📚 WJEC Year 11 Philosophy: Key Formulas & Principles Quick Reference | WJEC 11年级哲学：核心公式与原则速查手册
Welcome to your WJEC Year 11 Philosophy quick-reference guide. Just as mathematics relies on formulas to solve equations, philosophy often distills complex arguments into memorable logical structures. This handbook transforms key arguments and ethical principles into clear, digestible 'formulas' to help you revise efficiently for your exams. Each entry breaks down a core topic into its essential logical flow, definition, or test so that you can grasp the reasoning behind the ideas and recall them under pressure.
欢迎使用 WJEC 11 年级哲学速查手册。正如数学依赖公式来解方程，哲学也常将复杂的论证凝练成可记忆的逻辑结构。本手册将关键论证和伦理原则转化为清晰、易于消化的“公式”，帮助你在考前高效复习。每个条目都将一个核心主题拆解为其基本的逻辑流、定义或检验标准，让你能够掌握观点背后的推理过程，并在考试压力下准确回顾。
1. The Cosmological Argument: Formula of First Cause | 宇宙论论证：第一因公式
The Cosmological Argument follows this logical formula: Everything that begins to exist has a cause; the universe began to exist; therefore, the universe has a cause. This cause must itself be uncaused, eternal, and necessary — what believers call God. Aquinas' 'Second Way' chains it as: Cause1 → Cause2 → Cause3 … cannot go back infinitely; an infinite regress of causes is impossible, so a First Uncaused Cause (God) must exist.
宇宙论论证遵循此逻辑公式：一切开始存在之物皆有原因；宇宙开始存在；因此，宇宙有原因。此原因本身必是不被引起的、永恒且必然的——即信徒所称的上帝。阿奎那的“第二路”将其串联为：因₁ → 因₂ → 因₃ … 不能无限回溯；原因的无限回溯是不可能的，故必有一个第一不受动的推动者（上帝）。
Formally: If ΣCauses ≠ ∞, then ∃ God). This deductive move relies on the rejection of actual infinities in a causal series.
形式表达：若因果序列总和 ≠ ∞，则 ∃ 第一推动者（上帝）。这一演绎步骤依赖于对因果序列中实无限性的拒斥。
2. The Teleological Argument: Formula of Design | 目的论论证：设计公式
Paley' ner. The universe exhibits even greater complexity and purpose (e.g., the eye, planetary order) → therefore, the universe requires a supreme intelligent designer (God). The core inference fits: Design (complexity + purpose) → Designer.
佩利的钟表匠类比得出设计公式：一个各部分为某个目的协同运作的复杂物体（如表）→ 需要一个智能设计者。宇宙展示出更宏大的复杂性与目的性（如眼睛、行星秩序）→ 因此，宇宙需要一位至高的智能设计者（上帝）。核心推论可归纳为：设计（复杂性 + 目的性）→ 设计者。
Hume's critique can be expressed as a counter-formula: Design effect ∝ Designer features, so an imperfect universe implies an imperfect designer, not the God of classical theism. The leap from finite effect to infinite cause is a proportional error.
休谟的批判可表达为反向公式：设计结果与其设计者特征成正比，因此一个不完美的宇宙暗示一个不完美的设计者，而非古典有神论的上帝。从有限结果跃至无限原因是一种比例谬误。
3. The Ontological Argument: Anselm's Formula | 本体论论证：安瑟伦公式
Anselm's formula is a reductio ad absurdum: God is defined as 'that than which nothing greater can be conceived' we could conceive a greater being (one existing in reality). This contradicts the definition. Therefore, God must exist in reality. Formally: □(God is TTWNGCBC) → □∃ God.
安瑟伦的公式是一种归谬法：上帝被定义为“可设想之无与伦比者”（TTWNGCBC）。假设上帝仅存在于心灵中。存在于心灵且同时存在于现实的存有更为伟大。因此，若 TTWNGCBC 仅存在于心灵，我们便能设想一个更伟大者（在现实中存在的）。这与定义相矛盾。故上帝必存在于现实中。形式表达：□（上帝是 TTWNGCBC）→ □∃ 上帝。
Gaunilo’s 'Lost Island' counter-formula exposes the flaw: Define the greatest conceivable island; following Anselm's logic, it must exist in reality. Since this is absurd, the move from definition to existence is invalid without assuming God's necessary existence first.
高尼罗的“迷失岛”反向公式揭露了缺陷：定义可设想的最伟大岛屿；按安瑟伦的逻辑，它必存在于现实中。由于这显然是荒谬的，从定义到存在的推导若未先行假定上帝的必然存在则是无效的。
4. The Problem of Evil: Inconsistent Triad Formula | 恶的问题：不一致三元组公式
tions cannot all be true. If God is all-powerful and all-loving, He would eliminate all evil. Since evil exists, either God is not omnipotent, not omnibenevolent, or does not exist. The formula is: (Omnipotence ∧ Omnibenevolence ∧ Evil) → Logical Contradiction.
恶的逻辑问题呈现了一个不一致三元组：(1) 上帝全能；(2) 上帝全善；(3) 恶存在。这三个命题无法同时为真。若上帝全能与全善，祂理应消除一切恶。既然恶存在，则上帝要么不全能，要么不全善，要么不存在。公式为：（全能 ∧ 全善 ∧ 恶）→ 逻辑矛盾。
exists as a corruption, so God remains perfect. Formula: Free will → Possible moral evil → Soul-making; God's goodness is preserved because a world with free will and redemption is ultimately good.
奥古斯丁的神义论试图打破三元组：恶非实体，而是善的缺失（privatio boni），由自由意志的滥用引起。恶作为败坏存在，故上帝仍为完美。公式：自由意志 → 可能的道德恶 → 灵魂塑造；上帝的善得以保存，因一个拥有自由意志和救赎的世界最终是善的。
5. Utilitarianism: The Greatest Happiness Principle | 功利主义：最大幸福原则
Bentham' leasure) - Σ(Pain). The morally right action is the one that maximises net utility for all sentient beings affected. The formula: Action A is right iff A produces Max (ΣPleasureall - ΣPainall).
边沁的行为功利主义可表达为享乐计算：效用 = Σ(快乐) - Σ(痛苦)。道德上正确的行为，就是能为所有受影响的感性生命带来最大净效用的行为。公式：行为 A 是正确的，当且仅当 A 产生 Max（Σ快乐全体 - Σ痛苦全体）。
Mill' Pleasures × Quality weight) + (ΣLower Pleasures × Quality weight) - ΣPain. The principle remains: 'greatest happiness for the greatest number'.
密尔的修正引入了质的维度：高级快乐（智性、道德的）> 低级快乐（身体的）。于是公式变为：效用 =（Σ高级快乐 × 质量权重）+（Σ低级快乐 × 质量权重）- Σ痛苦。其核心原则仍是：“最大多数人的最大幸福”。
6. Kantian Ethics: The Categorical Imperative Formula | 康德伦理学：定言命令公式
Kant's first formulation of the Categorical Imperative acts as a universalizability test: ' to that maxim whereby you can at the same time will that it should become a universal law.' Formal test: Maxim M → Universalisable without contradiction? If yes, action is morally permissible; if no (contradiction in conception or will), the action is forbidden.
康德的第一定言命令公式作为可普遍化检验：“只依据那些你同时意欲其成为普遍法则的准则而行动。”形式检验：准则 M → 能否毫无矛盾地普遍化？若能，行为在道德上被许可；若否（构想中或意愿上出现矛盾），该行为被禁止。
The second formulation (humanity formula) states: '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.' Formula: Person ≠ Means-only; Agent must respect rational nature as an end-in-itself.
第二公式（人性公式）宣称：“务必如此行动，即无论是对待你自己人格中的人性，还是对待他人人格中的人性，永远同时当作目的，而绝不仅仅当作手段。”公式：人格 ≠ 纯工具；行动者必须尊重理性本性作为自在目的。
7. Situation Ethics: Agapeic Calculus | 情境伦理学：圣爱计算
Joseph Fletcher's Situation Ethics works on one principle: Agape (selfless, unconditional love) is the ultimate norm. The 'formula' for moral decision-making is: In situation S, do the most loving thing. There are four working principles: Pragmatism, Relativism, Positivism, Personalism. Love is the judge; no act is intrinsically right or wrong apart from love.
约瑟夫·弗莱彻的情境伦理学依据一个原则运作：圣爱（无私、无条件的爱）是终极规范。道德决策的“公式”是：在情境 S 中，做最具爱心的事。有四项工作原则：实用主义、相对主义、实证主义、人格主义。爱是判准；除爱之外，没有任何行为内在地是正确或错误的。
ct max(love, justice, personal wellbeing) for all involved. The consequentialist flavour means outcomes matter, but love alone measures utility. Even lying could be right if love demands it in the concrete situation.
因此，道德计算表达为：圣爱之举 = 为所有相关者最大化（爱、正义、人格福祉）的行为。其后果论色彩意味着结果举足轻重，但惟有爱衡量效用。若具体情境中爱的命令要求，撒谎亦可能正确。
8. Natural Law: Primary Precepts Formula | 自然法：基本戒律公式
Aquinas' Natural Law theory follows the formula: Eternal Law (God' self-evident goods). The five primary precepts are: preserve life, reproduce, educate offspring, live in society, and worship God. From these, secondary precepts are deduced via reason.
阿奎那的自然法理论遵循公式：永恒法（上帝的理性）→ 自然法（可由人类理性辨识）→ 基本戒律（自明的善）。五项基本戒律为：保存生命，生育繁衍，教育后代，在社会中生活，以及敬拜上帝。由此，次级戒律通过理性被推导出来。
The principle of double effect can be formulaically stated: An action having both good and evil effects is permissible if (a) the act itself is good or indifferent, (b) the good effect is intended and the evil merely tolerated, (c) the good effect is not achieved by means of the evil, and (d) there is a proportionate reason to allow the evil.
双重效果原则可以公式表达：一个兼有善恶效果的行为被许可，若 (a) 行为本身是善的或中性的，(b) 善效果被意图而恶效果仅被容许，(c) 善效果并非通过恶手段达成，且 (d) 存在相称的理由容许该恶效果发生。
9. Free Will and Determinism: The Compatibility Formula | 自由意志与决定论：相容性公式
s + laws of nature ∴ No alternative possibilities. Libertarianism counters: Some events (agent-caused) are uncaused, so free will exists. Formula: ∃ Agent-causation → free choice.
强决定论断言：决定论为真 → 自由意志为幻觉。简单公式：所有事件（包括选择）由先前的状态和自然法则决定 ∴ 没有其他可能性。自由意志论则反驳：某些事件（由行动者引起）并非被先行原因决定，故自由意志存在。公式：∃ 行动者引发 → 自由选择。
Compatibilism (soft determinism) proposes: Free will = acting according to one' hen you do what you want, without being forced, regardless of whether your desires are predetermined.
相容论（软决定论）主张：自由意志 = 依据本人未被强制的欲望行动，即使这些欲望本身是被决定的。公式：自由 = （内在原因 - 外在强制）。当你能做你想做的事且不受强制时，你便是自由的，无论你的欲望是否被预先决定。
10. Religious Experience: The Principle of Credulity | 宗教体验：轻信原则
n the absence of defeaters, probably X is present. Applied to God: S has an experience as of God → prima facie God exists. The formula: ExperienceGod + No defeaters → rational belief in God.
斯温伯恩的轻信原则为宗教体验提供了证成公式：若在一个主体 S 看来 X 在场，则在缺乏否决因素的情况下，很可能 X 确实在场。应用于上帝：S 拥有仿佛与上帝相遇的体验 → 初步看来上帝存在。公式：体验上帝 + 无否定因素 → 对上帝的理性信念。
The principle relies on the general reliability of our perceptual faculties unless shown otherwise. A defeat formula might be: ExperienceGod is unreliable if there are contradictory experiences, psychological explanations, or origin claims that reduce it to a natural phenomenon.
该原则依赖于我们知觉能力的一般可靠性，除非另有反证。否决公式可为：若存在相矛盾的体验、心理学解释，或者将该体验还原为自然现象的来源主张，则体验上帝 不可靠。
11. The Problem of the Soul: Mind-Body Dualism Formula | 灵魂问题：心身二元论公式
Descartes' conceivability argument for substance dualism can be expressed: I can clearly and distinctly conceive of myself existing without my body. Whatever is clearly and distinctly conceivable is metaphysically possible. ∴ It is possible that I exist without my body. ∴ I am not identical with my body; the mind is a separate substance. Formula: Mind ≠ Body; thought is the essence of mind, extension is the essence of body.
笛卡尔为实体二元论提出的可设想论证可表达为：我能清晰分明地设想自己独立于身体而存在。凡是清晰分明可设想者，都是形上学可能的。∴ 有可能我存在而身体不存在。∴ 我并非与身体同一；心灵是另一实体。公式：心灵 ≠ 身体；思维是心灵的本质，广延是身体的本质。
cess Y. Therefore, no separate substance is needed. The interaction problem for dualism is: If mind is non-physical, how does it cause physical actions? No formula bridges the gap without violating conservation laws.
唯物论的反向公式宣称：心理状态 = 脑状态。同一论：感觉 X = 神经过程 Y。因此，无需独立实体。二元论的交互问题在于：若心灵是非物质的，如何引发物理动作？任何公式若不违反守恒律则无法弥合此鸿沟。
12. Ethical Relativism vs. Objectivism: The Test Formula | 伦理相对主义与客观主义：检验公式
Cultural relativism formula: Moral rightness = Society's prevailing norms. Thus, 'X is right' means 'X is approved by my culture' . This seems counter-intuitive, so relativism is problematic as a formula for moral truth.
文化相对主义公式：道德正确性 = 社会的通行规范。因此，“X 是正确的”意味着“X 被我所在的文化认可”。反向检验：若相对主义为真，道德改革者（如威伯福斯）因反对通行规范而定义上即是错误的。这似乎违反直觉，故相对主义作为道德真理的公式是有问题的。
Ethical objectivism proposes: ∃ Mind-independent moral facts. Formula: If action A possesses property 'wrong' endent of opinion. This is often grounded in Natural Law or Divine Command: Morality = God' commands or rational nature; thus moral law is universal, not a matter of cultural taste.
伦理客观主义主张：∃ 独立于心灵之外的道德事实。公式：若行为 A 具有“错误”这一属性，则无论意见如何它都是错误的。这常奠基于自然法或神命论：道德 = 上帝的命令或理性本性；因此道德法则是普遍的，而非文化口味问题。
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