📚 CIE Year 9 Philosophy: Quick Reference Handbook of Formulas & Theorems | CIE Year 9 哲学：公式定理速查手册
This handbook presents key philosophical ideas as simplified formulas and logical structures, giving Year 9 CIE students a clear, memorisable toolkit. It covers deductive patterns, ethical principles, fallacies, and methods of inquiry, all expressed through concise symbolic notation and paired bilingual explanations.
本手册将关键哲学理念提炼为简化的公式与逻辑结构，为Year 9 CIE学生提供清晰、易记的工具箱。内容涵盖演绎模式、伦理原理、谬误与探究方法，均以简洁的符号表达，并配有双语对照解释。
1. The Philosophy Formula | 哲学的公式
ctured process: Question + Reasoned Argument + Critical Evaluation → Deeper Understanding.
哲学可以被看作一个结构化过程：问题 + 理性论证 + 批判性评估 → 更深层的理解。
It does not produce one final answer like a mathematical equation, but the pursuit itself follows a repeatable pattern, which we may call the 'philosophical formula'. Every debate in class, every essay you write, begins by identifying a question (e.g., 'What is knowledge?'), constructing arguments with premises and a conclusion, and then testing those arguments for weakness.
它不像数学方程那样产生唯一最终答案，但探究本身遵循一种可重复的模式，我们可以称之为“哲学公式”。课堂上的每一次辩论、你写下的每一篇论文，都始于确定一个问题（例如“知识是什么？”），用前提和结论构建论证，然后检验这些论证是否薄弱。
2. The Principle of Non-Contradiction | 非矛盾律
Formula: ¬(A ∧ ¬A) — a proposition cannot be both true and false at the same time and in the same respect.
公式：¬(A ∧ ¬A) —— 一个命题不能在同一时间、同一方面既为真又为假。
This principle is the bedrock of rational discourse. If someone says 'The desk is both completely wooden and completely metal in the same spot', you have a contradiction. Without this rule, arguments collapse into meaninglessness. In logic exercises, always check whether two premises assert A and not-A simultaneously; if they do, the set is inconsistent.
这条原理是理性对话的基石。若有人说“这张桌子在同一位置既完全是木头又完全是金属”，就出现了矛盾。没有这条法则，论证便会崩溃为无意义。在逻辑练习中，务必检查两个前提是否同时断言 A 以及非 A；如果如此，这一组前提便不一致。
3. Modus Ponens & Modus Tollens | 肯定前件式与否定后件式
Modus Ponens (Affirming the Antecedent):
肯定前件式：
If P → Q, and P is true, ∴ Q is true.
若 P → Q，且 P 为真，∴ Q 为真。
Example: If it rains (P), the ground is wet (Q). It rains. Therefore, the ground is wet. This form is always valid; truth of premises determines soundness.
例子：如果下雨（P），地面是湿的（Q）。下雨了。因此，地面是湿的。这种形式总是有效的；前提的真值决定其可靠性。
Modus Tollens (Denying the Consequent):
否定后件式：
If P → Q, and Q is false (¬Q), ∴ P is false (¬P).
若 P → Q，且 Q 为假（¬Q），∴ P 为假（¬P）。
Example: If the battery is charged (P), the phone turns on (Q). The phone does not turn on. Therefore, the battery is not charged. This is also a valid deductive form and appears frequently in CIE argument analysis questions.
例子：如果电池有电（P），手机就能开机（Q）。手机不能开机。因此，电池没有电。这也是一种有效的演绎形式，常出现在CIE论证分析题中。
4. The Categorical Syllogism Formula | 定言三段论公式
A syllogism moves from two premises to a conclusion. The classic valid pattern:
三段论由两个前提推出一个结论。经典的有效模式：
All A are B. All C are A. ∴ All C are B.
所有的 A 都是 B。所有的 C 都是 A。∴ 所有的 C 都是 B。
Example: All mammals are warm‑blooded. All whales are mammals. Therefore, all whales are warm‑blooded. The formula works as long as the 'middle term' (A) is distributed properly. A common mistake is the fallacy of the undistributed middle: 'All dogs are animals. All cats are animals. Therefore, all cats are dogs.' That is invalid because the middle term 'animals' is never connected in the right way to guarantee the conclusion.
例子：所有哺乳动物都是温血动物。所有鲸都是哺乳动物。因此，所有鲸都是温血动物。只要“中项”（A）周延得当，该公式就成立。常见错误是“中项不周延”谬误：“所有的狗都是动物。所有的猫都是动物。因此，所有的猫都是狗。”这是无效的，因为中项“动物”从未以正确方式联系起来以保证结论。
5. Validity & Soundness Formula | 有效性与可靠性公式
A concise way to remember the relationship:
记住关系的简洁方式：
Valid structure + True premises = Sound argument
有效结构 + 真前提 = 可靠论证
Validity only concerns the logical form: if the premises were true, the conclusion would have to be true. Soundness adds the extra layer that the premises are actually true in reality. For CIE exam answers, you must comment on both. You might say, 'The argument is valid because it follows modus ponens, but it is unsound because the first premise is factually incorrect.'
有效性仅关乎逻辑形式：如果前提为真，结论必然为真。可靠性则增加了额外一层要求——前提在现实中确实为真。在CIE考试答案中，你必须对这两者加以评述。你可以说：“该论证有效，因为它遵循肯定前件式，但它不可靠，因为第一个前提不符合事实。”
6. Ethical Formula: The Greatest Happiness Principle | 伦理公式：最大幸福原理
Utilitarian ethics, especially Bentham's version, can be expressed as:
功利主义伦理学，尤其是边沁的版本，可表达为：
Right action = Maximise Σ (Pleasure - Pain) for all affected
正确行为 = 为所有受影响者最大化 Σ（快乐 - 痛苦）
In this formula, Σ (the Greek sigma) stands for the sum of net happiness. Bentham proposed a 'felicific calculus' weighing intensity, duration, certainty, and extent. For a Year 9 revision, remember: the moral worth of an act is measured solely by its consequences on overall well‑being. A quick checklist: Does the action increase total happiness more than any alternative? If yes, a utilitarian would call it right.
在此公式中，Σ（希腊字母西格玛）代表净幸福的总和。边沁提出了“快乐计算法”，权衡强度、持续时间、确定性与范围。Year 9复习时记住：一个行为的道德价值仅由其带来的总体福祉后果衡量。快速核查清单：该行为是否比任何替代方案更能增加总幸福？如是，功利主义者便称之为正确。
7. The Categorical Imperative (Simplified) | 定言令式（简化版）
Kant’s central moral law can be reduced to a test formula:
康德的核心道德律可简化为一个检验公式：
Act only according to that maxim whereby you can, at the same time, will that it should become a universal law.
只依据你能同时意愿其成为普遍法则的准则去行动。
In application: (1) Identify the maxim of your action. (2) Universalise it — imagine everyone acts on it. (3) Test for contradiction. If universalising the maxim leads to a logical or practical contradiction, the act is morally impermissible. For instance, 'I will make a false promise to get money' cannot be universalised because the institution of promising would collapse. This contrasts sharply with consequentialist formulas: Kant asks about the form of the action, not the sum of outcomes.
实际应用：（1）确定你行为的准则。（2）将其普遍化——想象每个人都以此行动。（3）检验是否产生矛盾。若普遍化该准则导致逻辑或实践上的矛盾，该行为在道德上就是不允许的。例如，“为获得金钱而作虚假承诺”无法被普遍化，因为承诺制度会因此崩溃。这与后果论公式形成鲜明对比：康德询问行为的形式，而非结果的总和。
8. Fallacy Formulas: Disguised Bad Arguments | 谬误公式：伪装的坏论证
Many fallacies have identifiable structures. Recognising the formula helps avoid being misled:
许多谬误都有可识别的结构。识别公式有助于避免被误导：
- Ad Hominem: Attack the person, not the argument. Formula: 'You say P; you are flawed; therefore P is false.' —— 攻击人而非论点。公式：“你主张 P；你有缺陷；因此 P 为假。”
- Straw Man: Distort opponent's view (into a weaker version Q), then attack Q. Formula: 'Opponent claims P. I will interpret it as an extreme Q. Q is false. Therefore P is false.' —— 歪曲对方观点（弱化为 Q），然后攻击 Q。公式：“对方主张 P。我将其曲解为极端的 Q。Q 是错的。因此 P 是错的。”
- False Dilemma: Present only two options when more exist. Formula: 'Either A or B; not B; therefore A' (when C, D are also possible). —— 假两难：仅给出两个选项而实际存在更多。公式：“要么 A 要么 B；非 B；故 A”（但 C、D 等也可能）。
In CIE stimulus material, you can often spot these by asking: 'Does the reasoning depend on a hidden unfair simplification?' If yes, identify the fallacy by name using the pattern.
在CIE的阅读材料中，你常可通过提问“论证是否依赖于隐藏的不公简化？”来发现这些谬误。若是如此，即可用该模式说出谬误名称。
9. Socratic Method Formula | 苏格拉底式问答法公式
The Socratic method is a disciplined questioning technique:
苏格拉底式问答法是一种有纪律的提问技术：
Question → Answer → Counter‑example → Revised answer → Deeper insight
提问 → 回答 → 反例 → 修正回答 → 更深的洞见
This is not about winning a debate but about testing beliefs. For revision, recall the model: start with a definition (e.g., 'Justice is helping friends and harming enemies'). Then pose a counter‑example ('What if a friend is wrong?'). The initial definition is refined, moving closer to a more robust concept. In essays, you can demonstrate philosophical skill by showing how a concept withstands or fails under this iterative process.
这并非为了赢得辩论，而是检验信念。复习时可回忆此模型：从一个定义开始（如“正义是帮助朋友、伤害敌人”），然后提出反例（“若朋友做错了呢？”），初始定义得以修正，从而接近更坚实的概念。在论文中，你可用这种迭代过程来展示一个概念如何经受或未能经受检验，以此体现哲学技能。
10. The Thought Experiment Formula | 思想实验公式
Thought experiments are not random fantasies; they follow a structure:
思想实验并非随意的幻想，它们遵循一种结构：
ement (J) → Compare J with theory (T) → If J and T conflict, we must revise either J or T.
场景（S）隔离一个变量 → 直觉判断（J） → 将 J 与理论（T）比较 → 若 J 与 T 冲突，须修正其中之一。
For example, in the 'trolley problem', the scenario isolates whether causing harm as a side‑effect is morally different from intending harm. Your immediate judgement is tested against ethical principles like utilitarianism or the Doctrine of Double Effect. A complete CIE answer explains what the thought experiment reveals about the limits of a theory.
例如，在“电车难题”中，场景隔离了“将伤害作为副作用”与“有意造成伤害”是否在道德上不同。你的直觉判断将与功利主义或双重效果原则等伦理原则相检验。一份完整的CIE答案会解释该思想实验揭示了某一理论的何种局限。
11. Key Terminology at a Glance | 关键术语速查
| English Term | 中文术语 | Quick Formula / Definition |
|---|---|---|
| Premise | 前提 | A statement that supports a conclusion. |
| Conclusion | 结论 | The statement argued for, marked by '∴' or 'therefore'. |
| A priori | 先天的 | Knowledge independent of sense experience (e.g., 2+2=4). |
| A posteriori | 后天的 | Knowledge dependent on sense experience (e.g., 'the sky is blue'). |
| Empiricism | 经验主义 | All knowledge comes from sensory experience. |
| Rationalism | 理性主义 | Reason is the primary source of knowledge. |
| Consequentialism | 后果论 | Morality depends on outcomes: Right = best overall consequences. |
| Deontology | 义务论 | Morality depends on duty and rules, not consequences. |
12. Quick Revision Checklist | 快速复习清单
Before your assessment, run through these formula‑style questions:
评估前，请过一遍这些公式化的问题：
- Can I identify the logical form of an argument? (Modus ponens, modus tollens, syllogism?) —— 我能辨识论证的逻辑形式吗？（肯定前件、否定后件、三段论？）
- Do I distinguish validity from soundness? —— 我能区分有效性与可靠性吗？
- Can I apply the Greatest Happiness Principle and the Categorical Imperative to a scenario? —— 我能将最大幸福原理和定言令式应用于情境吗？
- Am I able to spot common fallacies by their structural formula? —— 我能通过结构公式识别常见谬误吗？
- Do I understand how a thought experiment isolates a variable and challenges a theory? —— 我理解思想实验如何隔离变量并挑战理论吗？
Mastering these patterns will turn philosophy from a vague discussion into a precise, exam‑ready discipline. Keep the formulas handy, practise with past paper scenarios, and always link abstract structures to concrete examples.
掌握这些模式，将使哲学从模糊的讨论转变为一门精确、适应考试的学科。随身记下这些公式，用历年试卷情境加以练习，并始终将抽象结构与具体例子联系起来。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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