Year 13 CIE Philosophy: Formula & Theorem Quick Reference Handbook | Year 13 CIE 哲学：公式定理速查手册

📚 Year 13 CIE Philosophy: Formula & Theorem Quick Reference Handbook | Year 13 CIE 哲学：公式定理速查手册

This quick reference handbook distills key arguments, logical forms, and ethical principles from the Year 13 CIE Philosophy syllabus into concise ‘formulae’ and ‘theorems’. It is designed as a rapid revision aid, covering epistemology, ethics, metaphysics of mind, and philosophy of religion. Each entry presents a core idea in a compact symbolic or structural form, followed by an explanation of its significance. Mastery of these schemas will equip you to analyse unseen stimuli and construct rigorous essays under timed conditions.

这本速查手册将 Year 13 CIE 哲学大纲中的关键论证、逻辑形式和伦理原则提炼成简洁的“公式”和“定理”。它旨在作为快速复习工具，涵盖认识论、伦理学、心灵形而上学和宗教哲学。每个条目都以紧凑的符号或结构形式呈现核心思想，随后解释其意义。掌握这些框架将使你能够分析陌生材料，并在限时条件下写出严谨的论文。

1. The JTB+ Formula for Knowledge | 知识论的JTB+公式

Knowledge was traditionally defined as Justified True Belief: S knows that p if and only if (i) p is true, (ii) S believes that p, and (iii) S is justified in believing that p. After Gettier cases, the formula becomes JTB + X, where X is a condition that rules out epistemic luck. The two leading candidates are (a) No false lemmas: S’s justification does not rest on any false belief. (b) Reliable process: S’s belief is produced by a cognitive process that reliably yields true beliefs.

知识传统上被定义为经过辩护的真信念：S知道p当且仅当（i）p为真，（ii）S相信p，且（iii）S有理由相信p。在盖梯尔案例之后，公式变为JTB + X，其中X是一个排除认知运气的条件。两个主要候选条件是：（a）无错误引理：S的辩护不依赖于任何错误信念。（b）可靠过程：S的信念由一个能可靠产生真信念的认知过程形成。

JTB formula: Ksp ↔ (p ∧ Bsp ∧ Jsp)

Gettier-proofed: Ksp ↔ (p ∧ Bsp ∧ Jsp ∧ ¬∃q(Fsq ∧ (Jsq → Jsp) ∧ ¬q))

The original JTB schema collapses under the weight of counterexamples where justification and truth accidentally align. Gettier showed that a belief can be justified and true yet still fall short of knowledge because the justification is disconnected from the truth-maker. The ‘no false lemmas’ fix states that the chain of reasoning must not contain any false intermediate proposition. The reliabilist fix, championed by Alvin Goldman, replaces internal justification with the external condition that the belief-forming mechanism is truth-conducive. Both repairs have their own weaknesses: the no-false-lemmas condition struggles with barn-façade cases, while reliabilism faces the generality problem.

原始的JTB框架在那些辩护与真值偶然吻合的反例下崩溃。盖梯尔表明，一个信念可能既有辩护又为真，但仍不算知识，因为辩护与使之成真的事实脱节。“无错误引理”修补方案规定，推理链条中不得包含任何错误中间命题。由阿尔文·戈德曼倡导的可靠主义修补方案，则用外在条件（信念形成机制是导向真理的）取代内在辩护。两种修补都有各自的弱点：无错误引理条件难以应对谷仓假象案例，而可靠主义面临普遍性问题。

2. Utilitarian Calculus: The Greatest Happiness Principle | 功利主义演算：最大幸福原则

Classical utilitarianism, formulated by Jeremy Bentham, evaluates the moral worth of an action by a single function: the net utility it produces. Utility is measured via the hedonic calculus, which aggregates pleasure and pain across seven dimensions: intensity, duration, certainty, propinquity, fecundity, purity, and extent. The decision rule is: choose the act A that maximises H = Σ (Iₚ × Dₚ × Cₚ) – Σ (Iₛ × Dₛ × Cₛ) over all sentient beings affected.

古典功利主义由杰里米·边沁提出，通过一个单一函数来评估行为的道德价值：即该行为产生的净功利。功利通过快乐计算法来衡量，该计算法跨七个维度汇总快乐与痛苦：强度、持续时间、确定性、远近程度、繁衍性、纯度和范围。决策规则是：选择能使H = Σ (Iₚ × Dₚ × Cₚ) – Σ (Iₛ × Dₛ × Cₛ) 在所有受影响的有情众生中最大化的行为A。

Hedonic Calculus: Hₐ = Σᵢ (Iᵢ × Dᵢ × Cᵢ) – Σⱼ (Iⱼ × Dⱼ × Cⱼ)

Mill’s qualitative hedonism modifies Bentham by introducing a distinction between higher and lower pleasures. The quantitative calculus then becomes a weighted sum: H’ = Σ wₖ × pₖ, where higher pleasures receive a greater weight wₖ determined by competent judges. This revision addresses the ‘swine objection’ that Bentham’s calculus reduces human life to mere animal gratification. The utilitarian formula always demands impartiality: ‘each is to count for one, and none for more than one.’

密尔的质性快乐主义修正了边沁，引入高级快乐与低级快乐的区分。定量计算随之变为加权和：H’ = Σ wₖ × pₖ，其中高级快乐获得由有资格的评判者确定的更大权重wₖ。这一修正回应了“猪的异议”——即边沁的计算法将人生降格为动物性的满足。功利主义公式始终要求不偏不倚：“每个算作一个，没有谁可以多于一个。”

3. Kant’s Categorical Imperative: The Universal Law Formula | 康德定言命令：普遍法则公式

Kantian ethics provides a rational decision procedure: act only on that maxim through which you can at the same time will that it should become a universal law. The test has two stages. First, formulate your maxim (M): ‘I will do action A in circumstances C in order to achieve purpose P.’ Second, universalise the maxim and check for contradictions: if the universalised maxim (UM) leads to a contradiction in conception or a contradiction in the will, the action is impermissible.

康德伦理学提供了一个理性决策程序：只依据你同时能够意愿其成为普遍法则的准则去行动。检验分两个阶段。首先，制定你的准则（M）：“在情境C下，我将做行为A以达到目的P。”其次，将准则普遍化并检测矛盾：如果普遍化后的准则（UM）导致概念上的矛盾或意愿上的矛盾，则该行为是不被允许的。

Categorical Imperative Test: ∀ M, ◇(M → UM) ? Permissible : Impermissible

A contradiction in conception occurs when the very act of universalising the maxim undermines its own possibility. For example, universalising the maxim of making a false promise to borrow money would destroy the institution of promising, such that no false promise could succeed. A contradiction in the will occurs when universalisation is logically possible but no rational agent could consistently will such a world – for instance, a world where no one helps others in distress, which would conflict with our rational need for assistance. The second formulation, the Humanity Formula, states: ‘Act so that you treat humanity always as an end, never merely as a means.’ This provides a direct constraint against deception and coercion.

概念上的矛盾发生在普遍化准则的行为本身会破坏其自身的可能性时。例如，普遍化“为了借钱而做虚假承诺”的准则将摧毁承诺制度，从而使任何虚假承诺都无法得逞。意愿上的矛盾发生在普遍化在逻辑上可能，但没有理性行为者能一贯地意愿这样一个世界——例如，一个人人都不帮助困境中他人的世界，这会与我们理性上对援助的需求相冲突。第二个人性公式表述是：“行动时，你总是同时把人当作目的，绝不仅仅当作手段。”这直接约束了欺骗和胁迫。

4. Aristotelian Virtue: The Doctrine of the Mean | 亚里士多德德性：中道学说

Virtue is a settled disposition to choose the intermediate between excess and deficiency relative to us, determined by phronesis (practical wisdom). The moral formula is not arithmetic but analogical: V = (R – D) / (E – D) tends to 0.5, where R is one’s actual emotional or action response, D is the deficiency, and E is the excess. The mean is relative to the agent and the situation, not a fixed midpoint.

德性是一种稳定的倾向，在我们自身相关的过度与不及之间选择中间，由实践智慧（phronesis）决定。道德公式不是算术的，而是类比的：V = (R – D) / (E – D) 趋向于0.5，其中R是一个人的实际情感或行为反应，D是不及，E是过度。中道是相对于行为者和情境而言的，而不是一个固定的中点。

Virtue	Deficiency	Excess
Courage	Cowardice	Rashness
Temperance	Insensibility	Self-indulgence
Liberality	Stinginess	Prodigality

Aristotle’s function argument underpins the theory of virtue: the good for a human is rational activity in accordance with virtue over a complete life. Eudaimonia (flourishing) is not a feeling but an activity of soul expressing reason. The mean is not mediocrity; in some cases, such as murder, there is no mean because the action is intrinsically vicious. Virtue requires not just right outward action but the right internal state – acting from a firm and unchanging character, choosing the act for its own sake, and taking pleasure in it.

亚里士多德的功能论证支撑德性理论：人的善是灵魂在完整一生中依据德性的理性活动。eudaimonia（繁荣）不是一种感受，而是灵魂合乎理性的现实活动。中道并非平庸；在某些情况下，例如谋杀，根本不存在中道，因为该行为内在地邪恶。德性不仅要求外在行为的正确，还要求内在状态的正确——从一个稳固不变的性格出发，为行为本身而选择它，并从中获得快乐。

5. The Logical Problem of Evil: Incompatibility Triad | 恶的逻辑问题：不相容三元组

The logical problem of evil challenges the coherence of theism by showing that the following three propositions cannot all be true: (1) God is omnipotent; (2) God is perfectly good; (3) Evil exists. The logical incompatibility is formalised as: (P1) A perfectly good being would prevent all evil it can. (P2) An omnipotent being can prevent all evil. (P3) Therefore, if a perfectly good omnipotent being exists, no evil exists. (P4) Evil exists. (C) Therefore, no perfectly good omnipotent being exists.

恶的逻辑问题通过表明以下三个命题不可能同时为真来挑战有神论的融贯性：（1）上帝是全能的；（2）上帝是全善的；（3）恶存在。逻辑不相容性被形式化为：（P1）一个全善的存在会阻止所有它能阻止的恶。（P2）一个全能的存在能够阻止所有恶。（P3）因此，如果存在一个全善全能的存在，就没有恶存在。（P4）恶存在。（C）因此，不存在全善全能的存在。

Incompatibility triad: {(∀x)Gx → (∀y)(Py → Rxy), (∀x)Ox → (∀y)Cy, ∃eEe} ⊨ ⊥

The free will defence, proposed by Alvin Plantinga, inserts a necessary condition: it is logically impossible for God to create free creatures who always choose good. Moral evil is the price of a greater good – significant free will. The defence does not aim to explain why evil exists; it shows only that the existence of God and evil is not logically contradictory. The evidential problem of evil, however, shifts the burden: even if evil is logically compatible with God, the amount and distribution of pointless suffering renders God’s existence improbable. This relies on Bayes’ theorem: P(G | E) = P(E | G) × P(G) / P(E). The sceptical theist counters by challenging our ability to infer P(E | G) – perhaps we are not in a position to know what God would or would not permit.

由阿尔文·普兰丁格提出的自由意志辩护插入了一个必要条件：上帝在逻辑上不可能创造出总是选择善的自由造物。道德恶是一种更高善的代价——即重要的自由意志。该辩护并不旨在解释恶为何存在；它只表明上帝的存在与恶之间不存在逻辑矛盾。然而，恶的证据性问题转移了负担：即使恶在逻辑上与上帝兼容，无意义苦难的数量和分布使得上帝存在的可能性极低。这依赖于贝叶斯定理：P(G | E) = P(E | G) × P(G) / P(E)。怀疑论有神论者通过挑战我们推断P(E | G)的能力来回应——或许我们无法知道上帝会或不会允许什么。

6. The Teleological Argument: Paley’s Watchmaker Inference | 目的论论证：佩利的钟表匠推理

The design argument proceeds by analogical reasoning: from a complex artefact (a watch) to a complex natural object (the eye), both exhibit marks of design – complexity of parts arranged for a purpose. The formal structure is: (P1) The watch exhibits complexity and functional arrangement; we infer a watchmaker. (P2) Natural organisms exhibit even greater complexity and functional arrangement. (C) Therefore, by analogy, the universe has a designer. The argument is abductive: the hypothesis of an intelligent designer is posited as the best explanation for apparent design.

设计论证通过类比推理进行：从一个复杂的人工制品（钟表）到一个复杂的自然物（眼睛），两者都显示出设计的标志——为某个目的而排列的复杂部件。其形式结构为：（P1）钟表展现出复杂性和功能性排列；我们推断存在钟表匠。（P2）自然生物展现出更复杂的复杂性和功能性排列。（C）因此，通过类比，宇宙有一位设计者。该论证是溯因的：智能设计者的假设被设定为对表面设计的最佳解释。

Design inference: Dₒ → C, C ↔ (F ∧ P); F&P unexplained by chance/physics → Dᵤ

Hume’s Dialogues anticipate multiple defeaters: (a) The analogy is weak – the universe is not palpably similar to a watch; it might be more like a vegetable or an animal that grows of itself. (b) The argument commits the fallacy of composition – inferring that because parts have a designer, the whole does. (c) Even if a designer were inferred, it would not lead to the perfect God of theism – the world is the ‘first rude essay of some infant deity’. Darwin’s theory of evolution by natural selection provides an alternative mechanism: complexity arises through random variation and natural selection, eliminating the need for an external designer. The modern Intelligent Design movement uses irreducible complexity and specified complexity as design criteria, but these remain contested.

休谟的《自然宗教对话录》预示了多种反驳：（a）类比薄弱——宇宙与钟表没有明显的相似性；它可能更像一株自发生长的植物或动物。（b）论证犯了合成的谬误——从部分有设计者推断整体也有。（c）即使推断出设计者，也无法得出有神论中完美的上帝——世界不过是“某个幼稚神祇最初的粗糙习作”。达尔文的自然选择进化论提供了一个替代机制：复杂性通过随机变异和自然选择产生，消除了对外部设计者的需求。现代智能设计运动使用不可化约的复杂性和特定复杂性作为设计标准，但这些仍存争议。

7. The Ontological Argument: Anselm’s Reductio | 本体论论证：安瑟伦的归谬法

Anselm defines God as ‘that than which nothing greater can be conceived’. The argument is a reductio ad absurdum: suppose God exists only in the understanding, not in reality. Then we could conceive of a being exactly like God but also existing in reality, which would be greater. That would mean we conceive of something greater than that than which nothing greater can be conceived – a contradiction. Therefore, God must exist in reality as well as in the understanding.

安瑟伦将上帝定义为“那无法设想有比之更伟大者”。该论证是一个归谬法：假设上帝只存在于理智中，而不存在于现实中。那么我们就能设想一个与上帝完全相同但也在现实中存在的存在者，而这个存在者会更伟大。这就意味着我们设想出某种比“那无法设想有比之更伟大者”更伟大的东西——这是一个矛盾。因此，上帝必定既存在于理智中也存在于现实中。

Ontological formula: ¬∃x (x > G); ∃ᵤ G → ∃ᵤ∃ᵣ G’ > G → ⊥; ∴ ∃ᵣ G

Gaunilo counters with the perfect island parody: we can conceive of a perfect island, so by Anselm’s logic it must exist, which is absurd. Anselm replies that the argument only works for necessary beings, not contingent islands. Descartes reformulates the argument: existence is a perfection, and God has all perfections, so God exists. Kant’s famous objection attacks this: ‘existence is not a predicate’ – it does not add to the concept of a thing. When we say ‘God exists’, we do not add a property to the concept of God; we posit that the concept is instantiated in the world. The ontological argument thus commits a category mistake. Alvin Plantinga’s modal version uses possible worlds: God exists in some possible world; if God is a maximally great being, he exists in every possible world, so he exists in the actual world. This version depends on the plausibility of the first premise.

高尼罗以完美岛屿的类比来反驳：我们可以设想一个完美岛屿，那么按照安瑟伦的逻辑它必然存在，这是荒谬的。安瑟伦回应称，该论证只适用于必然存在者，不适用于偶然的岛屿。笛卡尔重新表述了论证：存在是一种完善性，上帝拥有所有完善性，因此上帝存在。康德著名的反驳攻击了这一点：“存在不是谓词”——它并不增加事物的概念。当我们说“上帝存在”时，我们并未给上帝的概念添加一种属性；我们假设该概念在世界上有所例示。因此本体论论证犯了一种范畴错误。阿尔文·普兰丁格的模态版本使用可能世界：上帝在某个可能世界中存在；如果上帝是最大伟大的存在者，那么他在所有可能世界都存在，因此他在现实世界也存在。这个版本依赖于第一个前提的合理性。

8. Dualism: Descartes’s Divisibility Argument | 二元论：笛卡尔的可分性论证

Substance dualism holds that mind and body are fundamentally distinct substances. Descartes’s core argument rests on the principle of the indiscernibility of identicals (Leibniz’s Law): if two things are identical, they must share all properties. The argument runs: (P1) I know clearly and distinctly that my mind is indivisible. (P2) I know clearly and distinctly that my body is divisible. (P3) Therefore, mind and body have different properties. (C) By Leibniz’s Law, mind ≠ body.

实体二元论认为心灵和身体是根本不同的实体。笛卡尔的核心论证基于同一物的不可分辨原则（莱布尼茨律）：如果两个东西是同一的，它们必须共享所有属性。论证如下：（P1）我清楚分明地知道我的心灵是不可分的。（P2）我清楚分明地知道我的身体是可分的。（P3）因此，心灵和身体具有不同的属性。（C）根据莱布尼茨律，心灵 ≠ 身体。

Divisibility argument: (∀x)(∀y)(x=y → (Fx ↔ Fy)); Fm = indivisible; Fb = divisible; ∴ m ≠ b

The interaction problem is the most potent objection: how can an unextended, non-spatial substance causally interact with an extended, spatial body? Princess Elisabeth of Bohemia pressed this question, and Descartes’s appeal to the pineal gland merely relocates the mystery. The problem can be expressed as a trilemma: (1) Mind-body interaction occurs (evident from experience). (2) Substance dualism claims mind and body have no common properties. (3) Causal interaction requires a shared medium. Thus dualism seems to make interaction unintelligible. Epiphenomenalism, occasionalism, and parallelism are radical responses, but each surrenders some aspect of common sense.

交互问题是其最强有力的反驳：一个不具广延、非空间性的实体如何与一个具有广延、空间性的身体产生因果交互？波西米亚的伊丽莎白公主提出了这个问题，笛卡尔求助于松果腺只是转移了谜团。该问题可表述为一个三难困境：（1）心身交互确实发生（经验表明）。（2）实体二元论声称心灵与身体没有共同属性。（3）因果交互需要一个共享的介质。因此二元论似乎使交互无法理解。副现象论、偶因论和平行论是激进的回应，但它们各自放弃了常识的某些方面。

9. Physicalism: The Mind-Brain Identity Theorem | 物理主义：心脑同一论原理

Type-identity theory asserts that mental states are numerically identical to brain states: for every mental state M, there is some physical state P such that M = P. This is expressed as: ‘pain is identical to C-fibre firing’. The theory is motivated by considerations of causal closure: every physical effect has a sufficient physical cause. If mental states have physical effects, they must themselves be physical, otherwise we would have systematic overdetermination.

类型同一论断言心理状态在数值上等同于大脑状态：对于每种心理状态M，都有某种物理状态P使得M = P。这被表达为：“疼痛等同于C纤维放电。”该理论受到因果闭合考量的驱动：每个物理结果都有一个充分的物理原因。如果心理状态有物理结果，它们本身必须是物理的，否则我们将面临系统性过度决定。

Identity formula: ∀M ∃P (M ≡ P) ∧ (∃! causal role for M = causal role for P)

Two objections dominate. First, the multiple realisability objection: the same mental state (e.g., pain) can be realised by different physical substrates in different species (humans, octopuses, Martians). If pain is identical to C-fibre firing, then octopuses cannot feel pain unless they have C-fibres, which is empirically false. Functionalism is the natural successor: mental states are defined by causal roles, not physical constituents. Second, the knowledge argument (Jackson’s Mary) shows that physical facts about colour vision do not exhaust what it is like to see red. If Mary knows all physical facts but learns something new upon experiencing red, physicalism is incomplete. The physicalist replies either by denying that Mary acquires new factual knowledge (she gains only an ability, or she knew the fact under a different mode of presentation) or by embracing phenomenal concepts as physical concepts sui generis.

两大反驳占据主导。首先，多重可实现性反驳：相同的心理状态（如疼痛）可以在不同物种（人类、章鱼、火星人）中由不同物理基质实现。如果疼痛等同于C纤维放电，那么章鱼除非拥有C纤维，否则不能感到疼痛，这在经验上是错误的。功能主义是其自然继承者：心理状态由因果角色定义，而非物理构成物。其次，知识论证（杰克逊的玛丽）表明，关于颜色视觉的物理事实不能穷尽看到红色是什么感觉。如果玛丽知道所有物理事实，但在体验红色时学到新东西，那么物理主义就是不完整的。物理主义者要么否认玛丽获得了新的事实知识（她只获得了能力，或她以一种不同的呈现方式知道了该事实），要么接纳现象概念作为自成一类的物理概念。

10. Free Will and Determinism: The Consequence Argument | 自由意志与决定论：后果论证

The consequence argument seeks to show that if determinism is true, no one has free will (incompatibilism). The classical formulation by van Inwagen runs: (P1) No one has a choice about the past and the laws of nature. (P2) The past and the laws entail every future truth (determinism). (P3) Therefore, no one has a choice about any future truth. The underlying rule of inference is the transfer of powerlessness: if no one has a choice about A, and A entails B, then no one has a choice about B.

后果论证旨在表明，如果决定论为真，则没有人拥有自由意志（不相容论）。范·因瓦根的经典表述如下：（P1）没有人能对过去和自然法则有所选择。（P2）过去和法则蕴含每一个未来真理（决定论）。（P3）因此，没有人能对任何未来真理有所选择。其底层的推理规则是无力性的转移：如果没有人能对A有所选择，且A蕴含B，那么没有人能对B有所选择。

Consequence argument: □(P₀ ∧ L → F); N(P₀ ∧ L); ∴ N(F) (where N = ‘no choice about’)

Soft determinists (compatibilists) reject the transfer principle or reject the sense of ‘could have done otherwise’. For Ayer, an action is free if the agent would have done otherwise had they chosen to – a conditional analysis. This does not require that the agent could have chosen otherwise in a determined world. The liberty of spontaneity (doing what one wants without external constraint) is sufficient for moral responsibility. Hard determinists accept the incompatibilist conclusion and deny free will altogether, embracing a revisionary stance towards moral practices. Libertarians accept incompatibilism but assert that we do have free will, and therefore determinism is false. Agent-causal libertarianism posits a special kind of substance causation not reducible to event causation.

柔软决定论者（相容论者）拒绝转移原则，或拒绝“能够另行其事”的意义。对艾耶尔而言，一个行为是自由的，如果行为者是其自愿选择的产物——这是一种条件分析。这并不要求行为者在被决定的世界中能够另行选择。自发自由（在无外在约束下做自己想做的事）足以承担道德责任。强硬决定论者接受不相容论的结论并完全否认自由意志，对道德实践采取修正立场。自由意志论者接受不相容论，但断言我们确实拥有自由意志，因而决定论是错的。行为者因果自由意志论设定了一种不可化约为事件因果的特殊实体因果关系。

11. Meta-ethics: The Open Question Argument | 元伦理学：开放问题论证

G.E. Moore’s open question argument targets any attempt to define ‘good’ in naturalistic terms. The schema: for any proposed naturalistic definition D (e.g., ‘good = pleasure’), we can intelligibly ask, ‘Is D good?’ If the question is open – i.e., not closed by the meanings of the words – then D and ‘good’ are not synonymous. The naturalistic fallacy is the error of identifying a moral property with a natural property. Moore concludes that ‘good’ is a simple, non-natural, unanalysable property.

G.E.摩尔的开放问题论证针对任何试图用自然主义术语定义“善”的做法。其框架为：对于任何提议的自然主义定义D（例如，“善 = 快乐”），我们都能有意义地问：“D是善的吗？”如果该问题是开放的——即不被词语的含义所封闭——那么D与“善”就不是同义的。自然主义谬误就是将道德属性等同于自然属性的错误。摩尔得出结论：“善”是一种简单的、非自然的、不可分析的属性。

Open question test: ∀D (Def(D, good) → Open(‘Is D good?’)); ∴ ¬Def(D, good)

Contemporary non-naturalism and error theory both draw on Moore, though for different purposes. Mackie’s argument from queerness extends Moore’s insight to attack moral realism: if moral properties are non-natural, they would be entities of a very strange sort, and we would need a mysterious faculty of intuition to detect them. The better explanation of moral language is that it presupposes false objective values. Emotivism, by contrast, accepts the naturalistic fallacy but denies that moral utterances are truth-apt at all. Ayer’s verification principle: ‘stealing is wrong’ means nothing more than ‘Boo to stealing!’ in a peculiar tone. The Frege-Geach problem then challenges emotivism: how can moral expressions function meaningfully in unasserted contexts like conditionals if they are merely emotional ejaculations?

当代非自然主义和错误理论都借鉴了摩尔，尽管目的不同。麦基的离奇性论证扩展了摩尔的洞见，以攻击道德实在论：如果道德属性是非自然的，它们将是一种非常奇怪的实体，而且我们将需要一种神秘的直觉官能去察觉它们。对道德语言的更好解释是，它预设了虚假的客观价值。相反，情感主义接受自然主义谬误，但否认道德陈述具有真值。艾耶尔的证实原则：“偷窃是错误的”不过是以一种特别的语调说“偷窃，呸！”。接着，弗雷格-吉奇问题挑战了情感主义：如果道德表达仅仅是情感感叹，它们如何在条件句等非断言语境中具有意义地运作？

12. Religious Language: The Falsification Principle | 宗教语言：证伪原则

Anthony Flew applies Karl Popper’s falsification criterion to religious utterances. A statement is factually meaningful only if the speaker can specify what would count against it – what observation would show it to be false. Flew’s challenge to the theist: ‘What would have to occur or to have occurred to constitute for you a disproof of the love of, or of the existence of, God?’ If a believer qualifies every apparent counter-evidence (‘God’s love is inscrutable’), the claim ‘God loves us’ dies the death of a thousand qualifications – it becomes unfalsifiable and therefore vacuous.

安东尼·弗卢将卡尔·波普尔的证伪标准应用于宗教言说。一个陈述在事实上是有意义的，仅当说话者能具体说明什么能算作对它的反证——什么观察到的情况会表明它是假的。弗卢对有神论者的挑战是：“必须发生或曾发生什么，才会构成对上帝之爱或上帝存在的否证？”如果信仰者用限定语回应每一个表面上的反证（“上帝的愛不可测度”），那么“上帝爱我们”这个主张就会死于千般限定——它变得不可证伪，因而空洞无物。

Falsification test: S is cognitive ↔ ∃ observation O such that ¬O would refute S

R.M. Hare responds with the concept of the ‘blik’ – an unfalsifiable yet meaningful framework belief that shapes our entire interpretation of experience. A paranoid student who believes all dons are out to murder him has a blik; no evidence will change his interpretation. Religion, Hare argues, is a blik, not a hypothesis. Basil Mitchell uses the parable of the partisan and the stranger to argue that religious belief is cognitive because the believer does admit the problem of evil as counting against belief, even though they retain faith. The cumulative case approach of Mitchell shows that religious claims are on a continuum with other historical and metaphysical hypotheses, rather than being categorically meaningless.

R.M.黑尔以“blic”概念作为回应——这是一种不可证伪却有意义的框架性信念，塑造着我们对经验的整个解读。一个偏执的学生相信所有学监都想谋杀他，他拥有一个blic；没有任何证据能改变他的解读。黑尔认为，宗教是一个blic，而非一个假设。巴兹尔·米切尔用游击队员与陌生人的寓言来论证宗教信念是认知性的，因为信仰者确实承认恶的问题算作不利于信仰的因素，尽管他们仍保持信仰。米切尔的累积案例方法表明，宗教主张与其他历史及形而上学假设处于同一连续谱上，而非在范畴上无意义。

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