📚 Year 7 WJEC Philosophy: Formula & Theorem Quick Reference Handbook | Year 7 WJEC 哲学：公式定理速查手册
Welcome to your Year 7 WJEC Philosophy Quick Reference Handbook. Philosophy is not just about big questions — it also has its own 'formulas' and 'theorems' that help us think clearly, argue logically, and examine life. Think of this handbook as a toolkit: every logical law, ethical equation, and argument structure you need to revise is presented here in a simple, memorable form. Whether you are preparing for a class discussion, a written assessment, or simply want to sharpen your reasoning, these formulas will guide you step by step.
欢迎使用你的 Year 7 WJEC 哲学公式定理速查手册。哲学不仅是探讨大问题，它也有自己的“公式”和“定理”，帮助我们清晰地思考、有逻辑地论证并审视生活。把这份手册当作一个工具箱：你复习所需的每一条逻辑定律、每一个伦理等式、每一种论证结构，都以简单易记的形式呈现在这里。无论你是在准备课堂讨论、书面评估，还是只想提升推理能力，这些公式都将一步步指引你。
1. The Law of Non-Contradiction | 不矛盾律
Nothing can both be and not be at the same time and in the same respect. This fundamental law of logic is written as: ¬(P ∧ ¬P). It means a statement cannot be true and false simultaneously. For example, 'the door is open' and 'the door is not open' cannot both be true in exactly the same situation. This formula is the bedrock of all consistent thinking; if you ever catch yourself holding two contradictory beliefs, you must revise at least one of them to restore logical coherence.
任何事物不可能在同一时间和同一方面既是又不是。这条基本的逻辑定律可写作：¬(P ∧ ¬P)。它意味着一个命题不能同时为真又为假。例如，“门是开着的”和“门不是开着的”不可能在完全相同的情形下同时为真。这个公式是一切融贯思维的基础；如果你发现自己持有两个相互矛盾的信念，就必须至少修正其中一个，以恢复逻辑的一致性。
2. The Law of Excluded Middle | 排中律
For any statement P, either P is true or its negation ¬P is true — there is no third option. This is expressed as: P ∨ ¬P. When we reason, we assume there is no middle ground between a proposition and its denial. If someone says 'there might be a shade of grey' about whether it is raining, ask: is it raining, or is it not? The excluded middle forces clarity. In philosophy, this law helps us frame precise questions and reject vague answers that try to avoid committing to a definite position.
对于任一陈述 P，要么 P 为真，要么其否定 ¬P 为真——不存在第三种可能。这可表示为：P ∨ ¬P。当我们推理时，我们假设在一个命题与其否定之间没有中间地带。如果有人对“是否在下雨”说“可能有灰色地带”，那就问：到底在下雨，还是不在下雨？排中律迫使思考走向清晰。在哲学中，这条定律帮助我们提出精确的问题，并拒绝那些试图不采取确定立场的模糊回答。
3. The Golden Rule Formula | 黄金法则公式
The ethical instruction 'treat others as you would like to be treated' can be symbolised as a decision-making formula: If Action A toward Person X is acceptable when the roles are reversed, then A is morally permissible. More formally: G(A) = 1 if Aₓ→ᵧ is the same action you would consent to in reverse (Aᵧ→ₓ); otherwise G(A) = 0 rmula tests fairness by swapping perspectives. In Year 7 terms, before you borrow a friend' king, imagine the situation reversed. If you would not like it, G(A) = 0, so do not do it.
“你希望别人怎样对待你，你就怎样对待别人”这条伦理箴言，可以符号化为一个决策公式：如果角色互换后，针对某人 X 的行为 A 是你所能接受的，那么 A 在道德上就是可允许的。更正式地说：G(A) = 1，若 Aₓ→ᵧ 恰好是你反过来（Aᵧ→ₓ）也会同意的行为；否则 G(A) = 0。这个公式通过交换视角来检验公平性。用 Year 7 的话来说，在你随意借用朋友的铅笔之前，想象一下角色互换的情景。如果你不喜欢那样，G(A) = 0，那就不要做。
4. The Socratic Method Formula | 苏格拉底式提问公式
The Socratic method can be expressed as a recurring loop that uncovers deeper understanding. Step A: Clarify a claim — 'What exactly do you mean by X?' Step B: Probe implications — 'If that is true, does it also mean Y?' Step C: Test with a counterexample — 'Can you think of a case where X is true but Y is false?' Step D: Revise the claim — 'How would you adjust your original view?' The formula repeats until the definition is refined or the person realises they do not actually know. This structured inquiry is philosophy's most ancient and powerful problem-solving algorithm.
苏格拉底方法可以表示为一个不断揭示深层理解的循环。步骤 A：澄清主张——“你说的 X 到底是什么意思？”步骤 B：探究推论——“如果那是真的，是不是也意味着 Y？”步骤 C：用反例检验——“你能想到一个 X 为真但 Y 为假的情况吗？”步骤 D：修正主张——“你会如何调整你原来的观点？”这个公式不断重复，直到定义得到完善，或者对方意识到自己其实并不知晓。这种结构化的探究是哲学最古老也最有力的解题算法。
5. The Argument Structure: Premise → Conclusion | 论证结构：前提 → 结论
Every argument can be broken down like a mathematical equation: Premise 1 + Premise 2 + ... = Conclusion. An argument is a set of statements where some (premises) are offered as reasons to support another (the conclusion). The connective arrow is a 'therefore': P₁, P₂, ... ⊢ C. Spotting this skeleton inside any debate is your first step in philosophical analysis. Always ask: 'What are the reasons?' and 'What are they trying to prove?' If you cannot find at least one premise and a conclusion, you are not yet dealing with an argument.
每个论证都可以像数学等式一样拆解：前提1 + 前提2 + ... = 结论。论证就是一组陈述，其中一部分（前提）被用来作为支持另一部分（结论）的理由。连接箭头是“所以”：P₁, P₂, ... ⊢ C。在任何辩论中识别出这个骨架，是你进行哲学分析的第一步。永远要问：“理由是什么？”以及“他们试图证明什么？”如果你至少找不到一个前提和一个结论，那么你面对的就不是一个论证。
6. The Validity & Soundness Theorem | 有效性与可靠性定理
A valid argument is one where if the premises are true, the conclusion must be true. Validity depends purely on logical form, not on actual truth. A sound argument is a valid argument whose premises are actually true. The theorem: Soundness = Validity + True Premises. As a quick test, use a counterexample generator: can you imagine a world where the premises hold but the conclusion does not? If yes, the argument is invalid. Only sound arguments guarantee a true conclusion, making them the gold standard in philosophy.
一个有效论证是指：如果前提为真，那么结论必然为真。有效性纯粹取决于逻辑形式，与实际真假无关。而一个可靠论证，则是前提实际为真的有效论证。定理：可靠性 = 有效性 + 真实的前提。作为快速检验，可以使用反例生成器：你能想象一个世界，其中前提成立但结论不成立吗？如果能，该论证就是无效的。只有可靠论证才能保证结论为真，因此它们是哲学中的黄金标准。
7. Modus Ponens Rule | 肯定前件式（假言推理）
If P, then Q. P is true. Therefore, Q is true. This is one of the most common logical moves. In symbols: (P → Q) ∧ P ⊢ Q. For instance: 'If it is raining, the ground is wet. It is raining. Therefore, the ground is wet.' navoidable. This formula is the engine of prediction, explanation, and everyday reasoning.
如果 P，那么 Q。P 为真。所以，Q 为真。这是最常见的逻辑步骤之一。符号表示为：(P → Q) ∧ P ⊢ Q。例如：“如果下雨，地面就会湿。正在下雨。所以，地面是湿的。”肯定前件式是完全演绎的；只要条件句和前件为真，后件就无法避免。这个公式是预测、解释以及日常推理的引擎。
8. Modus Tollens Rule | 否定后件式
If P, then Q. Q is false. Therefore, P is false. Symbolically: (P → Q) ∧ ¬Q ⊢ ¬P. For example: ' the battery is charged, the phone will turn on. The phone does not turn on. Therefore, the battery is not charged.' firms, modus tollens denies and works backwards. This rule is invaluable for falsification — e does not occur. Be careful not to confuse it with the fallacy of denying the antecedent.
如果 P，那么 Q。Q 为假。所以，P 为假。符号表示：(P → Q) ∧ ¬Q ⊢ ¬P。例如：“如果电池有电，手机就会开机。手机没有开机。所以，电池没有电。”如果说肯定前件式是确认，那么否定后件式则是否定并逆向推理。这条规则在证伪中极有价值——通过证明预测的结果并未发生，来表明某事为错。注意不要把它与“否定前件”的谬误相混淆。
9. The Fallacy Identification Theorem | 谬误识别定理
A fallacy is an error in reasoning that makes an argument unsound, even if it looks convincing. The identification formula has three checks: (1) Relevance check: Are the premises actually connected to the conclusion? (2) Sufficiency check: Do the premises, if true, provide enough support? (3) Acceptability check: Would a reasonable person accept the premises? Use the mnemonic 'RSA'. Common fallacies include ad hominem (attacking the person instead of the argument) and straw man (misrepresenting a view to easily knock it down). Spotting fallacies keeps your own thinking clean and gives you a sharp defence against weak rhetoric.
谬误是推理中的错误，它使论证不可靠，即便它看起来很有说服力。识别公式包含三项检查：（1）相关性检查：前提真的与结论有关吗？（2）充分性检查：前提若为真，能提供足够的支持吗？（3）可接受性检查：一个理性的人会接受这些前提吗？可使用助记符“RSA”。常见的谬误包括人身攻击（攻击人而不是论点）和稻草人谬误（曲解对方的观点以便轻易击倒）。识别谬误能使你自己的思维保持清晰，并为你抵御空洞强辩提供一件利器。
10. The Utilitarian Calculus | 功利主义演算
Utilitarianism asks us to calculate the greatest happiness for the greatest number. A simplified 'felicific calculus' for Year 7 can be expressed as: U(Action) = (Total Pleasureₒᵤₜ − Total Painₒᵤₜ). Compare this figure for each possible action. If U(A) > U(B), action A is morally better. Consider sharing a box of chocolates: sharing produces a small pleasure for many (high total pleasure, low pain) while eating them all alone might produce more pleasure for one but zero for others. This formula encourages you to step outside your own viewpoint and weigh everyone's happiness equally.
功利主义要求我们计算最大多数人的最大幸福。一个为 Year 7 学生简化的“快乐演算”可以表示为：U(行动) = （总快乐ₒᵤₜ − 总痛苦ₒᵤₜ）。对每一个可能的行动，比较这一数值。若 U(A) > U(B)，行动 A 在道德上就更好。考虑分享一盒巧克力：分享为许多人带来小小的快乐（总快乐高，总痛苦低），而独自吃完可能给一个人带来更多快乐，但对其他人则为零。这个公式鼓励你跳出自己的视角，平等地衡量每个人的幸福。
11. The Categorical Imperative Formula | 绝对命令公式
Immanuel Kant's famous moral formula has two key versions for your toolkit. Version 1 (Universal Law): 'Act only according to that maxim whereby you can at the same time will that it should become a universal law.' Test your action: Could everyone do it without contradiction? If everyone broke promises, the very idea of a promise would collapse — so lying is forbidden. Version 2 (Humanity): 'Act so that you treat humanity, whether in your own person or in that of another, always as an end and never merely as a means.' The rule: Always respect persons as valuable in themselves. Use these as filters before deciding what to do.
伊曼努尔·康德著名的道德公式，在你的工具箱中有两个关键版本。版本一（普遍法则）：“只依据那些你能够同时意愿其成为普遍法则的准则去行动。”检验你的行动：所有人都能这样做而不产生矛盾吗？如果每个人都违背承诺，“承诺”这个概念本身就会崩溃——因此说谎是被禁止的。版本二（人性公式）：“你要如此行动，即无论在你的人格中还是在他人的人格中，始终把人当作目的，而绝不仅仅当作手段。”规则：永远尊重人本身的价值。在做决定之前，请用这两条过滤器衡量一番。
12. The Problem of Evil: Logical Consistency Check | 恶的问题：逻辑一致性检查
The problem of evil challenges the coexistence of a wholly good, all-powerful God and the presence of suffering. The logical inconsistency formula runs: (God is omnipotent ∧ God is omnibenevolent) → Evil should not exist. But evil exists. Thus, some conclude ¬(God omnipotent ∧ God omnibenevolent). The consistency check asks: can you add a third premise (e.g., 'free will allows greater goods') that removes the contradiction without denying any of the original attributes? Philosophers use this clash as a key exercise in testing worldviews for logical harmony. To master it, trace the premises and see if a contradiction genuinely follows, or if one premise can be reinterpreted without breaking the logical chain.
恶的问题对全善、全能的上帝与苦难的存在这对共存关系提出了挑战。逻辑不一致性的公式是：（上帝是全能的 ∧ 上帝是全善的）→ 恶不应该存在。但恶确实存在。因此，一些人得出结论：¬（上帝是全能的 ∧ 上帝是全善的）。一致性检验问的是：你能加上一个第三个前提（例如，“自由意志会带来更大的善”），在不否认原来任何属性的情况下消除这个矛盾吗？哲学家们把这一冲突当作检验世界观逻辑和谐性的关键练习。要掌握它，就追溯各个前提，看看矛盾是否真正必然出现，或者能否在不破坏逻辑链的情况下重新解释某一个前提。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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