Quantitative practice across statistics, engineering, and machine learning has been transformed by the automation of inference. Predictions are produced, validated, and deployed at scale and speed that human-mediated reasoning could not match. This shift intersects with a structural limit of reasoning that no methodological refinement dissolves: every inference rests on a finite specification of conditions, and what falls outside the specification does not appear as a widened uncertainty band -it does not appear at all. The choice of specification -the frame -is upstream of the inference and cannot be audited from inside the system that uses it. This paper offers a synthetic, application-oriented review. We argue that three categories of uncertainty operate in quantitative practice -aleatory, epistemic, and frame (or ontological) -and that the third, the residue of finite specification, is structurally invisible to formal analysis within the chosen frame and is the locus of most consequential failures. We trace why the limit applies equally to deductive and inductive reasoning, why no meta-level procedure dissolves the regress, and why current conditions of automated inference make epistemic humility -the practical disposition this argument supports -more, not less, important. We articulate the argument's specific resonances for five typical figures of contemporary quantitative work -the engineer, the statistician, the mathematician, the machine-learning practitioner, and the non-specialist recipient of expert claims -showing how the structural argument bears on each practice's natural defenses. The argument is not against rigor or against quantification; it is for distinguishing rigor earned within a frame from rigor with respect to the frame.

翻译：统计、工程和机器学习领域的量化实践已因推理自动化而彻底改变。预测以人类中介推理无法匹敌的规模和速度被生成、验证并部署。这一转变与推理的结构性极限相交汇——任何方法论的改进都无法消解这一极限：每一项推理都基于对条件的有限规定，而超出规定范围的部分不会表现为更宽的不确定带——它根本不会出现。规定的选择——即框架——位于推理上游，且无法从使用该系统的内部进行审计。本文提供一份综合性的应用导向综述。我们主张，在量化实践中存在三类不确定性——偶然性、认知性和框架性（或本体论性）——而第三类，即有限规定的残余，在所选框内对形式分析而言在结构上不可见，却是大多数重大失败的根源。我们追溯了为何这一极限同样适用于演绎和归纳推理，为何元层级的程序无法消除该回归，以及为何当前自动化推理的条件使得认识谦逊——这一论证所支持的实际态度——变得更为重要而非相反。我们阐述了该论证对当代量化工作中五种典型角色——工程师、统计学家、数学家、机器学习从业者以及专家主张的非专业接收者——的具体意义，展示了结构性论证如何影响每种实践的自然防御机制。这一论证并非反对严谨性或量化；而是旨在区分框架内获得的严谨与相对于框架本身的严谨。