Year 12 WJEC Philosophy: Formula and Theorem Quick Reference Handbook | WJEC 12年级哲学：公式定理速查手册

📚 Year 12 WJEC Philosophy: Formula and Theorem Quick Reference Handbook | WJEC 12年级哲学：公式定理速查手册

Philosophy may not have equations like physics, but it is built on rigorous logical structures, timeless definitions, and well-formed arguments that function as formulas and theorems. This handbook distils the Year 12 WJEC Philosophy syllabus into a collection of essential logical ‘formulae’ and philosophical ‘theorems’ — from the tripartite definition of knowledge to the structure of the ontological argument. Whether you are revising for AS Unit 1 (Philosophy of Religion) or Unit 2 (Mind and Epistemology), these ready-to-use schemas will sharpen your analytical writing and support your essay construction.

哲学也许不像物理学那样充满方程式，但它建立在严谨的逻辑结构、永恒的定义以及形式完好的论证之上，这些论证就像公式与定理一样运作。本手册将 WJEC 12 年级哲学大纲浓缩为一系列必备的逻辑“公式”和哲学“定理”——从知识的三元定义到本体论论证的结构。无论你是在复习 AS 第一单元（宗教哲学）还是第二单元（心灵与认识论），这些现成可用的模式都能提升你的分析写作能力，并为你的论文搭建提供支持。

1. The Tripartite Definition of Knowledge (JTB) | 知识的三元定义（JTB）

A standard formula for propositional knowledge held until Gettier’s challenge. According to the JTB analysis, a subject S knows a proposition p if and only if three conditions are met simultaneously.

在葛梯尔提出质疑之前，命题知识的标准公式一直如此。根据 JTB 分析，一个主体 S 知道命题 p，当且仅当同时满足三个条件。

S knows that p ⟷ [ (p is true) ∧ (S believes that p) ∧ (S is justified in believing that p) ]

This formula is treated as a necessary and sufficient condition schema: truth, belief, and justification together exhaust the concept of knowledge. If any one conjunct is missing, knowledge does not obtain.

该公式被视为一组充要条件的模式：真、信念和理由共同穷尽了知识的概念。只要缺少其中任何一项，就不构成知识。

2. Gettier Counterexamples: The JTB+? Formula | 葛梯尔反例：JTB+？公式

Gettier cases show that the JTB formula is not sufficient, because luck can intervene. A revised schema adds a ‘no false lemmas’ or ‘safety’ condition, but no single correction has gained universal acceptance.

葛梯尔案例表明 JTB 公式并非充分条件，因为运气可以介入。修正后的模式增添了一个“无假前提”或“安全性”条件，但没有任何单一修正获得普遍接受。

S knows that p ⟷ JTB(p) ∧ ¬∃q (q is false ∧ S’s justification for p depends on q)

The intuitive lesson is that knowledge cannot rest essentially on a falsehood. Many epistemologists now work with safety or virtue-theoretic templates.

直观的教训是，知识不能从根本上依赖于一个假命题。如今许多认识论者转而使用安全性或德性理论的模板。

3. The Ontological Argument: Anselm’s Logical Formula | 本体论论证：安瑟伦的逻辑公式

Anselm defines God as ‘that than which nothing greater can be conceived’ and builds a reductio ad absurdum. The logical core can be schematised.

安瑟伦将上帝定义为“无法设想有比之更伟大者”，并构建了一个归谬论证。其逻辑核心可以模式化。

1. God =_df the being such that no greater being can be thought.
2. If God exists only in the mind, then a greater being can be thought (one that exists in reality).
3. That leads to contradiction with (1).
∴ God exists in reality.

Gaunilo’s parody island uses the same formal structure to challenge the move from conception to real existence. This formula underpins all ontological proofs.

高尼罗的“迷失岛”戏仿使用了同样的形式结构来质疑从概念到实在存在的跨越。这一公式是所有本体论证明的基础。

4. The Cosmological Argument: Kalam Formula | 宇宙论论证：卡拉姆公式

The Kalam cosmological argument, defended by William Lane Craig, deploys a deductive chain with clear logical joints. It begins with the premise that everything that begins to exist has a cause.

由威廉·莱恩·克雷格辩护的卡拉姆宇宙论论证，使用了一条具有清晰逻辑关节的演绎链。它以“一切开始存在的事物都有原因”为前提。

1. ∀x (x begins to exist → x has a cause of its existence).
2. The universe began to exist.
3. ∴ The universe has a cause of its existence.
4. This cause must be uncaused, timeless, spaceless, and powerful — identified as God.

Whether premise (2) is supported by Big Bang cosmology or by philosophical arguments against actual infinities, the syllogism remains a central theorem in natural theology.

无论前提 (2) 是由大爆炸宇宙学支持，还是由反对实无穷的哲学论证支持，这一三段论始终是自然神学的核心定理。

5. The Teleological Argument: Paley’s Analogy Formula | 目的论论证（设计论证）— 佩利的类比公式

Paley’s design argument functions as an analogical inference: like effects have like causes. The formula connects observed complexity to a designer.

佩利的设计论证起着一个类比推理的作用：相似的结果有相似的原因。该公式将观察到的复杂性联系到一位设计者。

1. A watch exhibits complexity and purpose (C) and is known to be produced by an intelligent designer (D).
2. Natural organisms and the cosmos exhibit similar C⁺, even greater in degree.
3. ∴ Probably, nature/cosmos is also produced by an intelligent designer (D⁺).

Hume’s criticisms — such as the problem of alternative analogies and the unicity of the universe — are standard counter-formulae that weaken the inference.

休谟的批评——比如另类比拟的难题以及宇宙的独特性——是削弱此推论的标准反公式。

6. The Problem of Evil: Epicurus’ Logical Trilemma | 恶的问题：伊壁鸠鲁的逻辑三难

Often cited as a ‘trilemma’, this formula shows that the existence of evil is logically incompatible with the attributes of an all-LMN God (omnipotent, omnibenevolent, omniscient).

这通常被称为“三难推理”，该公式表明，恶的存在与一个全知、全能、全善的上帝的属性在逻辑上是不相容的。

1. If God is omnipotent, He can prevent all evil.
2. If God is omnibenevolent, He wants to prevent all evil.
3. Evil exists.
4. ∴ An omnipotent, omnibenevolent God does not exist. (Or not all three attributes hold simultaneously.)

Augustinian and Irenaean theodicies offer ‘solutions’ that adjust or reinterpret the premises, acting as rival philosophical theorems.

奥古斯丁式和伊里奈乌式的神正论提供了调整或重新解释前提的“解法”，它们本身是对抗性的哲学定理。

7. Deductive and Inductive Reasoning: Formal Structures | 演绎与归纳推理：形式结构

In philosophy, understanding the difference between validity and soundness is essential. A deductive argument is truth-preserving; an inductive argument is probability-raising.

在哲学中，理解有效性与健全性的区别至关重要。演绎论证是保真的；归纳论证是提高概率的。

Deductive: If premises are true, conclusion must be true. (Valid: P1 ∧ P2 → Conclusion)
Inductive: If premises are true, conclusion is probably true. (Strong: P1 ∧ P2 ↗ Conclusion)

The WJEC exam expects you to label arguments explicitly as ‘deductive and valid but unsound if a premise is false’ or ‘inductively strong but not demonstrative’.

WJEC 考试要求你明确地为论证贴上标签，如“演绎有效，但若一个前提为假则不够健全”或“归纳力度强，但不具有证明性”。

8. Modus Ponens and Modus Tollens | 肯定前件和否定后件

These are the two most fundamental deductive rules used across religious and epistemological arguments. Recognising their form allows instant evaluation of validity.

这是贯通宗教论证与认识论论证的两条最基本的演绎规则。认出它们的形式，就能立刻评估有效性。

Modus Ponens: P → Q, P ∴ Q
Modus Tollens: P → Q, ¬Q ∴ ¬P

Many mistakes in student essays come from asserting the consequent (P → Q, Q ∴ P) or denying the antecedent (P → Q, ¬P ∴ ¬Q), both of which are fallacious.

学生论文中的许多错误都源自肯定后件 (P → Q, Q ∴ P) 或否认前件 (P → Q, ¬P ∴ ¬Q)，这两种形式都是谬误。

9. The Problem of Induction – Hume’s Sceptical Theorem | 归纳问题 — 休谟的怀疑定理

Hume argues that inductive inferences cannot be rationally justified without circularity. The argument can be compressed into a dilemma.

休谟主张，归纳推理无法在不陷入循环的情况下得到理性辩护。该论证可以浓缩为一个二难推理。

1. All inductive arguments rely on the Uniformity Principle (UP): the future will resemble the past.
2. To justify UP, we must use either a deductive argument or an inductive argument.
3. Deduction cannot establish UP (it is not a logical truth).
4. Induction would presuppose UP (circular).
∴ Inductive reasoning cannot be rationally justified.

This theorem remains a watershed in epistemology and directly connects to the reliability of arguments for God’s existence based on experience.

这一定理是认识论的分水岭，并直接关系到基于经验的上帝存在论证的可靠性。

10. Cartesian Doubt and the Cogito Formula | 笛卡尔怀疑论与“我思故我在”公式

Descartes’ method of radical doubt seeks an indubitable foundation. The ‘Cogito’ emerges as the first certainty: I think, therefore I am.

笛卡尔的彻底怀疑方法寻求一个无可怀疑的根基。“我思故我在”作为第一个确定性浮现出来。

Even if an evil demon deceives me about all my beliefs, I must exist in order to be deceived.
¬(∃deception) → ¬(∃self) is impossible.
∴ I exist — so long as I am thinking.

The Cogito is not a syllogism; it is a performative intuition. It serves as the theorem from which Descartes reconstructs knowledge of the external world.

“我思”并非一个三段论，而是一次施行性的直观。它是笛卡尔重建外部世界知识所依据的定理。

11. Substance Dualism: Descartes’ Divisibility Argument | 实体二元论：笛卡尔的可分性论证

Descartes offers a formula distinguishing mind and body through their essential attributes: thought and extension.

笛卡尔提供了一个通过本质属性——思维与广延——来区分心灵与身体的公式。

1. Body is essentially divisible (extended substance).
2. Mind is essentially indivisible (thinking substance).
3. If X and Y are essentially different, they cannot be identical.
∴ Mind ≠ Body (substance dualism).

The ‘masked man’ fallacy and the interaction problem are standard criticisms that challenge the inference from conceivability to real distinctness.

“蒙面人”谬误和交互问题是标准的批评，它们挑战了从可设想性到真实区分的推论。

12. Physicalism: The Identity Theory Formulation | 物理主义：同一论公式

Mind-brain identity theory proposes that mental states are numerically identical with brain states, just as water is H₂O. The central formula is an identity statement, not a causal law.

心脑同一论主张，心理状态与大脑状态在数目上是同一的，就像水是 H₂O 一样。其核心公式是同一陈述，而非因果定律。

∀m (Mental state M → ∃b (Brain state B ∧ M = B))

Critics appeal to multiple realizability (Putnam): the same mental state can be realised by different physical substrates, which conflicts with the strict identity formula.

批评者诉诸多重可实现性（普特南）：同一心理状态可由不同的物理基质实现，这与严格的同一公式相冲突。

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