Year 12 Edexcel Philosophy: Formulae & Theorems Quick Reference | Edexcel 12年级哲学：公式定理速查手册

📚 Year 12 Edexcel Philosophy: Formulae & Theorems Quick Reference | Edexcel 12年级哲学：公式定理速查手册

Use this reference as a streamlined summary of the key logical forms, epistemic definitions, ethical principles, and argument structures that appear throughout the Year 12 Edexcel Philosophy specification. Each entry is presented as a 'formula' or 'theorem' to help you recall and apply these ideas quickly in essays and examinations. Understanding the precise logical shape of an argument often earns higher marks than a vague summary.

这份速查手册为你梳理了 Edexcel 12年级哲学大纲中反复出现的核心逻辑形式、知识论定义、伦理学原则以及论证结构。每个条目都以“公式”或“定理”的方式呈现，便于你在论文和考试中快速调用和准确应用。精准掌握论证的逻辑形态，通常比模糊概括更能赢得高分。

1. The JTB Formula for Knowledge | 知识的JTB公式

n believing that p. This is often written as K = J + T + B. However, Gettier cases show that these three conditions are not jointly sufficient, leading to the need for a fourth condition (e.g. no false lemmas).

命题知识的经典分析指出：S知道p，当且仅当 (i) p为真，(ii) S相信p，并且 (iii) S有理由相信p。这常被写作 K = J + T + B。然而，盖梯尔案例表明这三个条件并不构成充分条件，因此需要添加第四个条件（例如，没有虚假前提）。

2. Modus Ponens – Affirming the Antecedent | 肯定前件式

straightforward valid argument form: If P then Q; P; therefore, Q. Symbolically: P → Q, P ⊢ Q. Whenever you reconstruct a philosopher's reasoning, check if it follows this pattern. Descartes' ogito can be framed as: If I am thinking, then I exist; I am thinking; therefore, I exist.

最简洁的有效论证形式：如果P则Q；P成立；因此Q成立。符号化为：P → Q, P ⊢ Q。每当你重构哲学家的推理时，可以检查它是否遵循这一模式。笛卡尔的“我思”可表达为：如果我思考，那么我存在；我思考；因此我存在。

3. Modus Tollens – Denying the Consequent | 否定后件式

Another fundamental valid form: If P then Q; not Q; therefore, not P. Symbolically: P → Q, ¬Q ⊢ ¬ we cannot distinguish waking from dreaming (Descartes’ dream argument); therefore, we do not have knowledge of the external world.

另一个基本有效形式：如果P则Q；非Q；因此非P。符号化：P → Q, ¬Q ⊢ ¬P。这常被用于怀疑论论证。例如，如果我们拥有关于外部世界的知识，那么我们就能区分清醒与梦境；我们无法区分清醒与梦境（笛卡尔的梦境论证）；因此我们没有关于外部世界的知识。

4. Hypothetical Syllogism and Disjunctive Syllogism | 假言三段论与选言三段论

Hypothetical syllogism: If P then Q; if Q then R; therefore, if P then R. Disjunctive syllogism: Either P or Q; not P; therefore, Q. These patterns help navigate complex passages in Hume's fork or the problem of evil. The disjunctive form often appears when a theist says: either God has a reason for allowing evil or God does not exist; God exists; therefore, God has a reason.

假言三段论：如果P则Q；如果Q则R；因此，如果P则R。选言三段论：要么P要么Q；非P；因此Q。这些模式有助于梳理休谟的叉子或恶的问题中的复杂段落。选言形式常在神义论中出现：要么上帝有理由容许恶，要么上帝不存在；上帝存在；因此上帝有理由。

5. Hume's Fork – The Two Objects of Human Reason | 休谟的叉子——人类理性的两种对象

osteriori, contingent, known through experience, e.g. the sun will rise tomorrow). A statement that is neither a relation of ideas nor a matter of fact is, for Hume, 'sophistry and illusion'. This functions as a strict test for meaningfulness.

人类理性的所有对象分为两类：观念的关系（先天的、必然的、仅凭思想可知，如2+2=4）和事实（后天的、偶然的、通过经验可知，如太阳明天会升起）。对休谟而言，任何既不是观念关系也不是事实的陈述都是“诡辩和幻想”。这充当了一种严格的意义检验标准。

6. The Principle of Utility – The Greatest Happiness Formula | 功利原则——最大幸福公式

fected. The hedonic calculus attempts to quantify pleasure along dimensions of intensity, duration, certainty, propinquity, fecundity, purity, and extent. The formula is often summarised as: ‘the greatest happiness of the greatest number’.

行为功利主义：一个行为是正确的，当且仅当它最大化功利，功利 = 所有受影响者的快乐减去痛苦。快乐计算试图沿强度、持续时间、确定性、临近性、丰富性、纯度和范围等维度量化快乐。这个公式常被概括为：“最大多数人的最大幸福”。

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7. Kant's Categorical Imperative – The Universal Law Formula | 康德的定言命令——普遍法则公式

Act only according to that maxim whereby you can at the same time will that it should become a universal law. The test has two stages: (1) formulate the maxim of your action, (2) universalise it and check for contradictions in conception or in the will. A contradiction in conception yields a perfect duty (e.g. do not make false promises); a contradiction in the will yields an imperfect duty (e.g. help others).

只依据那些你能够同时意愿它成为普遍法则的准则而行动。检验分两步：(1) 构造你行动的准则，(2) 将其普遍化，检查是否存在构想上的矛盾或意志上的矛盾。构想上的矛盾产生完全义务（如不虚假承诺）；意志上的矛盾产生不完全义务（如帮助他人）。

8. The Teleological Argument – Paley's Watchmaker Theorem | 目的论论证——佩利的钟表匠定理

If an object exhibits complex, purposeful arrangement of parts (like a watch), then it must have an intelligent designer. The natural world exhibits far greater complexity and purpose. Therefore, the natural world has an intelligent designer (God). This is an argument by analogy, and its logical form can be challenged by Hume’s criticisms of the design argument and by Darwinian evolution.

如果一个物体表现出复杂、有目的的部分组合（如同钟表），那么它必定有一位智能设计者。自然界展现出远为巨大的复杂性和目的性。因此，自然界拥有一位智能设计者（上帝）。这是一个类比论证，其逻辑形式可以被休谟对设计论证的批判以及达尔文进化论所挑战。

9. The Problem of Evil – The Inconsistent Triad Theorem | 恶的问题——不相容三角定理

If God is omnipotent, omnibenevolent, and omniscient, then evil would not exist. Evil exists. Therefore, no such God exists. This is presented as an inconsistent set of propositions: (1) God is omnibenevolent, (2) God is omnipotent, (3) God is omniscient, (4) evil exists. Theodicies try to resolve the inconsistency by qualifying one of the attributes or redefining evil.

如果上帝是全能的、全善的、全知的，那么恶就不会存在。恶存在。因此，这样的上帝不存在。这表现为一组不一致的命题：(1) 上帝全善，(2) 上帝全能，(3) 上帝全知，(4) 恶存在。神义论尝试通过限定某个属性或重新定义恶来解决这种不一致。

10. Descartes' Cogito – The Indubitable Theorem | 笛卡尔的“我思”——不可怀疑的定理

‘I think, therefore I am’ (Cogito ergo sum) is immune to hyperbolic doubt. Even if an evil demon deceives me, I must exist in order to be deceived. The cogito is often taken as a self‑verifying proposition: the act of doubting it confirms it. It serves as the first secure foundation in Descartes’ rationalist epistemology.

“我思故我在” (Cogito ergo sum) 不受极端怀疑的影响。即使有一个邪恶的魔鬼欺骗我，我也必须存在才能被欺骗。“我思”常被视为一个自证实命题：怀疑它的行动本身就证实了它。它是笛卡尔理性主义认识论中第一个可靠的基础。

11. Aristotle's Virtue Theory – The Golden Mean Theorem | 亚里士多德的美德论——中庸定理

Moral virtue is a disposition to choose the mean relative to us, determined by reason as a person of practical wisdom would determine it. Each virtue lies between two vices (excess and deficiency). Courage is the mean between rashness and cowardice. The formula is contextual: the mean is not arithmetic but relative to the agent and the situation.

道德美德是一种选择相对于我们而言的中道的倾向，由理性决定，如同拥有实践智慧的人会做出的决定。每种美德都位于两种恶（过度与不足）之间。勇敢是鲁莽与怯懦的中道。这个公式与情境相关：中道不是算术平均，而是相对于主体和具体情况而言的。

12. Russell's Theory of Descriptions – The Logical Form Theorem | 罗素的摹状词理论——逻辑形式定理

A definite description such as ‘the present King of France’ does not refer to a non‑existent object; instead, the proposition ‘The present King of France is bald’ is analysed as: there exists an x such that x is King of France, there is at most one such x, and x is bald. This illustrates how surface grammar can mislead us about logical form, a key tool in analytic philosophy and useful when evaluating religious language.

像“当今法国国王”这样的确定摹状词并不指向一个非存在的对象；相反，“当今法国国王是秃头”这个命题被分析为：存在一个x，使得x是法国国王，至多存在一个这样的x，且x是秃头。这说明了表面语法如何误导我们关于逻辑形式的理解，这是分析哲学的关键工具，在评估宗教语言时非常有用。

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Published by TutorHao | Philosophy Revision Series | aleveler.com

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