📚 GCSE Eduqas Philosophy: Formula & Theorem Quick Reference Handbook | GCSE Eduqas 哲学：公式定理速查手册
This quick reference handbook gathers the essential logical structures, ethical calculi, and argument forms encountered in the GCSE Eduqas Religious Studies (Philosophy & Ethics) course. Think of each entry as a ‘formula’ that captures the core reasoning of a major philosophical idea, enabling you to recall and apply it effectively in your examination essays.
本速查手册汇集了 GCSE Eduqas 宗教研究（哲学与伦理学）课程中遇到的基本逻辑结构、伦理计算式和论证形式。每一条目都可以看作一个“公式”，它捕捉了重大哲学思想的核心推理过程，使你在考试论文中能够有效地回忆并加以运用。
1. The Greatest Happiness Principle | 最大幸福原则
Utilitarianism proposes a moral calculus: an act is right if it tends to promote happiness, wrong if it tends to produce the reverse of happiness. The basic formula weighs the sum of pleasure against the sum of pain, with everyone’s happiness counting equally.
功利主义提出了一种道德计算：若一种行为倾向于增进幸福，它就是对的；若倾向于产生幸福的反面，它就是错的。基本公式是用快乐的总和减去痛苦的总和，且每个人的幸福都同等重要。
Greatest Happiness = Σ (Pleasure – Pain) for all sentient beings affected
最大幸福 = 所有受影响的众生之 (快乐 – 痛苦) 总和
Bentham’s version uses a hedonic calculus based on intensity, duration, certainty, propinquity, fecundity, purity and extent. Mill refines this by distinguishing higher and lower pleasures. In the exam, you can apply the formula to issues such as animal testing, euthanasia or theft.
边沁的版本采用基于强度、持续时间、确定性、临近性、丰饶性、纯度和范围的苦乐计算。密尔通过区分高级快乐与低级快乐对此加以改进。考试中，你可以将此公式应用于动物实验、安乐死或盗窃等问题。
2. Kant’s Categorical Imperative (Universal Law Formula) | 康德的定言命令（普遍法则公式）
Kant’s deontological ethics requires that we act only according to that maxim which we can at the same time will that it should become a universal law. The test is logical consistency: if the maxim cannot be universalised without contradiction, the act is morally forbidden.
康德的义务论伦理学要求，我们只应按照那些我们同时能够意愿其成为普遍法则的准则去行动。其检验标准是逻辑一致性：若一个准则无法在不导致矛盾的情况下被普遍化，那么该行为在道德上就是被禁止的。
Act only if: Maxim → Universal Law, without contradiction in conception or will
仅当：准则 → 普遍法则，而不在构想或意愿中产生矛盾时，才可行动
For example, making a false promise to obtain money cannot become a universal law because the institution of promising would collapse. Always treat humanity, whether in your own person or in the person of any other, never simply as a means, but always at the same time as an end.
例如，为获取钱财而做虚假承诺不可能成为普遍法则，因为承诺这一制度将会崩溃。始终把人当作目的，而不仅仅是手段，无论是对你自己还是对任何他人。
3. Situation Ethics: Agape Calculus | 情境伦理学：圣爱计算
Joseph Fletcher’s situation ethics is summed up in one rule: do the most loving thing (agape) in each situation. The ‘formula’ prioritises love over any fixed law.
约瑟夫·弗莱彻的情境伦理学可概括为一个规则：在每一情境中做最有爱心（圣爱）的事。这一“公式”将爱置于任何固定律法之上。
Agape Decision = Maximise neighbour’s well-being, guided by the ruling norm of love
圣爱决策 = 在爱的统领规范下，最大化邻人的福祉
There are four working principles: pragmatism, relativism, positivism and personalism. The only absolute is agape love. This allows breaking moral rules if love demands it, for instance, lying to protect an innocent life.
有四项实用原则：实用主义、相对主义、实证主义和个人主义。唯一的绝对就是圣爱。如果爱有这样的要求，它允许打破道德规则，例如为了保护无辜的生命而说谎。
4. Natural Law: Primary Precepts | 自然法：首要准则
Aquinas’ Natural Law theory argues that reason can discover God’s eternal law through the primary precepts. The fundamental formula is: do good and avoid evil, which unfolds into five primary purposes natural to human nature.
阿奎那的自然法理论主张，理性可以通过首要准则发现上帝的永恒法。基本公式是：行善避恶，这展开为人类本性所固有的五项目的。
Primary Precepts = Worship God, Ordered Society, Reproduce, Learn, Defend the Innocent
首要准则 = 敬拜上帝、有序社会、繁衍后代、学习、保护无辜
Secondary precepts are derived from these through human reasoning. An act is morally right if it fulfils the natural purpose for which a faculty was designed. Apparent goods that lead away from the true human telos are morally wrong.
次要准则通过人类推理从这些首要准则中导出。如果一个行为实现了某一官能的天赋目的，那么它就是道德上正确的。那些偏离人类真正终极目的的虚假善在道德上是错误的。
5. The Teleological (Design) Argument | 目的论（设计）论证
The design argument reasons from evidence of order, purpose and complexity in the world to the existence of a designer. Paley’s watchmaker analogy forms a classic inferential formula.
设计论证从世界中的秩序、目的和复杂性推理出一位设计者的存在。佩利的钟表匠类比构成了一个经典的推论公式。
Ordered complexity → Mind-like designer (by analogy), therefore God exists
有序的复杂性 → 类心智的设计者（通过类比），因此上帝存在
Swinburne updates this with the argument from probability, suggesting that the universe’s fine-tuning is more likely if God exists than if He does not. Criticisms such as Hume’s (dysteleology, multiple designers, apprentice gods) challenge the inference.
斯温伯恩以概率论证更新了这一观点，提出如果上帝存在，宇宙的微调比起他不存在时更具可能性。休谟等人的批判（反目的论、多个设计者、学徒神）对这一推论提出了挑战。
6. The Cosmological Argument | 宇宙论论证
Cosmological arguments move from the existence of the cosmos to a transcendent cause. Aquinas’ ‘Second Way’ uses the formula of efficient causality to arrive at a necessary first cause.
宇宙论论证从宇宙的存在出发，推导出一个超越的原因。阿奎那的“第二路”运用动力因的公式，得出一个必然的第一因。
Chain of causes → No infinite regress → Uncaused First Cause → God
因果链 → 无无穷回溯 → 非受动的第一因 → 上帝
The Kalam version (Al-Ghazali, Craig) focuses on temporal beginning: everything that begins to exist has a cause; the universe began to exist; therefore the universe has a cause, which is God. Objections question whether the universe needs a beginning and whether the first cause must be God.
卡拉姆版本（安萨里、克雷格）聚焦于时间性的开端：一切开始存在的事物都有原因；宇宙开始存在；因此宇宙有一个原因，即上帝。反对意见质疑宇宙是否必须有一个开端，以及第一因是否必须是上帝。
7. The Problem of Evil – Logical Formulation | 恶的问题——逻辑表述
The logical problem of evil challenges the coherence of theism by setting three attributes of God against the existence of evil. The inconsistent triad is often presented as a formula of contradiction.
恶的逻辑问题通过将上帝的三种属性与恶的存在对立起来，挑战有神论的一致性。这一矛盾三联式常以矛盾公式的形式提出。
God is omnipotent ∧ God is omnibenevolent ∧ Evil exists → Contradiction
上帝全能 ∧ 上帝全善 ∧ 恶存在 → 矛盾
Mackie argues that if any two of these are true, the third must be false. Responses include the free will defence (Plantinga) that morally significant free will justifies the possibility of evil; and the greater good defence that a world with challenges is better than a sheltered world.
麦基认为，如果其中任意两项为真，则第三项必定为假。回应包括自由意志辩护（普兰丁格），即道德上有意义的自由意志使恶的可能性成为正当；以及更大善的辩护，即一个充满挑战的世界优于一个受庇护的世界。
8. Religious Experience: Weight of Evidence | 宗教体验：证据权重
Arguments from religious experience employ a principle of credulity or testimony. Swinburne’s principle of credulity states that we should accept that things are as they appear to be unless we have defeating evidence.
来自宗教体验的论证采用了轻信原则或证词原则。斯温伯恩的轻信原则指出，我们应该接受事物如其所呈现的样子，除非我们拥有推翻它的证据。
If S seems to experience X, then probably X exists, until counter-evidence shown
若 S 似乎体验到了 X，那么 X 很可能存在，直至出现反面证据
Cumulative testimony from many traditions increases the probability. Criticisms point to conflicting claims, psychological explanations (Freud’s projection, neuroimaging), and the possibility of deception. A cumulative case can still be built by weighing consistency, fruits, and phenomenological depth.
来自多种传统的累积证词增加了概率。批判指向相互冲突的主张、心理学解释（弗洛伊德的投射、神经影像）以及欺骗的可能性。你依然可以通过衡量一致性、所结的果实与现象学深度来构建累积论证。
9. The Verification Principle | 可证实原则
The verification principle, associated with logical positivism, states that a statement is meaningful only if it is either analytic (true by definition) or empirically verifiable. Religious language is often challenged on this basis.
与逻辑实证主义相关联的可证实原则主张，一个陈述只有当它是分析性的（依定义为真）或在经验上可证实时，才是有意义的。宗教语言常常在这一基础上受到挑战。
Meaningful statement = Analytic truth ∨ Empirically verifiable (in principle)
有意义的陈述 = 分析性真理 ∨ 经验上可证实（原则上）
Ayer’s strong verificationism ruled out God-talk as meaningless. Weak verificationism (Hick, Flew) and the falsification principle refined the challenge. Wittgenstein’s language games and Braithwaite’s conative approach offer alternative models of meaning for religious language.
艾耶尔的强证实论将关于上帝的言说视为无意义。弱证实论（希克、弗卢）和证伪原则对挑战进行了改进。维特根斯坦的语言游戏和布雷斯韦特的意动进路为宗教语言提供了其他意义模型。
10. The Free Will Defence | 自由意志辩护
The free will defence offers a logically possible reason why a good God might permit moral evil. It can be summarised as a conditional formula that preserves divine attributes while explaining genuine human choice.
自由意志辩护提供了一个逻辑上可能的理由，解释一位良善的上帝为何会容许道德上的恶。它可以被概括为一个条件式公式，它在解释真正的人类选择的同时，维护了上帝的属性。
Morally significant freedom > No moral evil (but requires possibility of evil)
道德上有意义的自由 > 无道德恶（但需要恶的可能性）
Plantinga argues that it is possible that God could not create a world with free creatures who always choose the good, meaning God remains omnipotent in the sense that He can do all logically possible things. Critics question why God could not have created free beings who always freely choose good, and whether the amount of evil is proportionate.
普兰丁格论证，上帝有可能不可能创造一个自由受造物永远选择善的世界，这意味着在上帝能做一切逻辑上可能之事的意义上，他仍是全能的。批评者质疑为何上帝不能创造永远自由地选择善的存在，以及恶的量是否成比例。
11. Dualism and Materialism: Mind-Body Formulae | 二元论与唯物主义：心身公式
Philosophy of mind explores the relationship between consciousness and the physical body. Substance dualism and reductive materialism offer two competing ‘equations’ for the self.
心灵哲学探索意识与物理身体的关系。实体二元论与还原唯物主义为自我提供了两种对立的“方程”。
Substance Dualism: Self = Non-physical mind (soul) + Physical body, interacting
实体二元论：自我 = 非物理的心灵（灵魂）+ 物理身体，二者相互作用
Materialism: Self = Brain states; mind = Neurochemical processes
唯物主义：自我 = 大脑状态；心灵 = 神经化学过程
Descartes’ conceivability argument suggests that because I can conceive of myself existing without a body, mind and body are distinct substances. Materialists like Ryle and Churchland reject the ‘ghost in the machine’ and argue that talk of the mental can be reduced to brain talk. The survival of consciousness after death hinges on which formula is accepted.
笛卡尔的可设想性论证指出，既然我能设想自己脱离身体而存在，那么心灵与身体就是不同的实体。赖尔和丘奇兰德等唯物主义者拒斥“机器中的幽灵”，主张关于精神的言说可被还原为关于大脑的言说。死后意识是否继续存在，取决于我们接受哪一个方程式。
12. Miracles: Hume’s Criteria | 奇迹：休谟的标准
Hume defines a miracle as a violation of the laws of nature by a particular volition of the Deity. His criteria for evaluating miracle claims form a practical ‘credibility formula’ based on evidence and probability.
休谟将奇迹定义为自然法则被神明的某种特殊意志干预所打破。他用以评价奇迹主张的标准形成了一个基于证据与概率的实用“可信度公式”。
Credibility of miracle report ∝ Number/quality of witnesses, inversely ∝ Probability against miracle
奇迹报告可信度 ∝ 证人的数量/质量，反比于奇迹发生的先验概率
Hume concludes that no testimony is sufficient to establish a miracle unless the testimony is of such a kind that its falsehood would be more miraculous than the fact it tries to establish. Swinburne counters that if God exists, miracles are not improbable, urging a more Bayesian approach. Wiles rejects the idea of arbitrary interventions, arguing they portray God as a capricious tyrant.
休谟的结论是，除非有这样一种证词——其虚假比其试图证实的事实本身更为不可思议，否则没有任何证词足以证实一个奇迹。斯温伯恩反驳说，如果上帝存在，奇迹并非不可概率，他主张一种更贝叶斯式的进路。威尔斯反驳任意干预的观点，认为这会描绘出一个反复无常的暴君形象。
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