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

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

Welcome to your Year 7 CAIE Philosophy quick reference guide. Although philosophy does not use mathematical formulas, it builds powerful tools for clear thinking—logical structures, argument patterns and ethical principles that work like ‘formulas’ for the mind. This handbook gathers the essential reasoning forms, fallacies and conceptual tools you will encounter, presented as a handy revision aid.

欢迎使用 Year 7 CAIE 哲学速查手册。哲学虽不用数学公式，却拥有一套让思维更清晰的强大工具——逻辑结构、论证模式和伦理原则，它们就像心智的“公式”。本手册汇集了你会遇到的基本推理形式、常见谬误与概念工具，是一份便捷的复习资料。

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1. Arguments: Premises and Conclusions | 论证：前提与结论

An argument in philosophy is a set of statements where some (premises) are intended to support another (the conclusion). Recognising this structure is the first ‘formula’ for analysing any piece of reasoning.

哲学中的论证是由若干陈述组成的集合，其中一部分（前提）用来支持另一部分（结论）。识别这一结构是分析任何推理的第一个“公式”。

Standard form: Premise 1, Premise 2, … therefore Conclusion. A simple example: All humans are mortal. (Premise 1) Socrates is a human. (Premise 2) Therefore, Socrates is mortal. (Conclusion)

标准形式：前提 1、前提 2……所以结论。一个简单例子：所有人都会死（前提 1）。苏格拉底是人（前提 2）。因此，苏格拉底会死（结论）。

Argument Formula: Premises → (support) → Conclusion

论证公式：前提 →（支持）→ 结论

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2. Deductive Reasoning: Modus Ponens | 演绎推理：肯定前件式

Modus Ponens is a valid deductive form. If a conditional statement (If P then Q) is accepted and the antecedent (P) is true, the consequent (Q) must be true. It guarantees the conclusion when the premises are true.

肯定前件式是一种有效的演绎形式。如果接受一个条件陈述（如果 P 则 Q）并且前件（P）为真，那么后件（Q）必然为真。当前提为真时，它能确保结论成立。

Formula: P → Q, P ⊢ Q

公式：P → Q，P ⊢ Q

Example: If it is raining, the ground is wet. It is raining. Therefore, the ground is wet. The strength lies in the logical connection, not the content.

示例：如果下雨，地面就湿。现在下雨。因此，地面湿。论证的力度在于逻辑联系，而不在于内容本身。

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3. Deductive Reasoning: Modus Tollens | 演绎推理：否定后件式

Modus Tollens denies the consequent. If P implies Q, and Q is false, then P must also be false. This form is powerful for testing hypotheses and eliminating false claims.

否定后件式通过否定后件来推理。如果 P 蕴含 Q，而 Q 为假，那么 P 一定也为假。这种形式在检验假设和排除错误主张时非常有用。

Formula: P → Q, ¬Q ⊢ ¬P

公式：P → Q，¬Q ⊢ ¬P

Example: If it is snowing, the roof is white. The roof is not white. Therefore, it is not snowing. Be careful: the premises must be reliably true for the argument to work in practice.

示例：如果下雪，屋顶是白色的。屋顶不是白色的。因此，没有下雪。注意：要让该论证在实际中有效，前提必须确实为真。

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4. Inductive Reasoning: From Specific to General | 归纳推理：从特殊到一般

Inductive reasoning moves from observed instances to a general conclusion. Unlike deductive arguments, inductive conclusions are probable, not certain. The ‘formula’ involves gathering evidence and making a reasonable generalisation.

归纳推理从观察到的事例推出一般性结论。与演绎论证不同，归纳结论是或然的，而非确定的。其“公式”包括收集证据并作出合理的概括。

Pattern: Instance₁, Instance₂, Instance₃… → General Rule (likely)

模式：事例₁、事例₂、事例₃…… → 一般规则（很可能）

Example: The sun has risen every day in recorded history. Therefore, the sun will rise tomorrow. This is a strong inductive argument, but it is not logically guaranteed.

示例：有记录以来每天都日出。因此，明天太阳也会升起。这是一个强归纳论证，但逻辑上并不保证绝对成立。

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5. Critical Thinking: The Importance of Definitions | 批判性思维：定义的重要性

Clear definitions are the ‘unit conversion’ of philosophy. Without precise definitions, arguments collapse into confusion. Always ask: What do we mean by this term? A good definition sets boundaries and avoids vagueness.

清晰的定义犹如哲学中的“单位换算”。没有精确的定义，论证就会陷入混乱。要始终追问：我们使用这个词到底是什么意思？好的定义设定界限并避免模糊。

Example: If we argue ‘stealing is wrong’, we must define ‘stealing’ and ‘wrong’. Does ‘stealing’ include borrowing without asking? Does ‘wrong’ mean illegal, harmful, or against a moral rule? Definitions shape the whole reasoning.

示例：如果我们论证“偷窃是错的”，就必须定义“偷窃”和“错”。“偷窃”是否包括未经许可的借用？“错”是指违法、有害还是违反道德规则？定义塑造了整个推理过程。

Definition Formula: Term = Essential Characteristics + Boundary Conditions

定义公式：术语 = 本质特征 + 边界条件

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6. Common Fallacies: Ad Hominem | 常见谬误：人身攻击

An ad hominem fallacy attacks the person making an argument rather than the argument itself. It sidesteps the reasoning and tries to discredit the source. This is a broken ‘formula’ that corrupts any debate.

人身攻击谬误攻击的是提出论证的人，而非论证本身。它绕开推理，试图贬低来源的可信度。这是一套被破坏的“公式”，会腐蚀任何讨论。

Fallacy Structure: ‘Your argument is wrong because you are X’

谬误结构：“你的论点是错的，因为你是 X”

Example: ‘You cannot trust her views on healthy eating because she once ate a burger.’ The claim about her eating habits does not refute the evidence she presents. Always separate the message from the messenger.

示例：“你不能相信她对健康饮食的看法，因为她曾经吃过汉堡。”关于她饮食习惯的说法并不能反驳她提出的证据。永远要把观点和说话的人分开。

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7. Common Fallacies: Straw Man | 常见谬误：稻草人

The straw man fallacy misrepresents someone’s argument to make it easier to attack. Instead of engaging with the real position, you create a distorted version—a ‘straw man’—and knock it down. This hides genuine disagreement.

稻草人谬误通过歪曲对方的论点使其更容易被攻击。你不去回应真实立场，而是制造一个扭曲的版本——“稻草人”——然后将其击倒。这掩盖了真正的分歧。

Straw Man Formula: Misrepresent Argument → Attack Distorted Version → Claim Victory

稻草人公式：歪曲论点 → 攻击扭曲版本 → 宣称胜利

Example: Person A says ‘We should spend more on libraries.’ Person B responds, ‘So you think we should ignore national defence and just buy books?’ Person B has replaced a moderate proposal with an extreme one. Fair critical thinkers restate the original view accurately before disagreeing.

示例：甲说“我们应该增加图书馆经费。”乙回应：“所以你认为我们应该忽视国防，只顾买书？”乙把一个温和的建议替换成了极端主张。公正的批判性思考者会在反驳之前先准确复述对方的原观点。

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8. Common Fallacies: False Dilemma | 常见谬误：虚假二分

A false dilemma presents only two options when more exist. It forces a choice between extremes and ignores the middle ground. Recognising this fallacy unlocks more thoughtful solutions.

虚假二分只给出两个选项，而实际上存在更多可能。它迫使人们在极端之间选择，无视中间地带。识别这一谬误可以开启更深思熟虑的解决方案。

False Dilemma Formula: ‘Either A or B; not A; therefore B’ (when C, D, E also exist)

虚假二分公式：“要么 A 要么 B；非 A；所以 B”（而实际上 C、D、E 也存在）

Example: ‘You either support this law completely, or you do not care about justice.’ This overlooks the possibility of supporting the goal but disagreeing with the specific rule. To avoid the fallacy, ask: Are there other alternatives? What spectrum of views exists?

示例：“你要么完全支持这项法律，要么不在乎正义。”这忽视了可能支持该目标但不同意具体规则的情形。要避免此谬误，可以追问：还有别的选择吗？可能存在哪些不同程度的观点？

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9. Evaluating Sources: Reliability and Bias | 评估信息来源：可靠性与偏见

Not all information is equal. A philosophical thinker must weigh sources using critical checks. Think of these questions as a reliability ‘formula’: Who produced this? Why? What evidence do they offer? Are other voices represented?

并非所有信息都等价。哲学思考者必须用批判性核查来权衡信息来源。可以把这些问题视为一条可靠性“公式”：谁制作的？为什么？他们提供了什么证据？是否呈现了其他声音？

Source Type	Reliability Indicators	Potential Bias
Academic article	Peer-reviewed, cites evidence	Funding source, author’s perspective
News report	Named sources, multiple witnesses	Political leaning, sensationalism
Social media post	Verifiable link, original context	Emotional appeal, unverified claims

Evaluation Formula: Credibility = Evidence Quality × Source Expertise ÷ Bias Effect

评估公式：可信度 = 证据质量 × 来源专业性 ÷ 偏见影响

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10. Ethical Thinking: The Greatest Happiness Principle | 伦理思维：最大幸福原则

Utilitarianism, developed by Jeremy Bentham and John Stuart Mill, offers a moral ‘formula’: the right action is the one that produces the greatest happiness for the greatest number. It asks us to calculate overall pleasure and pain.

由边沁和密尔发展的功利主义提供了一条道德“公式”：正确的行为就是能为最大多数人带来最大幸福的行为。它要求我们计算总的快乐与痛苦。

Utilitarian Formula: Right action = Maximise ∑ (Pleasure – Pain) for all affected

功利公式：正确行为 = 最大化所有受影响者的（快乐 – 痛苦）总和

In simple terms, before deciding, imagine a happiness scale. Option A brings 8 units of joy and 2 units of harm; Option B brings 5 units of joy and 1 unit of harm. A utilitarian would choose A because the net happiness (6) is higher than B’s net happiness (4). Critics point out that measuring happiness is difficult and that minority rights may be overlooked.

简而言之，在做决定前，想象一个幸福量表。选项 A 带来 8 单位快乐和 2 单位伤害；选项 B 带来 5 单位快乐和 1 单位伤害。功利主义者会选择 A，因为其净幸福（6）高于 B 的净幸福（4）。批评者指出，衡量幸福很困难，而且少数人的权利可能被忽视。

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11. Thought Experiment: The Trolley Problem | 思想实验：电车难题

The Trolley Problem is a famous ethical thought experiment. A runaway trolley is heading toward five people tied to the track. You can pull a lever to divert the trolley onto a side track, where one person is tied. Should you pull the lever? This tests utilitarian versus rule-based ethics.

电车难题是一个著名的伦理思想实验。一辆失控的电车冲向被绑在轨道上的五个人。你可以拉动拉杆让电车转向侧轨，那里绑着一个人。你应该拉杆吗？这考验了功利主义与基于规则的伦理观。

Pattern: Sacrifice one to save many? Or never use a person as a means?

模式：牺牲一人拯救多人？还是绝不把人当作手段？

There is no single correct answer. The problem reveals that moral ‘formulas’ can conflict. Utilitarians tend to pull the lever (5 lives > 1 life). Deontologists might refuse, arguing that intentionally causing harm is always wrong. Philosophy invites you to explore both paths.

这里没有唯一的正确答案。该问题揭示出道德“公式”可能相互冲突。功利主义者倾向于拉杆（5 条生命多于 1 条）。义务论者可能拒绝，理由是故意造成伤害永远是错的。哲学邀请你探索这两条路径。

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12. Socratic Questioning: Clarifying Ideas | 苏格拉底式提问：澄清观念

Socratic questioning is a disciplined method of probing thinking. Named after Socrates, it uses a sequence of questions to test assumptions, uncover definitions and examine evidence. It is the ultimate ‘formula’ for deeper understanding.

苏格拉底式提问是一种严谨的探究思考的方法。它因苏格拉底而得名，通过一连串问题来检验假设、发掘定义并考察证据。它是通向更深层理解的终极“公式”。

Question Sequence: Clarify → Probe Assumptions → Demand Evidence → Explore Implications

提问程序：澄清 → 探究假设 → 要求证据 → 探讨蕴含

• ‘What exactly do you mean by that?’ / “你那样说确切的意思是什么？”

• ‘What would be an example?’ / “能举个例吗？”

• ‘What are you assuming here?’ / “你这里假设了什么？”

• ‘What evidence supports this view?’ / “有什么证据支持这个观点？”

• ‘What might be the consequences of this idea?’ / “这个想法可能会带来什么后果？”

By repeatedly asking such questions, you sharpen your own thinking and help others clarify theirs—this is the living practice of philosophy.

通过反复提出这类问题，你可以磨砺自己的思考并帮助别人澄清他们的想法——这正是哲学的活生生的实践。

Published by TutorHao | Philosophy Revision Series | aleveler.com

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