📚 IGCSE Edexcel Philosophy: Formula and Theorem Quick Reference Handbook | IGCSE Edexcel 哲学：公式定理速查手册
This quick reference distils key philosophical arguments and ethical frameworks from the IGCSE Edexcel specification into memorable formulas, logical patterns, and conceptual shortcuts. Use these structures to analyse arguments, evaluate strengths and weaknesses, and craft precise exam responses.
这份速查手册将 IGCSE Edexcel 考纲中的核心哲学论证与伦理框架提炼为易记的公式、逻辑模式与概念捷径。运用这些结构来分析论证、评估优劣，并写出精准的考试答案。
1. The Teleological Argument Formula | 目的论论证公式
The Teleological Argument moves from perceived design to a designer. Paley’s watch analogy provides the classic inductive formula.
目的论论证由可感知的设计推向设计者。佩利的手表类比提供了经典的归纳公式。
Design Inference: Complexity + Purpose → Intelligent Designer
设计推理：复杂性 + 目的 → 智慧设计者
Premise 1: Human artefacts, such as a watch, exhibit intricate parts arranged for a purpose, and we know they have a designer.
前提 1：人造物品（如手表）展现出为某个目的而排列的精密部件，我们知道它们有设计者。
Premise 2: The natural world contains far greater examples of complex, purposeful arrangement, e.g., the human eye or bacterial flagellum.
前提 2：自然界包含着更为庞大的复杂、有目的排列实例，如人眼或细菌鞭毛。
Premise 3: Similar effects imply similar causes; therefore, the universe more strongly points to an intelligent cause.
前提 3：相似的结果意味着相似的原因；因此，宇宙更有力地指向一个智慧原因。
Conclusion: This supreme intelligent designer is what we call God.
结论：这位至高的智慧设计者就是我们所说的上帝。
Hume’s objections can also be expressed as contra-formulas: e.g., the universe might be more like a living organism than a machine, requiring no external designer.
休谟的反对也可表示为反公式：例如，宇宙可能更像一个生物体而非机器，无需外在设计者。
2. The Cosmological Argument Framework | 宇宙论论证框架
Cosmological arguments trace the existence of the universe back to a first cause or necessary being. Aquinas’ Third Way offers a concise logical skeleton.
宇宙论论证将宇宙的存在追溯至第一因或必然存在。阿奎那的第三路提供了一个简明的逻辑骨架。
Contingency → Dependency → Necessary Being (God)
偶然性 → 依赖性 → 必然存在（上帝）
Step 1: We observe that things in the universe are contingent – they come into being and pass away.
步骤 1：我们观察到宇宙中的事物是偶然的——它们生成并消灭。
Step 2: If everything were contingent, then at some point nothing would have existed, and nothing can come from nothing.
步骤 2：如果一切都是偶然的，那么在某个时刻曾一无所有，而无中不能生有。
Step 3: Therefore, there must exist a necessary being that contains its own reason for existence and causes all contingent beings.
步骤 3：因此，必有一个必然存在，其自身即包涵存在的理由，并导致所有偶然事物。
Kalam version formula: Everything that begins to exist has a cause; the universe began to exist; therefore, the universe has a cause (God).
卡拉姆版本公式：凡事有始皆有因；宇宙有始；因此，宇宙有因（上帝）。
Hume’s objection: The universe itself might be the necessary being; the argument commits the fallacy of composition.
休谟反对：宇宙自身可能就是必然存在；论证犯了合成谬误。
3. Anselm’s Ontological Argument | 安瑟伦的本体论论证
Anselm’s argument is a priori, attempting to deduce God’s existence from the very concept of God as ‘that than which nothing greater can be conceived’.
安瑟伦的论证是先天的，试图从“无法设想更伟大者”的上帝概念中演绎出上帝的存在。
Definition: God = The Greatest Conceivable Being (GCB)
定义：上帝 = 可设想的最伟大存在（GCB）
Premise 1: The GCB exists in the understanding (even the fool grasps it).
前提 1：GCB 存在于理智之中（连愚人也把握之）。
Premise 2: It is greater to exist in reality than in the understanding alone.
前提 2：存在于现实中比仅存在于理智中更为伟大。
Premise 3: If the GCB existed only in the understanding, we could conceive of a greater being (one existing in reality).
前提 3：如果 GCB 仅存在于理智，我们可以设想一个更伟大的存在（存在于现实中者）。
Conclusion: Therefore, the GCB must exist in reality, otherwise it would not be the greatest conceivable being.
结论：因此，GCB 必在现实中存在，否则它就不是可设想的最伟大存在。
Gaunilo’s ‘perfect island’ rebuttal shows the same logical form can ‘prove’ absurdities, challenging the validity of the a priori move.
高尼罗的“完美岛”反驳表明相同的逻辑形式可以“证明”荒谬之物，挑战了先天推演的有效性。
4. The Problem of Evil Logical Structure | 恶的问题逻辑结构
The logical problem of evil argues that the coexistence of an omnipotent, omnibenevolent God and evil is impossible. The evidential version lowers the claim to improbability.
恶的逻辑问题主张全能、全善的上帝与邪恶共存是不可能的。证据版本则降为不大可能。
Inconsistent Triad: God’s Omnipotence + God’s Omnibenevolence + Existence of Evil
不一致三元组：上帝全能 + 上帝全善 + 邪恶存在
Premise 1: If an omnipotent God exists, He can prevent all evil.
前提 1：若全能上帝存在，他能够阻止一切恶。
Premise 2: If an omnibenevolent God exists, He would want to prevent all evil.
前提 2：若全善上帝存在，他会愿意阻止一切恶。
Premise 3: There is evil (moral and natural suffering).
前提 3：存在恶（道德和自然苦难）。
Conclusion: Therefore, an omnipotent, omnibenevolent God does not exist.
结论：因此，既全能又全善的上帝不存在。
Common theodicy formula: Greater good defence: Evil is logically necessary for certain virtues (e.g., courage) or free will, so God’s allowance does not contradict His nature.
常见神正论公式：更大善防御：对于某些德性（如勇气）或自由意志，恶在逻辑上是必需的，因此上帝的允许与他的本性并不矛盾。
5. Utilitarianism: The Felicific Calculus | 功利主义：幸福计算
Bentham’s quantitative utilitarianism weighs pleasures and pains using a hedonic calculus. The goal is to maximise net utility for all affected.
边沁的量化功利主义运用快乐主义计算来权衡快乐与痛苦。目标是为所有受影响者最大化净效用。
Net Morality = Σ (Pleasure₁–Pain₁ + Pleasure₂–Pain₂ + …) over all sentient beings
净道德值 = Σ (快乐₁–痛苦₁ + 快乐₂–痛苦₂ + …) 对所有有感知者
Seven factors to quantify: Intensity, Duration, Certainty, Propinquity (nearness), Fecundity (will it produce more pleasure?), Purity (free from pain?), Extent (number affected).
七个量化因子：强度、持续时间、确定性、远近、丰产性（会带来更多快乐吗？）、纯度（无痛吗？）、广度（受影响人数）。
The principle of utility: Act so as to produce the greatest happiness for the greatest number. Each individual’s pleasure counts equally.
功利原理：行动以产生最多数人的最大幸福。每个人的快乐同等计入。
Mill’s qualitative shift formula: Higher intellectual pleasures count for more than lower bodily ones – ‘better to be Socrates dissatisfied than a fool satisfied’.
密尔的质量转变公式：高等智识快乐比低等身体快乐更有分量——“宁做不满足的苏格拉底，不做满足的愚人”。
6. Kant’s Categorical Imperative Formulations | 康德绝对命令的表述
Kant’s ethics are deontological: actions are right if they conform to rational duty, expressed through the categorical imperative. The most examined formulations work like moral litmus tests.
康德的伦理学是义务论的：行为若符合理性义务则为正当，由绝对命令表达。最常考的公式如同道德试纸。
Formula of Universal Law: Act only on that maxim which you can at the same time will to become a universal law.
普遍法则公式：只按照你同时能够意愿它成为一项普遍法则的准则去行动。
Test step 1: Formulate the maxim (e.g., ‘I may make a false promise to get money’).
检验步骤 1：表述准则（例如，“为获得金钱我可作虚假承诺”）。
Test step 2: Universalise it: ‘Everyone may make false promises for personal gain’.
检验步骤 2：普遍化：“人人可为私利作虚假承诺”。
Test step 3: Check for contradiction in conception (if universalised, promises would lose meaning) or contradiction in will (could not rationally will such a world).
检验步骤 3：检查概念矛盾（若普遍化，承诺将失去意义）或意愿矛盾（无法理性意愿这样一个世界）。
Formula of Humanity: Act in such a way that you treat humanity, whether in your own person or in the person of another, always as an end and never merely as a means.
人性公式：以这样的方式行动，即你总是将人性——无论是你自己人格中还是他人人格中的——视为目的，而不仅仅视为手段。
7. Aquinas’ Natural Law Primary Precepts | 阿奎那自然法的基本准则
According to Aquinas, God created the world with a built-in rational order, discoverable by reason. The primary precepts are the fundamental purposes towards which human nature inclines.
阿奎那认为上帝创造世界时内置了理性秩序，可由理性发现。基本准则是人性所趋向的根本目的。
Synderesis Rule: Do good and avoid evil → follow the natural inclinations
良知规则：行善避恶 → 遵循自然倾向
Primary Precept 1: Preservation of life (self-preservation and protection of the innocent).
基本准则 1：保存生命（自保与保护无辜者）。
Primary Precept 2: Reproduction and education of offspring (continuity of the species).
基本准则 2：繁衍与教育后代（物种延续）。
Primary Precept 3: Living in an ordered society (peace, justice, community).
基本准则 3：生活在有秩序的社会中（和平、正义、社群）。
Primary Precept 4: Worship of God (acknowledging the transcendent source).
基本准则 4：崇拜上帝（承认超越之源）。
Secondary precepts are derived by applying reason to the primary precepts in specific circumstances; these can change as situations vary, according to the doctrine of double effect.
次级准则是在具体情境中对基本准则进行理性推演而得；根据双重效果学说，这些可随境况变化。
8. Situation Ethics: The Agapeic Calculus | 情境伦理：以爱为本的计算
Fletcher’s situation ethics proposes one absolute norm: agape (self-giving love). All other rules, laws, and principles are relative to this love in each unique situation.
弗莱彻的情境伦理提出一个绝对规范：圣爱（无私给予的爱）。在所有独特处境中，其他规则、法律和原则都相对于此爱。
Love is the only intrinsic good; the right action = the most loving thing in the situation.
爱是唯一内在的善；正当的行为 = 在此情境中最有爱心之举。
Four working principles (the ‘positives’): Pragmatism (must work in practice), Relativism (rules serve love, not vice versa), Positivism (love is posited by faith), Personalism (persons first, not laws).
四项工作原则（“积极面”）：实用主义（实践中必须有效）、相对主义（规则服务于爱而非相反）、实证主义（爱由信仰所肯定）、位格主义（人优先于律法）。
Six fundamental propositions: e.g., ‘Love and justice are the same, for justice is love distributed.’ Only love is intrinsically good; love wills the neighbour’s good; love’s decisions are made situationally, not prescriptively.
六项基本命题：例如，“爱与正义是同一的，因为正义就是被分配的爱。” 唯有爱本身是内在善；爱意愿邻人的好处；爱的决定依据情境而非依规定作出。
Criticism formula: Situation ethics could collapse into antinomianism (no rules at all) or subjectivity, making moral evaluation inconsistent.
批评公式：情境伦理可能沦为反律法主义（全无规则）或主观主义，使道德评价不一致。
9. Descartes’ Cogito Ergo Sum | 笛卡尔“我思故我在”
Descartes employed radical doubt to establish an indubitable foundation for knowledge. The cogito is the first certainty of his rationalist epistemology.
笛卡尔以彻底怀疑为知识建立不可置疑的基础。“我思”是其理性主义认识论的首要确定性。
Cogito formula: If I am doubting, then I must exist as a thinking thing (Dubito, ergo sum).
我思公式：如果我在怀疑，那么我必然作为一个思想者而存在（我疑，故我在）。
Step 1: I can doubt the existence of my body, the physical world, and even mathematical truths (evil demon hypothesis).
步骤 1：我可以怀疑身体、物理世界乃至数学真理的存在（邪恶魔鬼假设）。
Step 2: The very act of doubting is a form of thinking (cogitatio).
步骤 2：而怀疑本身正是一种思想活动。
Step 3: It is impossible to doubt that I am thinking without thereby proving that I think.
步骤 3：怀疑“我在思想”是不可能的，因为这种怀疑恰恰证明我在思想。
Conclusion: Therefore, the proposition ‘I exist’ is necessarily true whenever uttered or conceived by me.
结论：因此，只要我陈述或构思“我存在”，这一命题必然为真。
Cartesian circle criticism: Descartes later uses clear and distinct ideas to prove God, and then uses God to guarantee clear and distinct ideas, forming a circular argument.
笛卡尔循环批评：笛卡尔后用清楚明白的观念来证明上帝，又用上帝来保证清楚明白的观念，形成循环论证。
10. Aristotle’s Four Causes Model | 亚里士多德四因说模型
Aristotle explained the nature of being and change through four types of cause. This aetiological model applies to any substance or object.
亚里士多德以四类原因来解释存在与变化的本质。这一原因论模型适用于任何实体或物体。
Complete Explanation (X) = Material Cause + Formal Cause + Efficient Cause + Final Cause
完满解释 (X) = 质料因 + 形式因 + 动力因 + 目的因
Material Cause: What something is made of (e.g., wood and stone of a house).
质料因：事物由什么构成（如房屋的木材和石块）。
Formal Cause: The essence or ‘what it is to be’ that thing (the plan or blueprint that makes wood a house).
形式因：该事物的本质或“是其所在”（使木料成为房屋的设计蓝图）。
Efficient Cause: The agent or process that brings it about (the builder and the act of building).
动力因：导致其产生的动因或过程（建造者与建造活动）。
Final Cause (Telos): The purpose or end for which it exists (shelter and comfort). For living things, the final cause is actualisation of potential.
目的因：其存在的目的或终点（遮风避雨与舒适）。对于生物，目的因即潜能之实现。
Aristotle’s Prime Mover functions as the ultimate final cause – pure actuality, drawing all things through attraction, not efficient causation. This ‘formula of desire’ makes the Prime Mover the final explanation for all motion.
亚里士多德的“第一推动者”作为终极目的因——纯粹现实性，通过吸引而非动力因拉动万物。这一“欲求公式”使第一推动者成为一切运动的终极解释。
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