AS CAIE Philosophy: Quick Reference Handbook of Formulas and Theorems | AS CAIE 哲学：公式定理速查手册

📚 AS CAIE Philosophy: Quick Reference Handbook of Formulas and Theorems | AS CAIE 哲学：公式定理速查手册

This handbook compiles the essential ‘formulas’ and ‘theorems’—the key arguments, principles, and logical patterns—needed for the AS CAIE Philosophy syllabus. Each entry is presented as a clear, modular statement, like an equation, to help you memorise and apply philosophical reasoning in your exams. Whether you are analysing the Teleological Argument or evaluating Utilitarianism, this quick reference will ground your essays in rigorous logical structure.

本手册汇编了 AS CAIE 哲学课程所需的“公式”和“定理”——核心论证、原则和逻辑模式。每个条目均以清晰、模块化的陈述形式呈现，如同方程式一般，帮助您在考试中记忆并运用哲学推理。无论您是在分析目的论论证还是评估功利主义，这份速查手册都将使您的论文具备严谨的逻辑结构。

1. Modus Ponens and Modus Tollens | 肯定前件与否定后件

Modus Ponens: If P then Q; P; therefore Q. Symbolically: (P → Q) ∧ P ⊢ Q. This is the most fundamental rule of deductive inference. For example: If it rains, the ground is wet. It rains. Therefore, the ground is wet.

肯定前件：若 P 则 Q；P 成立；因此 Q 成立。符号表示为：(P → Q) ∧ P ⊢ Q。这是最基础的演绎推理规则。例如：如果下雨，地面就会湿。下雨了。因此，地面湿了。

Modus Tollens: If P then Q; Not Q; therefore Not P. Symbolically: (P → Q) ∧ ¬Q ⊢ ¬P. Example: If the watch has a designer, it shows complex order. The watch does not show complex order (it is random). Therefore, it does not have a designer. This form is crucial for evaluating design arguments.

否定后件：若 P 则 Q；非 Q；因此非 P。符号表示为：(P → Q) ∧ ¬Q ⊢ ¬P。示例：如果手表有设计者，那么它会显示出复杂的秩序。手表没有显示复杂的秩序（它是随机的）。因此，它没有设计者。这种推理形式对于评估设计论证至关重要。

2. Fallacies: Affirming the Consequent and Denying the Antecedent | 谬误：肯定后件与否定前件

Affirming the Consequent: (P → Q) ∧ Q ⊢ P is invalid. The truth of Q does not guarantee the truth of P. For instance: If it is a dog, then it is a mammal. It is a mammal. Therefore, it is a dog. (It could be a cat.) This fallacy often appears in poorly formed cosmological arguments.

肯定后件谬误：(P → Q) ∧ Q ⊢ P 是无效的。Q 为真并不能保证 P 为真。例如：如果它是狗，那么它就是哺乳动物。它是哺乳动物。因此，它是狗。（它可能是猫。）这种谬误常出现在不严谨的宇宙论论证中。

Denying the Antecedent: (P → Q) ∧ ¬P ⊢ ¬Q is also invalid. Example: If it rains, the ground is wet. It does not rain. Therefore, the ground is not wet. (The ground could be wet from a sprinkler.) Recognising these fallacies is essential for critical analysis in AS Philosophy.

否定前件谬误：(P → Q) ∧ ¬P ⊢ ¬Q 同样无效。例子：如果下雨，地面就会湿。没有下雨。因此，地面不湿。（地面可能因为洒水器而湿。）识别这些谬误对于 AS 哲学考试中的批判性分析至关重要。

3. Direct Realism and the Argument from Illusion | 直接实在论与幻觉论证

Direct Realism claims: When an observer perceives an object O, O itself is directly and immediately present to the mind, and O exists mind-independently. The perceptual equation: Perception(O) → O exists. However, the Argument from Illusion challenges this by presenting cases where we perceive something that is not the real object (e.g., a straight stick looking bent in water).

直接实在论主张：当观察者感知对象 O 时，O 本身直接且立即地呈现于心灵，并且 O 是独立于心灵存在的。感知方程式为：感知(O) → O 存在。然而，幻觉论证对此提出质疑，指出在某些情况下，我们感知到的并非真实对象（例如，直棍在水中看起来是弯的）。

Formally, the argument poses: In an illusion, we perceive a sensible quality F (bentness), but the real object does not possess F. If we were directly aware of the real object, we would be aware of its actual qualities. Since we are aware of a non-actual quality, we must be aware of a sense-datum, not the physical object. Therefore, Direct Realism is false.

该论证的形式是：在幻觉中，我们感知到一种可感性质 F（弯曲），但真实对象并不具备 F。如果我们直接意识到真实对象，就会意识到其实际性质。既然我们意识到了非实际的性质，那么我们意识到的必定是感觉材料，而非物理对象。因此，直接实在论为假。

4. Locke’s Psychological Continuity Theory of Personal Identity | 洛克的人格同一性心理连续性理论

Locke’s formula: Person P₂ at time t₂ is the same person as P₁ at time t₁ if and only if P₂ remembers the thoughts and actions of P₁ (i.e., psychological continuity via memory). Symbolically: SamePerson(P₁,t₁, P₂,t₂) ↔ MemoryContinuity(P₁,P₂). This rejects bodily identity as the criterion.

洛克的公式：时间 t₂ 的人 P₂ 与时间 t₁ 的 P₁ 是同一个人，当且仅当 P₂ 记得 P₁ 的思想和行为（即通过记忆实现的心理连续性）。符号表示为：SamePerson(P₁,t₁, P₂,t₂) ↔ MemoryContinuity(P₁,P₂)。这否定了身体同一性作为标准。

Objections: Thomas Reid’s Brave Officer paradox shows transitivity of identity conflicts with memory lapses. Suppose the old general remembers being a brave officer, and the brave officer remembers being a flogged boy, but the general does not remember the flogged boy. By Locke’s criterion, the general is identical to the officer, the officer to the boy, but the general is not identical to the boy—violating transitivity. Thus the ‘memory formula’ alone is insufficient and must be replaced with overlapping chains of psychological connectedness (as in Parfit’s revision).

反对意见：托马斯·里德的“勇敢军官”悖论表明，同一性的传递性与记忆缺失相冲突。假设老将军记得自己曾是勇敢军官，军官记得自己是被鞭打的男孩，但将军不记得男孩。按洛克的标准，将军与军官同一，军官与男孩同一，但将军与男孩不同一——这违背了传递性。因此，仅凭“记忆公式”是不够的，必须代之以心理联系的重叠链条（如帕菲特修正的理论）。

5. Paley’s Design Argument (Teleological Argument) | 佩利的设计论证（目的论论证）

Paley’s analogical formula: A watch exhibits complex order with a purpose, so it must have a designer. The universe exhibits even greater complex order with apparent purpose, so by analogy, the universe must have a Designer (God). Form: Object X has property P (complex purposeful arrangement). The best explanation for P is intelligence. The universe has P. Therefore, the universe has an intelligent Designer.

佩利的类比公式：手表展现了具有目的的复杂秩序，因此它必定有一位设计者。宇宙展现出更加庞大的、具有目的的复杂秩序，因此通过类比，宇宙必定有一位设计者（上帝）。形式为：对象 X 具有属性 P（复杂的目的性安排）。对 P 的最佳解释是智能。宇宙具有 P。因此，宇宙有一位智能设计者。

Hume’s critiques: The analogy is weak—the universe is not sufficiently like a watch. Moreover, even if there is a designer, it does not prove the classical theistic God; it could be a team of gods, an infant deity, or an incompetent one. The argument also suffers from an inductive leap: we observe watch-makers, but we never observe universe-makers, so the inference to a Designer is not grounded in experience.

休谟的批判：类比很弱——宇宙并不足够像一个手表。此外，即使存在一位设计者，也无法证明这就是古典有神论的上帝；它可能是一群神、一个稚嫩的神或一个无能的神。这个论证还存在归纳上的跳跃：我们观察到手表制造者，但从未观察到宇宙制造者，因此向一位设计者的推论缺乏经验基础。

6. Anselm’s Ontological Argument | 安瑟伦的本体论论证

Anselm’s definition: God is ‘that than which nothing greater can be conceived’ (TT

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