📚 Year 7 CCEA Philosophy: Formula & Theorem Quick Reference | 7年级CCEA哲学：公式定理速查手册
Welcome to your Year 7 CCEA Philosophy quick reference. In mathematics and science, we use formulas and theorems to describe reliable patterns. Philosophy works in a similar way: it gives us logical forms, reasoning structures, and fundamental principles that act like formulas for clear thinking. This handbook collects the most important philosophical ‘formulas’ and ‘theorems’ you need to know for your CCEA course. Each entry includes a definition, a symbolic pattern, and an example to help you apply it.
欢迎使用你的7年级CCEA哲学速查手册。在数学和科学中，我们用公式和定理来描述可靠的模式。哲学也以类似的方式工作：它为我们提供逻辑形式、推理结构和基本原则，它们就像清晰思维的公式。本手册收集了你需要掌握的CCEA课程中最重要的哲学“公式”和“定理”。每个条目都包含定义、符号模式和帮助你应用的示例。
1. Modus Ponens (Affirming the Antecedent) | 肯定前件式（假言推理）
Modus ponens is a basic valid argument form. It states that if a conditional statement is true, and its antecedent is true, then its consequent must also be true. You can think of it as the ‘if-then’ engine of reasoning. The Latin name means ‘method of affirming’ because you affirm the first part to conclude the second part.
肯定前件式是一种基本的有效论证形式。它指出，如果一个条件语句为真，并且它的前件为真，那么它的后件也必定为真。你可以把它看作推理的“如果-那么”引擎。这个拉丁名称的意思是“肯定的方法”，因为你肯定第一部分从而推出第二部分。
| Pattern / 模式 | P → Q, P ∴ Q |
| Example (English) | If it is raining, the picnic is cancelled. It is raining. Therefore, the picnic is cancelled. |
| 示例（中文） | 如果下雨，野餐就会取消。正在下雨。所以，野餐被取消。 |
P → Q, P ∴ Q
2. Modus Tollens (Denying the Consequent) | 否定后件式
Modus tollens is the reverse companion of modus ponens. It works by denying the consequent of a conditional to conclude that the antecedent must be false. If the ‘then’ part is found to be false, then the ‘if’ part cannot be true. It is a powerful tool for eliminating possibilities.
否定后件式是肯定前件式的逆向伙伴。它通过否定条件语句的后件来推断前件一定为假。如果“那么”部分为假，那么“如果”部分就不可能为真。这是一个排除可能性的有力工具。
| Pattern / 模式 | P → Q, ¬Q ∴ ¬P |
| Example (English) | If the cake is fresh, it will taste sweet. The cake does not taste sweet. Therefore, the cake is not fresh. |
| 示例（中文） | 如果蛋糕是新鲜的，它吃起来就是甜的。蛋糕吃起来不甜。所以，蛋糕不新鲜。 |
P → Q, ¬Q ∴ ¬P
3. Hypothetical Syllogism (Chain Argument) | 假言三段论（链式推理）
This theorem allows you to chain conditionals together. If one statement implies a second, and that second implies a third, then the first implies the third directly. It is like linking dominoes; once you set the first, the last one falls through a logical chain.
这个定理允许你把多个条件语句连接起来。如果一个命题意味着第二个，而第二个意味着第三个，那么第一个就直接意味着第三个。这就像连接多米诺骨牌；一旦你推倒第一块，最后一块也会通过逻辑链条倒下。
| Pattern / 模式 | P → Q, Q → R ∴ P → R |
| Example (English) | If I study hard, I will pass the test. If I pass the test, I will celebrate. Therefore, if I study hard, I will celebrate. |
| 示例（中文） | 如果我努力学习，我就会通过考试。如果我通过考试，我就会庆祝。所以，如果我努力学习，我就会庆祝。 |
P → Q, Q → R ∴ P → R
4. Disjunctive Syllogism (Elimination) | 选言三段论（排除法）
When you face an ‘either-or’ choice and you can rule out one option, disjunctive syllogism allows you to conclude the remaining option must be true. It works with an inclusive ‘or’ meaning at least one of the two is true. The structure is simple but vital for decision-making and debate.
当你面对一个“要么…要么…”的选择，并且你可以排除其中一个选项时，选言三段论允许你推断剩下的那个选项必定为真。它适用于包容性的“或”，即两者中至少有一个为真。这个结构虽然简单，但对于决策和辩论至关重要。
| Pattern / 模式 | P ∨ Q, ¬P ∴ Q |
| Example (English) | The missing key is either in the kitchen or the hall. It is not in the kitchen. Therefore, the key is in the hall. |
| 示例（中文） | 丢失的钥匙要么在厨房，要么在走廊。不在厨房。所以，钥匙在走廊。 |
P ∨ Q, ¬P ∴ Q
5. Reductio ad Absurdum (Proof by Contradiction) | 归谬法（反证法）
This classic philosophical move assumes the opposite of what you want to prove, and then shows that this assumption leads to a contradiction or absurdity. Because contradictions cannot be true, the original claim must be true. It is used in mathematics, law and everyday reasoning.
这个经典的哲学方法假设你想证明的命题的反面，然后展示这个假设会导致矛盾或荒谬。因为矛盾不可能为真，所以原命题必定为真。这一方法被用于数学、法律和日常推理中。
| Structure / 结构 | Assume ¬P, derive a contradiction, therefore P. |
| Example (English) | Suppose the sun will not rise tomorrow. If that were true, all our predictions about day and night would be absurd. Therefore, the sun will rise tomorrow. |
| 示例（中文） | 假设太阳明天不会升起。如果那是真的，我们关于昼夜的所有预测都将变得荒谬。所以，太阳明天会升起。 |
(Assume ¬P → contradiction) ∴ P
6. Universal Instantiation (General to Particular) | 全称例示（从一般到个别）
This rule connects general statements with specific instances. If something is true for all members of a group, it must be true for any particular member you pick. It is the logical foundation for applying laws and principles to individual cases.
该规则将一般性陈述与具体的个例联系起来。如果某件事对一个群体的所有成员为真，那么它对你挑选的任何特定成员也一定为真。这是将法则和原理应用于个别情况的逻辑基础。
| Pattern / 模式 | ∀x (Fx) ∴ Fa |
| Example (English) | All humans are mortal. Socrates is a human. Therefore, Socrates is mortal. |
| 示例（中文） | 所有人都会死。苏格拉底是人。所以，苏格拉底会死。 |
∀x (Hx → Mx), Hs ∴ Ms
7. The Principle of Non-Contradiction | 不矛盾律
This is one of the most fundamental laws of thought. It states that a statement and its direct denial cannot both be true at the same time and in the same respect. You cannot consistently assert ‘It is raining’ and ‘It is not raining’ in the same place and moment. Every coherent argument respects this boundary.
这是最基本的思想法则之一。它指出，一个命题和它的直接否定不可能在同一时间、同一方面同时为真。你不能在同一地点、同一时刻一致地断言“正在下雨”和“没在下雨”。每一个连贯的论证都必须遵守这条界限。
| Symbolic Form / 符号形式 | ¬(P ∧ ¬P) |
| Explanation (English) | It is not the case that both P and not-P are true. |
| 解释（中文） | 并非P和非P同时为真。 |
¬(P ∧ ¬P)
8. Ockham’s Razor (The Principle of Parsimony) | 奥卡姆剃刀原理（简约原则）
Ockham’s Razor is a philosophical rule of thumb: do not multiply entities beyond necessity. In plain English, the simplest explanation that fits the facts is usually the best. It does not prove a theory, but it helps us choose between competing explanations by cutting away unnecessary assumptions.
奥卡姆剃刀是一条哲学经验法则：如无必要，勿增实体。用通俗的话说，最符合事实的最简解释通常是最好的。它并不能证明一个理论，但是通过削去不必要的假设，它帮助我们在互相竞争的解释中做出选择。
Simplest adequate explanation is preferred.
最简而充分的解释更受青睐。
9. The Socratic Elenchus (Cross-Examination Formula) | 苏格拉底式反诘法（问答公式）
The Socratic method is a disciplined questioning technique. It follows a formula: state a claim, probe for inconsistencies through a series of ‘what if’ questions, reveal a contradiction, and then refine the original claim. This dialectical pattern sharpens thinking and uncovers hidden assumptions.
苏格拉底方法是一种有纪律的提问技术。它遵循一个公式：提出一个主张，通过一系列“如果…会怎样”的问题探查其不一致性，揭露矛盾，然后修正原主张。这种辩证模式能磨砺思维，揭示隐藏的假设。
Claim → Question → Inconsistency → Refined Claim
主张 → 提问 → 不一致 → 修正后的主张
10. Cartesian Method of Doubt (The Doubt Formula) | 笛卡尔式怀疑法（怀疑公式）
Descartes gave us a radical formula for finding certainty: doubt everything that can possibly be doubted until you reach something indubitable. The famous outcome is ‘I think, therefore I am’ (Cogito, ergo sum). The method demonstrates that even if an evil demon deceives me, the very act of doubting proves my existence as a thinking being.
笛卡尔为我们提供了一个寻找确定性的激进公式：怀疑一切可以被怀疑的东西，直到你抵达某个无可怀疑的基点。其著名结论是“我思故我在”。这个方法表明，即使有一个邪恶精灵在欺骗我，怀疑这一行为本身就证明了我作为一个思考者的存在。
| Formula / 公式 | Doubt all → If I doubt, I think → If I think, I exist. |
| Result / 结果 | Cogito, ergo sum / 我思故我在。 |
Doubt → Thinking → Existence
11. The Greatest Happiness Principle (Utilitarian Calculus) | 最大幸福原则（功利计算）
Utilitarianism proposes a moral formula: the right action is the one that produces the greatest happiness for the greatest number. To decide, we weigh the pleasure and pain resulting from each possible choice. This principle turns ethics into a kind of calculation where we seek to maximise overall well-being.
功利主义提出了一个道德公式：正确的行为就是能为最大多数人带来最大幸福的行为。为了做出决定，我们衡量每个可能的选择所产生的快乐与痛苦。这条原则将伦理学变成了一种计算，我们力求使总体幸福最大化。
Action A is better than B if A produces more net happiness.
如果行为A产生的净幸福多于行为B，则A优于B。
12. The Categorical Imperative (Universal Law Formula) | 定言命令（普遍法则公式）
Kant offered a powerful ethical formula: act only according to that maxim whereby you can at the same time will that it should become a universal law. Before you act, ask yourself: ‘Can I rationally want everyone to act this way?’ If the answer is no, the action is morally prohibited. It tests the fairness of our motives.
康德提供了一个强大的伦理公式：只按照你同时能够意愿其成为一条普遍法则的准则去行动。在行动之前，问一问自己：“我能否理性地愿意所有人都这样做？”如果答案是否定的，那么该行为在道德上就是被禁止的。它检验我们动机的公正性。
Act only if your maxim can become universal law.
只有当你的准则可以成为普遍法则时，你才能行动。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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