📚 Year 7 CIE Philosophy Formula & Theorem Quick Reference Guide | 七年级CIE哲学公式定理速查手册
Philosophy uses clear structures and logical 'formulas' just like mathematics or science. This quick reference guide collects essential patterns of reasoning, ethical principles, and famous thought-experiment 'theorems' that every Year 7 CIE Philosophy student should know. Each entry follows a formula-style presentation: a concise logical or conceptual skeleton, followed by an explanation and an example.
哲学与数学或科学一样，也使用清晰的结构和逻辑“公式”。这份速查手册汇集了每位七年级CIE哲学学生都应掌握的基本推理模式、伦理原则以及著名的思想实验“定理”。每个条目均以公式风格呈现：先给出简洁的逻辑或概念骨架，再辅以解释和例子。
1. Modus Ponens (Affirming the Antecedent) | 肯定前件法
If P → Q, and P, ∴ Q.
Modus ponens is a fundamental rule of deductive logic. If a conditional statement ('if P then Q') is true, and the 'if' part (P) actually happens, then the 'then' part (Q) must follow. It guarantees a valid conclusion when the premises are true.
肯定前件是演绎逻辑的基本规则。如果条件陈述“若 P 则 Q”为真，且条件中的前件 P 确实成立，那么后件 Q 必然成立。当所有前提为真时，该形式确保结论有效。
- Premise 1: If it is raining, the pavement is wet. (P → Q)
- Premise 2: It is raining. (P)
- Conclusion: Therefore, the pavement is wet. (∴ Q)
前提一：若下雨，则人行道湿。(P → Q)
前提二：正在下雨。(P)
结论：所以人行道湿。(∴ Q)
2. Modus Tollens (Denying the Consequent) | 否定后件法
If P → Q, and ¬Q, ∴ ¬P.
Modus tollens works by denying the consequence. When we know that 'if P then Q' is true, but we also observe that Q is false (¬Q), we can logically conclude that P must also be false (¬P). It is a powerful tool for eliminating possibilities.
否定后件通过否定推论中的后件来运作。当我们知道“若 P 则 Q”为真，但同时观察到 Q 不成立 (¬Q)，就可以逻辑地推出 P 也不成立 (¬P)。这是消除可能性的有力工具。
- Premise 1: If the alarm had rung, I would be awake. (P → Q)
- Premise 2: I am not awake. (¬Q)
- Conclusion: Therefore, the alarm did not ring. (∴ ¬P)
前提一：若闹钟响了，我就会醒来。(P → Q)
前提二：我没有醒来。(¬Q)
结论：所以闹钟没有响。(∴ ¬P)
3. The Socratic Method Formula | 苏格拉底方法公式
Question → Critical Examination → Deeper Understanding
Socrates famously used a step-by-step questioning technique to test beliefs. The formula involves asking a series of 'What is X?' questions, exposing weaknesses in a definition, and then refining it. This process leads participants away from mere opinion towards clearer, more justified concepts.
苏格拉底以循序渐进的提问法来检验信念而闻名。该公式包含提出一系列“X 是什么？”的问题，暴露定义中的缺陷，然后加以修正。这个过程使参与者从单纯的意见走向更清晰、更有理由的概念。
- Step 1: Ask a big question, e.g., 'What is courage?'
- Step 2: Propose a definition: 'Courage is never retreating.'
- Step 3: Find a counter-example: 'Is a soldier who retreats to save lives not courageous?'
- Step 4: Refine the definition and repeat.
第一步：提出一个大问题，例如“什么是勇气？”
第二步：给出定义：“勇气就是永不退缩。”
第三步：寻找反例：“为挽救生命而撤退的士兵就不勇敢吗？”
第四步：修正定义，并重复上述过程。
4. Cogito Ergo Sum (I think, therefore I am) | 我思故我在
Doubt → Thinking → Existence
René Descartes searched for one absolutely certain truth. He imagined an evil demon deceiving him about everything. Yet, even if he was being deceived, he had to exist as a thinking thing to be deceived. The very act of doubting proves the existence of the self as a mind.
勒内·笛卡尔探求一项绝对确定的真理。他设想有一个邪恶的恶魔在一切事情上欺骗他。然而，即使他在受骗，也必定作为一个思维着的存在者才能被欺骗。怀疑这一行为本身就证明了自我作为心灵的存在。
- 'I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind.' – Descartes
- Formula: I cannot doubt that I am doubting. Doubting is a form of thinking. Hence, I must exist as a thinking thing.
“当我提出‘我存在’或在心中构想它时，它必然为真。”——笛卡尔
公式：我无法怀疑“我正在怀疑”这件事。怀疑是一种思考。因此，我必然作为一个思考者而存在。
5. Occam's Razor | 奥卡姆剃刀原理
Entities should not be multiplied beyond necessity.
Occam's Razor is a principle of simplicity. When faced with competing explanations for the same phenomenon, the one that makes the fewest assumptions is usually preferred. It does not prove truth but guides us towards more economical theories, avoiding unnecessary complexity.
奥卡姆剃刀是一条追求简洁的原则。当面对同一现象的多种竞争解释时，通常更倾向于假设最少的那一个。它并不证明真理，而是引导我们走向更经济的理论，避免不必要的复杂性。
- Example 1: If your lamp goes out, think 'the bulb blew' before 'a ghost switched it off.'
- Example 2: In science, we prefer a model of the solar system with simple ellipses rather than complex spirals unless forced by evidence.
例一：如果台灯灭了，先想“灯泡烧了”，而非“鬼魂关掉了它”。
例二：在科学中，除非有证据强力支持，否则我们更倾向于简单的椭圆轨道太阳系模型，而非复杂的螺旋形轨道。
6. The Golden Rule | 黄金法则
Treat others as you would like to be treated.
The Golden Rule is a foundational ethical formula found in many cultures and religions. It asks us to imagine ourselves in another person's situation before acting. It promotes empathy and fairness by making the self the standard for moral behaviour towards others.
黄金法则是在众多文化和宗教中都存在的一条基础伦理公式。它要求我们在行动之前，设想自己处于他人的处境。它以自我作为对待他人之道德行为的标准，从而促进同理心与公平。
- Positive form: 'Do to others what you want them to do to you.'
- Negative form (Confucius): 'Do not do to others what you do not want done to yourself.'
肯定形式：“你想别人怎样待你，你也要怎样待人。”
否定形式（孔子）：“己所不欲，勿施于人。”
7. Greatest Happiness Principle (Utilitarian Formula) | 最大幸福原则（功利主义公式）
Right action = the one that produces the greatest happiness for the greatest number.
Jeremy Bentham and John Stuart Mill proposed that morality is about maximising happiness and minimising suffering. This formula, sometimes called the utility calculus, weighs the total pleasure and pain an action causes. An action is right if it leads to a higher net happiness than any alternative.
杰里米·边沁与约翰·斯图亚特·密尔提出，道德在于最大化幸福、最小化痛苦。这一公式有时被称为“功利计算”，它权衡一个行动所带来的总体快乐与痛苦。如果某个行动带来的净幸福高于任何其他选择，它就是正确的行动。
- Calculation: Total utility = Sum of (pleasure – pain) for all affected individuals.
- Example: If telling a small lie saves someone's feelings and hurts no one, a utilitarian might argue it is right because it increases overall happiness.
计算式：总效用 = 所有受影响个体的（快乐 – 痛苦）之和。
例子：如果撒个小谎能保护他人感受且不伤害任何人，功利主义者可能会认为这是对的，因为它增加了总体幸福。
8. The Categorical Imperative (Kant's Formula) | 绝对命令（康德公式）
Act only according to that maxim whereby you can, at the same time, will that it should become a universal law.
Immanuel Kant's formula tests the morality of an action by asking whether the rule behind it could be applied universally without contradiction. If your personal maxim (the principle guiding your action) can rationally be willed as a law for everyone, then the action is moral. If it leads to a contradiction or a world you could not rationally desire, it is immoral.
伊曼努尔·康德的公式通过追问行动背后的规则能否被无矛盾地普遍应用，来检验行动的道德性。如果你的个人准则（指导行动的原则）在理性上能被意愿为众人的普遍法则，那么该行动就是道德的。如果它导致矛盾或产生一个你无法理性欲求的世界，那就是不道德的。
- Example of lying: If everyone made lying a universal law, trust would collapse, and the very act of lying would become impossible because no one would believe words. Thus, lying is always wrong according to this formula.
说谎的例子：如果每个人都把说谎当成普遍法则，信任就会崩溃，“说谎”本身也将变得不可能，因为没有人会相信言语。因此，根据这一公式，说谎永远都是错误的。
9. Hume's Fork | 休谟之分叉
All meaningful statements are either Relations of Ideas or Matters of Fact.
David Hume divided all meaningful knowledge into two forks. 'Relations of ideas' are truths that are certain purely by logic or definition (e.g., 'All bachelors are unmarried'). 'Matters of fact' are truths about the world known through experience, and their opposite is always possible (e.g., 'The sun will rise tomorrow'). This formula demands we ask: which fork does a claim belong to?
大卫·休谟将所有有意义的知识分为两个叉子。“观念关系”是仅凭逻辑或定义就确定的真理（例如“所有单身汉都未婚”）。“事实”则是通过经验得知的关于世界的真理，且其反面总是可能的（例如“太阳明天会升起”）。这个公式要求我们追问：某个主张属于哪一支叉？
- If a statement is neither a relation of ideas nor a matter of fact, Hume argued it is mere sophistry and illusion, to be committed to the flames.
如果某个陈述既非观念关系，亦非事实，休谟认为它就只是诡辩与幻象，应投进烈火中。
10. The Teleological Argument (Design Formula) | 目的论论证（设计公式）
Complexity + Purpose → Designer
The teleological argument, or argument from design, takes the form: if something shows complex parts working together for a purpose, it must have been designed by an intelligent being. William Paley used the analogy of a watch found on a heath: its intricate mechanism implies a watchmaker. Similarly, the universe's complexity points to a divine designer.
目的论论证，或称设计论证，采取如下形式：如果某物显示出复杂的部分协同运作以实现一个目的，那么它必定是由智能存在者设计的。威廉·佩利用荒地上发现的手表作类比：其精密结构暗示着一位钟表匠。同样，宇宙的复杂性指向一位神圣的设计者。
- Watch: gears + spring + glass case working to show time → implies a watchmaker.
- Universe: eye + planetary orbits + laws of physics → implies a cosmic designer.
手表：齿轮 + 发条 + 玻璃表壳协同显示时间 → 意味着存在钟表匠。
宇宙：眼睛 + 行星轨道 + 物理定律 → 意味着存在宇宙设计者。
11. Descartes' Evil Demon Hypothesis | 笛卡尔的恶魔假设
If I cannot rule out an evil demon, then I cannot be certain of the external world.
To test the foundations of knowledge, Descartes imagined a powerful, malicious demon whose sole purpose is to deceive him. The demon could create a completely convincing illusion of an external world. This formula radicalises scepticism: unless we can prove no such demon exists, all sensory knowledge might be a dream. It clears the ground for finding indubitable truth.
为检验知识的基础，笛卡尔设想了一个强大而恶意的恶魔，其唯一目的就是欺骗他。恶魔可以创造出完全令人信服的外部世界幻觉。这个公式将怀疑论推向极致：除非我们能证明不存在这样的恶魔，否则所有感官知识都可能是一场梦。它为寻找不可怀疑的真理扫清了基础。
- Premise: It is possible that an evil demon is deceiving me about everything I think I see, hear, or remember.
- Conclusion: Therefore, I cannot trust my senses as a sure foundation for knowledge.
前提：有可能存在一个邪恶恶魔，在我自以为看见、听见或记起的一切事情上欺骗我。
结论：因此，我不能将感官作为知识的可靠基础。
12. The Ship of Theseus (Identity Paradox) | 忒修斯之船（同一性悖论）
If all parts are replaced, is it still the same object?
Over time, every plank of the legendary ship of Theseus was replaced as it rotted. The philosophical puzzle asks: after all original planks are gone, is it the same ship? What if the old planks were kept in a warehouse and later reassembled—which is the true Ship of Theseus? This formula reveals the problem of identity through change and is a powerful tool for discussing what 'sameness' means.
随着时间流逝，传说中的忒修斯之船的每块木板都因腐烂而被替换。哲学谜题问道：在所有原始木板都被换掉后，它还是同一条船吗？如果旧木板被保存在仓库里，之后重新组装起来——哪一条才是真正的忒修斯之船？这个公式揭示了历经变化的同一性问题，是探讨“同一性”含义的有力工具。
- Argument: If sameness depends on continuous form, the restored ship is the original. If it depends on original material, the reassembled old planks form the original.
- This challenges our everyday assumptions about objects and selves.
论证：如果同一性取决于形式之连续，那么修复后的船就是原船。如果取决于原始材料，那么重新组装的旧木板构成了原船。
这个悖论挑战了我们对物体与自我的日常假设。
Published by TutorHao | 哲学 Revision Series | aleveler.com
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