📚 IGCSE WJEC Philosophy: Formulas and Theorems Quick Revision Guide | IGCSE WJEC 哲学：公式定理速查手册
Welcome to the IGCSE WJEC Philosophy Quick Revision Guide. This handbook condenses essential logical formulas, ethical principles, philosophical arguments, and core concepts into accessible 'theorems and formulas'. Designed as a rapid reference, it helps you recall, apply, and evaluate key ideas with confidence. Use these summaries to sharpen your revision and enhance exam performance.
欢迎使用 IGCSE WJEC 哲学速查手册。本手册将重要的逻辑公式、伦理原则、哲学论证和核心概念浓缩为易于查阅的“定理与公式”。作为快速参考工具，它帮助你自信地回忆、运用和评析关键观点。借助这些总结来强化复习，提升考试成绩。
1. Valid Forms of Deductive Argument | 演绎论证的有效形式
Modus Ponens (MP): Affirming the antecedent. The form: If P then Q; P is the case; therefore Q must be the case. A classic example: If it is raining, the streets are wet. It is raining. Therefore, the streets are wet.
肯定前件式：肯定前件。形式为：如果 P 则 Q；P 成立；因此 Q 必定成立。经典示例：如果下雨，街道会湿。正在下雨。因此街道湿了。
P → Q, P ⊢ Q
Modus Tollens (MT): Denying the consequent. If P then Q; Q is false; therefore P is false. Example: If the battery is charged, the phone turns on. The phone does not turn on. Therefore, the battery is not charged.
否定后件式：否定后件。如果 P 则 Q；Q 为假；因此 P 为假。示例：如果电池有电，手机开机。手机没有开机。因此电池没电。
P → Q, ¬Q ⊢ ¬P
Hypothetical Syllogism (HS): Chain argument. If P then Q; if Q then R; therefore if P then R. Example: If I study, I pass the exam. If I pass the exam, I graduate. So if I study, I graduate.
假言三段论：连锁论证。如果 P 则 Q；如果 Q 则 R；因此如果 P 则 R。示例：如果我学习，我通过考试。如果我通过考试，我毕业。所以如果我学习，我就毕业。
(P → Q), (Q → R) ⊢ (P → R)
Disjunctive Syllogism (DS): Denying a disjunct. Either P or Q; not P; therefore Q. Example: Either the keys are in my bag or I left them in the car. They are not in my bag. So I left them in the car.
选言三段论：否定一个选言支。要么 P 要么 Q；非 P；因此 Q。示例：钥匙要么在包里，要么落在车里。不在包里。所以落在车里。
P ∨ Q, ¬P ⊢ Q
Constructive Dilemma (CD): If P then Q, and if R then S; P or R is true; therefore Q or S. Example: If I take the train, I arrive by 10 am. If I drive, I arrive by 10:30 am. I either take the train or drive. So I arrive by 10 or by 10:30 am.
构造性二难推理：如果 P 则 Q，并且如果 R 则 S；P 或 R 为真；因此 Q 或 S。示例：如果乘火车，10点前到。如果开车，10点半到。我或者乘火车或者开车。所以我或者10点前到或者10点半到。
(P → Q), (R → S), P ∨ R ⊢ Q ∨ S
2. Common Logical Fallacies | 常见逻辑谬误
Ad Hominem: Attacking the person instead of the argument. Example: 'You cannot trust her opinion on climate change because she is not a scientist.' The flaw lies in dismissing the claim based on a personal trait.
人身攻击：攻击人而非论点。示例：“你不能相信她对气候变化的看法，因为她不是科学家。” 谬误在于根据个人特征否定主张。
Straw Man: Misrepresenting an opponent's position to make it easier to attack. Example: Person A argues for more public transport funding. Person B responds, 'Why do you want to leave rural communities completely isolated?' Person B distorts the original view.
稻草人谬误：歪曲对方立场，使之易于攻击。示例：A主张增加公共交通拨款。B回应：“你为什么想让乡村社区完全隔绝？” B扭曲了原观点。
Slippery Slope: Asserting that a small step will inevitably lead to a chain of extreme, unwanted events without sufficient evidence. Example: 'If we allow students to re-sit exams, next they will demand no exams at all, and education will collapse.'
滑坡谬误：声称一小步必然导致一系列极端的、不可取的后果，却无充分证据。示例：“如果我们允许学生补考，接下来他们会要求取消所有考试，教育将崩溃。”
False Dilemma: Presenting only two alternatives when more exist. Example: 'You are either with us or against us.' It ignores neutral or nuanced positions.
假两难推理：仅呈现两种选项，而实际上存在更多。示例：“你要么支持我们，要么反对我们。” 忽略了中立或细微的立场。
Begging the Question (Petitio Principii): The conclusion is assumed in one of the premises. Example: 'Reading is beneficial because it is good for you.' The premise simply rephrases the conclusion.
乞题谬误：结论已在前提中被假定。示例：“阅读是有益的，因为它对你好。” 前提只是换了个说法。
Appeal to Emotion: Manipulating emotional response instead of presenting a valid argument. Example: 'You must find the defendant guilty; think of the suffering of the victim’s family.'
诉诸情感：操纵情绪反应，而非给出有效论证。示例：“你必须判被告有罪；想想受害者家属的痛苦。”
3. Forms of Inductive Reasoning | 归纳推理形式
Inductive Generalisation: Drawing a general conclusion from a sample. The form: All observed Xs have property Y; therefore, probably all Xs have property Y. Example: Every crow I have seen is black; thus, all crows are probably black. Strength depends on sample size and representativeness.
归纳概括：从样本得出一般结论。形式：所有观察到的 X 都具有属性 Y；因此，可能所有 X 都具有 Y。示例：我见过的乌鸦都是黑的；所以所有乌鸦大概都是黑的。强度取决于样本大小和代表性。
Analogical Reasoning: Inferring that because two things are similar in some respects, they are similar in another respect. Formula: A has properties p, q, r, and s. B has properties p, q, r. Therefore, B probably also has s. Example: Earth and Mars are both planets with atmospheres, water history, and solid surfaces. Earth supports life. So Mars probably could support life.
类比推理：因两事物在某些方面相似，推断它们在另一属性上也相似。公式：A 有属性 p, q, r, s。B 有属性 p, q, r。因此 B 可能也有 s。示例：地球与火星都是具有大气层、有水历史、固态表面的行星。地球有生命。所以火星很可能也能支持生命。
Causal Reasoning (Mill’s Methods): Identifying causes. Method of Agreement: If two or more instances of the phenomenon have only one circumstance in common, that circumstance is the cause. Method of Difference: If an instance where the phenomenon occurs and an instance where it does not differ only in one factor, that factor is the cause.
因果推理（穆勒五法）：确定原因。契合法：如果现象发生的各个事例只有一个共同因素，则该因素为原因。差异法：如果现象发生与不发生的事例仅在一个因素上不同，则该因素为原因。
4. Core Principles of Ethical Theories | 伦理理论核心原则
The table summarises the central 'theorems' of each normative ethical theory, providing a quick primer for exam responses.
下表总结了各规范伦理理论的核心“定理”，为考试答题提供快速参考。
| Ethical Theory | 伦理理论 | Principal Formula | 核心公式 | Decision Rule | 决策准则 | Key Thinker | 关键人物 |
|---|---|---|---|
| Utilitarianism 功利主义 | Greatest Happiness Principle: maximise pleasure and minimise pain for all affected. 最大幸福原则：为所有受影响者最大化快乐、最小化痛苦。 | Choose the action that produces the highest net utility (hedonic calculus). 选择产生最大净效用的行动（快乐计算）。 | Jeremy Bentham, John Stuart Mill |
| Kantian Deontology 康德义务论 | Categorical Imperative (Universal Law formulation): Act only according to that maxim whereby you can at the same time will that it should become a universal law. 定言令式（普遍法则公式）：只按照你同时能够愿意其成为普遍法则的准则去行动。 | Test the maxim’s universalisability; never use persons merely as means. 检验准则的可普遍化性；绝不只把人当作手段。 | Immanuel Kant |
| Virtue Ethics 德性伦理 | Golden Mean: virtue lies in the intermediate between excess and deficiency relative to the situation. 中道原则：德性是相对于情境的过度与不及之间的适度。 | Act as a virtuous person would, cultivating practical wisdom (phronesis). 像有德之人那样行动，培养实践智慧。 | Aristotle |
| Divine Command Theory 神命论 | Morality is whatever God commands. 'Right' means commanded by God; 'wrong' means forbidden by God. 道德即神的命令。“正确”即神所命令的；“错误”即神所禁止的。 | Consult sacred texts or revelation. 查阅圣书或启示。 | Various religious traditions |
5. Philosophical Arguments for God’s Existence | 上帝存在的哲学论证
Anselm’s Ontological Argument (a priori formula): God is defined as the greatest conceivable being. Existence in reality is greater than existence in the understanding alone. Therefore, if God exists only in the understanding, we could conceive a greater being (one that exists in reality). Hence God must exist in reality.
安瑟伦的本体论论证（先验公式）：上帝被定义为可设想的最伟大存在者。在现实中存在比仅在理解中存在更伟大。因此，如果上帝仅存在于理解中，我们还能设想一位更伟大的存在者（即在现实中也存在）。所以上帝必然在现实中存在。
Gaunilo’s Objection (Reductio): Using the same reasoning, one could prove the existence of a perfect island. If the greatest conceivable island exists only in the mind, a greater island (existing in reality) could be conceived, so it must exist. This shows the logic is flawed because it leads to absurdity.
高尼罗的反驳（归谬）：用同样推理可证明最完美岛屿的存在。如果可设想的最伟大岛屿只存在于心中，就能设想更伟大的岛屿（在现实中存在），所以它必定存在。这表明逻辑有缺陷，导致荒谬。
Aquinas’ First Way (Cosmological – Motion/Change): Everything that is moved is moved by another. This chain cannot go back to infinity. Therefore there must be a first unmoved mover, which is God.
阿奎那的第一路论证（宇宙论 – 运动/变化）：凡运动之物皆被他物推动。这样的因果链不能无限回溯。因此必然存在一个第一推动者不被推动，这就是上帝。
Kalam Cosmological Argument: Everything that begins to exist has a cause. The universe began to exist. Therefore the universe has a cause, which is identified as God.
卡拉姆宇宙论论证：一切开始存在的事物都有其原因。宇宙开始存在。因此宇宙有一个原因，那被认为是上帝。
Paley’s Design Argument (Teleological): A watch’s complexity implies a watchmaker. Likewise, the complexity and apparent purpose in nature imply a divine designer.
佩利的设计论证（目的论）：手表的复杂性意味着钟表匠。同样，自然界的复杂性和明显的目的性意味着一位神圣设计者。
6. Fundamentals of Epistemology | 知识论基础
Classical Definition of Knowledge (JTB): Knowledge is justified true belief. S knows that P if and only if (i) P is true, (ii) S believes that P, and (iii) S is justified in believing that P.
知识的经典定义（JTB）：知识是得到确证的真信念。某人 S 知道 P 当且仅当 (i) P 为真，(ii) S 相信 P，(iii) S 有理由相信 P。
Gettier Problem: Counterexamples show that JTB is not sufficient for knowledge. A person might have justified true belief through luck or a mistaken intermediate step. Thus knowledge requires a fourth condition (e.g., no false lemmas).
盖梯尔问题：反例显示 JTB 对知识而言并不充分。某人可能因运气或错误的中间步骤而拥有确证的真信念。因此知识需要第四个条件（如，无虚假引理）。
Descartes’ Foundationalism: 'Cogito, ergo sum' (I think, therefore I am) serves as an indubitable foundation. Knowledge is built upon clear and distinct ideas derived from reason.
笛卡尔的基础主义：“我思故我在” 是不可怀疑的基石。知识建立在由理性获得的清晰明白的观念之上。
Hume’s Problem of Induction: Inductive inferences rely on the uniformity of nature, but that assumption cannot be justified without circularity. Hence inductive knowledge cannot be rationally justified.
休谟的归纳问题：归纳推理依赖自然的齐一性，但该假设若不加循环论证便无法被确证。因此归纳知识无法得到理性辩护。
7. Key Concepts in Metaphysics | 形而上学关键概念
Substance Dualism (Descartes): The mind and body are two distinct substances. The mind is non‑extended thinking substance; the body is extended non‑thinking substance. Interaction occurs at the pineal gland. Challenge: how can an immaterial mind cause physical changes?
实体二元论（笛卡尔）：心灵与身体是两种不同的实体。心灵是非广延的思维实体；身体是广延的非思维实体。交互发生在松果腺。挑战：非物质的心灵如何引起物理变化？
Physicalism: Everything that exists is physical or supervenes on the physical. Mental states are identical to brain states (identity theory) or functional states. Supported by neuroscientific correlations.
物理主义：一切存在物都是物理的，或随附于物理的。心理状态等同于大脑状态（同一论）或功能状态。得到神经科学相关性的支持。
Determinism vs. Free Will: Hard determinism holds that all events are causally determined, so free will is an illusion. Libertarianism asserts that the will is undetermined and genuinely free. Compatibilism (soft determinism) says free will is compatible with determinism as long as actions flow from our own desires without external coercion.
决定论与自由意志：强硬决定论认为所有事件都被因果决定，因此自由意志是幻象。自由意志论主张意志不被决定，是真正自由的。相容论（软决定论）声称只要行动源于自身欲望且无外部强制，自由意志就与决定论相容。
Personal Identity: What makes a person at time t2 identical to a person at t1? Psychological continuity theory (Locke): memory and mental states. Bodily continuity theory: the same human organism. Thought experiment: If your consciousness is uploaded to a computer, are you still you?
人格同一性：什么使时间 t2 的人与时间 t1 的人是同一个？心理连续性理论（洛克）：记忆与心理状态。身体连续性理论：同一人类有机体。思想实验：如果你的意识被上传到电脑，你还是你吗？
8. Philosophical Methods and Techniques | 哲学方法与技巧
Socratic Method (Elenchus): A cooperative dialogue involving questioning and critical examination. The formula is to elicit a definition, probe for inconsistencies, refine the thesis, and arrive at deeper understanding. Often exposes ignorance to stimulate genuine inquiry.
苏格拉底反诘法：一种合作式对话，通过提问和批判性检验进行。公式是引出定义、探查矛盾、修正论点、达到更深理解。常揭示无知以激发真正的探求。
Thought Experiments: Imaginary scenarios designed to test intuitions and theories. Famous examples: the Trolley Problem (a runaway trolley: pull the lever to sacrifice one and save five, or do nothing) tests utilitarian vs. deontological intuitions. The Brain in a Vat scenario challenges scepticism about the external world.
思想实验：为检验直觉和理论而设计的想象场景。著名例子：电车难题（失控电车：扳动拉杆牺牲一人救五人，或什么都不做）检验功利主义与义务论的直觉。缸中之脑场景挑战对外部世界的怀疑论。
Reductio ad Absurdum: Assuming the negation of the thesis leads to a contradiction or an absurdity; therefore the thesis must be true. Formula: To prove P, assume not‑P, derive a contradiction, conclude P.
归谬法：假定论题的反面会导出矛盾或荒谬；因此原论题必然为真。公式：要证明 P，假设非 P，导出矛盾，得出 P。
Conceptual Analysis: Clarifying a concept by breaking it down into necessary and sufficient conditions. For example, analysing 'knowledge' as JTB + X. This technique reveals hidden ambiguities and sharpens philosophical arguments.
概念分析：通过将概念分解为必要和充分条件来澄清它。例如，将“知识”分析为 JTB + X。此技巧揭示隐藏的模糊性，使哲学论证更精确。
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