📚 Year 13 OCR Philosophy: Formulas and Theorems Quick Reference | Year 13 OCR 哲学：公式定理速查手册
The study of philosophy of religion at Year 13 often demands memorising a series of logical structures, much like formulas in mathematics or the sciences. This quick reference distills the central arguments, critiques, and key concepts into schematic forms that capture their logical core. Whether you are revising the ontological argument, grappling with the problem of evil, or unpacking religious language, you can turn here for a crisp, diagrammatic representation of the essential reasoning – followed immediately by accessible explanation in both English and Chinese.
Year 13 阶段的宗教哲学学习常常要求记忆一系列逻辑结构，就像数学或科学中的公式一样。这份速查手册将核心论证、批判与关键概念提炼成图解式的形式，捕捉其逻辑核心。无论你是在复习本体论论证、探讨恶的问题，还是解析宗教语言，都可以在这里找到清晰、图表化的核心推理——并配有直白的中英双语解释。
1. The Ontological Argument – Anselm’s Formula | 本体论论证——安瑟伦的公式
God = that than which nothing greater can be conceived (the greatest conceivable being).
上帝 = 那无法设想比之更伟大的存在者（可设想的最伟大存在）。
Premise 1: God exists in the understanding (we have a concept of Him). Premise 2: If God existed only in the understanding, we could conceive a greater being – one that exists both in the understanding and in reality. Conclusion: Therefore, God must exist in reality, otherwise He would not be the greatest conceivable being.
前提1：上帝存在于理智中（我们拥有关于祂的概念）。前提2：如果上帝仅仅存在于理智中，我们就能设想一个更伟大的存在——一个同时在理智与现实世界中存在的存在。结论：因此，上帝必定存在于现实中，否则祂就不是可设想的最伟大存在。
Gaunilo’s 'Lost Island' counter-formula: By the same logic, we could 'prove' the existence of a perfect island – because the greatest conceivable island would have to exist in reality. Since the conclusion is absurd, Anselm’s form of reasoning must be flawed.
高尼罗的“迷失岛”反公式：按照同样的逻辑，我们可以“证明”一座完美岛屿的存在——因为可设想的最伟大的岛屿必定现实存在。既然结论是荒谬的，安瑟伦的推理形式必然有缺陷。
Kant’s objection: 'Exists' is not a predicate. Adding existence to a concept does not enlarge its content; therefore, a perfect being that lacks existence is no contradiction.
康德的反对：“存在”不是一个谓词。将存在加给一个概念并不会增加其内容；因此，一个缺乏存在的完美存在并不构成矛盾。
2. The Cosmological Argument – Aquinas’s First Three Ways | 宇宙论论证——阿奎那的前三路
the same pattern: an observed chain of dependency cannot go back infinitely; there must be a first uncaused cause, unmoved mover, or non-contingent being, and this everyone calls 'God'.
阿奎那的公式（五路论证）：（1）运动 → 第一推动者；（2）原因 → 第一动力因；（3）偶然性 → 必然存在。每一路都遵循相同模式：被观察到的依赖链条不可能无限回溯；必须有一个最初的无因之因、不被推动的推动者，或非偶然的存在，而这正是所有人所说的“上帝”。
David Hume’s critique: The universe itself may be a necessarily existent fact; we have no experience of the origin of worlds. Even if every part has a cause, the whole does not require an extra cause – the fallacy of composition.
大卫·休谟的批判：宇宙本身可能就是一个必然存在的事实；我们对世界的起源没有任何经验。即便每一个部分都有原因，整体并不需要一个额外的原因——这是合成谬误。
The Kalam version (formula): Everything that begins to exist has a cause; the universe began to exist; therefore, the universe has a cause – and this cause must be personal (God).
卡拉姆论证版本（公式）：一切开始存在的事物都有原因；宇宙开始存在；因此，宇宙有一个原因——而且这个原因必定是人格性的（上帝）。
3. The Teleological (Design) Argument – Paley’s Watchmaker | 目的论（设计）论证——佩利的钟表匠
Paley’s analogy formula: Watch : watchmaker :: universe : divine designer. If we find a watch in a heath, its complexity and purpose-ordering force us to infer an intelligent maker. Likewise, the natural world, with its far more complex arrangements, compels us to infer a cosmic designer – God.
佩利的类比公式：钟表之于制表匠，犹如宇宙之于神圣设计者。如果我们在荒野中捡到一块表，其复杂性和目的性安排迫使我们推论出一个智慧的制造者。同样，自然世界，其安排远更复杂，迫使我们推论出一个宇宙设计者——上帝。
Hume’s counter-formula (from Philo): The analogy is weak; the universe resembles an animal or a vegetable more than a machine. Moreover, even if a designer exists, we cannot infer infinite perfection – the world exhibits imperfection, suggesting a limited or apprentice deity, not the God of classical theism.
休谟的反公式（来自斐洛）：这个类比很薄弱；宇宙更类似于一个动物或植物，而非一部机器。此外，即使存在一个设计者，也无法推论出无限的完美——世界展示出缺陷，暗示着一位有限或学徒级的神明，而非古典有神论的上帝。
Darwin’s alternative mechanism: Apparent design is explained by natural selection working on random variation. Complex structures arise without any intentional purpose. Thus, the design argument fails to establish a supernatural designer.
达尔文的替代机制：看似的设计可以由自然选择作用于随机变异来解释。复杂的结构无需任何意向性目的即可出现。因此，设计论证未能确立一位超自然的设计者。
4. Religious Experience – Swinburne’s Principle of Credulity | 宗教经验——斯温伯恩的轻信原则
Swinburne’s formula: If it seems to a subject that x is present, then, in the absence of defeaters, probably x is present. Applied to religious experience, if it seems to a person that God is present, then – unless there are special considerations which undermine the experience – God is probably present.
斯温伯恩的公式：如果对某个主体而言似乎 x 在场，那么在缺乏否决因素的情况下，x 很可能就在场。应用于宗教经验：如果对一个人而言似乎上帝在场，那么——除非有削弱该经验的特殊考量——上帝很可能就在场。
Persistence and testimony strengthen the claim: widespread, cross-cultural, and morally transformative experiences resemble perceptual experiences of reality, making it rational to accept them as veridical unless refuted.
跨文化和持续性的见证加强了这一主张：广泛、跨文化且能带来道德转变的宗教经验类似于对现实的感知经验，在未被反驳之前，将其视为真确的乃是理性的。
Challenger’s formula: Experiences are interpreted through prior beliefs; the 'principle of credulity' is too permissive – it would justify hallucinations, alien abductions, and conflicting religious experiences. Neuroscience explains many experiences as brain events; the lack of independent verification remains a defeater.
挑战者的公式：经验总是经由先入之见诠释；“轻信原则”太过宽泛——它会让幻觉、外星人绑架和相互冲突的宗教经验都变得合理。神经科学将许多经验解释为大脑事件；缺乏独立验证始终是一个否决因素。
5. The Problem of Evil – Logical and Evidential Forms | 恶的问题——逻辑形式与证据形式
l; if all-good, He would want to prevent it. Yet evil exists → at least one of the attributes must be false, or God does not exist.
不相容三角（逻辑公式）：（1）上帝全能；（2）上帝全善；（3）恶存在。如果上帝全能，就能阻止恶；如果全善，就愿意阻止恶。然而恶存在 → 至少其中一种属性必然为假，或者上帝不存在。
Alvin Plantinga’s free will defence (formula): A world containing significantly free creatures who do more good than evil is better than a world with no free creatures. It is logically possible that even an omnipotent God could not create a world with free creatures who never choose evil. Therefore, the existence of God and evil is not logically contradictory.
普兰丁格的自由意志辩护（公式）：一个包含能行善多于做恶的显著自由造物的世界，优于一个没有自由造物的世界。在逻辑上可能的情况是，即便是全能的上帝，也无法创造一个自由造物永远不选择恶的世界。因此，上帝与恶的共存并非逻辑矛盾。
Evidential problem (Rowe’s formula): There exist instances of intense suffering that seem pointless and gratuitous; an all-loving God would not permit such evils unless they were necessary for a greater good. Since we see no outweighing good, it is more probable that God does not exist.
证据问题（罗的公式）：存在着似乎毫无意义且不必要的剧烈苦难；一位全然仁爱的上帝不会允许这类恶，除非它们为某种更大善所必需。既然我们看不到足以补偿的善，更可能的结论是上帝不存在。
6. Religious Language – Logical Positivism and Wittgenstein | 宗教语言——逻辑实证主义与维特根斯坦
Ayer’s verification principle (formula): A proposition is meaningful if and only if it is analytic (true by definition) or empirically verifiable. Religious claims like 'God exists' are neither; therefore, they are cognitively meaningless – pseudo-propositions expressing emotion, not fact.
艾耶尔的证实原则（公式）：一个命题有意义，当且仅当它是分析命题（依定义为真）或经验可证实的。诸如“上帝存在”这类宗教声称两者皆非；因此，它们在认知上无意义——是表达情感的伪命题，而非事实。
Hare’s 'blik' concept: Religious statements are not factual but express an interpretative framework through which a person sees the world. Two people with the same experiences can hold contradictory bliks; the language is meaningful as it guides action and attitude, but not in a scientific sense.
哈尔的“信念视域”概念：宗教陈述不是事实性的，而是表达了一个人用以观照世界的诠释框架。两个有着相同经验的人可以持有相互矛盾的信念视域；这种语言因为引导行动与态度而有意义，但并非在科学意义上。
Wittgenstein’s language games: Meaning arises from use within a form of life. Religious language belongs to its own language game with internal rules; it is inappropriate to judge it by the standards of science. The formula: Do not ask for the reference; look at how the words are woven into religious practice.
维特根斯坦的语言游戏：意义源于生活形式中的使用。宗教语言属于其自身的、具有内在规则的语言游戏；用科学的标准来评判它是不恰当的。公式：不要问所指为何；要看这些词语如何编织进宗教实践。
7. Miracles – Hume’s In Principle Argument | 神迹——休谟的“原则上”论证
Hume’s definition: A miracle is a violation of the laws of nature by a particular volition of the deity. His formula against belief: The evidence for accepting a miracle report must outweigh the evidence for the uniformity of nature. Since the uniform experience of nature provides a strong proof against miracles, no testimony is ever sufficient to establish one, unless its falsehood would be more miraculous than the fact.
休谟的定义：神迹是对自然法则的、由神祇特定意志带来的违背。他反对相信神迹的公式：接受神迹报告的证据必须压倒支持自然界一律性的证据。由于自然的一律性经验提供了反对神迹的强证明，没有任何证词足以确立一个神迹，除非证词的虚假比神迹本身更加不可思议。
Practical criteria: The witnesses must be numerous, educated, and of unquestioned integrity; yet in history, miracle claims come from ignorant and barbarous nations, and rival miracle stories cancel each other out.
实践判准：见证人必须为数众多、受过教育且诚信无虞；然而历史上，神迹声称多出自无知与野蛮的民族，且相互对立的神迹故事彼此抵消。
Swinburne’s counter-formula: The probability of a miracle depends on prior probability of God’s existence. If God’s existence is independently plausible, then miracles are not intrinsically improbable. Evidence for a resurrection, for instance, can be compelling if we have reason to think God would act in history.
斯温伯恩的反公式：神迹的概率取决于上帝存在的先验概率。如果上帝的存在有独立可信度，那么神迹本质上并非不可能。例如，倘若我们有理由认为上帝会在历史中行动，复活事件的证据就可能极具说服力。
8. Attributes of God – The Omnipotence Paradox | 上帝的属性——全能悖论
Classical formula: God is omnipotent, omniscient, and perfectly good. These attributes generate logical puzzles. The stone paradox: Can God create a stone so heavy that He cannot lift it? If He can, there is a stone He cannot lift (thus not omnipotent); if He cannot, there is something He cannot create (thus not omnipotent).
古典公式：上帝全能、全知、全善。这些属性引发了逻辑难题。石头悖论：上帝能否创造一块重到连祂自己也举不起来的石头？如果能，就有一块祂举不起来的石头（因此非全能）；如果不能，则有些东西祂造不出来（因此非全能）。
not a lack of power. The formula: Omnipotence = the power to bring about any logically possible state of affairs. So the paradox dissolves.
化解尝试：阿奎那将全能重新定义为能做一切逻辑上可能的事。创造一块逻辑上不可能的石头，并不代表能力的缺乏。公式：全能 = 实现任何逻辑上可能状态的能力。于是悖论消解。
The problem of omniscience and free will: If God knows infallibly what I will do tomorrow, then my action is necessitated; I cannot do otherwise, so I lack free will. This threatens moral responsibility and the free will defence.
全知与自由意志问题：如果上帝确然无误地知道我明天将做什么，那么我的行动就是被必然化的；我无法做出别样行动，从而缺乏自由意志。这危及道德责任以及自由意志辩护。
9. Life After Death – Resurrection and Dualism | 死后生命——复活与二元论
Resurrection formula (Christian materialism): Personal identity is preserved through the same body being transformed and raised by God. Continuity does not require an immaterial soul; it requires the will of God to re-create the person in a glorified body, with the same memories and character. The 'replica' problem asks: would a perfect replica be the same person?
复活公式（基督教物质主义）：人格同一性通过同一个身体被上帝转变并复活而得以保存。连续性并不需要非物质灵魂；它需要的是上帝的意志，将原人重新创造在一个荣耀的身体里，并附有相同的记忆与性格。“复制品”难题则问：一个完美的复制体还是同一个人吗？
Substance dualism (Plato, Descartes): The soul is a separate substance from the body. Death is the separation of the soul from the body; the soul then continues to exist in a disembodied state. Evidence from near-death experiences is often marshalled in support, but faces the hard problem of interaction – how can an unextended soul move a physical body?
实体二元论（柏拉图、笛卡尔）：灵魂是与身体分离的实体。死亡是灵魂与身体的分离；灵魂随后以脱离肉体的状态继续存在。濒死经验常被援引为证据，但面对“互动难题”——一个无广延的灵魂如何推动物质性的身体？
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