三段论推理的词项周延一致性规则在“分层抽样”和“酸”实例中的运用
Application of the Consistency Rule of Term Distribution in Syllogistic Reasoning to the Instances of "Stratified Sampling" and "Acid
李宏 湖北省十堰市郧阳中学
Li Hong Yunyang High School, Shiyan City, Hubei Province
"大项不当周延" (Illicit Major)：当大项（P）违反此规则时。
"Illicit Major": If the major term (P) violates this rule
一、案例：
展开剩余94%统计推断中 “分层抽样与样本代表性” 的错误推理（结论错误，推理无效）
Fallacious Reasoning in "Stratified Sampling and Sample Representativeness" in Statistical Inference (Incorrect Conclusion and Invalid Reasoning)
1.三段论构建（Construction of Syllogism）
大前提（一般原理）：所有分层抽样（M）的样本，都具有“代表性强（即样本分布接近总体分布）”（P）；（全称肯定判断，谓项 P 不周延）
Major Premise (General Principle): All samples obtained through stratified sampling (M) have high representativeness (i.e., the sample distribution is close to the population distribution) (P); (Universal affirmative judgment, where the predicate term P is undistributed)
小前提（特殊情况）：某调查采用简单随机抽样（S），不是分层抽样（M）；（单称否定判断）
Minor Premise (Specific Case): A certain survey adopts simple random sampling (S) and is not stratified sampling (M); (Singular negative judgment)
结论（推导结果）：某调查的样本（S）不具有 “代表性强”（P）。（单称否定判断，谓项 P 周延）
Conclusion (Derived Result): The sample of this survey (S) does not have high representativeness (P). (Singular negative judgment, where the predicate term P is distributed)
2.周延性与数学本质分析
Analysis of Distribution and Mathematical Essence
大项不当周延：大项 P “代表性强” 在大前提中是肯定谓项（不周延，仅说分层抽样属于代表性强的抽样，未说只有分层抽样），结论中是否定谓项（周延）；
Illicit Major: The major term P ("high representativeness") is an affirmative predicate in the major premise (undistributed, indicating only that stratified sampling belongs to sampling methods with high representativeness, not that it is the only such method) but becomes a negative predicate in the conclusion (distributed).
数学错误：简单随机抽样在总体均匀分布时，样本代表性可能极强（如从全校学生中随机抽 100 人调查身高，若学生身高分布均匀，样本能反映总体）；
Mathematical Error: When the population is uniformly distributed, simple random sampling can yield highly representative samples (e.g., randomly selecting 100 students from an entire school to survey height—if the students' height distribution is uniform, the sample can reflect the overall population).
学生易错点：将“分层抽样的优势（代表性强）” 误视为“分层抽样独有的性质”，忽略“其他抽样方法在特定条件下也能具备该优势”。
Common Misunderstanding Among Students: Mistaking "the advantage of stratified sampling (high representativeness)" for "a unique property of stratified sampling," while ignoring that "other sampling methods can also possess this advantage under specific conditions."
本质是对“抽样方法与性质的逻辑关系”理解不严谨。
Essentially, this stems from an imprecise understanding of the logical relationship between sampling methods and their properties.
二、三段论推理的词项周延一致性规则
Rule : Consistency of Term Distribution
规则：前提中不周延的项（未断定全部外延），结论中不得周延，否则犯“大项不当扩大”或“小项不当扩大”。
Rule: A term undistributed in the premises (i.e., not covering its entire extension) must not be distributed in the conclusion; otherwise, it commits the fallacy of "illicit major" or "illicit minor".
1.大项扩大反例：
大前提：鸟（M）会飞（P）（P不周延）
小前提：企鹅（S）不是鸟（M）
结论：企鹅（S）不会飞（P）
（错误原因：大项“飞”在前提不周延，结论中周延）
Counterexample:
Major Premise: Birds (M) can fly (P). (P undistributed)
Minor Premise: Penguins (S) are not birds (M).
Conclusion: Therefore, penguins (S) cannot fly (P).
(Fallacy: The major term "can fly" is undistributed in the premise but distributed in the conclusion, committing the "Fallacy of Illicit Major Term" .
2.小项扩大反例：
大前提：科学家（M）是理性的（P）
小前提：科学家（M）是勤奋的（S）
结论：所有勤奋的人（S）是理性的（P）
（错误原因：小项“勤奋的”在前提不周延，结论中周延）
Counterexample:
Major Premise: Scientists (M) are rational (P). (S undistributed)
Minor Premise: Scientists (M) are diligent (S). (S undistributed)
Conclusion: Therefore, all diligent people (S) are rational (P).
(Fallacy: The minor term "diligent" is undistributed in the premises but distributed in the conclusion, committing the "Fallacy of Illicit Minor" .
“小项不当周延”的逻辑错误案例
Case of the Logical Fallacy of "Illicit Minor"
三、化学推理中的实例分析
Instance Analysis in Chemical Reasoning
关于“酸”的构成推理
Reasoning about the Composition of "Acids"
1.错误推理：
Erroneous Reasoning:
前提：硫酸（S）是酸（M），并且硫酸（S）含有氧元素（P）。
Premise:Sulfuric acid (S) is an acid (M), and sulfuric acid (S) contains oxygen (P).
错误结论：所以，所有酸（S）都含有氧元素（P）。
Erroneous Conclusion:Therefore, all acids (S) contain oxygen (P).
2.逻辑剖析：
Logical Analysis:
找出小项 (S)：结论是“所有S是P”，所以小项S是“酸”。
Identify the Minor Term (S):The conclusion is "All S are P," so the minor term S is "acid."
检查小项的周延性：
Check the Distribution of the Minor Term (S):
在前提中，小项“酸（S）”处于单称肯定判断（“硫酸是酸”）的主项位置。
In the premise, the minor term "acid" (S) is the subject of a singular affirmative judgment("Sulfuric acid is an acid").
虽然单称判断通常视作全称处理，但这里的关键在于，前提只谈论了“硫酸”这一种酸，并没有断定“酸”这个整个类别的所有成员（如盐酸、氢氟酸等）都具有某属性。
Although singular judgments are often treated as universal, the key point here is that the premise discusses only one specific type of acid (sulfuric acid) and does not assert that all members of the entire category "acid" (such as hydrochloric acid or hydrofluoric acid) possess the property of containing oxygen.
因此，就“酸”这个类别而言，前提只涉及其一部分对象，小项实际上是不周延的。
Therefore, regarding the category "acid" as a whole, the premise addresses only part of its objects, meaning the minor term S is effectively undistributed in the premise.
在结论中，S（“酸”）却作为全称判断（“所有的酸”）的主项出现，从而变得周延了。
In the conclusion, however, S appears as the subject of a universal judgment ("all acids"), making it distributed.
谬误判定：此推理犯了 “小项不当周延”（或称“小项非法周延”）的逻辑错误，因为小项（“酸”）在前提中不周延，在结论中却变得周延，其范围被非法地从单个实例扩大到了整个类别。
Fallacy Identified:This reasoning commits the fallacy of "Illicit Minor"(or "Illicit Process of the Minor Term"), because the minor term ("acid") is undistributed in the premise but distributed in the conclusion, illicitly expanding its scope from a single instance to the entire class .
在结论“所有的酸都含有氧”中，这是一个全称肯定判断。小项“酸”作为这个全称判断的主项，是周延的。该结论因此断定了“酸”这个类别的全部外延。
In the conclusion "all acids contain oxygen," this is a universal affirmative judgment. The minor term "acids," functioning as the subject of this universal judgment, is distributed. The conclusion thereby asserts something about the entire extensionof the class "acids."
3.逻辑错误判定：
Logical Error Identified:
小项“酸”在前提中不周延（仅指一个特定实例，如硫酸），但在结论中变得周延了（指所有的酸）。
The minor term "acids" is undistributed in the premise (referring only to a specific instance, e.g., sulfuric acid), but becomes distributed in the conclusion (referring to all acids).
这构成了“小项不当周延”（或称“小项的非法周延过程”）的逻辑谬误。即使结论在事实上是正确的（在本例中并非如此），其推理过程本身也是无效的，因为该词项的周延范围被不当扩大了。
This constitutes the fallacy of "illicit minor" (or "illicit process of the minor term"). Even if the conclusion were factually correct (which it is not in this case), the reasoning process itself is invalid because the term's distribution has been improperly expanded.
正确的认知：
Correct Understanding:
并非所有酸都含有氧元素（如盐酸HCl）。要判断酸的组成，应依据其定义（电离出的阳离子全部是氢离子的化合物），而非不完全的举例。
Not all acids contain oxygen (e.g., hydrochloric acid, HCl). To determine the composition of an acid, one should rely on its definition (a compound that ionizes in water to yield hydrogen ions as the only positively charged ions), rather than incomplete examples.
Explorer of Innovative Thinking
Author: Li Hong
Yunyang High School, Shiyan City, Hubei Province
January 12, 2026
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