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

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

Philosophy may not feature the x’s and y’s of algebra, but its arguments rely on a rigorous architecture of logical formulas, inferential rules, and conceptual principles. This handbook distils the core logical machinery, valid argument forms, key philosophical principles, and the formalised structures of major arguments across epistemology, ethics, philosophy of religion, and metaphysics. Treat it as your essential quick-reference toolkit for AS CCEA Philosophy, enabling you to dissect, construct, and evaluate arguments with precision.

哲学虽不像代数那样满是 x 和 y，但其论证却建立在严谨的逻辑公式、推理规则和概念原则上。这本速查手册浓缩了核心逻辑工具、有效论证形式、关键哲学原则以及认识论、伦理学、宗教哲学和形而上学中各主要论证的形式化结构。将其视为你备战 AS CCEA 哲学的基本速查工具箱，助你准确剖析、构建和评估论证。

1. Propositional Logic Essentials | 命题逻辑精要

Propositional logic is the bedrock of philosophical analysis, using simple symbols to represent statements and connectives to express logical relationships. Below is the truth-table anatomy of the five fundamental connectives. In the tables, ‘1’ stands for True and ‘0’ for False.

命题逻辑是哲学分析的基石，它用简单符号代表语句，用联结词表达逻辑关系。以下是五种基本联结词的真值表剖析。表中 ‘1’ 代表真，’0′ 代表假。

Connective	Symbol	Truth-Table Pattern
Negation (not)	¬	P:1→0; P:0→1
Conjunction (and)	∧	(1∧1)=1; all others 0
Disjunction (or)	∨	(0∨0)=0; all others 1
Material Implication (if…then)	→	(1→0)=0; all others 1
Biconditional (iff)	↔	same as equality: (1↔1)=1, (0↔0)=1; others 0

The material conditional P → Q is false only when the antecedent P is true and the consequent Q is false. This minimal definition often surprises beginners but is essential for formal deduction.

实质条件句 P → Q 当前件 P 为真且后件 Q 为假时才为假。这一最低限度定义常令初学者意外，但对形式演绎至关重要。

Any propositional form that is true in every row of its truth table is a tautology, e.g., P ∨ ¬P (law of excluded middle). A contradiction is false in every row, e.g., P ∧ ¬P.

任何在真值表每一行都为真的命题形式便是重言式，如 P ∨ ¬P（排中律）。矛盾式则在每一行都为假，如 P ∧ ¬P。

---

2. Valid Argument Forms: The Engine of Proof | 有效论证形式：证明的引擎

These deductive forms guarantee that if the premises are true, the conclusion must be true. Internalising them is non-negotiable for AS philosophy success.

这些演绎形式确保若前提为真，结论必然为真。将其内化是 AS 哲学成功的必要条件。

Modus Ponens (Affirming the Antecedent): From P → Q and P, infer Q.

肯定前件式：由 P → Q 和 P，推出 Q。

P → Q, P ⊢ Q

Modus Tollens (Denying the Consequent): From P → Q and ¬Q, infer ¬P.

否定后件式：由 P → Q 和 ¬Q，推出 ¬P。

P → Q, ¬Q ⊢ ¬P

Hypothetical Syllogism: From P → Q and Q → R, infer P → R. This is a chain of conditionals.

假言三段论：由 P → Q 和 Q → R，推出 P → R。这是条件链。

P → Q, Q → R ⊢ P → R

Disjunctive Syllogism: From P ∨ Q and ¬P, infer Q (works symmetrically).

选言三段论：由 P ∨ Q 和 ¬P，推出 Q（对称有效）。

P ∨ Q, ¬P ⊢ Q

Constructive Dilemma: From (P → Q) ∧ (R → S) and P ∨ R, infer Q ∨ S. A powerful tool in complex arguments.

建设性二难推理：由 (P → Q) ∧ (R → S) 和 P ∨ R，推出 Q ∨ S。复杂论证中的利器。

(P → Q) ∧ (R → S), P ∨ R ⊢ Q ∨ S

These forms are often used to formalise classic philosophical moves, such as Descartes’ cogito implicitly relying on modus ponens after establishing ‘If I think, I exist’.

这些形式常被用来形式化经典哲学步骤，如笛卡尔的我思故我在，在确定「如果我思则我在」后隐含地使用了肯定前件式。

---

3. Common Formal and Informal Fallacies | 常见形式与非形式谬误

Spotting fallacies is as vital as constructing valid arguments. Here are the most examinable ones for AS CCEA, expressed as faulty inference patterns.

发现谬误与构建有效论证同样重要。以下是 AS CCEA 考试中最常见的谬误，以错误的推理模式表述。

Affirming the Consequent: P → Q, Q, therefore P. This invalid form seduces many reasoners.

肯定后件谬误：P → Q, Q，故 P。这一无效形式诱惑着许多推理者。

Invalid: P → Q, Q ⊢ P

Denying the Antecedent: P → Q, ¬P, therefore ¬Q. Another trap that ignores alternative causes for Q.

否定前件谬误：P → Q, ¬P，故 ¬Q。又一个忽略 Q 其他可能原因的陷阱。

Invalid: P → Q, ¬P ⊢ ¬Q

Begging the Question (Petitio Principii): The conclusion is assumed within the premises, making the argument circular. Formally: P, therefore P.

乞题谬误：结论暗含在前提之中，使论证循环。形式化为：P，故 P。

False Dilemma: Presents only two options when more exist. Form: P ∨ Q is falsely claimed, while R, S etc. are possible.

假两难谬误：仅呈现两个选项而实际上存在更多可能性。形式：错误地宣称 P ∨ Q 为真，而 R、S 等实为可能。

Straw Person: Misrepresenting an opponent’s argument (X) as a weaker version (Y) to attack it easily. Could be modelled as incorrectly asserting X → Y and then attacking Y.

稻草人谬误：将对手论证 (X) 曲解为较弱版本 (Y) 并轻松攻击。可模型化为错误地断定 X → Y 然后攻击 Y。

---

4. Epistemology: Key Principles and Distinctions | 认识论：关键原则与区分

AS epistemology demands mastery of the analytic-synthetic distinction, the a priori-a posteriori divide, and the definition of knowledge. Think of these as conceptual formulas.

AS 认识论要求掌握分析-综合区分、先天-后天之分以及知识的定义。请将这些视作概念公式。

The Classic JTB Formula: Knowledge = Justified True Belief. S knows that P iff (i) P is true; (ii) S believes that P; (iii) S is justified in believing that P.

经典 JTB 公式：知识 = 被证成的真信念。某人 S 知道命题 P 当且仅当 (i) P 为真；(ii) S 相信 P；(iii) S 有理由相信 P。

Gettier Cases as Counterexample Formula: A situation where JTB holds, but knowledge does not, due to accidental truth. No single formal fix exists, but the schema is: JTB + epistemic luck = not knowledge.

盖梯尔案例作为反例公式：JTB 满足但因偶然真而导致无知的情形。虽无单一形式修正法，但模式为：JTB + 认知运气 ≠ 知识。

Rationalism’s Core Thesis: Some substantive knowledge is innate or gained through reason alone, prior to sensory experience. Formula: ∃K such that K is synthetic a priori.

理性主义核心论题：某些实质性知识是与生俱来或仅凭理性先于感官经验获得的。公式：存在知识 K，且 K 为先天综合。

Empiricism’s Core Thesis: All knowledge of the world originates in sense experience; there are no innate ideas. Rejecting synthetic a priori for factual claims.

经验主义核心论题：一切关于世界的知识均源于感官经验；不存在天赋观念。拒斥关于事实的先天综合。

Hume’s Fork (Problem of Induction): Matters of fact cannot be deduced from reason alone; induction assumes the uniformity of nature, which itself cannot be proven without circularity. Principle: the future will resemble the past is not a logical truth.

休谟之叉（归纳问题）：事实问题不能单凭理性演绎；归纳假定自然齐一性，这一假定本身无法在不陷入循环的情况下被证明。原则：「未来将如同过去」并非逻辑真理。

---

5. Ethical Theories: Normative Formulas | 伦理学理论：规范公式

Each major ethical theory can be expressed as a fundamental formula or decision procedure. These are indispensable for CCEA ethical questions.

每种主要伦理学理论都可表述为一个基本公式或决策程序。这对 CCEA 伦理考题不可或缺。

Utilitarianism (Classical Hedonic Formula): An action is right if it maximises net utility, i.e., pleasure minus pain, for all affected. Bentham’s calculus: Quantity × Intensity × Duration × Certainty × Propinquity × Fecundity × Purity × Extent.

功利主义（经典快乐公式）：若一行动为所有受影响者最大化净效用（快乐减去痛苦），则其为正当。边沁的计量：量 × 强度 × 持续时间 × 确定性 × 邻近性 × 多产性 × 纯度 × 范围。

Kant’s Categorical Imperative (Universal Law Formula): “Act only according to that maxim whereby you can at the same time will that it should become a universal law.” Logically, if a maxim cannot be universalised without contradiction (in conception or in will), the act is impermissible.

康德绝对命令（普遍法则公式）：「只依据那种你同时能够愿意它成为普遍法则的准则去行动。」逻辑上，若一准则不可无矛盾地普遍化（构想中或意愿中），则该行为不许可。

Kant’s Humanity Formula: “Act in such a way that you treat humanity, whether in your own person or in the person of another, always at the same time as an end, never merely as a means.” This prohibits using rational agents instrumentally without their consent.

康德人性公式：「你要如此行动，以至无论是对你自己还是对别人，在任何时候都把人当作目的，而不仅仅当作手段。」这禁止未经同意将理性存在者当作工具使用。

Aristotelian Virtue Ethics Formula: An act is right if it is what a virtuous person would do, hitting the golden mean between two vices (excess and deficiency). Virtue is a disposition to choose the mean relative to us, determined by reason.

亚里士多德美德伦理学公式：若一行为为有德之人所做，且击中两恶（过度与不及）间的中道，则为正当。美德是依据理性选择相对于我们中道的气质。

---

6. Arguments for God’s Existence: Logical Structures | 上帝存在的论证：逻辑结构

The classic theistic proofs can be stripped to their logical skeletons. Master these templates for quick analysis in exams.

经典有神论证可被剥至逻辑骨架。掌握这些模板以在考试中快速分析。

Anselm’s Ontological Argument (Formalisation): (1) God is that-than-which-a-greater-cannot-be-conceived. (2) Existence in reality is greater than existence in the mind alone. (3) If God exists only in the mind, a greater being (existing in reality) could be conceived. (4) Therefore, God must exist in reality. Reductio ad absurdum form: assume God does not exist → contradiction with the definition.

安瑟伦本体论论证（形式化）：(1) 上帝是被设想为无与伦比之伟大者。 (2) 存在于现实比仅存在于心灵中更伟大。 (3) 若上帝仅存在于心灵，则能设想一更伟大者（存在于现实）。 (4) 故上帝必在现实中存在。归谬法形式：假设上帝不存在 → 与定义矛盾。

Aquinas’ Second Way (First Cause): (1) We observe efficient causes in a chain. (2) Nothing can be the cause of itself. (3) An infinite chain of causes would have no first cause, so no subsequent causes. (4) Therefore, there must be a first uncaused cause, which all call God. Formula: ¬(∃self-caused) ∧ ¬(∞ regress) ⊢ ∃first cause.

阿奎那第二路（第一因）：(1) 我们观察到动力因序列。 (2) 无物可自因。 (3) 无限因果链将无第一因，从而无后继原因。 (4) 故必有第一非受动因，人人称之为上帝。公式：¬(自因) ∧ ¬(无限回溯) ⊢ ∃第一因。

Paley’s Design Argument (Teleological): (1) The world exhibits complex order and purpose (like a watch). (2) Complex order with purpose implies an intelligent designer. (3) Therefore, the world has an intelligent designer (God). Analogical form: Watch : Watchmaker :: Universe : God.

帕雷的设计论证（目的论）：(1) 世界呈现复杂秩序与目的（如钟表）。 (2) 复杂秩序与目的蕴含理智设计者。 (3) 故世界有一理智设计者（上帝）。类比形式：钟表之于制表匠如同宇宙之于上帝。

Logical Problem of Evil (Inconsistent Triad): God is omnipotent, omnibenevolent, and evil exists. These are logically incompatible. Formal contradiction: If omnipotent, God can eliminate evil; if omnibenevolent, God would want to; so if both, evil would not exist. But evil exists; therefore such a God does not exist.

恶的逻辑问题（不一致三元组）：上帝全能、全善，而恶存在。三者逻辑上不相容。形式矛盾：若全能则能除恶，若全善则愿除恶，故若兼具则恶不应存在。但恶存在，故如此之上帝不存在。

---

7. Philosophy of Mind: Positions and Arguments | 心灵哲学：立场与论证

Mind theories often boil down to claims about whether mental states are reducible to physical states. Here are the formulas and key thought experiments.

心灵理论常归结为心理状态是否可还原为物理状态的主张。以下是公式及关键思想实验。

Substance Dualism: Mind and body are two distinct substances. Mind is non-physical, thinking substance; body is physical, extended substance. Formula: ∃ substances M (mental) and P (physical) such that M ≠ P and M can exist independently of P.

实体二元论：心灵与身体是两种不同的实体。心灵是非物理、思维实体；身体是物理、广延实体。公式：存在实体 M（心理）和 P（物理），M ≠ P 且 M 能独立于 P 存在。

Mind-Brain Identity Theory: Mental state types are identical to brain state types. For example, pain = C-fibre firing. Formula: ∀ mental state M, ∃ physical brain state B such that M = B. This is a type-type identity.

心脑同一论：心理状态类型等同于脑状态类型。例如，疼痛 = C 纤维激活。公式：∀ 心理状态 M，∃ 脑状态 B，使得 M = B。这是类型-类型同一。

Functionalism: Mental states are defined by their causal roles — what causes them and what they cause. Pain is whatever state results from bodily damage and causes avoidance behaviour. Formula: M = the functional role F (input→state→output) regardless of the physical substrate.

功能主义：心理状态由其因果角色定义——什么引起它们以及它们引起什么。疼痛是无论基底为何，凡由身体损伤引起并导致回避行为的状态。公式：M = 功能角色 F（输入→状态→输出），不论物理基质。

Mary’s Knowledge Argument (Against Physicalism): Mary knows all physical facts about colour vision but has never seen red. Upon seeing red, she learns new phenomenal facts. Therefore, not all facts are physical facts. Formula: Physical facts ⊉ all facts; qualia exist.

玛丽知识论证（反物理主义）：玛丽知道一切关于颜色视觉的物理事实但从未见过红色。见到红色时，她学到了新的现象事实。故非所有事实皆为物理事实。公式：物理事实集合不包含一切事实；存在感受质。

---

8. Metaphysics: Causation, Free Will and Identity | 形而上学：因果、自由意志与同一性

These principles frame debates on causation and personal identity – expressible in crisp conceptual formulas.

这些原则框定了关于因果关系和人格同一性的辩论——可用简洁概念公式表达。

Humean Constant Conjunction: We observe that event A is constantly followed by event B; we project necessary connection. Causation is ‘constant conjunction’ plus a mental habit. There is no rational proof of necessary causal connection.

休谟恒常联结：我们观察到事件 A 恒常被事件 B 跟随；我们投射出必然联系。因果只是「恒常联结」加上心理习惯。无必然因果联系的理性证明。

Determinism: Every event, including human actions, is necessitated by antecedent events and laws. Hard determinism formula: (Past states + Laws of nature) ⊢ every subsequent action. Thus, free will is an illusion.

决定论：每一事件，包括人类行为，都由先前事件和规律所必然决定。严格决定论公式：(过去状态 + 自然律) ⊢ 每一后续行为。故自由意志是幻象。

Compatibilism (Soft Determinism): Free will is compatible with determinism. A free act is one caused by the agent’s internal desires and beliefs without external constraint. Formula: Action A is free iff it is caused by the agent’s own volitions and is not externally coerced.

相容论（软决定论）：自由意志与决定论相容。一行为是自由的，若它由行动者内在欲望和信念引起且无外在强制。公式：行为 A 是自由的当且仅当它由行动者自身意志引起且不遭外力强迫。

Locke’s Psychological Continuity Theory of Personal Identity: Person P2 at time t2 is the same person as P1 at time t1 if and only if P2 remembers (or has psychological continuity with) the experiences of P1. Memory links forge identity.

洛克心理连续性人格同一性理论：时刻 t2 的人 P2 与时刻 t1 的人 P1 为同一个人当且仅当 P2 记得（或与 P1 的经验有心理连续性）。记忆链条锻造同一性。

---

Published by TutorHao | Philosophy Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）