📚 Year 10 CIE Philosophy Formula & Theorem Quick Reference | 公式定理速查手册
Welcome to your essential revision toolkit for CIE IGCSE Philosophy. This handbook distils philosophical theories, arguments and principles into concise 'formulas' and 'theorems'—just like those you memorise in mathematics or science, but here they capture logical structures, ethical rules and metaphysical claims. Use it to recall classical positions, evaluate strengths and weaknesses, and sharpen your exam technique. Each section presents a core area of the syllabus, pairing an English statement with its Chinese translation so you can master the terminology in both languages.
欢迎使用这本为 CIE IGCSE 哲学准备的必备复习手册。它将哲学理论、论证和原则提炼成简洁的“公式”和“定理”——就像你在数学或科学中记忆的那些一样，但这里捕捉的是逻辑结构、伦理规则和形而上学主张。用它来回忆经典立场、评估优缺点并磨炼考试技巧。每个部分都涵盖大纲的一个核心领域，将英文陈述与中文翻译配对，让你能掌握双语术语。
1. The JTB+ Formula for Knowledge | 知识的 JTB+ 公式
Knowledge = Justified True Belief + ¬(Gettier-style defeater)
Traditionally, propositional knowledge was defined as: S knows that P if and only if (i) P is true, (ii) S believes that P, and (iii) S is justified in believing P. This is written as Kp ⇔ p ∧ Bp ∧ Jp.
传统上，命题知识被定义为：S 知道 P，当且仅当 (i) P 为真，(ii) S 相信 P，并且 (iii) S 获确证地相信 P。这记作 Kp ⇔ p ∧ Bp ∧ Jp。
Gettier's counterexamples show that a person can have a justified true belief yet lack knowledge because of luck. The formula therefore requires an anti-luck condition. We write: Kp ⇔ p ∧ Bp ∧ Jp ∧ ¬G, where G stands for a Gettier-case factor (e.g. the truth depends on a fluke).
盖梯尔的反例表明，一个人可以持有确证的真信念却因运气而没有知识。因此公式需要反运气条件。我们写作：Kp ⇔ p ∧ Bp ∧ Jp ∧ ¬G，其中 G 代表盖梯尔式因素（例如真理依赖于偶然）。
Two rival theories about the source of knowledge can also be expressed as formulas. Rationalism: Innate Ideas + Reason → A Priori Knowledge. Empiricism: Sense Experience + Induction → A Posteriori Knowledge.
关于知识来源的两种竞争理论也可以表达为公式。理性主义：天赋观念 + 理性 → 先验知识。经验主义：感官经验 + 归纳 → 后验知识。
The problem of induction (Hume) reveals that the principle of the uniformity of nature cannot be justified without circularity, so empirical knowledge rests on a rationally unjustifiable assumption.
归纳问题（休谟）揭示，自然齐一性原则无法在不陷入循环的情况下得到证明，因此经验知识建立在一个理性上不可证明的假设之上。
2. The Cartesian Cogito and Method of Doubt | 笛卡尔的我思与怀疑方法
Cogito ergo sum (I think, therefore I am)
Descartes employed hyperbolic doubt to find an indubitable foundation for knowledge. Even if an evil demon deceived him about everything, the very act of being deceived proves that he exists as a thinking thing. Thus: Doubt → Thinking → Existence.
笛卡尔采用极端怀疑来为知识寻找一个不可怀疑的基础。即使有一个恶魔欺骗他关于的一切，被欺骗这一行为本身就证明了他作为一个思维物的存在。因此：怀疑 → 思考 → 存在。
The cogito is known clearly and distinctly, which Descartes takes as a general rule: Whatever is perceived clearly and distinctly must be true. He then tries to prove God's existence to guarantee that clear and distinct perceptions are reliable.
我思是被清楚分明地知觉到的，笛卡尔将此视为一条普遍规则：凡被清楚分明地知觉的必为真。然后他试图证明上帝的存在，以保证清楚分明的知觉是可靠的。
The evil demon hypothesis illustrates the challenge of global scepticism: If an all-powerful being deceives us, no empirical belief is safe. The cogito is the sole piece of knowledge that survives this extreme test.
恶魔假设例示了全局怀疑论的挑战：如果一个全能的存有欺骗我们，任何经验信念都不安全。我思是唯一能经受这一极端检验的知识。
3. The Ontological, Cosmological and Teleological Proofs | 本体论、宇宙论与设计论论证
Ontological: God = Being than which no greater can be conceived → God exists
Anselm's ontological formula: God is the greatest conceivable being. Existence in reality is greater than existence in the mind alone. Therefore, God must exist in reality, otherwise we could conceive a greater being (one that exists).
安瑟伦的本体论公式：上帝是可设想的最伟大存在。实际存在比仅存在于心中更伟大。因此，上帝必定实际存在，否则我们可以设想一个更伟大的存在（即实际存在的那个）。
Cosmological argument (Aquinas): g requires a cause → Infinite regress is impossible → A necessary first cause (God) exists. Kalam version: The universe began to exist; whatever begins to exist has a cause; therefore the universe has a cause (God).
宇宙论论证（阿奎那）：每个偶然物都需要一个原因 → 无限回溯不可能 → 存在一个必然的第一因（上帝）。卡拉姆版：宇宙开始存在；凡开始存在者皆有原因；因此宇宙有原因（上帝）。
Teleological / Design argument (Paley): stem with purpose → Analogy of the watch → An intelligent designer is the best explanation. In formulaic terms: Design-like features imply a designer.
设计论论证（佩利）：具有目的的复杂有序系统 → 手表类比 → 智慧设计者是最佳解释。用公式表达：类似设计的特征蕴含一位设计者。
Pascal's Wager uses decision theory: If you believe in God and God exists, infinite gain; if God does not exist, finite loss. Expected value of belief outweighs unbelief.
帕斯卡的赌注运用决策理论：若你信上帝且上帝存在，则无限收益；若上帝不存在，有限损失。信仰的期望值大于不信。
4. Mind-Body Duality and Physicalism | 身心二元论与物理主义
Substance Dualism: Mind ≠ Body | Physicalism: Mind = Brain states
Descartes' conceivability argument for dualism: I can conceive of myself existing without a body, but not without a mind. By Leibniz's law, if A has a property that B lacks, then A ≠ B. The mind is unextended and indivisible; the body is extended and divisible, so they are distinct substances.
笛卡尔为二元论提供的可设想性论证：我能设想自己无身体而存在，但不能设想自己无心而存有。根据莱布尼兹定律，若 A 具有 B 所没有的属性，则 A ≠ B。心灵是非广延和不可分的；身体是广延和可分的，所以它们是不同的实体。
Physicalism identifies mental states with physical states. The identity theory: Pain = C-fibres firing. Functionalism: mental states are defined by their causal roles. Both reduce the mental to the physical.
物理主义将心灵状态等同为物理状态。同一论：疼痛 = C-纤维发放。功能主义：心灵状态由其因果角色定义。两者都将心理还原为物理。
The Knowledge Argument (Mary the colour scientist) claims: Mary knows all physical facts about colour but learns a new fact upon seeing red for the first time. So there are non-physical facts, and physicalism is false. Formally: Complete physical knowledge + new fact upon experience → Physicalism incomplete.
知识论证（颜色科学家玛丽）主张：玛丽知道所有关于颜色的物理事实，但在第一次看到红色时学到了一个新事实。因此存在非物理事实，物理主义为假。形式上：完整的物理知识 + 经验后产生的新事实 → 物理主义不完整。
The possibility of philosophical zombies—beings physically identical to us but with no consciousness—also challenges physicalism: bies are conceivable → Physical properties do not entail consciousness → Physicalism false.
哲学僵尸的可能性——在物理上与我们完全相同但没有意识的存有——也挑战物理主义：僵尸可设想 → 物理属性不包含意识 → 物理主义假。
5. Freedom vs Determinism: The Compatibility Theorem | 自由与决定论：相容性定理
Hard Determinism: All events are causally determined → No free will
Determinism holds that every event, including human actions, has a sufficient cause. Hard determinism concludes that free will is an illusion. Incompatibilism formula: Determinism → ¬Free Will.
决定论认为每一事件，包括人类行动，都有充分原因。强硬决定论推断自由意志是一种幻觉。不相容论公式：决定论 → ¬自由意志。
Compatibilism (soft determinism) redefines free will: an action is free if it is caused by the agent's own desires and beliefs, without external coercion. The formula becomes: Free Action ⇔ (Caused by internal states) ∧ (Absence of constraint). Even in a deterministic world, we can be free.
相容论（温和决定论）重新定义自由意志：一个行动若是被行动者自身的欲求与信念所引起，且无外在强制，则它是自由的。公式变为：自由行动 ⇔ (由内在状态引起) ∧ (无强制)。即使在一个决定论的世界里，我们也可以是自由的。
Libertarianism posits that free will requires indeterminism: for an action to be free, the agent must have been able to do otherwise. This often appeals to agent causation or quantum indeterminacy. Free will → Indeterminism.
自由意志主义假定自由意志需要非决定论：一个行动要算是自由的，行动者必须本来能够做出另一选择。这常常诉诸行动者因果或量子不确定性。自由意志 → 非决定论。
Libet's experiments show brain activity initiating action before conscious awareness, which some take as evidence against free will. However, compatibilists reinterpret this: the agent's prior intentions are still part of the causal chain.
李贝特的实验显示，大脑活动先于有意识的觉知发起行动，有人将此作为反对自由意志的证据。然而相容论者重新解释：行动者的先在意向仍是因果链的一环。
6. Ethical Formulas: Utilitarianism, Deontology and Virtue Ethics | 伦理公式：功利主义、道义论与美德伦理
Principle of Utility: Right ⇔ Maximising net happiness for all affected
Bentham's act utilitarianism: Right action = the one that produces the greatest total pleasure minus pain. This is calculated using the felicific calculus, considering intensity, duration, certainty, etc. In symbols: U(A) = Σ(Pleasure) – Σ(Pain)[all affected].
边沁的行为功利主义：正确行动 = 产生最大总快乐减去痛苦的行动。这通过幸福计算来操作，考量强度、时长、确定性等。符号化：U(A) = Σ(快乐) – Σ(痛苦)[所有受影响者]。
Mill's rule utilitarianism adjusts for higher and lower pleasures: It is better to be a human dissatisfied than a pig satisfied. The quality of happiness matters, not just quantity.
密尔的规则功利主义根据更高级和更低级的快乐做出调整：宁做不满足的人，不做满足的猪。幸福的质而不是量至关重要。
Kant's deontology is based on the categorical imperative. First formulation: Act only according to that maxim whereby you can at the same time will that it should become a universal law. Second formulation: Act in such a way that you treat humanity, whether in your own person or in the person of another, always at the same time as an end, never merely as a means.
康德的道义论基于定言命令。第一公式：要只按照你同时能够愿意它成为一个普遍法则的那个准则去行动。第二公式：你要这样行动，把不论是你的人格中的人性，还是任何他人的人格中的人性，任何时候都同时当做目的，绝不仅仅当做手段。
Aristotle's virtue ethics focuses on character: Virtue = a mean between excess and deficiency. Courage is the mean between cowardice and rashness. Eudaimonia (flourishing) is the final end.
亚里士多德的美德伦理关注品格：德性 = 过度与不及之间的中道。勇敢是怯懦与鲁莽的中道。幸福（eudaimonia）是最终目的。
7. Political Philosophy: Social Contract and Justice Principles | 政治哲学：社会契约与正义原则
Social Contract: Legitimate authority ⇔ Consent of the governed
Hobbes: the state of nature is a war of all against all. Rational individuals consent to surrender their rights to a sovereign in exchange for security. Absolute sovereignty ⇔ Escape from state of nature.
霍布斯：自然状态是所有人对所有人的战争。理性个体同意将权利交给主权者以换取安全。绝对主权 ⇔ 脱离自然状态。
Locke's contract protects natural rights: life, liberty, and property. If government violates these, citizens may revolt. Government by consent + protection of natural rights → legitimate political order.
洛克的契约保护自然权利：生命、自由和财产。若政府侵犯这些权利，公民可以反抗。经同意的政府 + 保护自然权利 → 正当的政治秩序。
Rawls's theory of justice: principles are chosen behind a veil of ignorance in the original position. Principle (1): Equal basic liberties for all. Principle (2): Social and economic inequalities are justified only if they benefit the least advantaged and attach to positions open to all under fair equality of opportunity.
罗尔斯的正义论：原则在原初状态的无知之幕背后选取。原则 (1)：所有的平等基本自由。原则 (2)：社会和经济的不平等只有在对最不利者有利且在公平机会平等条件下职位向所有人开放时，才被允许。
The maximin rule: in the original position, rational agents would choose principles that maximise the minimum outcome, ensuring the worst-off are as well off as possible. This yields Rawls's principles.
最大最小值规则：在原初状态下，理性行动者会选择使最差结果尽可能好的原则，从而推导出罗尔斯的原则。
8. Logic and Thought Experiments Quick Reference | 逻辑与思想实验速查
Deduction: Premises true & valid form → Conclusion necessarily true
A valid deductive argument guarantees the conclusion if premises are true. Soundness requires both validity and true premises. Form: If P → Q, P, therefore Q (modus ponens). Fallacy of affirming the consequent: P → Q, Q, therefore P is invalid.
一个有效的演绎论证，若前提为真，则保证结论必然为真。可靠性既需要有效性也需要真的前提。形式：如果 P → Q，P，所以 Q（肯定前件）。肯定后件的谬误：P → Q，Q，所以 P 无效。
Inductive arguments make the conclusion probable: Strong induction + all true premises → Probable conclusion. The inductive leap is always risky. Causal reasoning often employs Mill's methods: method of difference, concomitant variation, etc.
归纳论证使结论很可能为真：强的归纳 + 所有真前提 → 或然结论。归纳飞跃始终有风险。因果推理常运用密尔方法：差异法、共变法等等。
Common informal fallacies: Ad hominem (attacking the person, not the argument); Straw man (misrepresenting a position to refute it easily); False dilemma (presenting only two options when more exist).
常见非形式谬误：人身攻击（攻击人而非论证）；稻草人（歪曲对方立场以便轻易驳斥）；错误二难（仅给出两个选项，实则另有他途）。
Key thought experiments: Trolley Problem – tests utilitarian vs deontological intuitions; Brain in a Vat – challenges the reality of the external world; Chinese Room – argues that syntax is not sufficient for semantics (against strong AI).
关键思想实验：电车难题——检验功利论与道义论的直觉；缸中之脑——挑战外部世界的真实性；中文屋——论证句法不足以产生语义（反对强人工智能）。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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