📚 A-Level OCR Philosophy: Quick Reference Handbook of Formulas and Theorems | A-Level OCR 哲学：公式定理速查手册
This revision guide collates the core logical structures, arguments and ethical principles that underpin the OCR A-Level Philosophy specification. Each entry is presented as a formulaic summary – a 'theorem' designed for rapid memorisation and precise application in essays. By distilling complex philosophical reasoning into concise forms, students can strengthen their analytical writing and secure high marks in both the Philosophy of Religion and Ethics components.
本复习手册汇集了支撑 OCR A-Level 哲学考纲的核心逻辑结构、论证与伦理学原则。每一个条目都以公式化的摘要——一种“定理”——呈现，旨在帮助快速记忆并在论文中精确运用。通过将复杂的哲学推理浓缩为简洁的形式，学生可以强化分析性写作，并在宗教哲学和伦理学两个部分中都获得高分。
1. Plato’s Theory of Forms | 柏拉图的理型论
Core Formula: ∀ objects in the material world (imperfect copies) ∃ a corresponding Form in the world of the Forms (perfect archetype). The Form of the Good illuminates all other Forms, just as the sun illuminates visible objects.
核心公式： 对于物质世界中的任何对象（不完美的摹本），在理型世界中均存在一个相应的理型（完美的原型）。善的理型犹如太阳照亮可见物体一般，照亮所有其他理型。
According to Plato, what we perceive through the senses is a shadow of true reality. A horse is a horse only because it partakes of the Form of Horse. Knowledge is a priori recollection of these Forms, accessed through reason. The Divided Line illustrates degrees of reality from eikasia (imaging) to noesis (understanding).
根据柏拉图，我们通过感官感知到的一切不过是真实存在的影子。一匹马之所以是马，只是因为它分有了马的理型。知识是对这些理型的先验回忆，通过理性获得。线段比喻展示了从想象到理智的不同实在程度。
2. Aristotle’s Four Causes | 亚里士多德的四因说
Formula for explaining any entity: de of) + Formal Cause (its essence or pattern) + Efficient Cause (the agent that brings it into being) + Final Cause (its telos, purpose).
解释任何实体的公式： 实体 = 质料因（由什么构成） + 形式因（其本质或模式） + 动力因（使其产生的施动者） + 目的因（其 telos，目的）。
Aristotle rejects the separate world of Forms. A statue’s material cause is marble, its formal cause is the shape of Athena, its efficient cause is the sculptor, and its final cause is to honour the goddess. The Prime Mover is pure actuality with no potentiality, moving the universe as a final cause – by attraction, not by mechanical push.
亚里士多德拒绝独立的理型世界。一座雕像的质料因是大理石，形式因是雅典娜的形状，动力因是雕刻家，目的因是尊崇女神。第一推动者是纯粹的现实，无任何潜能，它作为目的因推动宇宙——通过吸引，而非机械推动。
3. Ontological Argument (Anselm) | 本体论论证（安瑟伦）
Logical form:
P1: God is that-than-which-nothing-greater-can-be-conceived (the Greatest Conceivable Being, GCB).
P2: A being that exists both in the understanding (in intellectu) and in reality (in re) is greater than one existing only in the understanding.
C: Therefore, the GCB must exist in reality; otherwise it would not be the greatest conceivable.
逻辑形式：
P1：上帝是那不能设想有比之更伟大的存在者（可设想的无与伦比者，GCB）。
P2：既存在于理智中又存在于现实中的存在者，比仅存在于理智中的存在者更伟大。
C：因此，GCB 必然存在于现实之中；否则它就不是可设想的最伟大者。
Gaunilo’s parody reformulates the argument using a ‘perfect island’, showing that the same logical structure can ‘prove’ the existence of perfect absurdities. Kant’s retort: existence is not a predicate (a green apple has one more predicate than an apple; but a hundred real thalers do not contain the concept of a hundred possible thalers plus the predicate ‘existence’). The ontological argument thus commits a category mistake.
高尼罗的嘲讽用“完美的岛屿”重新表述了该论证，表明同样的逻辑结构可以“证明”荒谬至极的完美事物存在。康德的回应：存在不是谓词（一个青苹果比一个苹果多一个谓词；但一百个真实的塔勒并不包含一百个可能的塔勒的概念再加上“存在”这个谓词）。因此本体论论证犯了范畴错误。
4. Teleological Argument (Paley’s Watchmaker) | 设计论证（佩利的钟表匠）
Analogical formula:
P1: A watch shows complex parts arranged purposefully → it must have a watchmaker.
P2: The natural world exhibits even greater complex, purposeful arrangements (e.g., the eye).
C: Therefore, the natural world must have a supremely intelligent Designer (God).
类比公式：
P1：钟表展现复杂部件的有目的排列 → 必有一位钟表匠。
P2：自然界展现出甚至更复杂的、有目的的排列（例如眼睛）。
C：因此，自然界必然有一位拥有至高智慧的設計者（上帝）。
Hume’s criticisms, delivered through Philo, challenge the analogy: the world resembles a living organism or vegetable more than a machine; if God is analogous to a human mind, why not be an apprentice god or a team of gods? The epicurean hypothesis of random atomic swerves can also account for apparent design over infinite time. Darwin’s principle of natural selection provides a non-intentional mechanism that creates design without a designer.
休谟通过菲洛提出的批判挑战了这一类比：世界更类似一个活生生的有机体或蔬菜，而非机器；如果上帝类似于人类心智，何不假设是一个学徒神或一组神呢？伊壁鸠鲁的原子随机偏斜假说也可以在无限时间中解释看似设计之物。达尔文的自然选择原理则提供了一种无意向的机制，创造出无設計者的設計。
5. Cosmological Argument (Aquinas’ First Three Ways) | 宇宙论论证（阿奎那的前三种方式）
Way 1 (Motion):
(1) Some things are in motion. (2) Everything in motion is moved by another. (3) Infinite regress of movers is impossible. (4) Therefore, there must be a first mover, itself unmoved. ≡ God.
方式一（运动）：
（1）某些事物处于运动之中。（2）一切运动之物皆被他物推动。（3）推动者的无限回溯是不可能的。（4）因此，必有第一推动者，自身不被推动。≡ 上帝。
Way 2 (Causation): e but applied to efficient causes. No infinite regress of causes → a first uncaused cause.
Way 3 (Contingency): (1) Contingent beings exist (things that can not-exist). (2) If at some time nothing existed, nothing would exist now. (3) But things exist now. (4) Therefore, there must be a necessary being that never did not-exist, which is God.
方式二（原因）： 相同结构，应用于动力因。无法无限回溯的原因 → 第一无因之因。
方式三（偶然性）： （1）偶然存在者存在（能够不存在的事物）。（2）如果在某个时间点什么都不存在，那么现在什么都不会存在。（3）但事物现在存在。（4）因此，必然存在一个从不曾不存在的必然存在者，即上帝。
Hume and Russell attack the principle of sufficient reason and the validity of inferring a cause for the whole universe from our experience of parts. The fallacy of composition arises: because each member of the universe has a cause, it does not follow that the universe as a whole has a cause.
休谟和罗素攻击充足理由律，以及从我们对部分的经验推断整个宇宙有一原因的有效性。这引发了合成谬误：因为宇宙中的每个成员都有原因，并不能推出宇宙整体有原因。
6. The Problem of Evil | 恶的问题
The Inconsistent Triad (Epicurus, formulated by Hume):
(1) God is omnipotent. (2) God is omnibenevolent. (3) Evil exists. If God is willing but unable to prevent evil, He is not omnipotent. If able but unwilling, He is not omnibenevolent. If both willing and able, whence evil? These three propositions cannot all be true simultaneously.
不一致三元组（伊壁鸠鲁，经休谟系统表述）：
（1）上帝是全能的。（2）上帝是全善的。（3）恶存在。如果上帝愿意但无法阻止恶，则他并非全能。如果有能力但不愿意，则他并非全善。如果既愿意又有能力，恶从何来？这三项命题无法同时为真。
The logical problem of evil claims a contradiction exists. The evidential problem concedes that the existence of God and evil are logically compatible but argues that the sheer amount and gratuitous nature of suffering makes theism highly improbable. Theodicies are ‘formulas’ attempting to dissolve the contradiction. The free will defence (Plantinga) asserts that it is logically impossible for God to create free creatures who always freely choose good; therefore God cannot be blamed for moral evil. The soul-making theodicy (Irenaeus, Hick) proposes that evil is a necessary environment for spiritual growth.
恶的逻辑命题声称存在矛盾。恶的证据命题则承认上帝与恶在逻辑上兼容，但论证大量且无端的苦难使得有神论高度不可能。神义论是试图化解矛盾的“公式”。自由意志辩护（普兰丁格）断言，上帝在逻辑上不可能创造出总是自由选择善的自由受造物；因此道德恶不能归咎于上帝。灵魂塑造神义论（爱任纽、希克）指出，恶是灵魂成长的必要环境。
7. Religious Language | 宗教语言
Verification Principle (Ayer): A statement is meaningful only if it is either analytic (true by definition) or empirically verifiable (in principle). ‘God loves us’ is neither analytic nor verifiable, thus it is a pseudo-statement, mere emotive expression.
证实原则（艾耶尔）： 仅当一个陈述要么是分析命题（凭定义即真），要么是经验上可证实的（原则上可验证）时，它才是有意义的。“上帝爱我们”既非分析命题也非可证实命题，因此它是伪陈述，仅仅是情感表达。
Falsification Principle (Flew): A statement has meaning if the speaker can specify what would count as falsifying it. Religious believers allow nothing to count against ‘God loves us’, even massive suffering (they qualify it: ‘God’s love is inscrutable’). Thus the statement dies the death of a thousand qualifications and becomes vacuous.
证伪原则（弗卢）： 若说话者能指明怎样才算是证伪了一个陈述，该陈述才有意义。宗教徒不让任何事物驳斥“上帝爱我们”，即便面对巨大的苦难（他们会限定：“上帝的爱不可测度”）。因此该陈述死于千般限定的死亡，变得空洞无物。
Wittgenstein’s Language Games: Meaning emerges from use within a form of life. Religious language is its own autonomous language-game with internal criteria of sense, immune to external scientific verification. One can only understand it by participating in the believer’s form of life.
维特根斯坦的语言游戏： 意义源于在生活形式中的使用。宗教语言有其自身自主的语言游戏，拥有内部的意义标准，不受外部科学验证的免疫。只有参与到信徒的生活形式中，才能理解宗教语言。
8. Kantian Deontological Ethics | 康德义务论伦理学
Formula of the Universal Law (First Formulation of the Categorical Imperative):
“Act only according to that maxim whereby you can at the same time will that it should become a universal law.”
普遍法则公式（定言命令的第一表述）：
“要只按照你同时能够愿意它成为一条普遍法则的那个准则去行动。”
Test: (1) Contradiction in conception: if everyone followed the maxim, would the concept become self-defeating? E.g., a false promise would annihilate the institution of promises. (2) Contradiction in will: even if logically possible, can a rational agent consistently will such a world? E.g., a world where no one helps others cannot be willed because human beings inevitably need help.
检验：（1）概念上的矛盾：如果人人遵循此准则，该概念是否会自我挫败？例如，虚假承诺会摧毁承诺制度。（2）意志上的矛盾：即便逻辑上可能，理性行动者能否一贯地意愿这样一个世界？例如，无人帮助他人的世界不可意愿，因为人必然需要帮助。
Formula of the End in Itself: “Act in such a way that you treat humanity, whether in your own person or in any other, always at the same time as an end, never merely as a means.” Rational nature has dignity, not price.
目的本身公式： “你应当这样行动，即无论在你的人格还是在其他任何一个人的人格中，你都始终把人当作目的，而绝不仅仅当作手段来对待。”理性本性拥有尊严，而非价格。
9. Utilitarianism (Bentham and Mill) | 功利主义（边沁和密尔）
Principle of Utility (Bentham’s Hedonic Calculus): An action is right if it tends to maximize pleasure and minimize pain for the greatest number. The formula includes seven factors: intensity, duration, certainty, propinquity, fecundity, purity, and extent. Morality is quantifiable.
功利原则（边沁的快乐度量表）： 一个行为若是趋向于为最大多数人创造最大快乐并最小化痛苦，则是正确的。公式包含七个因子：强度、持续时间、确定性、邻近性、继生性、纯度和范围。道德是可量化的。
Mill amended Bentham’s quantitative scheme: pleasures are qualitatively distinct. He introduces the formula of higher and lower pleasures: “It is better to be a human being dissatisfied than a pig satisfied; better to be Socrates dissatisfied than a fool satisfied.” The competent judge test is used to determine which pleasures are of higher quality.
密尔修正了边沁的量化方案：快乐有质的区别。他引入了高等级与低等级快乐的公式：“做一个不满足的人胜于做一只满足的猪；做不满足的苏格拉底胜于做一个满足的傻瓜。” 胜任法官测试被用来判定何种快乐品级更高。
Act utilitarianism calculates the utility of each individual act. Rule utilitarianism (Mill can be interpreted this way) calculates which general rules, if universally followed, would maximise utility. Strong rule utilitarianism: never break rules even if an exception would bring more utility; weak rule: rules may be broken in extreme cases.
行为功利主义计算每个个别行为的效用。规则功利主义（密尔可被如此解读）计算哪些一般规则若被普遍遵守便会最大化效用。强规则功利主义：永不违反规则，即便例外情况能带来更多效用；弱规则：在极端情况下可以打破规则。
10. Natural Law Theory (Aquinas) | 自然法理论（阿奎那）
Four Tiers of Law Formula: the rational creature in the Eternal Law) → Human Law (positive law devised by societies).
四个层级法律公式： 永恒法（治理宇宙的神圣智慧） → 神法（于经文中启示） → 自然法（理性可及，理性受造物对永恒法的分有） → 人法（由社会制定的实证法）。
The Synderesis Rule: The primary precept is: “Good is to be done and pursued, and evil is to be avoided.” From this, reason derives five primary precepts based on natural inclinations: preservation of life, reproduction and education of young, living in society, seeking truth, and worshipping God. Secondary precepts are the logical applications of these.
良知规则： 首要诫命是：“行善避恶”。理性据此依据自然倾向推导出五项首要训令：保存生命、繁衍并教育后代、在社会中生活、追求真理、崇拜上帝。次要训令是这些训令的逻辑应用。
The doctrine of double effect provides a formula for resolving moral dilemmas: an act with both a good and a bad effect is permitted if (1) the act itself is good or neutral, (2) the good effect is intended and the bad merely foreseen, (3) the bad effect is not the means to the good effect, and (4) there is proportionate reason for permitting the bad effect.
双重效果学说提供了解决道德困境的公式：一个同时有善恶效果的行为被允许，若满足（1）行为本身是善的或中性的，（2）善果是意图的而恶果只是预见的，（3）恶果不是达成善果的手段，（4）有相称的理由容许恶果。
11. Situation Ethics (Fletcher) | 境遇伦理学（弗莱彻）
Agapeistic Calculus: There is only one absolute norm: agape (self-giving, unconditional love). The formula for moral judgment is: Love’s decision is made situationally, not prescriptively. The four working principles: pragmatism, relativism, positivism, personalism. Action is right if it serves love in that context – even if it breaks traditional moral rules.
爱之计算： 唯有一个绝对准则：agape（舍己、无条件的爱）。道德判断的公式是：爱的决定是境遇化的，而非规定性的。四项工作原则：实用主义、相对主义、实证主义、人格至上论。一个行为若在特定情境中服务了爱，便是正确的——即使它打破传统道德规则。
Fletcher’s six fundamental propositions operationalise the formula: (1) Only love is intrinsically good. (2) Love is the ruling norm of moral choice. (3) Love and justice are the same, for justice is love distributed. (4) Love wills the neighbour’s good whether we like him or not. (5) Only the end justifies the means; nothing else does. (6) Love’s decisions are made situationally, not prescriptively.
弗莱彻的六项基本命题将公式具体化：（1）唯有爱是内在善的。（2）爱是道德选择的统治性准则。（3）爱与正义等同，因为正义是被分配了的爱。（4）爱是意愿邻人的善，不论我们是否喜欢他。（5）唯有目的能证成手段，别无其他。（6）爱的决定是境遇化的，而非规定性的。
12. Free Will and Determinism | 自由意志与决定论
Hard Determinism Formula: All events, including human actions, are the necessary result of prior causes. Given antecedent conditions and the laws of nature, only one future is possible. Therefore, free will is an illusion. D’Holbach and more recently biological determinism exemplify this. This is incompatibilist: free will and determinism cannot coexist.
强决定论公式： 所有事件，包括人类行动，都是先行原因的必然结果。给定先行条件与自然法则，只有一種未来是可能的。因此，自由意志是假象。霍尔巴赫以及近期的生物决定论即是例证。这属于不兼容论：自由意志与决定论无法并存。
Libertarianism Formula: The agent is the undetermined first cause of a free action. Actions are caused by the agent, but the agent’s choice is not causally determined by prior events. This requires a special kind of causation (agent causation) or quantum indeterminacy. Moral responsibility demands this contra-causal freedom. (Associated with Kant, Campbell, some dualist views).
自由意志论公式： 行动者是自由行动的、非被决定的第一因。行动由行动者引发，但行动者的选择并非由先在事件因果决定。这需要一种特殊的因果类型（行动者因果）或量子不确定性。道德责任要求这种反对因果的自由。（关联康德、坎贝尔、某些二元论观点）。
Soft Determinism / Compatibilism (Hume): aint and the ability to act according to one’s own desires and will. An action is free if you could have done otherwise had you willed otherwise, even though your will itself is determined. The formula separates action from the will’s origin. Moral responsibility is preserved because punishment serves to modify future desires.
弱决定论 / 兼容论（休谟）： 自由 = 没有外在强制及按照自身欲求和意志行动的能力。一個行動是自由的，如果你若意愿不同就能做出不同行动，即使你的意志本身是被决定的。该公式将行动与意志的起源分开。道德责任得以保留，因为惩罚用于调整未来的欲求。
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