📚 Year 11 CIE Philosophy: Formula & Theorem Quick Reference Handbook | Year 11 CIE 哲学：公式定理速查手册
Welcome to your ultimate quick-reference guide for Year 11 CIE Philosophy. Here we distil key philosophical arguments, logical principles and ethical frameworks into clear 'formulas' and 'theorems' that you can apply directly to exam questions. Keep this handbook handy as you revise the nature of reality, knowledge, morality and religion.
欢迎使用这本终极速查手册，专为 Year 11 CIE 哲学准备。我们将关键的哲学论证、逻辑原理和伦理框架提炼成清晰的"公式"和"定理"，你可以直接运用于考试题目。在复习实在、知识、道德与宗教的本质时，请随身携带这本手册。
1. Valid Argument Forms & Logical Laws | 有效论证形式与逻辑法则
Modus Ponens (MP): P → Q, P ⊢ Q. If it is raining, the ground is wet. It is raining. Therefore, the ground is wet.
肯定前件（Modus Ponens）： 如果P则Q，P，所以Q。若下雨，则地湿。下雨了，因此地湿。
Modus Tollens (MT): P → Q, ¬Q ⊢ ¬ If it is raining, the ground is wet. The ground is not wet. Therefore, it is not raining.
否定后件（Modus Tollens）： P → Q，非Q，所以非P。若下雨则地湿。地不湿，因此没下雨。
Hypothetical Syllogism: (P → Q) ∧ (Q → R) ⊢ (P → R). If I study, I pass. If I pass, I celebrate. Therefore, if I study, I celebrate.
假言三段论： (P → Q) ∧ (Q → R) ⊢ (P → R)。如果我学习，我会通过。如果通过，我会庆祝。所以，如果我学习，我会庆祝。
Disjunctive Syllogism: (P ∨ Q) ∧ ¬P ⊢ Q. Either it is a cat or a dog. It is not a cat. Therefore, it is a dog.
选言三段论： (P ∨ Q) ∧ ¬P ⊢ Q。要么是猫要么是狗。不是猫，因此是狗。
Reductio ad Absurdum (RAA): Assume ¬P, derive a contradiction, therefore P. To prove Socrates is mortal, assume he is immortal, but all men die; contradiction, so he must be mortal.
归谬法： 假设非P，推导出矛盾，因此P。要证明苏格拉底会死，假设他永生，但所有人都会死；矛盾，所以他必有一死。
Law of Non-Contradiction: ¬(P ∧ ¬P). A proposition cannot be both true and false at the same time and in the same respect.
不矛盾律： ¬(P ∧ ¬P)。一个命题不能在相同时间和相同方面既真又假。
2. Common Logical Fallacies | 常见逻辑谬误
Affirming the Consequent: P → Q, Q ⊢ The ground is wet, therefore it is raining. (The ground could be wet for another reason.)
肯定后件： P → Q, Q ⊢ P（无效）。如果下雨，地湿。地湿了，所以下雨。（地湿可能是因为洒水车。）
Denying the Antecedent: P → Q, ¬P ⊢ ¬ wet. It is not raining, therefore the ground is not wet. (A sprinkler could make it wet.)
否定前件： P → Q, ¬P ⊢ ¬Q（无效）。如果下雨，地湿。没下雨，所以地不湿。（可能有洒水器。）
Ad Hominem: Attacking the person rather than the argument. 'You cannot trust her claim about climate change because she is not a scientist.'
人身攻击： 攻击人而非论证。"你不能相信她对气候变化的说法，因为她不是科学家。"
Straw Man: Misrepresenting an opponent's position to make it easier to attack. 'Vegetarians say eating any animal product is murder, but plants are living too, so they are hypocrites.'
稻草人谬误： 歪曲对方立场以方便攻击。"素食者说吃任何动物产品都是谋杀，但植物也有生命，所以他们虚伪。"
False Dilemma: Presenting only two options when more exist. 'Either you support the war or you are unpatriotic.'
假两难： 只给出两个选项，而实际上有更多选择。"要么支持战争，要么就是不爱国。"
3. Ontological Arguments | 本体论论证
Anselm's Argument (Logical Form): (1) God is by definition 'that than which nothing greater can be conceived'. (2) It is greater to exist in reality than to exist only in the mind. (3) If God exists only in the mind, then we can conceive of a greater being – one that exists in reality. (4) But then that being would be greater than God, which contradicts the definition. (5) Therefore, God must exist in reality.
安瑟伦论证（逻辑形式）： （1）上帝被定义为"无法设想有比之更伟大者"。（2）存在于现实中比仅存在于心灵中更伟大。（3）如果上帝只存在于心灵中，那么我们就能设想出一个更伟大者——一个存在于现实中的存在。（4）但这样一来，那个存在就会比上帝更伟大，这与定义矛盾。（5）因此，上帝必然存在于现实中。
Descartes' Version: (1) God is a supremely perfect being. (2) Existence is a perfection. (3) Therefore, God must possess existence, just as a triangle must have three angles. God necessarily exists.
笛卡尔版本： （1）上帝是至圆满的存在者。（2）存在是一种圆满性。（3）因此，上帝必定具备存在，就像三角形必定有三个角。上帝必然存在。
Key Objection (Kant): Existence is not a real predicate or perfection; it does not add anything to the concept of a thing. Saying 'God exists' does not enlarge the concept of God.
关键反驳（康德）： 存在不是真实的谓词或圆满性；它不给事物的概念增加任何内容。说"上帝存在"并没有扩大上帝的概念。
4. Cosmological Arguments | 宇宙论论证
Aquinas' First Way (Argument from Motion): (1) Some things are in motion (change). (2) Everything moved is moved by another. (3) This chain of movers cannot go back to infinity. (4) Therefore, there must be a first unmoved mover – and this everyone calls God.
阿奎那的第一路（运动论证）： （1）有些事物在运动（变化）中。（2）凡被推动者皆为他者所推动。（3）这个推动序列不能无限回溯。（4）因此，必有一个不被推动的第一推动者——这就是大家所说的上帝。
Kalam Cosmological Argument: (1) Everything that begins to exist has a cause. (2) The universe began to exist. (3) Therefore, the universe has a cause. (4) This cause must be God (as it is timeless, spaceless, immensely powerful).
卡拉姆宇宙论论证： （1）凡开始存在者皆有原因。（2）宇宙开始存在。（3）所以，宇宙有原因。（4）这个原因必然是上帝（因其无时间、无空间、极其强大）。
Logical Form of Kalam: (∀x)(Bx → Cx); Bu ⊢ Cu, where B = begins to exist, C = has a cause, u = universe.
卡拉姆的逻辑形式： (∀x)(Bx → Cx); Bu ⊢ Cu，其中B代表"开始存在"，C代表"有原因"，u代表宇宙。
5. Teleological Arguments (Design) | 目的论论证（设计）
Paley's Watchmaker Analogy: (1) A watch found on a heath exhibits complex parts arranged for a purpose. (2) The best explanation is a watchmaker who designed it. (3) The universe exhibits far greater complexity and purpose (e.g., the eye). (4) By analogy, the best explanation for the universe is a divine designer (God).
佩利的钟表匠类比： （1）在荒野里发现一块表，其复杂零件为目的而组合。（2）最佳解释是有一位设计它的钟表匠。（3）宇宙展现出更宏大的复杂性和目的性（如眼睛）。（4）类比之下，宇宙的最佳解释是一位神圣的设计者（上帝）。
Hume's Criticisms (Logical Undermining): (a) Weak analogy: The universe is not very like a watch; it is more like a living organism. (b) No experience of world-making: We have witnessed watches being made, but never worlds. (c) Even if a designer exists, it might not be the God of classical theism (could be a team, apprentice, or imperfect deity).
休谟的批评（逻辑削弱）： （a）类比脆弱：宇宙并不很像一块表；它更像一个有机体。（b）缺乏造世界的经验：我们见过表的制造，但从未见过世界的制造。（c）即使存在设计者，也未必是古典有神论的上帝（可能是一支团队、学徒或不完美的神）。
6. The Problem of Evil | 恶的问题
Inconsistent Triad (Logical Form): vent all evil). (3) Evil exists. These three propositions cannot all be true. Formally: (O ∧ B) → ¬E; E; therefore ¬(O ∧ lent, evil should not exist. Since evil exists, either God does not exist, or He lacks one
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