的理论，而是让人们沿着通向这种理论的最直接的可能路线进行探索。收敛的“直直性”是根据收敛到真实理论之前的历时认知成本来衡量的，例如经验方法随着数据的积累而改变其观点的次数，这些观点逆转发生的延迟时间，以及产生错误理论的总次数。刚才描述的一些严格的最优性定理已经被建立起来了。我们的建议是将这些结果推广到各个基本维度，更深入地研究它们对当代和历史实践的具体影响，并进行诊断性计算机模拟，以研究标准统计和机器学习策略在模型选择方面的收敛效率。因此，建议的工作涉及到概念细化、数学、方法和基于计算机生成的随机数据的模拟研究的平衡组合。对于科学方法中一个突出的奥秘，开发一种新的、以真理为导向的解释，其智力价值是显而易见的。没有什么问题能比这更广泛、更深刻地关系到美国国家科学基金会的使命了。就更广泛的影响而言，奥卡姆剃刀对科学家、理科生和广大公众来说都是一个谜，对科学哲学来说也是一个谜。所提出的解释简单而鼓舞人心，就其大纲而言，足以作为简单性在科学中的作用的标准教科书解释。

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.