📚 Philosophy Formulas & Theorems Quick Reference | 哲学公式定理速查手册
Welcome to your Philosophy Formulas & Theorems Quick Reference! Just like in maths or science, philosophy has its own 'formulas' – not for numbers, but for thinking clearly, building solid arguments, and making good choices. This handbook gathers the most important reasoning patterns, ethical principles, and logic rules you will meet in Year 7 OCR Philosophy. Keep it handy whenever you need to revise how to spot a fallacy, test an argument, or apply a moral 'theorem'.
欢迎来到你的哲学公式定理速查手册！就像数学或科学一样，哲学也有自己的“公式”——不过不是为了数字，而是为了清晰思考、构建坚实的论证和做出好的选择。这本手册汇集了你将在七年级OCR哲学中遇到的最重要的推理模式、伦理原则和逻辑规则。当你需要复习如何识别谬误、检验论证或应用道德“定理”时，随时翻阅它。
1. The Modus Ponens Formula | 肯定前件式推理公式
ets you draw a conclusion from a conditional statement and its trigger. Think of it as the 'if-then-release' rule. If you know that 'If P, then Q' is true, and you also know that P is true, you can safely conclude Q. Form: P → Q, P ⊢ Q.
肯定前件式是一个基本的逻辑模式，它能让你从一个条件语句及其触发条件得出结论。可以把它看作“如果-那么-释放”规则。如果你知道“如果P，那么Q”为真，并且你也知道P为真，就可以安全地得出结论Q。形式：P → Q, P ⊢ Q。
- Example: If it is raining, the grass is wet. It is raining. Therefore, the grass is wet.
- 示例：如果下雨，草地就会湿。现在下雨了。因此，草地是湿的。
This formula works in one direction only. Reversing it leads to a fallacy, so always check the arrows!
这个公式只在一个方向上有效。颠倒它会导致谬误，所以要时刻检查箭头方向！
2. The Modus Tollens Formula | 否定后件式推理公式
but the expected outcome (Q) is absent, then the trigger (P) cannot be true. Form: P → Q, ¬Q ⊢ ¬P.
否定后件式是肯定前件式的另一面。如果一个条件语句为真，但预期的结果（Q）没有出现，那么触发条件（P）就不可能为真。形式：P → Q, ¬Q ⊢ ¬P。
- Example: If the alarm is set, the light flashes red. The light is not flashing red. Therefore, the alarm is not set.
- 示例：如果警报被设置，灯就会闪烁红色。灯没有闪烁红色。因此，警报没有被设置。
This is a powerful tool for eliminating possibilities. Just remember that the absence of the effect removes the cause, not the other way round.
这是排除可能性的强大工具。只需记住，结果的缺失推翻了原因，而不是反过来。
3. The Hypothetical Syllogism Chain | 假言三段论链接公式
When you have a chain of 'if-then' statements, you can cut out the middle and link the ends. If P implies Q, and Q implies R, then P implies R. Form: (P → Q) ∧ (Q → R) ⊢ (P → R). This is like a logical domino effect.
当你有一连串的“如果-那么”语句时，你可以去掉中间环节，把两端连接起来。如果P蕴含Q，并且Q蕴含R，那么P蕴含R。形式：(P → Q) ∧ (Q → R) ⊢ (P → R)。这就像逻辑多米诺骨牌效应。
- Example: If I study, I pass the test. If I pass the test, I get a reward. Therefore, if I study, I get a reward.
- 示例：如果我学习，我就能通过测试。如果我通过测试，我就能得到奖励。因此，如果我学习，我就能得到奖励。
Chains can be any length, but every link must be true for the whole chain to hold.
链条可以是任意长度，但每个环节都必须为真，整个链条才成立。
4. The Disjunctive Syllogism (This or That) | 选言三段论（非此即彼公式）
When you face an 'either A or B' situation and you can rule out one option, the other becomes certain. Form: A ∨ B, ¬A ⊢ B (or: A ∨ B, ¬B ⊢ A). This works only if the 'or' is exclusive or exhaustive.
当你面对“要么A要么B”的情况，并且可以排除其中一个选项时，另一个就确定了。形式：A ∨ B, ¬A ⊢ B（或：A ∨ B, ¬B ⊢ A）。这仅在“或”是排他性的或穷尽了所有选项时才有效。
- Example: The door is either locked or unlocked. It is not locked. Therefore, it is unlocked.
- 示例：门要么锁着要么没锁。门没有锁着。因此，门没锁。
Be careful: in everyday language 'or' sometimes means 'one or the other, but not both', while in logic we must clarify. This formula is a quick eliminator.
注意：在日常语言中，“或”有时意味着“一个或另一个，但不同时”，而在逻辑中我们必须明确。这个公式是一个快速排除工具。
5. The Conjunction Rule (And Introduction) | 合取引入规则（与公式）
If you have two separate true statements, you can join them into one compound statement using 'and'. Form: A, B ⊢ A ∧ B. This might seem simple, but it is the basis of building more complex arguments.
如果你有两个独立的真陈述，你可以用“且”将它们合并成一个复合陈述。形式：A, B ⊢ A ∧ B。这看起来很简单，但它是构建更复杂论证的基础。
- Example: The sun is shining. The birds are singing. Therefore, the sun is shining and the birds are singing.
- 示例：阳光灿烂。鸟儿在歌唱。因此，阳光灿烂且鸟儿在歌唱。
Both parts must be true for the whole conjunction to be true – if one part is false, the conjunction is false.
两个部分都必须为真，整个合取式才为真——如果一部分为假，合取式就为假。
6. The De Morgan Deconversion Theorems | 德摩根转换定理
De Morgan's laws help you transform 'not (A and B)' and 'not (A or B)' into clearer forms. They are like logical spectacles that bring hidden structure into focus.
德摩根定律帮助你转换“并非（A且B）”和“并非（A或B）”为更清晰的形式。它们就像逻辑眼镜，让隐藏的结构聚焦。
| Expression 表达式 | Equivalent Form 等价形式 |
|---|---|
| ¬(A ∧ B) | ¬A ∨ ¬B |
| ¬(A ∨ B) | ¬A ∧ ¬B |
English memory aid: 'The negation of a conjunction is the disjunction of the negations.' Flip 'and' to 'or' and negate each part.
中文记忆口诀：“合取的否定等于否定的析取。” 把“且”变成“或”，并对每一部分取否定。
- Example: It is not true that (I have cake and ice cream). So, either I don't have cake or I don't have ice cream.
- 示例：并非（我有蛋糕和冰淇淋）。所以，要么我没有蛋糕，要么我没有冰淇淋。
7. The Utilitarian Calculus (Bentham's Happiness Formula) | 功利主义演算（边沁的幸福公式）
In ethics, Jeremy Bentham proposed a 'felicific calculus' to measure the rightness of an action: the greatest happiness for the greatest number. While not a math formula, it follows a weighing pattern: Action A produces more total pleasure minus pain than Action B, therefore A is morally preferable.
在伦理学中，杰里米·边沁提出了一个“幸福计算法”来衡量一个行为的正确性：最大多数人的最大幸福。虽然不是一个数学公式，但它遵循一个权衡模式：行为A产生的总快乐减去痛苦大于行为B，因此A在道德上更可取。
Factors to weigh: intensity, duration, certainty, proximity, fecundity, purity, and extent. (You can remember them as 'IDCPFPE'.)
需要权衡的因素：强度、持续时间、确定性、临近性、衍生性、纯度和范围。（你可以把它们记作“IDCPFPE”。）
- Quick check: Would the world contain more net happiness if everyone acted this way? If yes, the action passes the utilitarian test.
- 快速检验：如果每个人都这样做，世界会包含更多的净幸福吗？如果是，这个行为就通过了功利主义检验。
8. The Categorical Imperative Test (Kant's Universalizability Formula) | 定言律令检验（康德的普遍化公式）
Immanuel Kant's ethical theorem states: 'Act only according to that maxim whereby you can at the same time will that it should become a universal law.' Imagine your personal rule as a formula: if an action's principle cannot be consistently willed for everyone without contradiction, it is morally wrong.
伊曼努尔·康德的伦理定理指出：“只依照那个你同时愿意它成为普遍法则的准则去行动。” 把你的个人规则想象成一个公式：如果一个行为的原则不能被无矛盾地意愿为每个人都采用，那它在道德上就是错误的。
- Example: Making a false promise to get money. If everyone made false promises, the institution of promising would collapse – a contradiction. Therefore, it fails the test.
- 示例：为了获得钱财而做虚假承诺。如果每个人都做虚假承诺，承诺制度就会崩溃——一种矛盾。因此，它没有通过检验。
This formula does not calculate consequences but checks for rational consistency.
这个公式不计算结果，而是检查理性的融贯性。
9. The Fallacy Formula: Affirming the Consequent | 谬误公式：肯定后件
lows this invalid pattern: P → Q, Q, therefore P. Just because the effect occurs, it doesn't mean the suspected cause is true – there could be other causes.
最常见的推理错误之一遵循这个无效模式：P → Q, Q，因此P。仅仅因为结果发生了，并不意味着假定的原因就是真实的——可能还有其他原因。
- Example: If it's a swan, it's white. This bird is white. Therefore, it's a swan. (It could be a goose.)
- 示例：如果它是天鹅，它就是白色的。这只鸟是白色的。因此，它是天鹅。（它可能是只鹅。）
Memorise this as the 'backwards-if trap'. Always ask: Could Q have happened another way?
把这记作“反向如果陷阱”。始终要问：Q 会不会是其他原因造成的？
10. The Socratic Questioning Loop | 苏格拉底式提问循环
native viewpoints → Examine implications. Repeat. This is the engine of philosophical thinking, summarised as: Question, Reason, Reflect.
不是一个数学公式，而是一个有条理的探究循环：澄清概念 → 探究假设 → 探索理由和证据 → 考虑替代观点 → 检视后果。重复。这就是哲学思维的引擎，概括为：提问、推理、反思。
Use this loop whenever you encounter a philosophical claim or a real-life dilemma. It helps you avoid jumping to conclusions and builds deeper understanding.
每当你遇到一个哲学主张或现实困境时，使用这个循环。它帮助你避免过早下结论，并建立更深刻的理解。
11. The Principle of Charity (Interpretation Maxim) | 宽容原则（解释准则）
When analysing an argument, restate it in its strongest, most reasonable form before criticising it. Formula: Reconstruct the other person's argument so that it is as plausible as possible (without distorting their meaning), then evaluate. This principle sidesteps 'straw man' fallacies.
在分析一个论证时，先把它重述为最强、最合理的形式，然后再批评它。公式：重建他人的论证，使其尽可能合理（不扭曲其原意），然后评价。这个原则能避开“稻草人”谬误。
- Quick rule: 'Interpret others as you would have your own arguments interpreted.'
- 快速规则：“要像你希望自己的论证被解读那样去解读别人。”
Applying charity makes philosophical discussion fairer and more productive.
应用宽容原则会让哲学讨论更公平、更富有成效。
12. The Cartesian Method of Doubt | 笛卡尔怀疑方法
Descartes' strategy: systematically doubt everything that can possibly be doubted until you find something indubitable. The 'formula' is: Imagine an evil demon (or a powerful deception) that makes all your senses unreliable. If a belief survives this extreme scepticism, it counts as a foundation for knowledge. His result: 'I think, therefore I am' (Cogito ergo sum) is the first certainty.
笛卡尔的策略：系统地怀疑一切可以怀疑的东西，直到找到无可置疑的事物。“公式”是：想象一个邪恶的恶魔（或强大的欺骗）让你的所有感官都不可靠。如果一个信念能经受住这种极端怀疑主义，它就可以作为知识的基础。他的结果：“我思故我在”是第一个确定性。
Use this method to test beliefs: Can you find any reason to doubt it? If you can, it's not a foundational truth. This is the beginning of rationalism.
用这个方法检验信念：你能找到怀疑它的任何理由吗？如果能，它就不是一个基础真理。这是理性主义的开端。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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