📚 IGCSE CCEA Philosophy: Formula & Theorem Quick Reference | IGCSE CCEA 哲学：公式定理速查手册
This quick-reference handbook condenses the essential logical forms, ethical principles, and philosophical arguments required for IGCSE CCEA Philosophy. Each section presents a memorable 'formula' so you can reconstruct the structure of an argument quickly in an exam.
本速查手册浓缩了 IGCSE CCEA 哲学所需的核心逻辑形式、伦理原则与哲学论证。每一节都以好记的“公式”呈现，帮助你在考试中快速重构论证结构。
1. Modus Ponens & Modus Tollens | 肯定前件与否定后件
Modus ponens is a valid deductive form: if the antecedent holds, the consequent must follow. It is often written as 'affirming the antecedent'.
肯定前件（Modus Ponens）是一种有效演绎形式：如果前件成立，后件必然随之成立。它常被称为 '通过肯定前件来推理'。
P → Q; P; ∴ Q
Example: If it rains, the picnic is cancelled. It rains. Therefore, the picnic is cancelled.
示例：如果下雨，野餐取消。现在下雨。因此，野餐取消。
Modus tollens works by denying the consequent. It is also deductively valid and is common in philosophical disproofs.
否定后件（Modus Tollens）通过否定后件来推理。它同样是有效的演绎形式，常用于哲学中的反证。
P → Q; ¬Q; ∴ ¬P
Example: If God exists, there is no gratuitous evil. There is gratuitous evil. Therefore, God does not exist.
示例：如果上帝存在，就没有无端邪恶。存在无端邪恶。因此，上帝不存在。
2. Hypothetical Syllogism & Disjunctive Syllogism | 假言三段论与选言三段论
Hypothetical syllogism chains conditionals. It lets you combine two 'if... then...' statements into one longer conditional.
假言三段论将条件句链接起来。它使你能把两个 '如果……那么……' 陈述合并为一个更长的条件句。
P → Q; Q → R; ∴ P → R
Example: If students revise, they remember key arguments. If they remember key arguments, they write better essays. Therefore, if students revise, they write better essays.
示例：如果学生复习，他们就能记住关键论证。如果他们记住关键论证，他们就能写出更好的论文。因此，如果学生复习，他们就能写出更好的论文。
Disjunctive syllogism eliminates one option in a disjunction. It is valid when the disjunction is exhaustive.
选言三段论排除析取中的一个选项。当析取是穷尽时，该推理有效。
P ∨ Q; ¬P; ∴ Q
Example: Either the mind is physical or the mind is non-physical. The mind is not non-physical. Therefore, the mind is physical.
示例：要么心灵是物理的，要么心灵是非物理的。心灵不是非物理的。因此，心灵是物理的。
3. Formal and Informal Fallacies | 形式谬误与非形式谬误
Two invalid conditional forms must be avoided in exam answers: affirming the consequent and denying the antecedent.
考试答案中必须避免两种无效条件推理：肯定后件与否定前件。
Affirming the consequent: P → Q; Q; ∴ P (invalid)
Denying the antecedent: P → Q; ¬P; ∴ ¬Q (invalid)
Example of affirming the consequent: If it rains, the grass is wet. The grass is wet. Therefore, it rains. This ignores sprinklers or dew.
肯定后件示例：如果下雨，草是湿的。草是湿的。因此，下雨了。这忽略了洒水器或露水。
Informal fallacies attack the person, distort the opponent's view, or present only two options when more exist.
非形式谬误包括人身攻击、歪曲对方观点，或在存在更多选项时只给两个选项。
- Ad hominem: attacking the person, not the argument. | 人身攻击：攻击人而非论证。
- Straw man: misrepresenting a view to make it easier to attack. | 稻草人：歪曲观点使其更易攻击。
- False dilemma: forcing a choice between two extremes. | 假两难：迫使在两个极端间选择。
- Begging the question: assuming the conclusion in the premises. | 丐题：在前提中预设结论。
4. Utilitarian Calculus | 功利主义计算
Classical utilitarianism evaluates an action by its consequences. The core principle is the greatest happiness principle.
古典功利主义根据后果评价行为。其核心原则是最大幸福原则。
Right action = action that maximises total happiness (pleasure − pain) for all affected
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