📚 Year 7 OCR Philosophy: Quick Reference Formulas & Theorems | 七年级 OCR 哲学：公式定理速查手册
Philosophy is often about clear thinking, and like mathematics, it has its own ‘formulas’ – patterns of reasoning that help us argue well and spot mistakes. This quick reference guide brings together the most important logical forms, ethical principles, and classic philosophical theorems you will meet in Year 7 OCR Philosophy. Each entry gives you the English name, the symbolic structure where possible, and a plain explanation. Use it to check your understanding, prepare for assessments, or simply to sharpen your mind.
哲学关乎清晰的思维，和数学一样，它也有自己的“公式”——帮助我们有效论证并识别错误的推理模式。这份速查手册汇集了你在七年级 OCR 哲学课程中会遇到的、最重要的逻辑形式、伦理原则和经典哲学定理。每个词条都给出了英文名称、符号结构（如适用）和通俗的解释。你可以用它来检查自己的理解、准备测评，或者仅仅是用来磨练你的思维。
1. Modus Ponens | 肯定前件式
If P implies Q, and P is true, then Q must be true. This is perhaps the most basic valid argument form.
如果 P 蕴含 Q，且 P 为真，那么 Q 必定为真。这也许是最基本的有效论证形式。
P → Q
P
∴ Q
Example: If it is raining (P), the grass is wet (Q). It is raining (P). Therefore, the grass is wet (Q).
示例：如果下雨 (P)，那么草地会湿 (Q)。正在下雨 (P)。因此，草地湿了 (Q)。
The argument is valid because the conclusion follows logically from the premises. However, if the premises are false, the conclusion might still be false even if the argument is valid.
该论证是有效的，因为结论逻辑上从前提推导出来。然而，如果前提为假，即使论证有效，结论也可能为假。
2. Modus Tollens | 否定后件式
If P implies Q, and Q is false, then P must be false. This form is equally valid and often used to test a claim.
如果 P 蕴含 Q，且 Q 为假，那么 P 必定为假。这一形式同样有效，常被用来检验某个说法。
P → Q
¬Q
∴ ¬P
Example: If the alarm works (P), it will ring at 7 am (Q). It did not ring at 7 am (¬Q). Therefore, the alarm does not work (¬P).
示例：如果闹钟正常工作 (P)，它就会在早上7点响铃 (Q)。它没有在7点响铃 (¬Q)。因此，闹钟不工作了 (¬P)。
In philosophical analysis, modus tollens is powerful for challenging assumptions: show that a predicted outcome did not happen, and you can reject the initial claim.
在哲学分析中，否定后件式是挑战假设的有力工具：表明预期的结果并未发生，你就可以拒绝最初的陈述。
3. Hypothetical Syllogism | 假言三段论
If P implies Q, and Q implies R, then P implies R. This allows us to chain conditionals together.
如果 P 蕴含 Q，且 Q 蕴含 R，那么 P 蕴含 R。这让我们能够把条件语句串联起来。
P → Q
Q → R
∴ P → R
Example: If I study (P), I will understand the topic (Q). If I understand the topic (Q), I will pass the test (R). Therefore, if I study (P), I will pass the test (R).
示例：如果我学习 (P)，我会理解这个主题 (Q)。如果我理解这个主题 (Q)，我会通过考试 (R)。因此，如果我学习 (P)，我会通过考试 (R)。
Hypothetical syllogism is used repeatedly in philosophy to build long chains of reasoning, such as in ethical arguments about the consequences of actions.
假言三段论在哲学中反复使用，用来构建长链条的推理，例如在关于行为后果的伦理论证中。
4. Disjunctive Syllogism | 选言三段论
If either P or Q is true, and P is false, then Q must be true. This simple reasoning underlies many ‘process of elimination’ arguments.
如果 P 或 Q 为真，并且 P 为假，那么 Q 必定为真。这种简单的推理是许多“排除法”论证的基础。
P ∨ Q
¬P
∴ Q
Example: Either the butler (P) or the gardener (Q) is the culprit. It is not the butler (¬P). Therefore, the gardener (Q) is the culprit.
示例：要么是管家 (P)，要么是园丁 (Q) 是罪犯。不是管家 (¬P)。因此，园丁 (Q) 是罪犯。
In philosophical dilemmas, presenting an exclusive disjunction can force a choice, but one must always ensure the alternatives are truly exhaustive.
在哲学困境中，提出一个互斥的选言命题可以迫使人做出选择，但我们必须确保所列的选项的确是穷尽的。
5. Affirming the Consequent (Fallacy) | 肯定后件式 (谬误)
If P implies Q, and Q is true, concluding P is a logical mistake. The truth of Q does not prove P.
如果 P 蕴含 Q，且 Q 为真，就得出 P 为真的结论，这是一个逻辑错误。Q 为真并不能证明 P。
P → Q
Q
∴ P (INVALID)
Example: If it is raining (P), the grass is wet (Q). The grass is wet (Q). Therefore, it is raining (P). ← This is invalid because a sprinkler could have wet the grass.
示例：如果下雨 (P)，草地会湿 (Q)。草地湿了 (Q)。因此，正在下雨 (P)。← 这是无效的，因为洒水器也可能把草地弄湿。
Recognising this fallacy is essential in Year 7 philosophy; many real-world arguments mistakenly reverse a conditional this way.
识别这一谬误在七年级哲学中至关重要；许多现实世界的论证都以这种方式错误地颠倒了条件关系。
6. Denying the Antecedent (Fallacy) | 否定前件式 (谬误)
If P implies Q, and P is false, concluding Q is false is also a fallacy. Q might still be true for other reasons.
如果 P 蕴含 Q，且 P 为假，就得出 Q 为假的结论，这也是一种谬误。Q 仍有可能因为其他原因而为真。
P → Q
¬P
∴ ¬Q (INVALID)
Example: If I am in London (P), I am in England (Q). I am not in London (¬P). Therefore, I am not in England (¬Q). ← This is false because I could be in Manchester, still in England.
示例：如果我在伦敦 (P)，那么我在英格兰 (Q)。我不在伦敦 (¬P)。因此，我不在英格兰 (¬Q)。← 这是错误的，因为我可能在曼彻斯特，仍然在英格兰。
This fallacy often appears when people mistakenly treat a sufficient condition as a necessary one.
这种谬误经常出现在人们错误地把充分条件当作必要条件的时候。
7. Descartes’ Cogito (Theorem) | 笛卡尔“我思”定理
René Descartes, searching for a firm foundation for knowledge, arrived at the famous proposition ‘I think, therefore I am’ (Cogito, ergo sum). Even if an evil demon is deceiving him about everything, the very act of being deceived proves that he exists as a thinking thing.
勒内·笛卡尔在探寻知识的稳固基础时，得出了著名的命题“我思故我在”(Cogito, ergo sum)。即便有一个恶意的魔鬼在一切事情上欺骗他，被欺骗的这个行为本身就证明了他作为一个思考者的存在。
I am thinking → I must exist
This is not a formal logical theorem in the mathematical sense, but a philosophical ‘theorem’ – a foundational insight that resists all doubt.
这不是一个数学意义上的形式逻辑定理，而是一个哲学“定理”——一个抵抗所有怀疑的根本洞见。
In Year 7, it introduces the idea of self-evident truths and the method of radical doubt: reject anything that can possibly be doubted until you find something indubitable.
在七年级的课程中，它引出了不证自明的真理这一概念，以及激进怀疑的方法：摒弃一切可能被怀疑的东西，直到你找到某个不可怀疑之物。
8. The Principle of Utility (Formula) | 功利原则 (公式)
In Ethics, Jeremy Bentham’s utilitarianism can be roughly expressed as: an action is right if it produces the greatest happiness for the greatest number. This can be imagined as a cost-benefit analysis where you weigh pleasure against pain.
在伦理学中，杰里米·边沁的功利主义可以大致表述为：如果一个行为能为最大多数人带来最大的幸福，那么它就是正确的。这可以想象成一种成本效益分析，在其中你权衡快乐与痛苦。
Right action = Max(∑ pleasure − ∑ pain) across all affected
While Year 7 does not require exact calculation, understanding this ‘formula’ helps us analyse moral dilemmas: a lie might be justified if it prevents great suffering, but only if the total happiness really increases.
虽然七年级并不要求精确计算，但理解这个“公式”有助于我们分析道德困境：如果一个谎言能防止极大的痛苦，那么它可能是正当的，但前提是总幸福确实增加了。
Critics point out that measuring happiness is difficult, and that the principle may ignore justice or individual rights.
批评者指出，测量幸福是困难的，而且这一原则可能忽视了正义或个体权利。
9. Kant’s Categorical Imperative (First Formulation) | 康德的绝对命令 (第一种表述)
Immanuel Kant proposed a different ethical ‘formula’: ‘Act only according to that maxim whereby you can at the same time will that it should become a universal law.’ If you cannot coherently imagine everyone doing what you propose, the action is morally wrong.
伊曼努尔·康德提出了一个不同的伦理“公式”：“只依据那些你能够同时愿意它成为一条普遍法则的准则去行动。”如果你无法连贯地想象每个人都按照你的提议去行动，那么该行为在道德上就是错误的。
Permissible if: Your rule (maxim) can be universalised without contradiction
Example: Is it acceptable to break a promise? If everyone broke promises whenever it suited them, the institution of promising would collapse. Therefore, breaking a promise cannot be a universal law and is impermissible.
示例：违背诺言是可接受的吗？如果每个人都随心所欲地违背诺言，那么承诺这一习俗就会崩溃。因此，违背诺言不能成为一条普遍法则，是不被允许的。
Kant’s imperative is like a logical consistency test for morality, a neat ‘theorem’ that Year 7 students can practise applying to everyday choices.
康德的绝对命令就像是针对道德的逻辑一致性测试，一个简洁的“定理”，七年级学生可以练习将其应用于日常的选择。
10. The Problem of Evil (Logical Formula) | 恶的问题 (逻辑公式)
The classic logical challenge to the existence of an all-powerful, all-knowing, and all-good God can be expressed as an inconsistent triad. If God exists, then evil should not exist. But evil does exist. Therefore, at least one of God’s attributes must be false.
针对全能、全知、全善的上帝存在这一命题，经典的逻辑挑战可以被表达为一个不一致的三元组。如果上帝存在，那么恶就不应该存在。但恶确实存在。因此，上帝的属性中至少有一个必定为假。
1) God is all-powerful (can prevent evil)
2) God is all-good (wants to prevent evil)
3) Evil exists
→ These three cannot all be true simultaneously
In Year 7 Religious Philosophy, this is a key ‘formula’ for debate. Some respond by denying premise 2 (God allows evil for a greater good) or premise 3 (evil is an illusion). The logical form remains a powerful tool.
在七年级的宗教哲学中，这是辩论的一个关键“公式”。有些人通过否认前提 2（上帝允许恶是为了更大的善）或前提 3（恶是一种幻觉）来回应。而这个逻辑形式仍然是一个有力的工具。
11. Occam’s Razor (Principle of Parsimony) | 奥卡姆剃刀 (简约原则)
This is not a strict theorem but a philosophical rule of thumb: ‘Do not multiply entities beyond necessity.’ When you have multiple explanations for a phenomenon, the simplest one (with fewest assumptions) is most likely to be correct.
这不是一个严格的定理，而是一个哲学上的经验法则：“如无必要，勿增实体。”当你对某个现象有多种解释时，最简洁的那个（假设最少的那个）最可能是正确的。
Prefer the explanation with fewer unexplained elements
Example: If your homework disappears, you could assume a ghost stole it (many extra assumptions about ghosts) or that you left it in your locker (one simple assumption). Occam’s Razor favours the locker.
示例：如果你的作业不见了，你可以假设是一个幽灵偷走了它（需要许多关于幽灵的额外假设），或者你把它忘在了储物柜里（一个简单假设）。奥卡姆剃刀倾向于储物柜的解释。
In logical analysis, this principle helps eliminate unnecessarily complex theories.
在逻辑分析中，这一原则有助于消除不必要的复杂理论。
12. The Socratic Method (Formula for Inquiry) | 苏格拉底式方法 (探究公式)
Socrates’ approach to philosophy can be distilled into a procedural ‘formula’: pose a question, listen to the answer, then ask clarifying questions that expose contradictions or unrecognised assumptions. Repeat until a clearer definition or truth emerges.
苏格拉底的哲学方法可以被提炼成一个程序化“公式”：提出一个问题，听取回答，然后提出揭示矛盾或未被意识到的假设的澄清性问题。重复此过程，直到一个更清晰的定义或真理浮现出来。
Question → Answer → Cross-examine for consistency → Revised definition → (loop)
This is the living ‘formula’ of philosophical dialogue. In Year 7 classrooms, it is practised through group discussions and Socratic circles, turning every student into a philosopher.
这是哲学对话的活的“公式”。在七年级的课堂上，它通过小组讨论和苏格拉底圈来实践，把每个学生变成哲学家。
The Socratic method teaches that philosophy is not just about memorising theorems, but about applying them in the search for wisdom.
苏格拉底式方法教导我们，哲学不仅仅是记住定理，更是将它们应用于对智慧的追寻。
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