AS WJEC Philosophy: Quick Reference Formulas & Theorems | AS WJEC 哲学：公式定理速查手册

📚 AS WJEC Philosophy: Quick Reference Formulas & Theorems | AS WJEC 哲学：公式定理速查手册

In AS WJEC Philosophy, understanding key arguments and principles often involves recognising their underlying logical structure. This quick reference handbook presents essential “formulas” and “theorems” that capture the core of philosophical reasoning across topics such as epistemology, ethics, philosophy of religion, and mind. Each entry condenses a central idea into a symbolic or structured form, helping you memorise, apply, and evaluate philosophical arguments with precision.

在 AS WJEC 哲学中，理解关键论证和原理通常需要识别其底层逻辑结构。这本速查手册呈现了一些核心“公式”和“定理”，浓缩了认识论、伦理学、宗教哲学和心灵哲学等课题的哲学推理精华。每个条目将中心思想凝练为符号化或结构化的形式，帮助你有条理地记忆、应用和评估哲学论证。

---

1. The JTB Formula for Knowledge | 知识的 JTB 公式

K(S, P) ↔ (True(P) ∧ Belief(S, P) ∧ Justified(S, P))

The JTB formula states 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. This tripartite definition was long taken as the standard account of propositional knowledge.

JTB 公式表明，主体 S 知道命题 P，当且仅当 P 为真，S 相信 P，且 S 的相信是有辩护理由的。这种三元定义长期被视为命题知识的标准解释。

In WJEC Philosophy, you must be able to explain each component: truth as a mind-independent fact, belief as a subjective mental state, and justification as the evidence or reasons that support the belief. The formula captures the traditional necessary and jointly sufficient conditions for knowledge.

在 WJEC 哲学中，你必须能解释每一个组成部分：真理是独立于心灵的事实，信念是一种主观的心理状态，辩护是支持信念的证据或理由。该公式抓住了传统上对知识的必要条件与联合充分条件。

However, Gettier cases demonstrate that there are situations where JTB holds yet we intuitively deny knowledge, suggesting the formula is insufficient. The formula therefore serves as a foundation for deeper epistemological exploration.

然而，盖梯尔案例表明，存在 JTB 成立但我们直觉上否认知识的情形，这暗示该公式并不充分。因此，这一公式充当了更深入的认识论探索的基础。

---

2. Gettier-Style Counterexample Formula | 盖梯尔式反例公式

∃ case: True(P) ∧ Belief(S, P) ∧ Justified(S, P) ∧ ¬Knowledge(S, P)

A Gettier case is a scenario where all three JTB conditions are satisfied, yet the belief is true only by luck, so we do not attribute knowledge. The logical formula above expresses the possibility that JTB is not sufficient for knowledge.

盖梯尔案例是这样一种情形：三个 JTB 条件都得到满足，但该信念只是碰巧为真，因此我们不将它归为知识。上面的逻辑公式表达了 JTB 不是知识的充分条件的可能性。

For example, S believes ‘the person who will get the job has ten coins in their pocket’ based on strong justification about Jones. By coincidence, S himself gets the job and also has ten coins. The belief is justified and true, but it is not knowledge because it depends on a lucky coincidence.

例如，S 基于关于琼斯的强辩护而相信“得到那份工作的人口袋里有十个硬币”。巧合的是，S 自己得到了那份工作而且也有十个硬币。该信念得到辩护且为真，但它不是知识，因为它依赖于一次幸运的巧合。

Gettier cases force a revision of the JTB formula, leading to proposed fourth conditions such as ‘no defeaters’ or reliance on reliable cognitive processes. Recognising this logical pattern is essential for Unit 1 epistemology questions.

盖梯尔案例迫使人们修正 JTB 公式，从而提出了第四条件，比如“不存在否决项”或依赖可靠的认知过程。识别这种逻辑模式对第一单元的认识论问题至关重要。

---

3. Cartesian Cogito Formula | 笛卡尔“我思”公式

Doubt(I, anything) → Exist(I)

Descartes’ famous conclusion “I think, therefore I am” can be formulated as: if I am doubting the existence of anything, then I must exist in order to perform that act of doubting. Even an evil demon cannot deceive me about my own existence while I am thinking.

笛卡尔著名的结论“我思故我在”可被形式化为：如果我在怀疑任何事物的存在，那么我必定存在，因为正是我在进行这一怀疑活动。即便有一个邪恶的恶魔，在我正在思考的时候，它也无法欺骗我关于我自身的存在。

This formula underscores the indubitable foundation of knowledge: the very act of doubting confirms the existence of the doubter. It is not a deductive argument from a general premise but a self-verifying insight.

该公式凸显了知识不可怀疑的基础：怀疑活动本身就证实了怀疑者的存在。这不是一个从一般前提演绎推出的论证，而是一条自我证实的洞见。

In AS exam essays, you can use this logical form to explain how Descartes establishes a first certainty after radical doubt. The formula shows that the cogito is performative rather than inferential.

在 AS 考试论文中，你可以用这个逻辑形式来解释笛卡尔如何在彻底怀疑之后建立起第一个确定性。该公式表明，“我思”是践言式的，而非推理式的。

---

4. Anselm’s Ontological Argument Formula | 安瑟伦本体论论证公式

G = ιx ∀y (y≠x → ¬(y > x))
(ExistInUnderstanding(G) ∧ ¬ExistInReality(G)) → ∃z (z > G) → Contradiction
∴ ExistInReality(G)

Anselm defines God as the greatest conceivable being (that than which nothing greater can be conceived). The formula captures the reductio: if God exists only in the understanding, we can conceive of a greater being that exists also in reality, contradicting the definition.

安瑟伦将上帝定义为可设想的最伟大存在（没有比之更伟大的可设想之物）。该公式捕捉了归谬过程：如果上帝只存在于理智中，我们就能设想一个更伟大的存在——它也在现实中存在，这就与定义发生矛盾。

Purely symbolic: G = the greatest conceivable being; existence in reality is greater than existence in understanding alone; therefore, God must exist in reality. This is an a priori argument that attempts to deduce God’s existence from the concept of God.

纯粹符号表示：G = 可设想的最伟大存在；现实中的存在比单纯在理智中的存在更伟大；因此，上帝必定在现实中存在。这是一种试图从上帝概念推出上帝存在的先验论证。

Kant objects that existence is not a predicate, while Gaunilo parodies the argument with a perfect island. Nevertheless, the logical structure remains a central topic in philosophy of religion, and this formula helps you reconstruct the reasoning accurately.

康德反驳说存在不是一个谓词，而高尼罗用完美海岛来戏仿该论证。尽管如此，这一逻辑结构仍然是宗教哲学的核心主题，而这个公式有助于你准确地重构其推理。

---

5. Cosmological Argument (First Cause) Formula | 宇宙论论证（第一因）公式

∀x (Contingent(x) → ∃y (Cause(y, x)))
Contingent(universe)
¬∃ infinite regress of causes
∴ ∃z (Necessary(z) ∧ ¬Contingent(z) ∧ Cause(z, universe))

The cosmological argument rests on the principle that every contingent fact requires a cause. The universe is a contingent fact, and an infinite chain of causes is impossible; therefore, there must be a necessary first cause, identified with God.

宇宙论论证依赖于这一原则：每个偶存事实都需要一个原因。宇宙是一个偶存事实，而无限的原因链条是不可能的；因此，必定存在一个必然的第一因，这即被认为是上帝。

Aquinas’ second way uses the idea of efficient causation. The formula shows that if we reject an actual infinite regress, we must arrive at a first uncaused cause. This cause is not contingent but necessary.

阿奎那的第二路论证使用了动力因的概念。该公式说明，如果我们拒绝实无限的回溯，就必定要到达一个第一因，它没有原因，因而不是偶存的，而是必然的。

Hume and Russell challenge whether ‘every contingent fact has a cause’ applies to the universe as a whole, arguing that the fallacy of composition may be involved. The formula helps you identify exactly where the criticism bites.

休谟和罗素质疑“每一个偶存事实都有原因”是否适用于整个宇宙，主张这可能犯下构成谬误。该公式帮助你精准地识别批评的发力点。

---

6. Teleological Argument (Design) Formula | 设计论论证公式

(Complex(X) ∧ Purposeful(X) ∧ Orderly(X)) → ∃y (Designer(y) ∧ Created(y, X))
Complex(universe) ∧ Purposeful(universe) ∧ Orderly(universe)
∴ ∃y (Designer(y) ∧ Created(y, universe))

The teleological argument infers a designer from the appearance of complexity, purpose, and order in the natural world. Paley’s watch analogy suggests that just as a watch requires a watchmaker, the universe requires a divine designer.

设计论论证从自然界呈现出的复杂性、目的性和秩序中推出有设计者。佩利的钟表类比表明，正如钟表需要钟表匠，宇宙也需要一位神圣的设计者。

The symbolic formulation captures the inference to the best explanation: the properties of the universe are such that the existence of a designer is the best explanation. This argument is inductive and analogical rather than deductive.

这一符号化表述捕捉了通向最佳解释的推理：宇宙的性质令“存在设计者”成为最佳解释。该论证是归纳和类比的，而不是演绎的。

Critics, including Hume and Darwin, question the analogy and provide alternative explanations such as natural selection. Recognising the conditional form helps you assess whether the antecedent truly necessitates the consequent.

包括休谟和达尔文在内的批评者质疑这种类比，并提供了诸如自然选择等替代解释。识别这种条件式形式有助于你评估前件是否真的必然推出后件。

---

7. Logical Problem of Evil Formula | 恶的逻辑问题公式

∃x (God(x) ∧ Omnipotent(x) ∧ Omnibenevolent(x) ∧ Omniscient(x)) → ¬∃y (Evil(y))
∃y (Evil(y))
∴ ¬∃x (God(x) ∧ Omnipotent(x) ∧ Omnibenevolent(x) ∧ Omniscient(x))

The logical problem of evil asserts that the existence of an all-powerful, all-loving, and all-knowing God is logically incompatible with the existence of evil. If such a God existed, evil would not exist; but evil does exist, so such a God cannot exist.

恶的逻辑问题断言，一位全能的、至善的、全知的上帝与恶的存在在逻辑上不相容。如果这样一位神存在，恶就不会存在；但恶确实存在，因此这样一位神不可能存在。

This deduction is a modus tollens: if God then no evil; evil; therefore no God. The formula sharpens the need for a theodicy that either denies the reality of evil or reinterprets the divine attributes.

这是一次否定后件推理：如果有上帝则无恶；有恶；所以无上帝。该公式凸显了提出神义论的必要，即要么否定恶的真实性，要么重新解释神的属性。

Plantinga’s free will defence responds by challenging the premise that an omnibenevolent God would necessarily prevent all evil, as moral evil may be a necessary consequence of free will. The formula sets the stage for this debate.

普兰丁格的自由意志辩护通过挑战“至善的上帝必然阻止一切恶”这个前提来回应，因为道德之恶可能是自由意志的必然结果。该公式为这场辩论搭建了舞台。

---

8. Utilitarian Calculus (Bentham/Mill) | 功利主义计算公式（边沁/密尔）

U(A) = Σₚ (Pleasureₚ(A) − Painₚ(A))
Right(A) ↔ ∀B ≠ A (U(A) ≥ U(B))

Classical utilitarianism proposes that the moral worth of an action is determined by its total utility, defined as the sum of all pleasure minus pain it produces for all affected parties. The action with the highest net utility is the right one.

古典功利主义认为，一个行为的道德价值由其总效用决定，效用即该行为为所有受影响方带来的快乐减去痛苦的总和。产生最高净效用的行为就是正确的行为。

This formula is the core of Bentham’s felicific calculus and Mill’s greatest happiness principle. It requires impartial consideration of every individual’s happiness, treating each as one and none as more than one.

这一公式是边沁的快乐计算和密尔的最大幸福原则的核心。它要求不偏不倚地考虑每个个体的幸福，人人算一，无人算多。

In WJEC ethics, you need to evaluate the strengths of this quantitative approach as well as objections, such as the problem of measuring utility, the demands of impartiality, and the potential to justify intuitively immoral actions. The formula provides a precise target for these criticisms.

在 WJEC 伦理学中，你需要评价这种量化方法的优点以及反对意见，比如效用难以度量的问题、不偏不倚的要求之高，以及它可能为直觉上不道德的行为辩护。该公式为这些批评提供了一个精确的靶子。

---

9. Kant’s Categorical Imperative (Universal Law Formula) | 康德的定言命令（普遍法则公式）

Permissible(A) ↔ ◇ Universalize(Maxim of A) without contradiction
in will or in conception

Kant’s first formulation of the categorical imperative requires that one act only according to that maxim through which one can at the same time will that it become a universal law. An action is morally permissible if its maxim can be consistently universalised.

康德对定言命令的第一表述要求，只按照你同时意愿它成为一项普遍法则的准则去行动。如果一个行为的准则能够被一贯地普遍化，这一行为在道德上就是被允许的。

The formula captures the test of universalisability: conceive a world where everyone adopts the same maxim; if this leads to a contradiction in conception (e.g., false promising makes promising impossible) or a contradiction in the will (the agent cannot rationally will such a world), the action is forbidden.

该公式捕捉了普遍化检验：设想一个人人采取同一准则的世界；如果这在概念上产生矛盾（例如虚假承诺会使承诺成为不可能），或在意志上产生矛盾（行为者无法理性地意愿这样一个世界），则此行为被禁止。

This logical structure is essential for distinguishing perfect duties (maxims that cannot even be conceived as universal law) from imperfect duties (maxims that can be conceived but not rationally willed universalised). The formula offers a decision procedure based on consistency.

这一逻辑结构对于区分完全义务（其准则甚至无法被设想为普遍法则）和不完全义务（其准则可被设想但无法被理性地意愿普遍化）至关重要。该公式提供了一种基于一致性的决策程序。

---

10. Mind-Brain Identity Theory Formula | 心脑同一论公式

∀M (MentalState(M) → ∃B (BrainState(B) ∧ M = B))

Type identity theory claims that every type of mental state is strictly identical to some type of brain state. Mental phenomenon M, such as pain, is nothing over and above a specific configuration of neural activity B.

类型同一论主张，每一类心理状态都严格等同于某一类大脑状态。心理现象 M，例如疼痛，除开特定配置的神经活动 B 之外什么也不是。

This formula encapsulates a reductive physicalist solution to the mind-body problem. It denies any ontological distinction between mind and matter, holding that mental terms refer to physical processes.

该公式概括了身心问题的一种还原物理主义解决方案。它否认心灵与物质之间有任何本体论上的区分，主张心理词汇指的就是物理过程。

One major objection is multiple realizability: the same mental state can be realized by different brain states across species or even within an individual, challenging the identity claim. The formula highlights why identity theory must be defended at the type level.

一个主要的反对是多重可实现性：同一种心理状态可以在不同物种甚至同一个体身上由不同的大脑状态实现，这挑战了同一性主张。该公式凸显了为何同一论必须在类型层面上进行辩护。

---

11. Substance Dualism (Descartes’ Argument) Formula | 实体二元论（笛卡尔论证）公式

(◇(Mind(I) exists ∧ ¬Body(I) exists)) → (Mind(I) ≠ Body(I))

Descartes argues that he can clearly and distinctly conceive of himself as a thinking thing without a body, while the reverse is not similarly conceivable. This conceptual possibility, given Leibniz’s law, implies that mind and body are distinct substances.

笛卡尔论证说，他可以清晰分明地设想自己是一个没有身体的思考之物，而相反的情况则无法类似地设想。根据莱布尼茨律，这种概念上的可能性意味着心灵与身体是不同的实体。

The formula relies on the principle of the indiscernibility of identicals: if A = B, then every property of A is a property of B. Since the mind has the property ‘can possibly exist without the body’ while the body lacks it, they cannot be identical.

该公式依赖不可分辨物的同一性原则：如果 A = B，那么 A 的每一个性质都是 B 的性质。由于心灵具有“可能无身体而存在”的性质而身体不具有，它们不可能是同一个东西。

Critics target the move from conceivability to possibility and question whether ‘clearly and distinctly

Published by TutorHao | AS 哲学 Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）