📚 Year 9 OCR Philosophy: Quick Reference Handbook of Formulas and Theorems | Year 9 OCR 哲学：公式定理速查手册
In philosophy, just as in mathematics, certain structures and principles can be expressed as 'formulas' or 'theorems' — repeatable patterns of reasoning that help us analyse arguments, evaluate ethical dilemmas, and understand abstract concepts. This quick reference handbook gathers the most important logical forms, epistemic definitions, ethical calculi, and metaphysical arguments from the Year 9 OCR Philosophy course. Each entry is presented with a clear symbolic or structural outline, followed by an explanation and worked example where relevant. By treating these core ideas as tools to be applied, you can sharpen your critical thinking and build confidence for class discussions and written assessments.
在哲学中，正如数学一样，某些结构和原则可以表达为"公式"或"定理"——即可重复的推理模式，帮助我们分析论证、评估伦理困境并理解抽象概念。本速查手册汇集了Year 9 OCR哲学课程中最重要的逻辑形式、认识论定义、伦理计算以及形而上学论证。每个条目都先给出清晰的符号化或结构化轮廓，再附以解释和相应示例。通过像使用工具一样运用这些核心思想，你可以磨砺批判性思维，并为课堂讨论和书面考核建立信心。
1. Modus Ponens (Affirming the Antecedent) | 肯定前件式
ctive argument form: If P, then Q. P is true. Therefore, Q is true. Symbolically, P → Q, P ⊢ Q.
肯定前件式是一种有效的演绎论证形式：如果P则Q。P为真。因此，Q为真。符号表示为 P → Q，P，所以 Q。
Example: If Socrates is human, then he is mortal. Socrates is human. Therefore, Socrates is mortal.
示例：如果苏格拉底是人，那么他是会死的。苏格拉底是人。因此，苏格拉底是会死的。
2. Modus Tollens (Denying the Consequent) | 否定后件式
another valid form: If P, then Q. Q is false. Therefore, P is false. Symbolically, P → Q, ¬Q ⊢ ¬P.
否定后件式是另一种有效形式：如果P则Q。Q为假。因此，P为假。符号表示为 P → Q，非Q，所以非P。
Example: If it is raining, the street is wet. The street is not wet. Therefore, it is not raining.
示例：如果下雨，街道是湿的。街道没有湿。因此，没有下雨。
3. Disjunctive Syllogism | 选言三段论
Disjunctive syllogism works with an 'or' statement: P or Q. Not P. Therefore, Q. Symbolically, P ∨ Q, ¬P ⊢ Q.
选言三段论处理"或"语句：P或Q。非P。因此，Q。符号表示为 P ∨ Q，非P，所以 Q。
Example: Either the butler committed the crime or the maid did. The butler did not commit the crime. Therefore, the maid committed the crime.
示例：要么管家犯了罪，要么女仆犯了罪。管家没有犯罪。因此，女仆犯了罪。
4. Hypothetical Syllogism | 假言三段论
ditionals: If P, then Q. If Q, then R. Therefore, if P, then R. Symbolically, P → Q, Q → R ⊢ P → R.
假言三段论将条件命题串联起来：如果P则Q。如果Q则R。因此，如果P则R。符号表示为 P → Q，Q → R，所以 P → R。
Example: If I study, I will pass the exam. If I pass the exam, I will graduate. Therefore, if I study, I will graduate.
示例：如果我学习，我会通过考试。如果我通过考试，我会毕业。因此，如果我学习，我会毕业。
5. The Tripartite Definition of Knowledge (JTB) | 知识的三元定义 (JTB)
Knowledge is traditionally defined as justified true belief. A subject S knows that proposition P if and only if: (i) P is true; (ii) S believes that P; and (iii) S is justified in believing that P. This is often called the JTB account.
知识传统上被定义为确证的真信念。一个主体S知道命题P，当且仅当：(i) P为真；(ii) S相信P；(iii) S有理由相信P。这常被称为JTB理论。
While the JTB formula captures many cases, Edmund Gettier showed that there can be justified true belief without knowledge, prompting ongoing debate.
尽管JTB公式涵盖了许多情形，但埃德蒙·盖梯尔指出可能存在没有知识的确证真信念，由此引发了持续争论。
6. The Principle of Utility | 功利原则
The principle of utility, central to utilitarianism, states that an action is right if it promotes the greatest happiness for the greatest number. This 'greatest happiness principle' acts as a decision-making formula: evaluate an action by summing the pleasures and pains it produces for all affected.
功利原则，作为功利主义的核心，主张一个行为是正当的，当它促进最大多数人的最大幸福。这一"最大幸福原则"相当于一个决策公式：通过将该行为对全体受影响者产生的快乐与痛苦加总来评估它。
7. Bentham's Felicific Calculus | 边沁的幸福计算
Jeremy Bentham proposed a hedonic calculus to quantify pleasure and pain. The value of a pleasure or pain is determined by seven dimensions:
杰里米·边沁提出了一种量化快乐与痛苦的计算法。一个快乐或痛苦的价值由以下七个维度决定：
- Intensity: How strong is the sensation?
- Duration: How long does it last?
- Certainty: How likely is it to occur?
- Propinquity: How soon will it occur?
- Fecundity: Will it be followed by more of the same?
- Purity: Will it be followed by the opposite sensation?
- Extent: How many people are affected?
中文对应：
- 强度：这种感觉有多强烈？
- 持续时间：它能持续多久？
- 确定性：它发生的可能性有多大？
- 邻近性：它多久之后会发生？
- 丰产性：它会带来更多同类感觉吗？
- 纯度：它会不会被相反的感觉所跟随？
- 范围：有多少人会受到影响？
8. The First Formulation of the Categorical Imperative | 绝对命令的第一公式
Immanuel Kant's first formulation of the categorical imperative is the Formula of Universal Law: "Act only according to that maxim whereby you can at the same time will that it should become a universal law." To test an action, formulate its principle and ask whether it can be consistently willed as a law for everyone.
伊曼努尔·康德的绝对命令第一公式为普遍法则公式："只依据那些你可以同时愿意它成为一条普遍法则的准则去行动。"要检验一个行为，将其原则形式化，并追问它是否能被一贯地意愿为适用于每个人的法则。
Example: If you consider making a false promise, imagine everyone making false promises. The practice would undermine trust and become self-defeating, so the maxim cannot be universalised.
示例：如果你考虑做虚假承诺，想象每个人都做虚假承诺。这一行为会摧毁信任并自相矛盾，因此该准则不能被普遍化。
9. The Second Formulation of the Categorical Imperative | 绝对命令的第二公式
The second formulation is the Formula of Humanity: "Act in such a way that you treat humanity, whether in your own person or in the person of another, always at the same time as an end and never merely as a means." This demands respect for rational beings as intrinsically valuable.
第二公式为目的公式："你要这样行动，把不论是你自身中的人性还是任何他人中的人性，总是同时当作目的，而绝不仅仅当作手段。"这一公式要求尊重理性存在者自身拥有的内在价值。
10. Anselm's Ontological Argument (Logical Form) | 安瑟伦的本体论论证（逻辑形式）
Anselm of Canterbury defines God as "that than which nothing greater can be conceived." His argument can be expressed as a reductio ad absurdum: (1) God exists in the mind. (2) Suppose God exists only in the mind. (3) Then a greater being could be conceived — one that exists both in the mind and in reality. (4) But this would mean that the greatest conceivable being is not the greatest, which is a contradiction. (5) Therefore, God must exist in reality.
坎特伯雷的安瑟伦将上帝定义为"无法设想有比之更伟大的存在者"。他的论证可表达为归谬法：(1) 上帝存在于心中。(2) 假设上帝只存在于心中。(3) 那么就能设想一个更伟大的存在者——既存在于心中又存在于现实中。(4) 但这意味着可设想的最伟大者并非最伟大，矛盾。(5) 因此，上帝必然存在于现实中。
11. The Problem of Evil (Epicurus' Trilemma) | 恶的逻辑问题（伊壁鸠鲁三难）
The logical problem of evil challenges the existence of an omnipotent, omnibenevolent God given the existence of evil. It is often traced to Epicurus: (1) If God is willing to prevent evil but not able, He is not omnipotent. (2) If He is able but not willing, He is malevolent. (3) If He is both able and willing, then why does evil exist? (4) If He is neither able nor willing, why call Him God? The argument suggests that the existence of any evil is logically incompatible with such a God.
恶的逻辑问题挑战全能、全善之上帝的存在与恶的共存。该论证常追溯至伊壁鸠鲁：(1) 如果上帝愿意阻止恶却做不到，则祂并非全能。(2) 如果祂做得到却不愿意，则祂并非全善。(3) 如果祂既能又愿，恶何以存在？(4) 如果祂既不能又不愿，为何称祂为上帝？该论证指出，任何恶的存在都与这样一位上帝在逻辑上不相容。
12. Ockham's Razor | 奥卡姆剃刀
Ockham's Razor is a methodological principle of simplicity: "Entities should not be multiplied beyond necessity." In argument analysis, it advises that, all else being equal, the explanation requiring the fewest assumptions is to be preferred.
奥卡姆剃刀是一条关于简单性的方法论原则："如无必要，勿增实体。"在论证分析中，它建议在所有条件相同的情况下，应优先选择假设最少的解释。
Example: If your homework disappears, rather than positing invisible goblins, it is simpler to assume you misplaced it — applying Ockham's Razor strips away unnecessary suppositions.
示例：如果你的作业不见了，与其假设存在隐形小妖，不如假设你把它放错了地方——这正合奥卡姆剃刀，剔除不必要的假定。
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