Formula & Theorem Quick Reference Handbook for Year 7 CIE Philosophy | Year 7 CIE 哲学：公式定理速查手册

📚 Formula & Theorem Quick Reference Handbook for Year 7 CIE Philosophy | Year 7 CIE 哲学：公式定理速查手册

Welcome to your essential quick reference guide for Year 7 CIE Philosophy. This handbook distils the core logical structures, argument patterns, and conceptual frameworks you will encounter into clear, memorable ‘formulae’ and ‘theorems’. Philosophy is not about memorising equations in the traditional sense, but it does rely on rigorous patterns of reasoning that can be expressed in structured form. Each entry below pairs an English explanation with its Chinese equivalent, ensuring you grasp the concept from both linguistic angles.

欢迎使用 Year 7 CIE 哲学的必备速查手册。本手册将你将会遇到的核心逻辑结构、论证模式和概念框架提炼为清晰易记的”公式”与”定理”。哲学并非传统意义上的记忆方程式，但它确实依赖于可以用结构化形式表达的严谨推理模式。以下每个条目都将英文解释与中文对应，确保你从两个语言角度理解概念。

1. The Socratic Formula for Questioning | 苏格拉底式提问公式

The Socratic method follows a structured pattern of inquiry to uncover assumptions and test beliefs. The formula proceeds as: Clarify the concept → Probe for evidence → Examine alternative views → Consider implications → Reflect on the original question. This recursive process forms the backbone of philosophical dialogue and critical thinking in the CIE classroom.

苏格拉底方法遵循结构化的探究模式，以揭示假设并检验信念。该公式进行如下：澄清概念 → 探寻证据 → 审视替代观点 → 考虑含义 → 反思原初问题。这一递归过程构成了CIE课堂中哲学对话与批判性思维的支柱。

Step 1: What exactly do we mean by ‘X’? / 第一步：”X”的确切含义是什么？
Step 2: What reasons support this claim? / 第二步：什么理由支持这一主张？
Step 3: Could the opposite be true? / 第三步：相反的情况是否可能为真？
Step 4: If this is true, what follows? / 第四步：如果这是真的，会得出什么？
Step 5: Has our understanding deepened? / 第五步：我们的理解是否深化了？

2. Aristotle’s Syllogism Structure | 亚里士多德三段论结构

A syllogism is the fundamental logical formula where a conclusion is drawn from two given propositions, called premises. The classic structure follows: Major Premise (All A are B) + Minor Premise (C is A) → Conclusion (Therefore, C is B). Mastering this pattern helps you construct valid arguments and identify flawed reasoning in philosophical texts.

三段论是基本的逻辑公式，从两个给定的命题（称为前提）中得出结论。经典结构如下：大前提（所有A都是B）+ 小前提（C是A）→ 结论（因此，C是B）。掌握这一模式有助于你构建有效论证，并识别哲学文本中的缺陷推理。

Component / 组成部分	Example / 示例
Major Premise / 大前提	All humans are mortal. / 所有人都会死。
Minor Premise / 小前提	Socrates is a human. / 苏格拉底是人。
Conclusion / 结论	Therefore, Socrates is mortal. / 因此，苏格拉底会死。

3. The Argument Validity Theorem | 论证有效性定理

An argument is valid if and only if the conclusion logically follows from the premises. The theorem states: Validity ≠ Truth. A valid argument can have false premises and a false conclusion, yet still be logically correct in structure. The key test is: IF the premises were true, would the conclusion necessarily be true? This distinction between validity and soundness is a cornerstone of CIE philosophical analysis.

一个论证有效，当且仅当结论从前提中合乎逻辑地得出。该定理指出：有效性 ≠ 真实性。一个有效的论证可以拥有假的前提和假的结论，但在结构上仍然是逻辑正确的。关键检验在于：如果前提为真，结论是否必然为真？有效性与健全性之间的这一区分，是CIE哲学分析的基石。

Validity Formula: If (P₁ ∧ P₂ ∧ … ∧ Pₙ), then C must follow. / 有效性公式：如果 (P₁ ∧ P₂ ∧ … ∧ Pₙ)，则C必然得出。

4. The Ethical Decision-Making Framework | 伦理决策框架

When confronting an ethical dilemma, apply the four-quadrant formula: Action → Intention → Consequences → Universal Principle. Evaluate each quadrant in turn before reaching a moral judgement. This framework synthesises deontological (duty-based) and teleological (outcome-based) approaches, both examined in the CIE syllabus.

面对伦理困境时，应用四象限公式：行为 → 意图 → 后果 → 普遍原则。在得出道德判断之前，依次评估每个象限。这一框架综合了义务论（基于责任）和目的论（基于结果）的方法，两者均在CIE教学大纲中考查。

Quadrant 1: What is the action itself? Is it inherently right or wrong? / 第一象限：行为本身是什么？它在本质上是对还是错？
Quadrant 2: What is the intention behind the action? / 第二象限：行为背后的意图是什么？
Quadrant 3: What are the likely consequences for all affected? / 第三象限：对所有受影响者可能产生的后果是什么？
Quadrant 4: Can this be universalised as a rule for everyone? / 第四象限：这能否被普遍化为适用于所有人的规则？

5. The Mind-Body Distinction Principle | 心身区分原则

The principle of dualism, most famously argued by Descartes, can be expressed as: Mental substances are non-physical and indivisible; physical substances are extended and divisible. Therefore, Mind ≠ Body. This formula initiates the core philosophical problem of consciousness examined at Year 7 level, prompting questions about identity and personal existence.

二元论原则，最为著名的由笛卡尔论证，可以表述为：心灵实体是非物质的且不可分割的；物质实体是有广延的且可分割的。因此，心灵 ≠ 身体。这一公式开启了七年级水平所探讨的意识这一核心哲学问题，引发关于同一性和个人存在的追问。

Dualism Theorem: Mental states have no spatial location; physical states do. Therefore, they are distinct. / 二元论定理：心理状态没有空间位置；物理状态有。因此，它们是不同的。

6. Plato’s Theory of Forms as an Equation | 柏拉图理型论的方程式表述

Plato’s metaphysical framework can be expressed relationally: Particular object = Imperfect copy of its corresponding Form. The Form of Beauty itself is perfect, eternal, and unchanging, whereas a beautiful painting participates in that Form imperfectly. Understanding this relation helps you grasp the CIE philosophy topic of appearance versus reality.

柏拉图的形而上学框架可以用关系式表达：具体事物 = 其对应理型的不完美摹本。美之理型本身是完美的、永恒的、不变的，而一幅美丽的画作则不完满地分有了那个理型。理解这一关系有助于你掌握CIE哲学中表象与实在的主题。

World of Being / 存在的世界	World of Becoming / 生成的世界
Perfect, eternal Forms / 完美、永恒的理型	Imperfect, changing particulars / 不完美、变化的具体事物
Grasped by reason / 由理性把握	Perceived by senses / 由感官感知

7. The Empiricism Formula for Knowledge | 经验主义的知识公式

Empiricism asserts that all knowledge originates in sensory experience. The formula runs: Sense perception → Simple ideas → Complex ideas → Knowledge. John Locke described the mind at birth as a tabula rasa, a blank slate, upon which experience writes. This contrasts with rationalism, which holds that reason alone can yield knowledge independently of the senses.

经验主义主张所有知识都源于感觉经验。公式进行如下：感官知觉 → 简单观念 → 复杂观念 → 知识。约翰·洛克将出生时的心灵描述为一块白板，经验在其上书写。这与理性主义形成对比，后者认为理性可以独立于感官产生知识。

Empiricist Formula: No idea in the mind that was not first in the senses. / 经验主义公式：心灵中没有先于感官存在的观念。

8. The Principle of Sufficient Reason | 充足理由原则

Formulated by Leibniz, the Principle of Sufficient Reason states: For every fact or true proposition, there must be a sufficient reason why it is so and not otherwise. In argumentation, this translates to a practical formula: Every claim requires justification, and no belief should be held without adequate grounds. This principle underpins the CIE philosophy emphasis on reasoned justification in essays and discussions.

由莱布尼茨提出的充足理由原则指出：对于每一个事实或真命题，必然有一个充足理由说明它为什么是这样而不是那样。在论证中，这转化为一个实践公式：每个主张都需要理由支持，任何信念都不应在没有充分根据的情况下持有。这一原则支撑了CIE哲学在论文和讨论中对理据性论证的强调。

Claim: X is true. / 主张：X是真的。
Required: Provide reason R such that R explains why X is true. / 要求：提供理由R，使得R解释为什么X是真的。
Insufficient: ‘Because I think so’ or ‘Because it is obvious’. / 不充分：”因为我是这么想的”或”因为这很明显”。

9. The Utilitarian Calculus | 功利主义计算

Bentham’s utilitarian principle proposes a formula for moral evaluation: An action is right if it produces the greatest happiness for the greatest number. Quantitatively, one can think of it as: Total Net Happiness = Σ(Pleasure) − Σ(Pain), summed over all affected individuals. While simplified for Year 7, this introduces the consequentialist logic central to CIE ethics modules.

边沁的功利主义原则提出了道德评估的公式：一个行为是正确的，如果它为最大多数人带来最大幸福。在数量上，可以将其视为：总净幸福 = Σ(快乐) − Σ(痛苦)，对所有受影响的个体求和。虽然为七年级做了简化，但这引入了CIE伦理学模块中核心的后果论逻辑。

Greatest Happiness Principle: Maximise pleasure, minimise pain, across all sentient beings. / 最大幸福原则：在所有有感知的存在中，最大化快乐，最小化痛苦。

10. The Categorical Imperative Test | 定言令式检验

Kant’s ethical formula requires you to test any proposed action against a universal law: Act only according to that maxim whereby you can at the same time will that it should become a universal law. This is not a mathematical formula but a rational test procedure. If universalising your maxim leads to a contradiction, the action is morally impermissible.

康德的伦理公式要求你将任何提议的行为与一条普遍法则进行对照检验：只按照那个你同时能够意愿其成为普遍法则的准则去行动。这不是一个数学公式，而是一个理性的检验程序。如果你的准则的普遍化会导致矛盾，那么该行为在道德上是不可允许的。

Test steps / 检验步骤:

1. Formulate the maxim of your action. / 表述你行为的准则。
2. Universalise it: imagine everyone acts on it. / 将其普遍化：想象每个人都按照它行动。
3. Check for contradiction in conception or in will. / 检查在构想上或意愿上是否有矛盾。
4. If contradiction → impermissible; if none → permissible. / 如果有矛盾 → 不允许；如果没有 → 允许。

11. The Relativism vs. Absolutism Distinction | 相对主义与绝对主义的区分

This conceptual formula clarifies a recurring tension in CIE philosophy: Moral Relativism holds that ethical truths are relative to culture, individual, or historical context; Moral Absolutism holds that certain ethical principles are universally and objectively valid. The distinction can be framed as: ‘Is X wrong always and everywhere, or does it depend?’ Understanding this polarity is essential for structuring comparative essays.

这一概念性公式澄清了CIE哲学中反复出现的张力：道德相对主义认为伦理真理相对于文化、个体或历史语境而言；道德绝对主义认为某些伦理原则是普遍且客观有效的。这一区分可以概括为：”X是永远且在各地都是错的，还是取决于具体情况？”理解这一对立对于构建比较性论文至关重要。

Relativism / 相对主义	Absolutism / 绝对主义
Truth depends on perspective. / 真理取决于视角。	Truth is independent of perspective. / 真理独立于视角。
‘Right’ varies across cultures. / “对”因文化而异。	‘Right’ is constant across cultures. / “对”在不同文化中恒常不变。

12. The Logical Fallacy Identification Formulae | 逻辑谬误识别公式

Philosophical reasoning requires vigilance against common fallacies. Each fallacy has a recognisable pattern. Ad Hominem: Rejecting an argument by attacking the person making it, rather than addressing the argument itself. Straw Man: Misrepresenting an opponent’s position to make it easier to attack. Formula: Original argument A is distorted into a weaker version A’, and A’ is refuted instead of A.

哲学推理需要对常见谬误保持警惕。每种谬误都有可识别的模式。人身攻击：通过攻击提出论证的人来拒绝一个论证，而不是针对论证本身。稻草人谬误：歪曲对手的立场以使其更容易攻击。公式：原始论证A被扭曲为较弱的版本A’，而A’被驳倒以代替A。

Ad Hominem Pattern: ‘You are X, therefore your argument is wrong.’ / 人身攻击模式：”你是X，所以你的论证是错的。”
Straw Man Pattern: ‘You said X, which really means Y, and Y is clearly wrong.’ / 稻草人模式：”你说了X，这实际上意味着Y，而Y显然是错的。”
False Dilemma Pattern: ‘Either A or B; there is no third option.’ / 假两难模式：”要么A，要么B；没有第三种选择。”
Begging the Question: The conclusion is assumed in the premise. / 循环论证：结论在前提中已被假设。

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Formula & Theorem Quick Reference Handbook for Year 7 CIE Philosophy | Year 7 CIE 哲学：公式定理速查手册