GCSE WJEC Philosophy: Formula & Theorem Quick Reference Handbook | GCSE WJEC 哲学：公式定理速查手册

📚 GCSE WJEC Philosophy: Formula & Theorem Quick Reference Handbook | GCSE WJEC 哲学：公式定理速查手册

Philosophy may not be full of equations in the mathematical sense, but its arguments and principles can be expressed with the clarity of formulae. This quick reference handbook re‑frames key concepts from the WJEC GCSE Philosophy specification as memorable ‘formulae’ and structured ‘theorems’. Use these summaries to check your understanding, compare theories, and apply ethical and metaphysical ideas with precision. Each entry pairs an English explanation with a Chinese paraphrase, ensuring you grasp both the logic and the language required for exam success.

哲学或许不像数学那样充满方程式，但其论证与原则同样可以像公式一样清晰地表达出来。这本速查手册将 WJEC GCSE 哲学大纲中的核心概念重新编排成便于记忆的“公式”和结构化的“定理”。你可以利用这些摘要检验理解、比较理论，并精准运用伦理学和形而上学的思想。每个条目都配有英文解释与中文复述，确保你同时掌握考试所需的逻辑与语言。

1. Utilitarianism: The Greatest Happiness Formula | 功利主义：最大幸福公式

Utilitarianism asserts that the moral worth of an action is determined solely by its contribution to overall utility – the balance of pleasure over pain. In its classical Benthamite form, we can express this as a hedonistic calculus.

功利主义主张，一个行为的道德价值完全取决于它对总体功利——即快乐超过痛苦的平衡——的贡献。在其经典的边沁形式中，我们可以将这一思想表达为享乐计算法。

Moral worth = Σ (pleasure – pain) for all sentient beings affected

道德价值 = 对所有受影响的有情众生产生的(快乐 – 痛苦)之和

Bentham’s hedonic calculus further breaks this down into seven factors: intensity, duration, certainty, propinquity, fecundity, purity, and extent. Mill later refined the theory by distinguishing higher intellectual pleasures from lower physical ones, adding a qualitative dimension.

边沁的快乐计算法进一步将这一公式分解为七个因子：强度、持续时间、确定性、临近性、繁殖力、纯度和范围。密尔后来区分了高级的理智快乐与低级的身体快乐，为理论增添了定性维度。

Thinker	Formula emphasis	思想家	公式侧重
Bentham	Quantity of pleasure (hedonic calculus)	边沁	快乐的量（快乐计算法）
Mill	Quality over quantity; higher pleasures	密尔	质胜于量；高级快乐
Singer	Preference satisfaction = interest fulfilment	辛格	偏好满足 = 利益实现

When applying the formula, remember that act utilitarianism calculates each act individually, whereas rule utilitarianism calculates the happiness produced by adopting a general rule.

在运用该公式时，需记住行为功利主义逐项计算每个行为，而规则功利主义则计算采纳一条普遍规则所产生的快乐。

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2. Kant’s Categorical Imperative: Universalizability Test | 康德的定言命令：可普遍化检验

Kantian ethics is deontological: the morality of an action depends not on its consequences but on whether it conforms to rational duty. The first formulation of the categorical imperative provides a logical test for any maxim.

康德伦理学是义务论的：行为的道德性不取决于其后果，而取决于它是否符合理性义务。定言命令的第一公式为任何准则提供了一个逻辑检验。

Act only on that maxim whereby you can at the same time will that it should become a universal law.

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。

If universalising a maxim leads to a contradiction in conception (e.g. false promising, where the practice of promising would break down) or a contradiction in the will (a state of affairs you could not rationally will), the act is impermissible. The formula of humanity adds that we must never treat rational beings merely as means but always as ends in themselves.

如果将一条准则普遍化会导致概念上的矛盾（例如虚假承诺——一旦普遍化，承诺制度就会崩溃）或意愿上的矛盾（一种你无法理性愿意的事态），那么该行为就是不容许的。人性公式补充说，我们决不能仅仅将理性存在者当作手段，而要始终将其视为目的本身。

• Formula of Universal Law: Can I will this maxim as a universal law without contradiction?
• Formula of Humanity: Does this action treat persons as ends, never merely as means?
• 普遍法则公式：我能否毫无矛盾地愿意此准则成为普遍法则？
• 人性公式：此行为是否将人视为目的，而绝非仅仅当作手段？

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3. Natural Law: Primary Precepts & Double Effect | 自然法：基本律令与双重效果

Aquinas’ Natural Law theory holds that morality is grounded in the rational nature of human beings and the purpose they can discern through reason. The primary precepts are the fundamental principles that guide all moral action.

阿奎那的自然法理论认为，道德植根于人类的理性本性和他们通过理性可辨识的目的。基本律令是指导一切道德行为的根本原则。

Primary precepts: Preserve life, reproduce, educate the young, live in society, worship God.

基本律令：保存生命、繁衍、教育后代、在社会中生活、敬拜上帝。

Secondary precepts are derived from these by practical reasoning. The doctrine of double effect provides a formula for deciding cases where a single action has both good and bad effects:

次级律令是通过实践理性从基本律令中推导出来的。双重效果原则为处理一个行为同时带来好效果和坏效果的情况提供了公式：

An action with both good and bad effects is permissible only if: (1) the act itself is morally good or neutral; (2) the bad effect is not intended, only foreseen; (3) the good effect is not produced by the bad effect; (4) there is a proportionate reason for allowing the bad effect.

兼具好坏效果的行为，仅在满足以下条件时才是容许的：（1）行为本身在道德上是善的或中性的；（2）坏效果并非意图造成，仅仅是预见到；（3）好效果不是通过坏效果产生的；（4）有相称的理由容许坏效果发生。

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4. Situation Ethics: Agape Calculus | 情境伦理学：圣爱计算

Joseph Fletcher’s situation ethics rejects both legalism and antinomianism in favour of a single absolute norm: agape, or unconditional Christian love. The only rule is love; everything else is relative to that principle in each situation.

约瑟夫·弗莱彻的情境伦理学拒斥律法主义与反律法主义，转而拥护一个绝对的唯一规范：agape，即无条件的基督教之爱。唯一的规则就是爱；其他一切都根据具体情境服从于这一原则。

Agapeic calculus: What is the most loving thing to do in this situation for all those concerned?

圣爱计算：在此情境下，为了所有相关方的最大益处，最富有爱心的做法是什么？

Fletcher lists six fundamental propositions, including: love is always good, love is the only norm, love and justice are the same, and the end justifies the means. The working principle is pragmatism, relativism, positivism, and personalism.

弗莱彻列出了六个基本命题，包括：爱总是善的、爱是唯一的规范、爱与正义是同一的、目的可以证明手段。其工作原则是实用主义、相对主义、实证主义与人格主义。

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5. The Cosmological Argument: Cause & Contingency | 宇宙论论证：因果与偶然性

The cosmological argument seeks to demonstrate the existence of God from the fact of the universe’s existence. Its logical form can be summarised as a chain of cause or dependence.

宇宙论论证试图从宇宙存在这一事实来证明上帝的存在。其逻辑形式可以概括为一个因果或依存的链条。

Aquinas’ Third Way: Contingent beings depend on a necessary being. If everything is contingent, at some time nothing existed – but if there was ever nothing, nothing could come from it. Therefore, a necessary being (God) must exist.

阿奎那的第三路：偶然存在者依赖于一个必然存在者。若万物皆为偶然，则某一时刻将无一物存在——但若曾空无一物，则无物能从中产生。因此，必然存在者（上帝）必定存在。

Kalam version: Everything that begins to exist has a cause; the universe began to exist; therefore, the universe has a cause (God). Hume and Russell challenge the argument by questioning the assumption that every cause must have a further cause, and the move from a cause within the universe to a transcendent cause.

卡拉姆版本：一切开始存在的事物都有一个原因；宇宙开始存在；因此，宇宙有一个原因（上帝）。休谟与罗素则质疑一切原因必有进一步原因的假定，以及由宇宙内部的原因推出超越原因的跳跃。

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6. The Teleological Argument: Design & Probability | 设计论证：设计与概率

The teleological argument infers a designer from the order, complexity, and apparent purpose in the world. Paley’s watchmaker analogy is the classic formulation.

设计论证从世界的秩序、复杂性和看似的目的性推出设计者的存在。佩利的钟表匠类比是经典的表述形式。

If a watch requires a watchmaker, the far more complex natural world requires a supreme designer – God.

如果一只表需要一位制表匠，那么远为复杂的自然界就需要一位至高的设计者——上帝。

Modern forms, such as Swinburne’s probability argument, treat the existence of ordered laws as more likely under theism than under naturalism. Hume’s criticisms: we cannot analogise the universe to a machine; even if there is a designer, it need not be the God of classical theism; the design argument cannot account for imperfections and evil.

现代形式，如斯温伯恩的概率论证，将有秩序的规律存在视为在有神论下比在自然主义下更可能。休谟的批评有：我们无法将宇宙类比为一部机器；即使有设计者，它也未必是古典有神论的上帝；设计论证无法解释不完善与恶的存在。

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7. The Ontological Argument: Existence as Predicate | 本体论论证：存在作为谓词

Anselm’s ontological argument is an a priori proof that defines God as ‘that than which nothing greater can be conceived’ and argues that such a being must exist in reality, because existence in reality is greater than existence in the understanding alone.

安瑟伦的本体论论证是一个先验证明，它将上帝定义为“无法设想有比之更伟大的存在者”，并论证说这样的存在者必然在现实中存在，因为在实际中存在的伟大性胜过仅在理智中存在。

God = that than which no greater can be conceived. If God exists only in the mind, we could conceive a greater being that also exists in reality. Therefore, God must exist in reality.

上帝 = 无法设想有比之更伟大的存在者。若上帝仅存在于心灵中，我们便能设想一个同时也在现实中存在的更伟大者。因此，上帝必在现实中存在。

Gaunilo’s ‘perfect island’ parody and Kant’s objection that existence is not a real predicate remain the classic rebuttals. Descartes reformulated the argument using the idea of existence as a perfection, but Kant’s critique largely undermines this move.

高尼罗的“完美岛屿”戏仿以及康德关于存在并非真实谓词的反对，依然是经典的反驳。笛卡尔将存在视为一种完善性来重构论证，但康德的批判在很大程度上瓦解了这一思路。

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8. The Problem of Evil: Inconsistent Triad | 恶的问题：不一致三元组

The logical problem of evil states that the existence of an omnipotent, omnibenevolent God is logically incompatible with the existence of evil. J. L. Mackie formalised this as the inconsistent triad:

恶的逻辑问题指出，一个全能、全善的上帝其存在与恶的存在在逻辑上是不相容的。麦基将其形式化为不一致三元组：

The three propositions – God is omnipotent, God is wholly good, and evil exists – cannot all be true. Any two are consistent, but the third must be rejected.

三个命题——上帝是全能的、上帝是全善的、恶是存在的——不可能同时为真。任意二者可相容，但必须否定第三个。

The free will defence argues that moral evil results from the misuse of free will, which is a greater good. The evidential problem of evil, highlighted by Rowe, points to the sheer amount and distribution of seemingly pointless suffering as evidence against God’s existence. Theodicies such as Irenaeus’ soul‑making theodicy attempt to explain suffering as necessary for moral and spiritual development.

自由意志辩护认为，道德之恶源于自由意志的误用，而自由意志本身是一个更大的善。由罗维所强调的恶的证据问题，则指出大量且分布不公的看起来无意义的痛苦，构成了反对上帝存在的证据。伊里奈乌的灵魂塑造神义论等神义论尝试将苦难解释为道德与灵性成长的必经之路。

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9. Religious Experience: Principle of Credulity & Testimony | 宗教经验：轻信原则与见证

Arguments from religious experience claim that personal encounters with the divine provide direct evidence for God’s existence. Swinburne’s principle of credulity asserts that, in the absence of special considerations, things are probably as they seem to be. Applied to religious experience: if someone seems to perceive God, that experience should be accepted as veridical unless we have good reason to doubt it.

来自宗教经验的论证声称，与神的亲身遭遇为上帝存在提供了直接证据。斯温伯恩的轻信原则主张，在没有特殊理由的情况下，事物很可能就是它们显现出来的样子。应用于宗教经验：如果某人似乎感知到了上帝，那么该经验就应被视为真实的，除非我们有充分理由怀疑它。

If a subject S has a seeming experience E of x, then S is justified in believing x exists, unless defeaters are present.

若主体 S 对 x 拥有一个看似经验的 E，则 S 有正当理由相信 x 存在，除非存在否定因子。

The principle of testimony further holds that, other things being equal, we should believe what others tell us. Critics such as Feuerbach and Freud argue that religious experiences can be explained naturalistically – as projections of human wishes or manifestations of psychological states.

见证原则进一步主张，在其他条件等同的情况下，我们应该相信他人的告诉。费尔巴哈和弗洛伊德等批评者则认为，宗教经验可以被自然地解释——人类愿望的投射或心理状态的表现。

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10. Sanctity of Life vs Quality of Life: Ethical Equations | 生命神圣性与生命质量：伦理方程

In bioethical debates on abortion and euthanasia, two competing principles clash. The sanctity of life principle holds that all human life is intrinsically valuable and must never be deliberately taken. The quality of life principle weighs the value of a life by its capacity for consciousness, relationships, and the avoidance of suffering.

在关于堕胎与安乐死的生命伦理辩论中，两条相互冲突的原则彼此碰撞。生命神圣性原则认为，所有人的生命都具有内在价值，绝不可被故意剥夺。生命质量原则则根据生命的意识能力、人际关系和免于痛苦的程度来衡量其价值。

Sanctity of Life: Intrinsic worth of a human being → Absolute prohibition of direct killing.

生命神圣性：人的内在价值 → 绝对禁止直接杀害。

Quality of Life: Worth of a life = Σ (capacities + experiences) → Permits termination in cases of extreme suffering or no conscious capacity.

生命质量：生命价值 = Σ（能力 + 体验） → 在极度痛苦或毫无意识能力时容许终止生命。

Natural law and Kantian ethics (formula of humanity) tend to support the sanctity of life approach, while utilitarianism and situation ethics lend themselves more to quality-of-life judgements, depending on the expected balance of happiness.

自然法和康德伦理学（人性公式）倾向于支持生命神圣性路径，而功利主义和情境伦理学则更容易导向生命质量的判断，这取决于预期幸福的平衡。

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11. Abortion & Euthanasia: Key Arguments | 堕胎与安乐死：关键论证

The debate over abortion often hinges on the concept of personhood. A ‘potentiality principle’ can be formulated: if an entity has the potential to develop into a person, it has a right to life. Opponents counter that potential is not actual and that bodily autonomy overrides.

堕胎的争论往往围绕人格概念展开。可以形式化为一个“潜能原则”：若一个实体具有发展成人的潜能，则它享有生命权。反对者则反驳说，潜能并非现实，且身体自主权优先。

Pro-Life: Foetus = person (from conception) → Abortion = killing an innocent person.

反堕胎：胎儿 = 人（自受孕起） → 堕胎 = 杀害无辜者。

Pro-Choice: Personhood requires capacities like self-awareness → Early foetus is not a person → Woman’s autonomy dominates.

赞成选择：人格需要自我意识等能力 → 早期胎儿不是人 → 妇女的自主权占主导。

In euthanasia, the distinction between active and passive, voluntary and non‑voluntary is crucial. The ‘acts and omissions doctrine’ states that letting die is sometimes permissible while killing is not. However, James Rachels’ equivalence thesis argues that there is no moral difference between killing and letting die when the motivation and outcome are identical.

在安乐死中，主动与被动、自愿与非自愿的区分至关重要。“作为与不作为原则”指出，放任死亡有时是容许的，而杀害则不然。然而，詹姆斯·雷切尔的等价论题认为，在动机与结果相同的情况下，杀害与任其死亡之间并无道德差别。

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12. Animal Rights: Speciesism & Moral Status | 动物权利：物种主义与道德地位

Peter Singer argues that the principle of equal consideration of interests requires us to give equal weight to the like interests of all beings capable of suffering, regardless of species. The formula he employs is an extension of utilitarian calculus beyond the boundary of humanity.

彼得·辛格主张，利益的平等考量原则要求我们对所有能感受痛苦的存在的相似利益给予同等权重，不论物种如何。他所采用的公式是将功利计算扩展到人类边界之外。

Equal consideration: If a being can suffer, there is no non‑arbitrary ground for excluding its suffering from moral calculation.

平等考量：若一个存在能够感受痛苦，则没有任何非任意的理由将其痛苦排除在道德计算之外。

Singer’s anti‑speciesism challenges traditional views that only humans have moral status. Contrastingly, contractarianism and anthropocentric views (e.g. Aquinas, Kant) restrict direct moral duties to rational beings, though they may permit indirect duties regarding animals. Regan’s animal rights view, based on the concept of ‘subjects‑of‑a‑life’, grants inherent value to certain animals.

辛格的反物种主义挑战了只有人类才具有道德地位的传统观点。与之对照，契约论和人类中心主义观点（如阿奎那、康德）将直接的道德义务限于理性存在者，尽管它们可能允许对动物负有间接义务。雷根的动物权利观点，基于“生命主体”这一概念，赋予了某些动物以固有价值。

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