📚 AS Cambridge Philosophy: Quick Reference Handbook of Key Concepts and Arguments | AS 剑桥哲学：关键概念与论证速查手册
In philosophy, mastering the subject requires a firm grasp of central definitions, arguments, and logical forms—much like the formulas and theorems in mathematics. This quick reference handbook collects the “theorems” you must know for the AS Cambridge Philosophy syllabus, covering epistemology, ethics, logic, and the philosophy of religion. Each entry presents the concept precisely and is followed by its Chinese translation, enabling rapid review and bilingual consolidation.
在哲学中，精通这门学科需要牢固掌握核心定义、论证和逻辑形式——就像数学中的公式和定理一样。本速查手册汇总了 AS 剑桥哲学大纲中你必须掌握的“定理”，涵盖认识论、伦理学、逻辑学和宗教哲学。每个条目都以精确的方式呈现概念，并附有中文译文，便于快速复习和双语巩固。
1. The Tripartite Definition of Knowledge | 知识的三元定义
The classical account, often associated with Plato, defines knowledge as justified true belief (JTB). Formally: a subject S knows a proposition P if and only if (i) P is true, (ii) S believes that P, and (iii) S is justified in believing P.
经典解释通常归功于柏拉图，将知识定义为证成的真信念（JTB）。形式化表述：一个主体 S 知道命题 P，当且仅当 (i) P 为真，(ii) S 相信 P，(iii) S 对相信 P 有证成。
These conditions are often summarised in the following biconditional:
这些条件常用以下双条件式总结：
K(S, P) ↔ B(S, P) ∧ T(P) ∧ J(S, P)
| Condition (English) | 条件 (中文) |
|---|---|
| Truth – The proposition is objectively true. | 真——命题在客观上为真。 |
| Belief – The subject accepts the proposition. | 信念——主体接受该命题。 |
| Justification – The subject possesses adequate reasons or evidence. | 证成——主体持有充分的理由或证据。 |
This tripartite analysis formed the orthodox view until the 1960s, when counterexamples exposed its weakness.
这一三元分析曾构成正统观点，直到 20 世纪 60 年代反例暴露了它的弱点。
2. The Gettier Problem and No-False-Lemma | 盖梯尔问题与无假前提条件
Edmund Gettier (1963) demonstrated that justified true belief is not sufficient for knowledge. In his classic cases, a subject forms a justified true belief that is true merely by epistemic luck. For instance, Smith has strong evidence for “Jones owns a Ford” and deduces “Either Jones owns a Ford or Brown is in Barcelona”. Unbeknownst to Smith, Jones does not own a Ford, but Brown coincidentally is in Barcelona.
Edmund Gettier (1963) 证明，证成的真信念不足以构成知识。在他的经典案例中，主体形成了一个证成的真信念，但该信念的真仅仅来自认知运气。例如，史密斯有充分证据相信“琼斯拥有一辆福特”，并由此推导出“或者琼斯拥有一辆福特，或者布朗在巴塞罗那”。史密斯不知道琼斯并没有福特，但布朗恰好在巴塞罗那，使得析取命题为真。
One prominent response adds a fourth condition—the no-false-lemma condition: S knows that P if (i) S believes P, (ii) P is true, (iii) S is justified in believing P, and (iv) S’s justification does not rest on any false proposition.
一个著名的回应增加了第四个条件——无假前提条件：S 知道 P，如果 (i) S 相信 P，(ii) P 为真，(iii) S 对 P 的信念有证成，(iv) S 的证成不依赖于任何假命题。
While this condition handles many original Gettier cases, subsequent examples have shown that the project of adding ad hoc conditions faces continuing challenges.
虽然该条件处理了许多原始盖梯尔案例，但后来的例子表明，添加特设条件的做法仍面临持续的挑战。
3. Internalism vs Externalism | 内在主义与外在主义
Internalists about justification contend that the factors that make a belief justified must be cognitively accessible to the subject through reflection. If a subject cannot be aware of what justifies her belief, the belief is not genuinely justified for her. Externalists deny this requirement: justification can depend on factors outside the subject’s conscious reach, such as the reliability of the belief-forming process.
关于证成的内在主义者主张，使信念得以证成的因素必须是主体通过反思可以认知抵达的。如果主体无法意识到是什么证成了她的信念，那么这个信念对她而言就不是真正被证成的。外在主义者否认这一要求：证成可以取决于主体意识不可及的因素，例如信念形成过程的可靠性。
Externalism is often motivated by reliabilism, which identifies a justified belief with one produced by a truth-conducive cognitive process. In reliabilism, what matters is the actual reliability, not the subject’s awareness of it.
外在主义常常由可靠主义推动，可靠主义将证成的信念等同于由导向真理的认知过程所产生的信念。在可靠主义那里，重要的是实际的可靠性，而不是主体对此的意识。
This debate shapes responses to scepticism and influences theories of knowledge.
这一争论塑造了对怀疑论的回应，并影响着知识论。
4. Foundationalism vs Coherentism | 基础主义与融贯主义
Foundationalism claims that the structure of justified beliefs resembles a building: all non-basic beliefs derive their justification from basic beliefs, which are self-justifying or non-inferentially justified. Basic beliefs halt the regress of justification. Classic candidates include beliefs about immediate sensory experiences (e.g., “I am appeared to redly”) and self-evident truths.
基础主义主张，证成信念的结构像一座建筑：所有非基础信念都是从基础信念那里获得证成的，而基础信念是自我证成的或非推理地得到证成的。基础信念终止了证成的回溯。经典的候选者包括关于直接感觉经验的信念（如“我似乎看到了红色”）和自明真理。
Coherentism denies the need for basic beliefs. It holds that a belief is justified if and only if it coheres with the subject’s entire web of beliefs. Justification is a matter of mutual support and consistency within the system.
融贯主义否认基础信念的必要性。它主张，一个信念是证成的，当且仅当它与主体整个信念之网相融贯。证成是系统内的相互支持和一致性问题。
The classical regress argument states that if every justified belief requires another justified belief as its basis, then an infinite regress, a circle, or an arbitrary stopping point appears. Foundationalism reacts by positing basic beliefs; coherentism accepts a virtuous circularity.
经典的回溯论证指出，如果每一个证成的信念都需要另一个证成的信念作为其依据，那么就会出现无限回溯、循环或武断的终止点。基础主义的回应是设定基础信念；融贯主义则接受一种良性的循环。
5. Reliability Theory of Knowledge | 知识的可靠理论
Reliabilism replaces the justification component with a reliability condition: S knows that P if and only if P is true, S believes that P, and S’s true belief is produced by a cognitive process that reliably leads to true beliefs. Reliability is typically understood as a high truth ratio in the relevant possible worlds.
可靠主义用可靠性条件替代了证成部分：S 知道 P，当且仅当 P 为真，S 相信 P，并且 S 的真信念是由一个可靠地导向真信念的认知过程所产生的。可靠性通常被理解为在相关可能世界中具有较高的真值比率。
K(S, P) ↔ T(P) ∧ B(S, P) ∧ Reliable(process)
A reliable process is one that yields mostly true beliefs, e.g., perception in good light, clear memory, and deductive reasoning. Unreliable processes include wishful thinking and guessing.
可靠的认知过程是那些产生多半为真信念的过程，例如良好光线下的感知、清晰的记忆和演绎推理。不可靠的过程则包括一厢情愿的思考和猜测。
Reliabilism elegantly handles many Gettier cases by noting that the belief-forming process was unreliable in the specific circumstances, even if the final belief happened to be true.
可靠主义优雅地处理了许多盖梯尔案例，因为它指出，尽管最终信念碰巧为真，但信念形成过程在特定情境下并不可靠。
6. Deductive Validity and Soundness | 演绎有效性与健全性
A deductive argument is valid if it is logically impossible for the premises to be true while the conclusion is false. Validity concerns the structure of the argument, not the actual truth of the premises.
一个演绎论证是有效的，如果在逻辑上不可能前提为真而结论为假。有效性涉及论证的结构，而不是前提的实际真值。
Valid: If Premises are true, Conclusion must be true (truth-preserving).
An argument is sound if it is both valid and all of its premises are actually true. Soundness guarantees a true conclusion.
一个论证是健全的，如果它既有效又所有前提事实上为真。健全性保证了结论为真。
Common valid forms include Modus Ponens and Modus Tollens:
常见的有效形式包括肯定前件和否定后件：
Modus Ponens: P → Q, P ⊢ Q
Modus Tollens: P → Q, ¬Q ⊢ ¬P
These forms are foundational to philosophical analysis and are tested implicitly in evaluating ethical and metaphysical arguments.
这些形式是哲学分析的基础，在评估伦理学和形而上学论证时会被隐性地考查。
7. The Principle of Utility | 功利原则
Jeremy Bentham’s principle of utility states that an action is morally right if it tends to promote the greatest happiness for the greatest number. Happiness is understood as pleasure and the absence of pain.
边沁的功利原则指出，一个行为在道德上是对的，如果它倾向于促进最大多数人的最大幸福。幸福被理解为快乐和痛苦的缺失。
Happiness = Σ (Pleasure) − Σ (Pain)
Bentham proposed a hedonic calculus to measure the value of pleasures, considering seven dimensions:
边沁提出了幸福计算来度量快乐的价值，考虑七个维度：
| Dimension (English) | 维度 (中文) |
|---|---|
| Intensity | 强度 |
| Duration | 持续时间 |
| Certainty | 确定性 |
| Propinquity (remoteness) | 远近 |
| Fecundity (chance of being followed by more pleasure) | 丰产性（带来更多快乐的可能性） |
| Purity (chance of not being followed by pain) | 纯度（后不随痛苦的可能性） |
| Extent (number of people affected) | 范围（受影响的人数） |
John Stuart Mill later refined the theory, arguing for qualitative distinctions between higher and lower pleasures, famously stating that it is better to be a human being dissatisfied than a pig satisfied.
约翰·斯图尔特·密尔后来完善了这一理论，主张高等快乐与低等快乐之间存在质的区别，并提出那句名言：宁愿做一个不满足的人，也不做一头满足的猪。
8. The Categorical Imperative (First Formulation) | 定言令式（第一公式）
Immanuel Kant’s first formulation of the categorical imperative is: “Act only according to that maxim whereby you can at the same time will that it should become a universal law.”
康德定言令式的第一个公式是：“只按照你同时能够意愿它成为一条普遍法则的格准去行动。”
Max
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