📚 IGCSE AQA Philosophy: Formula & Theorem Quick Reference | IGCSE AQA 哲学：公式定理速查手册
In IGCSE AQA Philosophy, students encounter arguments and ethical theories that can be structured as logical ‘formulas’ or patterns of reasoning. This quick reference handbook presents key philosophical positions and moral theorems in a concise, formula-like format to aid revision. Each entry breaks down a major argument or principle into its essential components, premises, and conclusions.
在IGCSE AQA哲学课程中，学生会接触到各种论证和伦理理论，这些都可以构建成逻辑“公式”或推理模式。本速查手册以简洁的公式化形式呈现关键的哲学立场和道德定理，便于复习。每个条目将一个重要论证或原则分解为其基本组成部分、前提和结论。
1. The Teleological (Design) Argument | 目的论（设计）论证
The Design Argument infers the existence of God from the appearance of purpose and complexity in the natural world. Its classical formulation, as advanced by William Paley's watchmaker analogy, can be rendered as a conditional sequence.
设计论证从自然界表现出的目的性和复杂性推导出神的存在。其经典表述（如威廉·佩利的手表类比）可表述为一个条件序列。
Intricate Order + Purpose → Intelligent Designer 精细秩序 + 目的 → 智慧设计者
Premise 1: The universe exhibits intricate order, regularity, and purposeful complexity — much like a watch.
前提1：宇宙展现出精细的秩序、规律性和有目的的复杂性——很像一块手表。
Premise 2: Such complexity and purpose are never the product of chance; they invariably point to an intelligent mind.
前提2：这种复杂性和目的从来不是偶然的产物；它们总是表明存在着智慧心智。
Premise 3: The universe is far more complex and purposeful than any human artefact.
前提3：宇宙比任何人造物都更复杂、更具目的性。
Conclusion: Therefore, the universe must have been designed by a supremely intelligent and powerful designer — God.
结论：因此，宇宙必定是由一位拥有至上智慧与能力的设计者——神——所设计的。
2. The Cosmological Argument (First Cause) | 宇宙论论证（第一因）
The Cosmological Argument holds that the existence of the universe requires a first cause or necessary being. Aquinas' 'Second Way' and the Kalam version both follow a similar reductio ad absurdum of infinite regress.
宇宙论论证主张，宇宙的存在需要一个第一因或必然存在者。阿奎那的‘第二路’和卡拉姆版本都遵循了对无限回溯的归谬推理。
No infinite regress of causes → Uncaused First Cause 无因果无限回溯 → 无因的第一因
Premise 1: Everything that exists has a cause or explanation for its existence (principle of sufficient reason).
前提1：每个存在的事物都有其存在的原因或解释（充足理由律）。
Premise 2: An infinite chain of dependent causes is impossible, because if there were no first cause, there would be no subsequent causes and nothing would exist now.
前提2：无限的依赖原因链条是不可能的，因为如果没有第一因，就不会有后续的原因，现在也就不会有任何事物存在。
Premise 3: There exists a chain of dependent causes (the universe).
前提3：存在着一个依赖原因链条（宇宙）。
Conclusion: Therefore, there must be a first cause that is itself uncaused, and this we call God.
结论：因此，必定有一个自身不被引起的第一个原因，我们称之为神。
3. The Logical Problem of Evil (Inconsistent Triad) | 恶的逻辑问题（不一致三元组）
The logical problem of evil challenges the coherence of the theistic deity. J.L. Mackie formalised it as an inconsistent triad: three statements that cannot all be true simultaneously.
恶的逻辑问题挑战了有神论神祇的一致性。J.L.麦基将其形式化为一个不一致三元组：三句话无法同时为真。
Omnipotence ∧ Omnibenevolence ∧ Evil → Contradiction 全能 ∧ 全善 ∧ 恶存在 → 矛盾
Statement 1: God is omnipotent (all-powerful).
陈述1：上帝是全能的。
Statement 2: God is omnibenevolent (all-loving).
陈述2：上帝是全善的。
Statement 3: Evil exists.
陈述3：恶存在。
If God is all-powerful, God can prevent evil. If God is all-loving, God would want to prevent evil. Yet evil exists. Therefore, such a God does not exist (at most two of the three can be true).
如果神是全能的，他能够阻止恶；如果神是全善的，他会愿意阻止恶。然而恶存在。因此，这样的神不存在（三条中最多只能有两条为真）。
4. The Free Will Defence Formula | 自由意志辩护公式
A major theodicy defends the existence of evil by appealing to the greater good of free will. The formula justifies moral evil as the price of genuinely free moral agents.
一种主要的神义论通过诉诸自由意志这一更大的善来为恶的存在辩护。该公式将道德恶解释为真正自由的道德主体所必须付出的代价。
Free will (greater good) + Misused freedom → Moral evil 自由意志（更大的善）+ 被滥用的自由 → 道德恶
Premise 1: Genuine love and moral goodness require free choice.
前提1：真正的爱和道德善需要自由选择。
Premise 2: If humans are genuinely free, they must have the capacity to choose evil.
前提2：如果人类真正自由，就必须具有选择恶的能力。
Premise 3: The value of a world with free beings who sometimes choose evil outweighs a world of automata.
前提3：一个拥有有时会选择恶的自由存在的世界的价值，高于一个全是自动机器的世界。
Conclusion: Therefore, God allows moral evil to preserve the greater good of free will.
结论：因此，神允许道德恶的存在，是为了维护自由意志这一更大的善。
5. The Ontological Argument (Anselm) | 本体论论证（安瑟伦）
Anselm's ontological argument is an a priori proof that moves from the concept of God to his existence. It can be presented as a reductio ad absurdum of denying God's existence.
安瑟伦的本体论论证是一个从上帝的概念推出其存在的先天证明。它可以被呈现为对否认上帝存在这一立场的归谬法。
Greatest conceivable being + Existence as perfection → Necessary existence 可设想的最伟大者 + 存在是完美 → 必然存在
Premise 1: God is defined as 'that than which nothing greater can be conceived'.
前提1：上帝被定义为‘无法设想有比之更伟大者的那个存在’。
Premise 2: This being exists in the mind (even the fool understands the concept).
前提2：这个存在存在于心灵中（连愚顽人也理解这个概念）。
Premise 3: It is greater to exist in reality than to exist in the mind alone.
前提3：存在于现实中，比仅存在于心灵中更伟大。
Conclusion: If God existed only in the mind, we could conceive of something greater (the same being existing in reality), which contradicts the definition. Thus God must exist in reality.
结论：如果上帝只存在于心灵中，我们就能设想一个更伟大者（同一个存在同时存在于现实中），这就与定义矛盾。因此上帝必然在现实中存在。
6. The Principle of Credulity (Religious Experience) | 轻信原则（宗教经验）
Richard Swinburne's principle of credulity provides an epistemic formula for treating religious experiences as prima facie evidence. It shifts the burden of proof onto the sceptic.
理查德·斯温伯恩的轻信原则提供了一个认识论公式，将宗教经验视为初步证据。它将举证责任转移到了怀疑者一方。
If it seems that X is present → Probably X is present (unless defeaters) 如果似乎X在场 → 则很可能X在场（除非有否决条件）
Core formula: A person is rationally justified in believing that things are as they seem to be, in the absence of special considerations (e.g. the subject was intoxicated, or the claim is overwhelmingly improbable).
核心公式：在没有特殊考虑（如主体处于醉酒状态，或该主张极度不可能）的情况下，一个人在理性上有理由相信事物就是它们所呈现的样子。
Combined with the principle of testimony, we should generally trust what others report about their experiences unless we have positive reasons for doubt.
结合证词原则，我们通常应当相信他人所报告的体验，除非我们有积极的理由去怀疑。
7. Utilitarian Hedonic Calculus | 功利主义苦乐计算法
Jeremy Bentham's act utilitarianism proposes a quantitative hedonic calculus to determine the morality of an action. The 'formula' sums pleasures and pains across all affected persons.
杰里米·边沁的行为功利主义提出了一套量化苦乐计算法来判定行为的道德性。该‘公式’将所有受影响者的快乐与痛苦进行加总。
Net utility = Σ (Pleasure - Pain) for all affected 净功利 = Σ（快乐 - 痛苦） 对所有受影响者
Seven factors: Intensity, Duration, Certainty, Propinquity (nearness), Fecundity (chance of more pleasure), Purity (chance of no mixture of pain), and Extent (number of people).
七项因素：强度、持续时间、确定性、邻近性（远近）、多产性（带来更多快乐的机会）、纯粹性（不掺杂痛苦的机会）和范围（受影响的人数）。
The right action is the one that maximises net pleasure over pain for the greatest number. This is a consequentialist 'formula': rightness is a function of outcomes only.
正确的行为是那个能为最大多数人带来最大净快乐超出痛苦的行为。这是一个后果论的‘公式’：行为对错仅由结果决定。
8. Kant's Categorical Imperative (Universal Law) | 康德的定言命令（普遍法则）
Immanuel Kant's deontological ethic is grounded in the categorical imperative, a rational test for moral maxims. Its first formulation provides a clear decision procedure.
伊曼努尔·康德的义务论伦理以定言命令为基础，这是一个对道德准则的理性检验。其第一表述提供了一个清晰的决策程序。
Maxim universalisable without contradiction → Morally permissible 准则可普遍化而无矛盾 → 道德上允许
Formula: 'Act only according to that maxim whereby you can at the same time will that it should become a universal law.'
公式：‘只按照那同时能够意愿其成为普遍法则的准则去行动。’
A maxim fails if universalising it leads to a contradiction in conception (e.g. false promising) or a contradiction in will (e.g. failing to help others). The second formulation treats humanity always as an end, never merely as a means.
如果普遍化一项准则会导致概念上的矛盾（如虚假承诺）或意愿上的矛盾（如不帮助他人），该准则就不成立。第二表述要求总是将人本身作为目的，而绝不仅仅作为手段。
9. Virtue Ethics: The Golden Mean | 美德伦理：中道
Aristotle's virtue ethics characterises moral goodness as a disposition to choose the intermediate between excess and deficiency. Each virtue is flanked by two vices.
亚里士多德的美德伦理将道德上的善描述为一种在过度与不足之间进行选择的倾向。每一种美德都伴随着两个恶行。
Virtue = Mean (midpoint) between Vice of excess and Vice of deficiency 美德 = 中道（过度与不足之恶的中间点）
Table of virtues:
美德表：
| Sphere of action (领域) | Vice of deficiency (不足之恶) | Virtue (美德) | Vice of excess (过度之恶) |
|---|---|---|---|
| Fear & confidence | Cowardice | Courage | Rashness |
| Pleasure & pain | Insensibility | Temperance | Licentiousness |
| Giving & spending money | Stinginess | Generosity | Prodigality |
Moral action is not derived from rules or consequences but from the agent's phronesis (practical wisdom) in hitting the mean relative to the situation.
道德行为并非源于规则或后果，而是源于行为者依据情境击中中道的实践智慧（phronesis）。
10. Logical Inference Forms: Modus Ponens & Modus Tollens | 逻辑推理形式：肯定前件与否定后件
Philosophical reasoning relies on valid deductive forms. Two fundamental inference patterns appear repeatedly in arguments for and against religious and ethical claims.
哲学推理依赖于有效的演绎形式。两种基本的推理模式反复出现在关于宗教和伦理主张的论证中。
Modus Ponens: If P then Q; P → Q Modus Tollens: If P then Q; ¬Q → ¬P
Modus Ponens (affirming the antecedent): If P then Q. P is true. Therefore, Q is true. Example: If design exists, a designer exists. Design exists. Therefore, a designer exists.
肯定前件（Modus Ponens）：如果P则Q。P为真。因此Q为真。例：如果设计存在，设计者就存在。设计存在。因此设计者存在。
Modus Tollens (denying the consequent): If P then Q. Q is false. Therefore, P is false. Example: If an all-loving God exists, gratuitous evil would not exist. Gratuitous evil does exist. Therefore, an all-loving God does not exist.
否定后件（Modus Tollens）：如果P则Q。Q为假。因此P为假。例：如果全善的神存在，无缘无故的恶就不会存在。无缘无故的恶存在。因此全善的神不存在。
ying the antecedent are invalid. These formal templates keep arguments logically rigorous.
谬误提醒：肯定后件（如果P则Q；Q，因此P）和否定前件是无效的。这些形式模板使论证保持逻辑严谨。
11. The Euthyphro Dilemma | 欧绪弗洛两难
The Euthyphro dilemma, from Plato's dialogue, poses a fundamental challenge to divine command theory. It can be expressed as a forced choice between two unpalatable options.
源自柏拉图对话录的欧绪弗洛两难对神令论提出了根本挑战。它可以表达为一个在两个都难以接受的选择之间的强制抉择。
Good ↔ God's command? 善 ↔ 神的命令？
Horn 1: Is an action right because God commands it? If so, morality becomes arbitrary — God could command cruelty and it would be 'good'.
角1：一个行为是正当的，因为神命令它吗？如果是，道德就变成了任意的——神可以命令残忍行径，那也将是‘善’的。
Horn 2: Does God command an action because it is right? If so, there is a standard of goodness independent of God, thus undermining divine sovereignty.
角2：神命令一个行为，是因为它本身是正当的吗？如果是，那么就存在一个独立于神的善的标准，从而削弱了神的主权。
This dilemma forces the theist to either abandon the objectivity of morality or limit God's omnipotence. Modified divine command theories attempt to resolve it by grounding goodness in God's unchanging nature.
这个两难迫使有神论者要么放弃道德的客观性，要么限制神的全能。修正的神令论试图通过将善的根基建立在神的不变本性中来化解它。
12. The Moral Argument for God's Existence | 上帝存在的道德论证
The moral argument infers God as the best explanation for the existence of objective moral values and duties. Kant and later philosophers developed this line of reasoning into a practical postulate.
道德论证通过推论上帝是客观道德价值和义务存在的最佳解释。康德和后来的哲学家将这条推理路线发展成一个实践公设。
Objective moral law → Moral lawgiver 客观道德律 → 道德立法者
Premise 1: Objective moral facts exist (e.g. torturing children for fun is really wrong, independent of opinion).
前提1：客观的道德事实存在（例如，为取乐而折磨儿童真的是错的，无关乎人的意见）。
Premise 2: The best explanation for objective moral facts is a transcendent, personal source of moral obligation.
前提2：对客观道德事实的最佳解释是一个超验的、人格性的道德义务来源。
Premise 3: Naturalism cannot ground unconditional duties, because nature is indifferent to moral value.
前提3：自然主义无法为无条件的义务奠基，因为大自然对道德价值漠不关心。
Conclusion: Therefore, a transcendent moral lawgiver (God) probably exists.
结论：因此，很可能存在一位超验的道德立法者（神）。
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