📚 Year 9 WJEC Philosophy: Formulas & Theorems Quick Revision Guide | Year 9 WJEC 哲学：公式定理速查手册
In philosophy, we do not work with numbers and chemical equations, but we do use logical patterns, ethical principles and arguments that behave like 'formulas'. This quick revision guide collects the most important 'formulas' and 'theorems' you will encounter in the Year 9 WJEC Philosophy course. Each section presents a central idea as a structured formula, explains how it works, and gives you the paired English and Chinese explanations needed to master the material. Keep this handbook close as you explore the big questions about God, ethics and meaning.
在哲学中，我们不与数字和化学方程式打交道，但我们会使用逻辑模式、伦理原则和论证，它们就像“公式”一样运作。这份速查手册汇集了你将在 Year 9 WJEC 哲学课程中遇到的最重要的“公式”与“定理”。每个小节都将一个核心思想呈现为一个结构化的公式，解释其运作方式，并为你提供配对的中英文解释，以便掌握这些材料。在探索关于上帝、伦理和意义的大问题时，请把这份手册放在手边。
1. The Design Argument Formula | 设计论证公式
ct of an intelligent designer. A watch → a watchmaker; the natural world (e.g., the human eye) → a divine designer.
目的论论证使用一个简单的条件公式：如果某物表现出复杂性、秩序和目的，那么它极有可能是智慧设计者的产物。钟表 → 钟表匠；自然界（例如人眼） → 一位神圣的设计者。
(Complexity ∧ Purpose ∧ Regularity) → Intelligent Designer
- English: Paley's watch analogy: finding a watch on a heath leads us to infer a watchmaker, even if we have never seen one made. The universe is far more intricate, so by analogy we infer a cosmic designer.
- 中文：佩利的钟表类比：在荒野上发现一块表，我们会推断存在钟表匠，即便从未见过制造过程。宇宙更为精妙，因此通过类比我们推断有一位宇宙设计者。
- English: Critics point to evolution by natural selection as an alternative 'designer-free' formula: complex organisms arise through random mutation and environmental selection over deep time.
- 中文：批评者指出，通过自然选择的进化是一个替代的“无设计者”公式：复杂生物体在漫长的时间中通过随机突变和环境选择而产生。
2. The Cosmological Argument Formula | 宇宙论论证公式
The Cosmological Argument works like a causal chain formula. It holds that every event or thing has a cause; an infinite chain of causes is impossible; therefore a First Cause must exist, and this is identified as God.
宇宙论论证类似于一条因果链公式。它认为每一个事件或事物都有一个原因；无限的因果回溯是不可能的；因此必然存在一个第一因，并被认定是上帝。
∀x (x exists → x has a cause), ¬∃ an actual infinite series → ∃ First Cause (God)
- English: Aquinas' Second Way: we observe a sequence of efficient causes in the world. If you remove a cause, you remove its effect. To avoid an infinite regress, there must be a first uncaused cause. This we call God.
- 中文：阿奎那的第二路：我们观察到世界上有效率因的序列。如果移除一个原因，便移除了其结果。为避免无限回溯，必有一个不被其他原因推动的第一因。我们称其为上帝。
- English: A key challenge: why must the first cause be the God of classical theism? Could it be an impersonal force? And does the universe itself necessarily need a beginning?
- 中文：一个重要挑战：为何第一因必定是古典有神论的上帝？它可能是一种非人格的力量吗？宇宙本身必须有开端吗？
3. The Ontological Argument Formula | 本体论论证公式
The Ontological Argument is a logical, a priori 'formula' that attempts to define God into existence. It states: God is the greatest conceivable being. Existence in reality is greater than existence only in the mind. Therefore, God must exist in reality.
本体论论证是一个逻辑的、先验的“公式”，试图通过定义证明上帝存在。它声称：上帝是可设想的最伟大存在。在现实中存在比仅在心灵中存在更伟大。因此，上帝必然在现实中存在。
than which nothing greater can be conceived → Existence in intellectu & in re → God exists
- English: Anselm's version: even the fool who says 'God does not exist' understands the concept of a supremely perfect being. But a perfect being lacking existence would be less than perfect. So God must exist.
- 中文：安瑟伦的版本：即使说“上帝不存在”的愚人也理解一个最完美存在的概念。但一个缺乏存在性的完美之物将不那么完美。因此上帝必须存在。
- English: Gaunilo replied using the perfect island: one can define a perfect island, but that does not make it exist. Kant later argued that existence is not a predicate that adds to the concept of a thing.
- 中文：高尼罗用完美岛屿回应：可以定义一座完美岛屿，但这并不能使它存在。康德后来论证，存在不是一个可以附加到事物概念上的谓词。
4. The Problem of Evil Logical Formula | 恶的逻辑问题公式
The logical problem of evil presents an inconsistency formula: If God is all-powerful, all-loving and all-knowing, then evil should not exist. Evil does exist. Therefore, such a God does not exist. This is sometimes called the inconsistent triad.
恶的逻辑问题提出了一个不一致公式：如果上帝全能、全爱、全知，则恶不应存在。恶确实存在。因此，这样的上帝不存在。这有时被称为不一致三角。
(Omnipotence ∧ Omnibenevolence ∧ Omniscience) ∧ (Evil exists) → Contradiction
- English: Epicurus formulated it: If God is willing but unable to prevent evil, He is not omnipotent. If able but unwilling, He is not benevolvent. If willing and able, whence cometh evil?
- 中文：伊壁鸠鲁的表述：如果上帝愿意但无法阻止恶，则非全能。如果能够但不愿意，则非全爱。如果愿意且能够，恶又从何而来？
- English: A theistic response formula is the 'greater good defence': evil is logically necessary for certain higher goods, such as free will, moral courage and soul-making. A world with free beings that sometimes choose wrongly is better than a world of automata.
- 中文：有神论的一个回应公式是“更大的善辩护”：恶在逻辑上对于某些更高的善是必要的，比如自由意志、道德勇气和灵魂塑造。一个拥有自由却有时犯错的世界优于一个全是机器人的世界。
5. The Utilitarian Calculus | 功利主义计算
Classical Utilitarianism operates as a happiness-maximising formula. The right action is the one that produces the greatest net balance of pleasure over pain for all affected. This can be expressed as a simple utilitarian sum.
古典功利主义运作起来就像一个幸福最大化公式。正确的行为是能为所有受影响者带来最大快乐净余额的行为。这可以表示为一个简单的功利主义总和。
Total Happiness = Σ (Pleasure units – Pain units) for all sentient beings
- English: Bentham's felicific calculus considered seven factors: intensity, duration, certainty, propinquity, fecundity, purity and extent. The action with the highest total is the moral duty.
- 中文：边沁的苦乐计算考虑了七个因素：强度、持续时间、确定性、远近、衍生性、纯度和范围。总量最高的行为即为道德义务。
- English: Mill refined the formula by distinguishing higher (intellectual) pleasures from lower (physical) pleasures. 'It is better to be a human being dissatisfied than a pig satisfied.'
- 中文：密尔通过区分高级（精神）快乐和低级（肉体）快乐改进了公式。“宁做不满足的人，不做满足的猪。”
6. Kant's Categorical Imperative Formula | 康德绝对命令公式
Kant's moral law is not a calculation of consequences but a principle of universalisation. The first formulation is a logical test: Act only according to that maxim whereby you can at the same time will that it should become a universal law without contradiction.
康德的道德法则不是结果的计算，而是一条普遍化原则。第一个表述是一个逻辑测试：只按照你同时能够愿意它成为一条普遍法则的准则去行动，而不致产生矛盾。
Maxim → Test: Can it be universalised without contradiction? If yes → Permissible; If no → Impermissible
- English: The lying promise example: if everyone made false promises, the institution of promising would collapse, so the maxim cannot be universalised. Therefore, lying promises are wrong. The formula reveals duties by logical consistency.
- 中文：虚假承诺的例子：如果每个人都作出虚假承诺，承诺制度将崩溃，因此该准则不能被普遍化。所以虚假承诺是错误的。该公式通过逻辑一致性揭示义务。
- English: The second formula treats humanity as an end in itself, never merely as a means. This gives us an absolute protection of rational beings: do not exploit or use people.
- 中文：第二个公式要求将人当作目的本身，而绝不仅仅当作手段。这赋予理性存在者绝对的保护：不要剥削或利用他人。
7. Moral Relativism Formula | 道德相对主义公式
Moral relativism can be captured by a contextual truth formula: A moral judgement of the form 'Action X is right' is true only relative to a particular cultural or personal framework. There is no universal, cross-cultural moral metric.
道德相对主义可以用一个语境真值公式来概括：具有“行为 X 是正确的”这一形式的道德判断，只有相对于特定的文化或个人框架才为真。不存在普遍的、跨文化的道德标尺。
Truth-value of moral statement S = f(culture, historical period, individual perspective)
- English: Cultural relativism observes that different societies hold different moral codes. The 'formula' tells us we cannot legitimately judge another culture's practices by our own standards, because morality is culturally defined.
- 中文：文化相对主义观察到，不同社会持有不同的道德准则。这个“公式”告诉我们，不能合法地用我们自己的标准去评判另一文化的习俗，因为道德是由文化定义的。
- English: A major criticism is the reformer's dilemma: if morality is entirely relative to culture, then moral reformers like Martin Luther King Jr. would be automatically wrong when criticising their own society's norms.
- 中文：一个主要批评是改革者困境：如果道德完全相对于文化，那么像马丁·路德·金这样的道德改革者在批评自己社会的规范时，就会自动是错的。
8. Pascal's Wager Formula | 帕斯卡的赌注公式
Pascal's Wager treats belief in God as an expected value calculation. It uses a decision matrix: if you believe and God exists, the reward is infinite (heaven); if you disbelieve and God exists, the punishment is infinite. The rational choice is to believe.
帕斯卡的赌注把信仰上帝看作一个期望值计算。它使用一个决策矩阵：如果你相信而上帝存在，奖赏是无限（天堂）；如果你不相信而上帝存在，惩罚是无限的。理性的选择是相信。
Expected value (believe) = ∞, Expected value (disbelieve) = -∞ → Choose belief
| Choice / God exists? | God exists | God does not exist |
|---|---|---|
| Believe | Infinite reward | Limited loss |
| Disbelieve | Infinite punishment | Limited gain |
- English: The wager is not a proof of God but a prudential argument: given the possible outcomes, the safest bet is to live as though God exists. Many philosophers object that one cannot simply decide to believe, and that the wager assumes only one possible God.
- 中文：该赌注并不是对上帝的证明，而是一个审慎论证：考虑到可能的结果，最安全的赌注就是活得仿佛上帝存在。许多哲学家反对说，人无法简单地决定去相信，而且该赌注只假设了一种可能的上帝。
9. The Religious Experience Evidence Formula | 宗教经验证据公式
The argument from religious experience proposes a direct experiential formula: If a person sincerely has an experience that seems to be of God, and there is no overriding reason to doubt it, then it is reasonable to believe that God exists. These experiences are treated as analogous to sensory perception.
来自宗教经验的论证提出了一个直接经验公式：如果一个人真诚地拥有看似来自上帝的经验，且没有压倒性的理由去怀疑，那么相信上帝存在就是合理的。这些经验被视为类似于感官知觉。
Experiencer testimony + principle of credulity → Justified belief in God
- English: Richard Swinburne's principle of credulity suggests we should trust our experiences unless we have a defeater. If millions testify to a sense of divine presence, this cumulatively strengthens the case for God.
- 中文：理查德·斯温伯恩的轻信原则表明，除非我们有否决理由，否则应该相信自己的经验。如果数百万人见证了神圣的存在感，这会累积地加强上帝存在的论据。
- English: Challenges ask whether religious experiences are merely psychological projections, wish-fulfilment or explainable through neuroscience. The formula only works if the experience genuinely originates from a transcendent reality.
- 中文：挑战在于，宗教经验是否仅仅是心理投射、愿望满足或可通过神经科学解释。只有当经验真正源于超越的实在时，这个公式才有效。
10. The Miracles Verification Formula | 奇迹验证公式
Hume's approach to miracles gives us a probability formula: a miracle is a violation of the laws of nature by a supernatural agent. Testimony for a miracle must be weighed against the uniform evidence for natural law. A wise person proportions belief to the evidence.
休谟处理奇迹的方法给我们一个概率公式：奇迹是超自然动因对自然法则的违反。关于奇迹的证据必须与支持自然法则的一致证据相权衡。一个明智的人会根据证据比例来调整其信念。
P(Miracle|Testimony) > P(Natural law violation event) only if testimony is overwhelmingly strong
- English: Hume's maxim: 'no testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavours to establish.' This sets a very high evidential bar.
- 中文：休谟的格言：“没有任何证词足以建立一个奇迹，除非该证词的虚假性比它试图建立的事实更加不可思议。”这设定了一个很高的证据门槛。
- English: Modern miracle claims are tested by historical criteria. The resurrection of Jesus, for instance, is debated through the 'minimal facts' approach that seeks historically attested events open to natural or supernatural explanation.
- 中文：现代的奇迹声称通过历史标准来检验。例如，耶稣的复活通过“最低限度事实”方法进行辩论，该方法寻找历史上可证伪的事件，这些事件可用自然或超自然的方式解释。
11. Natural Law Primary Precepts Formula | 自然法首要规条公式
Aquinas' Natural Law theory offers a practical reasoning formula based on the synderesis rule: do good and avoid evil. From this, we derive the primary precepts: preservation of life, reproduction, education of the young, living in society, and worshipping God.
阿奎那的自然法理论提供了一个基于良知规则（趋善避恶）的实践推理公式。由此我们推导出首要规条：保存生命、繁衍后代、教育幼儿、社会生活、敬拜上帝。
Synderesis: Good must be done and evil avoided → Primary Precepts → Secondary Precepts
- English: The 'formula' works by reflection on natural inclinations. Because we naturally seek to live, to reproduce and to seek truth, these inclinations reveal the divine plan for human flourishing. The secondary precepts are the detailed rules derived from these.
- 中文：该“公式”通过对自然倾向的反思而起作用。因为我们自然地寻求生存、繁衍和寻求真理，这些倾向揭示了人类繁荣的神圣计划。次级规条就是从这些倾向推导出的详细规则。
- English: The doctrine of double effect is a sub-formula: an action causing a bad effect is permissible if the intention is good, the bad effect is not directly intended, and there is a proportionate reason. For example, saving a mother's life even if it sadly results in the loss of the unborn child.
- 中文：双重效果论是一个子公式：如果意图是善的，坏效果不是直接意图的，且有相称的理由，那么引起坏效果的行为是允许的。例如，拯救母亲的生命，即使不幸导致未出生婴儿的死亡。
12. Situation Ethics Agapeic Formula | 情境伦理学的爱佳法公式
Joseph Fletcher's Situation Ethics relies on a single central formula: The ruling norm of Christian decision-making is love (agape) and nothing else. Each situation is unique, so the sole absolute is to calculate the most loving outcome.
约瑟夫·弗莱彻的情境伦理学依赖于一个单一的核心公式：基督教决策的最高准则是爱（佳爱），别无其他。每个情境都是独特的，因此唯一的绝对就是要计算出最有爱心的结果。
ape (unselfish love) = sole intrinsic good → Act so as to maximise agape in each situation
- English: Fletcher proposed four working principles: pragmatism, relativism, positivism and personalism. The decision-making 'formula' asks: 'What is the most loving thing to do in this specific situation?' Love is justice distributed.
- 中文：弗莱彻提出了四项运作原则：实用主义、相对主义、实证主义和位格主义。决策的“公式”会问：“在这个具体情境中，最有爱心的事情是什么？”爱是分配的正义。
- English: Critics argue that abandoning moral rules makes ethical reasoning unpredictable and may justify terrible actions if they are claimed to be motivated by love. A formula relying purely on context can be manipulated.
- 中文：批评者认为，抛弃道德规则会使伦理推理不可预测，并且如果声称是由爱驱动的，可能会使可怕的行为合理化。一个纯粹依赖情境的公式容易被操纵。
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