CCEA Year 11 Philosophy: Quick Reference Formula & Theorem Handbook | CCEA 11 年级哲学：公式定理速查手册

📚 CCEA Year 11 Philosophy: Quick Reference Formula & Theorem Handbook | CCEA 11 年级哲学：公式定理速查手册

Welcome to your go‑to quick reference for the key logical forms, arguments, and ethical principles you need in Year 11 CCEA Philosophy. Just like a maths formula sheet, this handbook turns core philosophical content into clear, structured ‘formulae’ to help you analyse, evaluate, and write high‑grade exam answers.

欢迎使用这份为你准备的 CCEA 11 年级哲学速查手册，涵盖关键逻辑形式、论证结构和伦理原则。就像数学公式表一样，本手册将核心哲学内容转化为清晰、结构化的“公式”，帮助你进行分析、评价，并写出高分考试答案。

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1. Logical Toolkit: Valid Argument Forms | 逻辑工具箱：有效论证形式

Philosophical arguments rely on logic. Learn these fundamental inference patterns to spot and build convincing reasoning.

哲学论证依赖于逻辑。掌握以下基本推理模式，以识别并构建有说服力的推理。

Modus Ponens (Affirming the Antecedent)
If P, then Q. P is true. Therefore, Q is true.
Symbolically: P → Q, P ∴ Q

肯定前件式 (Modus Ponens)
如果 P 则 Q。P 为真。因此 Q 为真。
符号化：P → Q，P ∴ Q

Modus Tollens (Denying the Consequent)
If P, then Q. Q is false. Therefore, P is false.
Symbolically: P → Q, ¬Q ∴ ¬P

否定后件式 (Modus Tollens)
如果 P 则 Q。Q 为假。因此 P 为假。
符号化：P → Q，¬Q ∴ ¬P

Hypothetical Syllogism
If P, then Q. If Q, then R. Therefore, if P, then R.
Symbolically: P → Q, Q → R ∴ P → R

假言三段论
如果 P 则 Q。如果 Q 则 R。因此如果 P 则 R。
符号化：P → Q，Q → R ∴ P → R

Master these as the ‘algebra’ of philosophy – they underpin every major argument.

掌握这些作为哲学的“代数”——它们是每一个重要论证的基础。

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2. The Ontological Argument (Anselm) | 本体论论证（安瑟伦）

Anselm’s a priori argument for God’s existence defines God and deduces necessary existence from that definition.

安瑟伦关于上帝存在的先天论证从定义上帝出发，由该定义推导出必然存在。

Formula 1: The Concept of God
God = ‘that than which nothing greater can be conceived’ (TTWNGCBC).

公式 1：上帝的概念
上帝 = “无法设想有比之更伟大者” (TTWNGCBC)。

Formula 2: Existence in Reality vs. in the Understanding
If TTWNGCBC exists only in the mind, then I can conceive a greater being – one that exists in reality too.
Therefore, TTWNGCBC must exist in reality, otherwise it is not the greatest conceivable.

公式 2：现实中的存在 vs. 理智中的存在
如果 TTWNGCBC 仅存在于心中，那么我就能设想一个更伟大的存在——一个也在现实中存在的。
因此，TTWNGCBC 必然在现实中存在，否则它就不是可设想的最伟大者。

Premise 1: God is TTWNGCBC. Premise 2: To exist in reality is greater than to exist in the mind alone. Conclusion: God exists in reality.

前提 1：上帝是 TTWNGCBC。前提 2：在现实中存在比仅在心中存在更伟大。结论：上帝在现实中存在。

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3. Cosmological Argument (Aquinas’ First Three Ways) | 宇宙论论证（阿奎那的前三种证明）

Aquinas argues from observed features of the world to a necessary first cause, using a posteriori reasoning.

阿奎那从观察到的世界特征出发，运用后天推理，推导出必然的第一因。

Formula: The Way of Motion (First Way)
Everything moved is moved by another. An infinite regress of movers is impossible. Therefore, there must be a first, unmoved mover – God.

公式：运动之证明（第一路）
凡运动者皆为另一物所推动。无限追溯推动者是不可能的。因此，必须有一个第一、不被推动的推动者——上帝。

Formula: The Way of Causation (Second Way)
Every effect has a cause. If you remove the cause, you remove the effect. No infinite causal chain. Therefore, a first efficient cause exists – God.

公式：因果之证明（第二路）
每个结果都有其原因。若除去原因，便除去结果。不存在无限的因果链。因此，存在第一动力因——上帝。

Formula: The Way of Contingency (Third Way)
Contingent beings exist (they can not‑exist). If everything were contingent, at some time nothing would have existed, and then nothing would exist now. Since things exist now, there must be a necessary being – God.

公式：偶然性之证明（第三路）
偶然存在物存在（它们可能不存在）。如果一切都是偶然的，那么在某个时刻就什么都没有存在过，那么现在也将什么都没有。既然现在有事物存在，就必须有一个必然存在——上帝。

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4. Teleological (Design) Argument (Paley’s Watchmaker) | 目的论（设计）论证（佩利的钟表匠）

Paley’s analogy argues that complexity and purpose in nature point to an intelligent designer.

佩利的类比论证认为，自然界中的复杂性与目的性指向一位智慧的设计者。

Formula: The Watch Analogy
Watch : complexity + purpose → watchmaker
Universe : complexity + purpose (e.g., the eye) → ?
Conclusion: Universe → intelligent designer (God).

公式：钟表类比
钟表：复杂性 + 目的 → 钟表匠
宇宙：复杂性 + 目的（如眼睛） → ？
结论：宇宙 → 智慧设计者（上帝）。

Formula: Design Qua Regularity + Design Qua Purpose
Design Qua Regularity: laws of nature, planetary orbits → law‑giver.
Design Qua Purpose: parts fitted for a function (eyeball arranged for sight) → purpose‑giver.

公式：规律性设计与目的性设计
规律性设计：自然规律、行星轨道 → 立法者。
目的性设计：部件为特定功能而配置（眼球为视觉而安排） → 目的赋予者。

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5. Problem of Evil & Theodicies | 恶的问题与神正论

The logical and evidential challenge that evil and suffering pose to the existence of an all‑powerful, all‑loving God.

恶与苦难对全能、全善的上帝存在构成的逻辑和证据挑战。

Logical Problem Formula (Inconsistent Triad)
God is omnipotent.
God is omnibenevolent.
Evil exists.
These three statements cannot all be true. If God can and wants to stop evil, evil would not exist. Yet it does. Therefore, such a God does not exist.

逻辑问题公式（不相容三元组）
上帝全能。
上帝全善。
恶存在。
这三个陈述不能同时为真。如果上帝能且愿阻止恶，恶就不会存在。但恶确实存在。因此，这样的上帝不存在。

Augustinian Theodicy – Formula
Evil = privation of good (not a substance). Original sin → all share Adam’s guilt → suffering is just punishment. God’s grace saves some. Therefore, God remains just and loving.

奥古斯丁神正论——公式
恶 = 善的缺乏（非实体）。原罪 → 全人类承继亚当的罪责 → 苦难是公义的惩罚。上帝的恩典拯救部分人。因此，上帝仍是公义和慈爱的。

Irenaean Theodicoy – Formula
Humanity created imperfect (in the image, but not yet likeness of God). Soul‑making through suffering → moral and spiritual growth. Evil is a necessary condition for free, mature love. Thus, God’s goodness is compatible with evil.

爱任纽神正论——公式
人被造为不完美（有上帝的形象，但尚未成为样式）。通过苦难塑造灵魂 → 道德与灵性成长。恶是自由、成熟之爱的必要条件。因此，上帝的良善与恶相容。

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6. Religious Experience as Argument | 宗教经验作为论证

Arguments from religious experience claim that direct personal encounters with the divine justify belief in God.

来自宗教经验的论证主张，个人与神明的直接相遇可为相信上帝提供正当理由。

Formula: Principle of Credulity (Swinburne)
If a person seems to perceive X, then, in the absence of defeaters, it is rational to believe X exists. Applied to God: if I have an experience that seems to be of God, I am justified in believing God exists unless there is evidence against it.

公式：轻信原则（斯温伯恩）
如果一个人似乎感知到 X，那么在没有否决理由的情况下，相信 X 存在是理性的。应用于上帝：如果我有一个似乎是关于上帝的经验，我就有理由相信上帝存在，除非有反证。

Formula: The Cumulative Case
No single argument proves God, but the combination of ontological, cosmological, teleological, and experiential arguments builds a strong cumulative case.

公式：累计论证
没有任何单一论证能证明上帝，但本体论、宇宙论、目的论和经验论证的结合构建了一个强大的累计论证。

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7. Moral Argument for God’s Existence | 道德论证

This argument deduces God’s existence from the apparent objectivity of moral laws.

该论证从道德律看似客观的特性推导出上帝的存在。

Kant’s Postulate Formula
The universe is just in the end (summum bonum) → requires an afterlife and a judge who ensures happiness proportioned to virtue → God must exist.

康德的公设公式
宇宙终将是公正的（至善） → 这要求来世和一位确保幸福与德行成比例的审判者 → 上帝必须存在。

Lewis’ Argument from Moral Law
There is an objective moral law that all humans recognise. A law implies a law‑giver. This law‑giver cannot be physical. Therefore, a non‑physical moral law‑giver (God) exists.

刘易斯的道德律论证
存在一个所有人类都认识的客观道德律。法律意味着立法者。这个立法者不可能是物质的。因此，一位非物质的道德立法者（上帝）存在。

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8. Utilitarianism – Calculus of Happiness | 功利主义——幸福的计算

Utilitarianism judges actions by their consequences; the right action maximises overall happiness.

功利主义根据后果评判行为；正确的行为能最大化总体幸福。

Bentham’s Hedonic Calculus Formula
Happiness = Intensity × Duration × Certainty × Propinquity × Fecundity × Purity × Extent
When comparing actions, sum the hedons (units of pleasure) minus the dolors (units of pain) for each affected person.

边沁的苦乐计算公式
幸福 = 强度 × 持续时间 × 确定性 × 迫切度 × 丰富度 × 纯度 × 范围
比较行为时，计算每个受影响者的乐单位（hedons）减去苦单位（dolors）的总和。

Mill’s Qualitative Amendment
Pleasures differ in quality, not just quantity. Higher pleasures (intellect, moral) outweigh lower pleasures (physical). ‘Better to be Socrates dissatisfied than a pig satisfied.’

密尔的质性修正
快乐有质量差异，而不只是数量差异。高级快乐（智识、道德）胜过低级快乐（身体）。‘宁做不满足的苏格拉底，也不做满足的猪。’

Act vs. Rule Utilitarianism
Act: Ask of each act: ‘Does it maximise utility?’ Rule: Follow rules that, if universally adopted, would maximise utility (e.g., ‘Do not lie’).

行为功利主义 vs. 规则功利主义
行为：对每一行为问：“它是否最大化功利？”规则：遵循那些若被普遍采纳便会最大化功利的规则（例如‘不撒谎’）。

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9. Kantian Deontology – The Categorical Imperative Formula | 康德义务论——定言令式公式

Kant’s ethics is based on duty and rational principles, not consequences.

康德的伦理学基于义务和理性原则，而非后果。

Formula 1: The Universal Law Formula
Act only according to that maxim whereby you can at the same time will that it should become a universal law. Test: Can I rationally will that everyone does X in the same situation?

公式 1：普遍法则公式
只依据那些你同时愿意其成为普遍法则的准则而行动。检验：我能理性地意愿在相同情境下每个人都这样做吗？

Formula 2: The Humanity Formula
Act so that you treat humanity, whether in your own person or in that of another, always as an end and never merely as a means.

公式 2：人性公式
如此行动，以至于不论是在自己的人格中还是在他人的人格中，你始终将人性作为目的，而绝不仅仅作为手段。

Contradiction Tests
Contradiction in conception: a maxim like ‘make false promises’ cannot be universalised because promising would become meaningless. Contradiction in will: some maxims pass the first test but cannot rationally be willed (e.g., refusing to help others).

矛盾检验
设想中的矛盾：例如“做虚假承诺”这一准则不能被普遍化，因为承诺行为本身将失去意义。意愿中的矛盾：某些准则通过了第一项检验，但在理性上无法被意愿（例如拒绝帮助他人）。

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10. Sanctity of Life vs. Quality of Life: Principles | 生命的神圣性与生命质量：原则

These contrasting principles shape ethical debates on abortion, euthanasia, and embryo research.

这些对立的原则塑造了关于堕胎、安乐死和胚胎研究的伦理辩论。

Sanctity of Life Formula
Human life is sacred because: Created in imago Dei (image of God) → intrinsic worth from conception to natural death → never permissible to intentionally end innocent life.

生命神圣性公式
人的生命是神圣的，因为：人是按上帝的形象 (imago Dei) 造的 → 从受孕到自然死亡具有内在价值 → 绝不允许故意终结无辜的生命。

Quality of Life Formula
Moral worth is tied to personhood characteristics: consciousness, rationality, self‑awareness, capacity to communicate, ability to value one’s own existence. When these are absent or irretrievably lost, it may be morally permissible to end life.

生命质量公式
道德价值与位格特征相联系：意识、理性、自我意识、交流能力、珍视自身存在的能力。当这些特征不存在或不可挽回地丧失时，终结生命在道德上可能是可允许的。

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11. Natural Law Ethics (Aquinas) – Primary & Secondary Precepts | 自然法伦理学（阿奎那）——基本诫命与次要诫命

Aquinas’ Natural Law theory derives moral rules from the purpose built into human nature by God.

阿奎那的自然法理论从上帝赋予人性的内在目的中推导出道德规则。

Formula: Synderesis Rule
Do good and avoid evil. This is the first, self‑evident principle of practical reason.

公式：良知 (Synderesis) 规则
行善避恶。这是实践理性的首要自明原则。

Primary Precepts (derived from natural inclinations)
1. Preserve life (self‑preservation)
2. Reproduce (conjugal, education of offspring)
3. Educate (seek truth about God, live in society)
4. Live in an ordered society
5. Worship God

基本诫命（源自自然倾向）
1. 保存生命（自我保护）
2. 繁衍（婚姻、教育后代）
3. 教育（寻求关于上帝的真理，在社会中生活）
4. 生活在有秩序的社会中
5. 敬拜上帝

Secondary Precepts
These are more specific rules derived from primary precepts, such as ‘Do not murder’ (from preserve life).

次要诫命
这些是从基本诫命中推导出的更具体的规则，例如“不可杀人”（源于“保存生命”）。

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12. Situation Ethics – Agape Calculus | 情境伦理学——仁爱计算

Joseph Fletcher’s Situation Ethics proposes that only one absolute rule exists: love (agape), and all other rules are relative to the situation.

约瑟夫·弗莱彻的情境伦理学主张，只存在一条绝对规则：爱（agape），所有其他规则都视情境而定。

Formula: The Four Working Principles
Pragmatism, Relativism, Positivism, Personalism. Combined: The loving thing to do is worked out case‑by‑case.

公式：四项运作原则
实用主义、相对主义、实证主义、人格主义。组合起来：充满爱心的事在具体情境中逐一确定。

Formula: The Six Fundamental Propositions
Only love is intrinsically good; the ruling norm is love; love and justice are the same; love wills the neighbour’s good whether we like him or not; only the end justifies the means; love’s decisions are made situationally.

公式：六项基本命题
唯有爱是内在的善；支配性规范是爱；爱与正义是同一的；爱愿邻舍的善，无论我们是否喜欢他；唯独目的能证明手段的正当性；爱的决定在具体情境中做出。

Agape = unconditional, self‑giving love → Agent must calculate the most loving outcome in each unique situation.

Agape = 无条件的、自我奉献的爱 → 行为者必须在每一个独特情境中计算出最具爱心的结果。

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