📚 Year 11 AQA Philosophy: Formula & Theorem Quick Reference | AQA 哲学：公式定理速查手册
Philosophy at GCSE level often involves mastering key arguments as if they were logical formulas. Each theistic proof, ethical theory, or logical dilemma can be broken down into premises and conclusions, making them easier to recall in an exam. This quick reference presents the core 'formulae' of the AQA Philosophy syllabus in a structured, bilingual format, helping you see the logical skeleton of each idea.
GCSE 阶段的哲学考试常常要求学生像掌握数学公式一样掌握核心论证。每一个有神论证明、伦理理论或逻辑难题都可以拆解为前提与结论，从而在考试中更容易回忆与运用。这份速查手册以结构化的双语形式梳理 AQA 哲学大纲的核心“公式”，帮你直观把握每一个思想的逻辑骨架。
1. The Cosmological Argument Formula | 宇宙论论证公式
The Cosmological Argument, particularly Aquinas' First Way, can be expressed as a chain of causation that cannot regress infinitely. It is an a posteriori argument moving from observable motion to a first unmoved mover.
宇宙论论证，尤其是阿奎那的第一推动者论证，可以表达为一条不能无限回溯的因果链。这是一个从可观察的运动推导出第一推动者的后天论证。
P1: Some things are in motion (change).
P2: Whatever is moved is moved by another.
P3: This chain of movers cannot go on to infinity.
∴ There must exist a first unmoved mover (God).
The formula relies on the rejection of an infinite regress of movers. If each mover requires a prior mover, an infinite chain would mean no first mover, and thus no subsequent motion. Since motion exists, a first mover is logically necessary.
这个公式依赖于拒绝推动者的无限回溯。如果每个推动者都需要在先的推动者，那么无穷的链条意味着根本没有第一推动者，从而也就没有任何后续的运动。既然运动存在，第一推动者在逻辑上就是必要的。
2. The Teleological Argument Formula | 目的论论证公式
Paley's watchmaker analogy gives a classic design argument structure. The argument infers an intelligent designer from apparent order and purpose in the world.
佩利的钟表匠类比提供了一个经典的设计论证结构。该论证从世界中明显的秩序与目的推导出智能设计者的存在。
P1: The natural world exhibits complexity, order, and purpose (e.g. the eye).
P2: Such characteristics are always produced by an intelligent designer in human artefacts (e.g. a watch).
P3: Similar effects imply similar causes.
∴ The natural world has an intelligent designer (God).
Hume and Mill criticised the analogy, arguing that the universe is too unique for such a comparison and that observed flaws (evil) contradict the notion of a perfect designer. Darwin's theory of evolution provides an alternative explanation of apparent design through natural selection.
休谟和密尔批评了这一类比，认为宇宙太过独特，无法这样比较，而且可以观察到的缺陷（恶）与完美设计者的概念相矛盾。达尔文的进化论通过自然选择为表面上的设计提供了另一种解释。
3. The Ontological Argument Formula | 本体论论证公式
Anselm's ontological argument is a priori, attempting to deduce God's existence from the very concept of God as 'that than which nothing greater can be conceived'.
安瑟伦的本体论论证是先天的，试图从“不可设想比之更伟大的存在”这一上帝概念中直接演绎出上帝的存在。
P1: God is defined as 'that than which nothing greater can be conceived'.
P2: It is greater to exist both in the mind and in reality than in the mind alone.
P3: If God existed only in the mind, we could conceive of a greater being (one that also existed in reality).
∴ God must exist in reality.
Gaunilo's parody of the perfect island challenges the logic, suggesting that using the same formula one could prove the existence of any perfect thing. Kant's objection is that existence is not a predicate; adding 'existence' to the concept of a thing does not actually add to its description.
高尼罗用完美的岛屿来戏仿这一逻辑，表明用同样的公式可以证明任何完美事物的存在。康德的反对意见是：存在不是一个谓词；给一个事物的概念加上“存在”并没有真正充实其描述内容。
4. The Problem of Evil Logical Structure | 恶的问题逻辑结构
The logical problem of evil presents an inconsistency within classical theism between the attributes of God and the existence of evil.
恶的逻辑问题揭示了古典有神论内部上帝的属性与邪恶存在之间的不一致性。
P1: If God exists, God is omnipotent, omniscient, and omnibenevolent.
P2: An omnipotent God can prevent all evil.
P3: An omniscient God knows how to prevent all evil.
P4: An omnibenevolent God would wish to prevent all evil.
P5: Evil exists.
∴ God as defined does not exist.
J.L. Mackie argues that these premises are logically inconsistent. To avoid the conclusion, a theist must either deny one of God's attributes or deny that evil really exists. Plantinga's free will defence suggests that it is logically impossible for God to give free will and simultaneously guarantee that no evil occurs, thus breaking the deductive chain.
麦克基认为这些前提在逻辑上不相容。要回避这一结论，有神论者必须要么否定上帝的某一属性，要么否认恶的真实存在。普兰丁格的自由意志辩护提出，上帝不可能既赐予自由意志，又同时保证绝无邪恶发生，从而切断了演绎链条。
5. Theodicies: Augustinian and Irenaean Formulas | 神义论：奥古斯丁与爱任纽公式
Augustine's theodicy frames evil as a privation, not a substance, while Irenaeus sees evil as necessary for soul-making. Both seek to reconcile God's goodness with the existence of evil.
奥古斯丁的神义论把恶界定为善的缺乏而非实体，而爱任纽把恶视为灵魂成长的必需。两者都试图调和上帝之善与恶的存在。
created everything good; evil entered through the Fall (free will). Original sin explains moral evil, and natural evil is a consequence of the broken order. Thus, God is not to blame.
Augustine's view relies heavily on a literal reading of Genesis and the transmission of original sin. Critics argue that an omnibenevolent God could have created free beings who always choose good, and the idea that all humanity is punished for Adam's sin seems unjust.
奥古斯丁的观点高度依赖于对《创世记》的字面解读和原罪的传递。批评者指出，一位全善的上帝本可以创造出永择善行的自由生命，而且全人类因亚当的罪而受罚似乎并不公正。
Irenaeus: Soul-making theodicy. Evil is required for humans to develop into the 'likeness' of God through moral struggle. The world is a 'vale of soul-making'.
Hick develops this view, arguing that a world without challenges would prevent genuine moral and spiritual growth. However, the sheer intensity of suffering often seems disproportionate to any educative purpose, challenging the soul-making formula.
希克发展了这一观点，认为一个没有挑战的世界将阻碍真正的道德和灵性成长。然而，许多苦难的极端程度与任何教育目的似乎都不成比例，这使灵魂成长公式受到挑战。
6. Religious Experience Argument Form | 宗教经验论证形式
The argument from religious experience moves from the testimony of individuals to the probable existence of a divine reality, relying on the principle of credulity.
宗教经验论证从个人的见证出发，依据轻信原则，推导出神圣实在很可能存在。
P1: A person has a powerful, self-authenticating experience which seems to be of God.
P2: In the absence of defeaters, we should trust the way things seem to be (Principle of Credulity).
P3: There are no publicly available defeaters that uniformly discredit all religious experiences.
∴ It is reasonable to believe that God exists, based on such experiences.
Swinburne's Principle of Testimony extends this: we should also trust what others tell us about their experiences unless we have reasons to doubt. Critics point to conflicting religious experiences across traditions, psychological explanations (Freud), and the possibility of deception.
斯温伯恩的见证原则延伸了这一思想：除非有理由怀疑，否则我们也应当相信他人对其经验的陈述。批评者则指出不同宗教传统之间存在冲突的宗教经验，心理学解释（弗洛伊德），以及欺骗的可能性。
7. Ethical Theories: Utilitarianism Calculus | 伦理理论：功利主义计算
Bentham's Act Utilitarianism is founded on the Hedonic Calculus, a formula for quantifying pleasure and pain to determine the morally right action.
边沁的行动功利主义建立在快乐计算法之上，这是一种将快乐和痛苦量化的公式，用以确定道德上正确的行为。
Principle of Utility: An action is right if it produces the greatest happiness for the greatest number.
| Calculus Factor | 计算要素 | Description | 描述 |
|---|---|
| Intensity | How strong is the pleasure? |
| Duration | How long will it last? |
| Certainty | How likely is the pleasure to occur? |
| Propinquity | How soon will it occur? |
| Fecundity | Will it be followed by more pleasure? |
| Purity | Will it be followed by pain? |
| Extent | How many people are affected? |
Mill's Rule Utilitarianism modified the formula by distinguishing between higher and lower pleasures, arguing that the quality of pleasure matters. The calculus is applied not to individual acts directly, but to general rules that maximise happiness over time.
密尔的规则功利主义通过区分高级快乐与低级快乐修正了这一公式，主张快乐的质很重要。快乐计算不再直接应用于个别的行为，而是应用于那些能够实现长远幸福最大化的普遍规则。
8. Kantian Ethics: Categorical Imperative Formulation | 康德伦理学：绝对命令公式
Kant's ethical system is deontological, basing morality on rational duty rather than consequences. The Categorical Imperative provides the logical test for moral maxims.
康德的伦理体系是义务论的，将道德建立在理性责任而非后果之上。绝对命令为道德准则提供了逻辑检验标准。
Formula of Universal Law (First Formulation):
"Act only according to that maxim whereby you can at the same time will that it should become a universal law."
This formula requires a test of universalisability and of contradiction in conception or in will. A lying promise fails the test because if 'making false promises' were universalised, the very institution of promising would collapse, making the maxim self-defeating.
这一公式要求进行可普遍化检验，并检查概念上的矛盾或意愿上的矛盾。虚假承诺不能通过检验，因为如果“作出虚假承诺”被普遍化，承诺这一制度本身就会崩溃，使得该准则自相矛盾。
Formula of Humanity (Second Formulation):
"Act in such a way that you treat humanity, whether in your own person or in the person of another, always at the same time as an end and never simply as a means."
This formulation emphasises the inherent dignity and rationality of all persons. Using someone merely as a means violates their autonomy. Kant argues that morality flows from the rational will of autonomous agents legislating the moral law for themselves.
这一公式强调所有人与生俱来的尊严与理性。仅仅将人当作手段来利用就侵犯了人的自主性。康德认为，道德是自主的理性主体为自己立法、出自理性意志的行为。
9. Situation Ethics: Agapeic Calculus | 情境伦理学：圣爱计算
Situation Ethics, proposed by Joseph Fletcher, is a teleological theory that places agape (selfless, unconditional Christian love) as the sole absolute. Every situation is judged by what best serves love.
弗莱彻提出的情境伦理学是一种目的论理论，将圣爱（无私、无条件的基督教之爱）作为唯一绝对的原则。每一个情境都以最有助于实现爱为标准来判断。
The master formula: Do the most loving thing in the situation.
Only one absolute: Agape.
Four working principles: Pragmatism, Relativism, Positivism, Personalism.
Pragmatism requires that the outcome must work in practice. Relativism insists that rules are relative to love and not absolute. Positivism affirms that love is a matter of faith and commitment, not just reason. Personalism puts persons, not laws, at the centre of ethics.
实用主义要求结果必须在实践中可行。相对主义强调规则相对于爱而非绝对。实证论主张爱需要信仰和委身，而不仅仅是理性。人格至上论则把人而非律法置于伦理学的中心。
Fletcher used the term 'agapeic calculus' to describe the process of calculating which action maximises love, though he insisted that this is not a rigid numerical system like Bentham's. The theory is flexible but criticised for being unpredictable and potentially justifying any action in the name of love.
弗莱彻使用“圣爱计算”一词来描述计算哪种行为能最大程度实现爱的过程，尽管他坚称这不是像边沁那样的刻板数字体系。该理论非常灵活，但也因不可预测性以及可能以爱之名合理化任何行为而受到批评。
10. Euthyphro Dilemma Logical Scheme | 游叙弗伦两难逻辑图式
The Euthyphro Dilemma, taken from Plato's dialogue, questions whether morality is grounded in God's commands or exists independently. It remains a key challenge for Divine Command Theory.
游叙弗伦两难源于柏拉图的对话录，质问道德究竟是建立在上帝的命令之上，还是独立于上帝而存在。它至今仍是神命论面临的关键挑战。
(1) Is an action right because God commands it?
→ Morality becomes arbitrary; God could command cruelty and it would be good.
(2) Does God command an action because it is right?
→ Rightness exists independently of God, limiting God's sovereignty.
This dilemma suggests that if God's commands are the sole foundation of morality, then whatever God wills is right by definition, making 'goodness' empty. On the other horn, if God simply recognises an external standard, then God is not the ultimate source of morality.
这个两难表明，如果上帝的命令是道德的唯一根基，那么上帝所定意的任意行为都因定义而成为善，这使得“善”的概念变得空洞。而在另一边，如果上帝只是认出了一个外在的标准，那么上帝就不是道德的终极源头。
Modified Divine Command Theory attempts to resolve this by locating goodness in God's unchanging, loving nature rather than in arbitrary commands. Thus, God commands what is consistent with His own character, bridging the horns of the dilemma.
修正的神命论试图将善植根于上帝那不变且充满爱的本性之中，而非任意的命令，从而化解这个两难。这样，上帝的命令与祂自己的性情相一致，在两难之间架起了桥梁。
11. The Design Argument: Fine-Tuning Formula | 设计论证：精细调谐公式
The fine-tuning argument is a modern teleological argument based on the precise conditions that permit life. Even slight variations in fundamental constants would make life impossible.
精细调谐论证是一种现代目的论论证，其依据是允许生命存在的各种极其精确的条件。哪怕基本常数发生极微小的变动，生命都会变得不可能。
P1: The universe's physical constants (gravitational force, cosmological constant, etc.) are 'fine-tuned' to an extraordinary degree for life.
P2: This fine-tuning is due either to necessity, chance, or design.
P3: It is not due to necessity (there is no known law requiring these values).
P4: It is highly improbable to be due to chance alone.
∴ Design by an intelligent creator is the best explanation.
Critics propose the multiverse hypothesis as an alternative: if there are a vast number of universes with varying constants, we would inevitably find ourselves in one that supports life. This challenges the leap from improbability to design.
批评者提出多重宇宙假说作为替代解释：如果存在海量的宇宙，拥有各不相同的常数，那么我们必然会发现自己身处一个支持生命的宇宙中。这挑战了从不具可能性到设计的跳跃性推论。
12. The Logical Structure of Miracles as Proof | 神迹作为证据的逻辑结构
A miracle is typically defined as an event that breaks a law of nature and is attributed to a divine agent. Hume's definition and critique form the logical backbone of this debate.
神迹通常被定义为违反自然规律并被归于神圣作为的事件。休谟的定义和批评构成了这一争论的逻辑主干。
A miracle = "a transgression of a law of nature by a particular volition of the Deity" (Hume).
Test Equation (Hume): 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.
Hume's argument against miracles rests on a weighing of probabilities: we have constant and uniform experience of laws of nature, against the fallible testimony of humans claiming miracles. The wise person always proportions their belief to the evidence.
休谟反驳神迹的论证基于概率的权衡：我们对自然规律拥有恒定而一致的经验，而声称神迹的人只提供了容易出错的见证。明智者总是根据证据的比例来调节其相信程度。
Wiles responds not by denying miracles outright, but by arguing that a truly omnibenevolent God would not perform isolated miracles (like healing one person) while allowing so many other innocent people to suffer. Such arbitrariness is incompatible with divine love.
怀尔斯并非全盘否定神迹，而是主张：一个真正全善的上帝不会在容许无数其他无辜者受苦的同时，只施行个别神迹（如医治一人）。这种随机性与神圣之爱不相容。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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