📚 Year 12 CAIE Philosophy: Key Arguments and Concepts Quick Reference Guide | Year 12 CAIE 哲学：公式定理速查手册
This handbook distils the core 'formulae' (logical argument patterns) and 'theorems' (defining philosophical principles) that appear throughout the CAIE AS-Level Philosophy syllabus (9990). Just as a mathematician memorises standard transformations, a philosophy student must internalise these structures to recognise, analyse, and evaluate arguments with precision. Each entry singles out an essential definition, a deductive form, or a classic objection, pairing it with its symbolic representation where possible.
本速查手册提炼了 CAIE AS 哲学大纲（9990）中反复出现的核心“公式”（逻辑论证模式）和“定理”（规定性的哲学原理）。正如数学学习者必须熟记标准变换，哲学考生也需要内化这些结构，以便精准地识别、分析与评价论证。每一条目拣选一个关键定义、一种演绎形式或一种经典反驳，并尽可能配以符号表达。
1. The Tripartite Definition of Knowledge (JTB) | 知识的三元定义 (JTB)
The classical analysis maintains that a subject S knows a proposition p if and only if p is true, S believes that p, and S is justified in believing that p. Symbolically:
经典分析认为，认知者 S 知道命题 p 当且仅当 p 为真、S 相信 p，并且 S 有确证地相信 p。符号表达为：
Ksp ↔ (Tp ∧ Bsp ∧ Jsp)
This formula served as the undisputed 'theorem' of epistemology until Edmund Gettier showed in 1963 that justified true belief is not sufficient for knowledge. In a standard Gettier case, S has a justified true belief that p, but the belief is true only by accident, violating the intuition that knowledge excludes epistemic luck.
这一公式曾被视为认识论中无可争议的“定理”，直到埃德蒙·盖提尔于 1963 年证明，有确证的真信念并非知识的充分条件。在典型的盖提尔案例中，S 拥有一个有确证的真信念 p，但该信念为真仅出于偶然，从而违背了知识应当排除认知运气的直觉。
Gettier's counterexample can be expressed as a negation of sufficiency: even if Tp, Bsp, and Jsp all hold, ¬Ksp may be the case. Consequently, the JTB account is not a complete definition; alternative analyses add conditions such as the 'no false lemmas' clause or appeal to reliable belief-forming processes (reliabilism).
盖提尔的反例可以表达为对充分性的否定：即使 Tp、Bsp 与 Jsp 皆成立，¬Ksp 仍可能为真。因此，JTB 这一说明并非一个完整的定义；替代性分析会补充“无误导前提”条款，或诉诸可靠的信念形成过程（可靠论）。
2. Modus Ponens and Modus Tollens | 肯定前件与否定后件推理
Philosophical argument often turns on two simple yet powerful deductive forms. Modus ponens (MP) affirms the antecedent of a conditional: if p then q; p; therefore q. Modus tollens (MT) denies the consequent: if p then q; not q; therefore not p.
哲学论证常常围绕两个简洁而有力的演绎形式展开。肯定前件式 (MP) 肯定条件句的前件：如果 p 那么 q；p；所以 q。否定后件式 (MT) 否定条件句的后件：如果 p 那么 q；非 q；所以非 p。
MP: (p → q), p ⊢ q
MT: (p → q), ¬q ⊢ ¬p
The validity of these forms is unconditional: if the premises are true, the conclusion must be true. Recognising them is essential when evaluating arguments for God's existence or against scepticism, where thinkers frequently deploy MT to refute a problematic consequence.
这两个形式的有效性是无条件的：如果前提为真，结论必然为真。在评价上帝存在论证或反驳怀疑论时，识别它们至关重要，因为思想家们经常运用 MT 去推翻一个问题重重的推论。
3. The Problem of Perception: Direct vs. Indirect Realism | 知觉问题：直接实在论与间接实在论
Direct realism (DR) asserts the intuitive thesis: the immediate objects of perception are mind-independent physical objects. The Argument from Illusion challenges DR by pointing to cases where an object appears to have a property it does not actually possess, e.g., a straight stick looks bent in water. The argument can be formalised:
直接实在论 (DR) 维护一条直觉论题：知觉的直接对象是独立于心灵存在的物理实体。幻觉论证向 DR 发起挑战，它指出在某些情况下，对象看似具有某种它并不实际拥有的属性，例如一根直棍在水中看起来是弯的。该论证可以形式化为：
(1) In illusion, we perceive an F-appearing object that is not F.
(2) What we perceive must be the way it appears.
(3) Therefore, we perceive something mind-dependent (a sense-datum).
Indirect realism accepts that we perceive sense-data, which represent physical objects. Its main theorem is that perception is mediated by representational intermediaries, but it then faces the veil-of-perception scepticism: if we only ever experience sense-data, how can we justify the belief that a mind-independent world exists?
间接实在论接受我们感知的是感觉材料，这些感觉材料又表征着物理对象。其主要“定理”就是知觉由表征性中介所中介，但随之而来的是知觉之幕的怀疑论：倘若我们只能体验感觉材料，又怎能确证一个独立于心灵的世界存在呢？
4. The Principle of Induction and Hume's Problem | 归纳原理与休谟问题
Induction underpins all empirical science: we observe that n instances of F have been G, and infer that all Fs are G, or at least that the next F will be G. The inference relies on the Principle of the Uniformity of Nature (PUN): the future will resemble the past.
归纳推理支撑着一切经验科学：观察到 n 个 F 均为 G，进而推论所有 F 都是 G，或者至少下一个 F 将是 G。这一推论依赖于自然齐一性原则 (PUN)：未来将与过去相仿。
(PUN) ∀x (Fx → Gx) is supported by past instances, but PUN itself is presupposed.
David Hume showed that induction cannot be justified deductively — for it is not a contradiction to imagine the future changing — and any inductive justification of induction would be circular. This is the 'Humean theorem' of induction: there is no non-circular rational justification for expecting the unobserved to resemble the observed. Responses either attempt to embed induction in a probabilistic framework or accept a pragmatic, naturalistic stance.
大卫·休谟指出，归纳既无法演绎地证明——因为想象未来发生改变并不自相矛盾——而用归纳来证明归纳则陷入循环。这就是休谟式的归纳“定理”：期望未观察到的事物与已观察到的相似，并不存在一种非循环的理性确证。各种回应要么尝试将归纳嵌入概率框架，要么接受一种实用的自然主义立场。
5. The Verification Principle | 可证实性原则
Logical positivism's Verification Principle (VP) sought to demarcate meaningful statements from metaphysical nonsense. A sentence is cognitively meaningful iff it is either analytic (true by definition) or empirically verifiable (in principle).
逻辑实证主义的可证实性原则 (VP) 力图划清有意义的陈述与形而上学的废话之间的界限。一句话具有认知意义当且仅当它要么是分析的（因定义而真），要么是（原则上）经验上可证实的。
Meaningful(p) ↔ (Analytic(p) ∨ EmpiricallyVerifiable(p))
The fatal objection, often presented as a self-application modus tollens, is that VP itself is neither analytic nor empirically verifiable. If VP is true but meaningless by its own criteria, then VP is self-refuting; if VP is false, it is simply false. Either way, the strong verificationism collapses unless weakened to a more modest criterion of linguistic significance.
对其致命的反驳——经常被呈现为一种自我适用的否定后件推理——是 VP 本身既非分析的，也非经验上可证实的。如果 VP 为真却按其自身标准没有意义，则 VP 自我驳斥；如果 VP 为假，那它就是假的。无论哪种情形，强证实主义都会崩溃，除非它被弱化为一个更温和的语言意义标准。
6. The Cosmological Argument: Aquinas' First Way | 宇宙论论证：阿奎那的第一方式
Thomas Aquinas’ First Way argues for an unmoved mover from the fact of change (motion). The logical structure can be reconstructed as:
托马斯·阿奎那的第一方式从变化（运动）的事实出发，论证一个不动的推动者。其逻辑结构可以重构为：
(1) Some things in the world are in a state of motion (change).
(2) Whatever is in motion is put into motion by another.
(3) This series of movers cannot go on to infinity, or else there would be no first mover and hence no subsequent motion.
(4) Therefore, there must exist a first unmoved mover, which everyone understands to be God.
The core philosophical 'formula' is the denial of an infinite causal regress: ¬PossInfRegress → ∃ each member is explained by the previous, the whole series may be accounted for without a first term.
其核心的哲学“公式”是对无穷因果回溯的否定：¬PossInfRegress → ∃FirstCause。批评者，最著名的是休谟，质疑前提 (2)，并挑战无穷回溯不可能这一假设，他们指出如果序列中的每一成员都被前一个所解释，那么即使没有第一项，整个序列也可能已得到说明。
7. The Teleological Argument: Paley's Watchmaker | 目的论论证：佩利的钟表匠
William Paley's design argument proceeds by analogy: finding a watch on a heath would compel us to infer a watchmaker; likewise, the complex purposeful order of the natural world (e.g., the eye) implies a Divine Designer.
威廉·佩利的设计论证采用类比推理：如果在荒地上发现一块手表，我们将不得不推断有一位制表匠；同样，自然世界（如眼睛）复杂而具有目的性的秩序暗示着一位神圣设计者。
Analogical Structure: ComplexOrder(Watch) → Designer(Watch)
ComplexOrder(Universe) → Designer(Universe) = God
David Hume’s counter-criticisms function as a series of 'disanalogy' objections: the universe is not sufficiently like a watch to licence the inference; perhaps the universe more closely resembles a vegetable or an animal, where order springs from internal principles rather than external design. Furthermore, even if one grants a designer, the argument does not establish the singular, omnipotent, benevolent God of classical theism; the poor design in nature may suggest an apprentice deity or a committee.
大卫·休谟的反驳批评犹如一套“类比失当”异议：宇宙并不足够类似于一块手表，因而不能许可这样的推理；也许宇宙更像一株植物或一个动物，其秩序源于内部原理而非外在设计。再者，即便承认一位设计者，该论证也未能确立古典有神论中唯一、全能、至善的上帝；自然中的拙劣设计反而可能指向一位学徒神或一个委员会。
8. The Problem of Evil: The Deductive Argument | 恶的问题：演绎论证
The logical problem of evil aims to demonstrate an inconsistency between the existence of a God who is omnipotent, omnibenevolent, and omniscient, and the existence of evil. The deductive formulation is powerful because it deploys modus tollens:
恶的逻辑问题意在证明：一位全能、全善且全知的上帝的存在与恶的存在之间存在不一致性。其演绎表述十分有力，因为它运用了否定后件推理：
(OmniGod → ¬Evil) ∧ Evil ⊢ ¬OmniGod
If God exists with those attributes, evil ought not to exist; but evil does exist; therefore, such a God does not exist. The standard 'free will defence' (Plantinga) counters that it is logically possible that even an omnipotent God cannot create a world containing morally significant free creatures without the possibility of moral evil. The defence shows that the existence of evil is not logically incompatible with God’s existence, transforming a logical problem into an evidential one.
如果具有那些属性的上帝存在，恶就不应当存在；但恶确实存在；所以那样的上帝不存在。标准的“自由意志辩护”（普兰丁格）反驳说，逻辑上可能甚至全能上帝也不能创造一个包含有道德意义的自由受造物却不带有产生道德恶的可能性的世界。该辩护表明，恶的存在与上帝存在在逻辑上并非不相容，从而将一个逻辑问题转化为了一个证据性问题。
9. Free Will and Determinism: The Consequence Argument | 自由意志与决定论：后果论证
Determinism states that for every event E, there exists a prior state of the universe S and laws of nature L such that S and L together necessitate E. Incompatibilists deploy the Consequence Argument to conclude that determinism rules out free will:
决定论主张，对每一个事件 E，存在一个在先的宇宙状态 S 与自然律 L，使得 S 与 L 共同必然导致 E。不相容论者运用后果论证得出结论：决定论排除了自由意志。
Determinism = ∀E ∃S,L (S ∧ L □→ E)
No agent has a choice about S or L; therefore, no agent has a choice about the consequences of S and L, including their own actions.
Compatibilists reject this equation, offering a conditional analysis: an agent acts freely if they could have done otherwise had they willed to do otherwise, and their action flows from their own desires without coercion. The compatibilist 'theorem' thus divorces free will from the impossibility of doing otherwise in exactly the same circumstances, redefining freedom as the capacity to act according to one's own motives.
相容论者拒斥此等式，并给出一个条件句分析：一个行动者自由地行动，如果倘若他意愿做别的事情他就能够做别的事情，并且其行动源自自身欲望且无外部强制。相容论的“定理”由此将自由意志与在完全相同的环境中不可能做出别样行动的可能性分离开来，将自由重新定义为按照自身动机行动的能力。
10. Personal Identity: The Psychological Criterion | 人格同一性：心理标准
Against bodily continuity theories, John Locke proposed that personal identity consists in continuity of memory: a person at time t2 is the same as a person at time t1 if and only if the later person can remember the earlier person's experiences. This psychological criterion has been refined to include overlapping chains of psychological connectedness (Parfit).
针对身体连续性理论，约翰·洛克提出人格同一性在于记忆的连续性：时间 t2 的人与时间 t1 的人是同一人，当且仅当后来者能够回忆起前者的经历。这一心理标准已被精细化为包含心理联系的重叠链条（帕菲特）。
PI(Locke): Personₜ₂ = Personₜ₁ ↔ Remembers(Personₜ₂, Experiencesₜ₁)
Serious objections target transitivity and duplication. If A remembers B's experiences and B remembers C's, but A does not remember C's, identity can be lost. Moreover, Parfit's teletransportation thought experiment creates two psychologically continuous streams from one brain, forcing us to ask whether personal identity can be 'divided'. These puzzles suggest that identity is not a deep further fact but rather a matter of degree and description — a conclusion with radical implications for survival and ethics.
严肃的反对意见瞄准传递性和复制问题。如果 A 记得 B 的经验，B 记得 C 的经验，但 A 不记得 C 的，则同一性可能丢失。此外，帕菲特的心灵传送思想实验从一个大脑中创造了两条心理连续之流，迫使我们去追问人格同一性是否可以被“分割”。
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