📚 Year 9 CCEA Philosophy: Formula & Theorem Quick Reference Guide | 九年级CCEA哲学：公式定理速查手册
Philosophy is not just about big ideas – it is also about clear thinking. Just like mathematics has formulas for solving problems, philosophy has reasoning patterns, argument structures, and conceptual tools that help us analyse ideas, evaluate arguments, and build our own positions. This quick reference guide collects the most useful 'formulas' and 'theorems' you will encounter in your Year 9 CCEA Philosophy studies. Take these mental shortcuts with you into every discussion, debate, and essay.
哲学不仅仅是关于宏大思想——它也是关于清晰思考。就像数学有解题公式一样，哲学也有推理模式、论证结构和概念工具，帮助我们分析观点、评价论证以及建立自己的立场。这本速查手册汇集了你在九年级CCEA哲学学习中会遇到的最有用的“公式”和“定理”。把这些思维捷径带进每一次讨论、辩论和写作中吧。
1. Logic Basics: Modus Ponens & Modus Tollens | 逻辑基础：肯定前件与否定后件
Valid argument forms are like reliable machines: if you put in true premises, you always get a true conclusion. Two fundamental forms are Modus Ponens and Modus Tollens.
有效的论证形式就像可靠的机器：如果你输入真实的前提，总会得出真实的结论。两个基本形式是肯定前件和否定后件。
Modus Ponens (Affirming the Antecedent): If P, then Q. P is true. Therefore, Q is true.
肯定前件：如果P，那么Q。P是真的。所以，Q是真的。
Example: If it is raining (P), the ground is wet (Q). It is raining. Therefore, the ground is wet.
例子：如果下雨（P），地面就会湿（Q）。正在下雨。所以，地面是湿的。
Modus Tollens (Denying the Consequent): If P, then Q. Q is false. Therefore, P is false.
否定后件：如果P，那么Q。Q是假的。所以，P是假的。
Example: If the alarm is set (P), the light is on (Q). The light is off. Therefore, the alarm is not set.
例子：如果警报器设置了（P），灯就会亮（Q）。灯没亮。所以，警报器没有设置。
Memorise these two 'proof' shapes – they appear everywhere in philosophical writing.
记住这两种“证明”形状——它们出现在哲学写作的各个角落。
2. Syllogisms: Hypothetical & Disjunctive | 各类三段论：假言与选言
A syllogism is a three-step argument built from two premises and one conclusion. Two special types help us handle 'if-then' chains and 'either-or' choices.
三段论是由两个前提和一个结论组成的三步论证。两种特殊类型帮助我们处理“如果—那么”链条和“要么—要么”的选择。
Hypothetical Syllogism: If P, then Q. If Q, then R. Therefore, if P, then R.
假言三段论：如果P，那么Q。如果Q，那么R。所以，如果P，那么R。
Example: If I study (P), I understand the topic (Q). If I understand the topic, I pass the test (R). Therefore, if I study, I pass the test.
例子：如果我学习（P），我就理解课题（Q）。如果我理解课题，我就通过考试（R）。所以，如果我学习，我就通过考试。
Disjunctive Syllogism: Either P or Q. Not P. Therefore, Q. (Works the other way too.)
选言三段论：要么P，要么Q。非P。所以，Q。（反过来也成立。）
Example: Either we go by bus or by train. We don't go by bus. Therefore, we go by train.
例子：要么我们乘公交车，要么乘火车。我们不乘公交车。所以，我们乘火车。
These structures ensure your reasoning stays tight when dealing with chains of causes or limited options.
这些结构确保你在处理因果链或有限选项时，推理保持严密。
3. Fallacies: Ad Hominem, Straw Man, Slippery Slope | 逻辑谬误：人身攻击、稻草人、滑坡
A fallacy is a flawed argument pattern that appears convincing but is logically invalid. Recognizing fallacies is your defence against manipulation.
谬误是一种缺陷的论证模式，看似令人信服但逻辑上无效。识别谬误是你抵御操控的防线。
Ad Hominem (To the Person): Rejecting a claim by attacking the person making it, rather than the argument itself.
人身攻击：通过攻击主张者而非论证本身来反驳一个说法。
Formula: 'You say X, but you are bad/stupid/biased, so X is false.' This is always irrelevant to the truth of X.
公式：“你说了X，但你是坏的/愚蠢的/有偏见的，所以X是错的。”这与X的真实性永远无关。
Straw Man: Misrepresenting someone's argument to make it easier to attack.
稻草人：错误地转述某人的论点，使其更容易被攻击。
Real argument: 'We should regulate social media gently.' Straw man: 'So you want zero rules and total chaos?'
真实论点：“我们应该轻轻监管社交媒体。”稻草人：“所以你想要零规则和完全混乱？”
Slippery Slope: Claiming a small first step will inevitably lead to an extreme negative outcome, without proof.
滑坡谬误：声称一小步会导致不可避免的极端负面结果，而没有证据。
Structure: A → B → C → ... → terrible Z. Each link must be justified, not just assumed.
结构：A → B → C → ... → 糟糕的Z。每一步都必须被证明，而不能只是假设。
4. The Principle of Charity & Steelmanning | 厚道原则与最强版本重构
In philosophy, we don't just defeat our opponent's weakest arguments; we engage with the strongest possible version. The Principle of Charity asks us to interpret another person's argument in its most reasonable form before criticising it.
在哲学中，我们不只是击败对手最弱的论点；我们要针对最强的版本来讨论。厚道原则要求我们在批评之前，将他人的论证解读为最合理的形式。
Steelmanning Formula: 1. Restate the opponent's view as clearly and generously as you can. 2. Add any missing premises that would make it stronger. 3. Only then engage with critique.
最强版本重构公式：1. 尽可能清晰、宽厚地重述对方观点。2. 补充任何缺失的会使它更强的前提。3. 然后才进行批判。
This is not about being 'nice' – it is an intellectual standard. If you can refute the steelman, you have truly engaged with the idea.
这不是关于“友善”——这是一种智识标准。如果你能反驳最强版本，你就真正触及了这个想法。
5. Occam's Razor | 奥卡姆剃刀
Also called the principle of parsimony, Occam's Razor is a rule of thumb for choosing between competing explanations: the simplest explanation, with the fewest assumptions, is often the best.
又称简约原则，奥卡姆剃刀是选择竞争性解释的一条经验法则：最简单的解释，即假设最少的，往往是最好的。
Formula: When you have two theories that explain the same data equally well, choose the one that makes the fewest unnecessary assumptions.
公式：当你有两个理论同样好地解释相同数据时，选择那个没有多余假设的。
Example: After hearing hoofbeats, think horses, not zebras – unless you are in Africa. Don't multiply entities beyond necessity.
例子：听到蹄声时，想到马，而不是斑马——除非你在非洲。如无必要，勿增实体。
This razor cuts through conspiracy theories and overly complex arguments in ethics, science, and everyday reasoning.
这把剃刀能切穿阴谋论，以及伦理、科学和日常推理中过于复杂的论证。
6. Ethical Frameworks: Consequentialism & Deontology | 伦理框架：后果论与义务论
When evaluating moral actions, philosophers often use two big 'formulas'. They act as lenses through which we judge right and wrong.
在评价道德行为时，哲学家常常使用两大“公式”。它们如同透镜，让我们判断对与错。
Consequentialism (especially Utilitarianism): An action is right if it produces the best overall consequences, usually measured by the greatest happiness for the greatest number.
后果论（特别是功利主义）：如果一个行为产生最好的总体后果，通常是以最多数人的最大幸福来衡量，那么它就是对的。
Formula: Right Action = Maximise Pleasure, Minimise Pain for all affected.
公式：正确的行为 = 为所有受影响者最大化快乐，最小化痛苦。
Deontology (Duty Ethics): An action is right if it follows a moral rule or duty, regardless of the consequences. Think of the Golden Rule: 'Act only according to that maxim whereby you can at the same time will that it should become a universal law.' (Kant)
义务论（责任伦理）：如果一个行为遵守了道德规则或责任，它就是对的，无论后果如何。想想黄金法则：“只依照你同时能够愿意它成为普遍法则的准则去行动。”（康德）
Formula: Right Action = Follow the Duty (e.g., don't lie, keep promises) × Universalisability.
公式：正确的行为 = 遵守责任（例如不说谎、遵守承诺）× 可普遍化。
7. The Socratic Method: Questioning the Formula | 苏格拉底方法：提问的公式
The Socratic method is a formula for uncovering truth through disciplined questioning. Instead of stating your view directly, you ask a series of questions that lead your conversation partner to examine their own beliefs.
苏格拉底方法是通过有纪律的提问来揭示真相的一种公式。你不是直接陈述自己的观点，而是提出一系列问题，引导对话伙伴审视他们自己的信念。
Basic Template: 1. Ask for a definition of a key concept (e.g., 'What is courage?'). 2. Find a counterexample that challenges the definition. 3. Refine the definition. 4. Repeat until you reach a deeper understanding or acknowledge the limits of your knowledge.
基本模板：1. 询问关键概念的定义（例如，“什么是勇气？”）。2. 找一个挑战该定义的反例。3. 完善定义。4. 重复，直到达到更深的认知或承认你知识的局限。
This method is the engine of all philosophical inquiry – it is a ‘formula’ that generates wisdom rather than just answers.
这种方法是所有哲学探究的引擎——它是一种生成智慧而不仅仅是答案的“公式”。
8. The Tripartite Definition of Knowledge | 知识的三元定义
simple equation: Knowledge = Justified True Belief. This is often called the JTB formula.
几个世纪以来，哲学家用一个简单的等式定义知识：知识 = 证成的真信念。这常被称为JTB公式。
Components:
- Belief: You must accept the proposition as true.
- Truth: The proposition must actually be true.
- Justification: You must have good reasons or evidence for holding that belief.
组成部分：
- 信念：你必须接受该命题为真。
- 真相：该命题实际上必须是真实的。
- 证成：你必须有充分理由或证据持有该信念。
While later 'Gettier problems' showed this formula can be incomplete, it remains the starting point for all discussions about what it means to know something.
虽然后来的“盖梯尔问题”表明这个公式可能不完整，但它依然是一切关于“认识某事意味着什么”的讨论起点。
9. Paradoxes: A Quick Glance | 悖论速览
Paradoxes are mental short-circuits: they use apparently sound reasoning to reach a contradiction. They are not just puzzles; they force us to revise our assumptions.
悖论是思维短路：它们用看似合理的推理得出矛盾。它们不仅是谜题，它们迫使我们修正自己的假设。
Ship of Theseus: If you replace every plank of a ship over time, is it still the same ship? Formula: Identity = Σ parts? But parts change.
忒修斯之船：如果你随时间替换船上的每一块木板，它还是同一艘船吗？公式：同一性 = 所有部分之和？但部分会变。
Liar Paradox: 'This statement is false.' If it is true, then it is false; if it is false, then it is true. A self-referential loop with no stable truth-value.
说谎者悖论：“这句话是假的。”如果它是真的，那么它就是假的；如果它是假的，那么它就是真的。一个没有稳定真值的自我指涉循环。
Paradoxes are the 'bugs' in our conceptual software – studying them sharpens logical precision.
悖论是我们概念软件中的“bug”——研究它们能磨砺逻辑的精确性。
10. Critical Thinking Formula: Argument = Premises + Conclusion | 批判性思维公式：论证 = 前提 + 结论
The most fundamental formula in philosophy: every argument can be broken down into premises (reasons) and a conclusion (claim). Learning to extract this structure from any text is the first step to thinking critically.
哲学中最基本的公式：每一个论证都可以分解为前提（理由）和结论（主张）。学习从任何文本中提取这个结构是批判性思维的第一步。
Formula: Premise 1: ... Premise 2: ... (and so on) {symbol for 'therefore'} Conclusion: ...
公式：前提1：... 前提2：... （等等）{表示“因此”的符号} 结论：...
To evaluate an argument, ask:
1. Are the premises true?
2. Do the premises logically support the conclusion? (Validity)
3. Are there any hidden assumptions?
评价一个论证，要问：
1. 前提真实吗？
2. 前提是否在逻辑上支持结论？（有效性）
3. 有没有隐藏的假设？
This formula turns everyday disagreements into structured discussions you can actually resolve.
这个公式把日常的分歧变成了你真正可以解决的结构化讨论。
11. Diagramming Arguments: The Visual Formula | 论证图解：视觉公式
Sometimes drawing an argument helps more than writing it. Argument mapping uses arrows and numbers to show how premises link together to support sub-conclusions and the main conclusion.
有时候，把论证画出来比写出来更有帮助。论证图示使用箭头和数字来展示前提如何连接在一起，支撑子结论和主结论。
Basic syntax: n Conclusion; Co-premises cluster together with a bracket before pointing to their target.
基本语法：前提 → 子结论1 → 主结论；协同前提用一个括号聚在一起，然后指向它们的目标。
When you map arguments, weak links and missing steps become visible instantly. It's a powerful revision strategy for your philosophy essays.
当你绘制论证图示时，薄弱环节和缺失步骤会立即显现。这对你的哲学论文来说是一种强大的复习策略。
12. The 'Why' Chain: Infinite Curiosity Formula | “为什么”链条：无限好奇公式
Young children ask 'Why?' repeatedly, and philosophers do the same. A 'Why' chain presses a question until you hit fundamental reasons or reveal an unexamined assumption.
小孩子不断问“为什么？”，哲学家也这样做。“为什么”链条持续追问下去，直到你触及根本理由或揭示一个未经审视的假设。
Technique: Start with a statement you believe is true. Ask: 'Why is that true?' Provide a reason. Then ask: 'Why is that reason true?' Continue until you reach a principle that no longer admits further justification (a foundation) or you see a circular justification.
技巧：从一个你相信为真的陈述开始。问：“为什么它是真的？”提供一个理由。然后问：“为什么那个理由是真的？”继续下去，直到你达到一个不再允许进一步证成的原则（基础），或者你发现了一个循环论证。
This 'formula' turns passive knowing into active, grounded understanding – a core aim of CCEA Philosophy.
这个“公式”把被动知道变成主动的、有根基的理解——这是CCEA哲学的核心目标。
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