📚 Year 7 Cambridge Philosophy: Formula & Theorem Quick-Reference Handbook | Year 7 剑桥哲学：公式定理速查手册
Philosophy might seem like a subject of endless questions and no fixed answers, but underneath the big ideas lie powerful patterns – formulas and theorems of thought that help us think clearly, argue fairly, and understand the world. This quick-reference handbook collects eight essential ‘thinking formulas’ used by philosophers across history. Each entry gives you the core idea in a compact form, a simple explanation, and a practical example. Keep it handy for your Year 7 Cambridge Philosophy lessons, debates, and any time you want to sharpen your reasoning.
哲学看似一门充满无尽问题且没有固定答案的学科，但在那些宏大思想背后，隐藏着强大的思考模式——这就是帮助我们清晰思考、公平论辩和理解世界的思维公式与定理。这本速查手册汇集了历史上哲学家们使用过的八个核心“思维公式”。每个条目都以简洁的形式给出核心理念，附有浅显的解释和实际例子。在你学习 Year 7 剑桥哲学课程、参与辩论或任何想要锻炼推理能力的时候，都可以随时翻阅。
1. The Syllogism Formula | 三段论公式
Syllogism: If A ⇒ B and B ⇒ C, then A ⇒ C.
A syllogism is the basic building block of logical reasoning. It connects two statements to reach a necessary conclusion. If the first statement (premise) is true and the second premise is true, the conclusion must be true. Aristotle first formalised this pattern, and it remains the foundation of valid argument. For example: ‘All humans are mortal’ (A ⇒ B). ‘Socrates is a human’ (B ⇒ C). Therefore, ‘Socrates is mortal’ (A ⇒ C). This formula helps you spot faulty reasoning when one of the connections is missing or when the middle term isn’t properly shared.
三段论是逻辑推理的基本构件。它将两个陈述连接起来，得出一个必然的结论。如果第一个前提为真，第二个前提也为真，那么结论必定为真。亚里士多德最早形式化了这一模式，它至今仍是有效论证的基石。例如：“所有人都会死”（A ⇒ B）。“苏格拉底是人”（B ⇒ C）。因此，“苏格拉底会死”（A ⇒ C）。这个公式能帮你发现推理中的错误：当其中一个连接缺失，或者中项没有被正确共享时，论证就会失效。
2. Socratic Questioning Formula | 苏格拉底式提问公式
Socratic Method: Claim → Question → Clarify → Contradiction? → Refine Claim.
Socrates didn’t write down his philosophy; he asked questions until people saw the weaknesses in their own beliefs. This formula captures his famous method. Start with a claim someone makes, then ask a series of clarifying questions. Often this reveals a contradiction or an unexpected consequence. The aim isn’t to win an argument but to move closer to truth by peeling away assumptions. In a classroom discussion, you might use it: ‘Justice means giving everyone what they deserve.’ Then ask, ‘What if what someone deserves is harmful to others?’ By testing the claim, you refine it or discover you need a whole new definition.
苏格拉底并没有写下自己的哲学，他通过不断提问，让人们看清自己信念中的弱点。这个公式就捕捉了他著名的方法。从某人的主张开始，然后问一系列澄清性的问题。这往往会揭示出一个矛盾或一个意想不到的后果。目的不是赢得争论，而是通过剥离假设来更接近真理。在课堂讨论中，你可以这样用：“正义就是给予每个人他们应得的东西。”然后问：“如果某人应得的东西对他人有害呢？”通过检验主张，你既可能使它得到完善，也可能发现你根本需要一个全新的定义。
3. Cartesian Certainty Formula | 笛卡尔确定性公式
Cogito: I think, therefore I am (D = I think → I exist).
René Descartes set out to doubt everything that could possibly be doubted – the evidence of the senses, the reality of the physical world, even mathematical truths. Eventually he arrived at one indubitable truth: even if an evil demon is deceiving him about everything, he must exist in order to be deceived. This gave him the famous certainty formula ‘Cogito, ergo sum’ – I think, therefore I am. From this rock-solid starting point, he rebuilt knowledge. For Young philosophers, the lesson is about foundational certainty: before you build a big system of beliefs, find one thing you can be absolutely sure of, and build outwards from there.
勒内·笛卡尔决心怀疑一切可能被怀疑的东西——感官的证据、物理世界的实在性，甚至数学真理。最终，他找到了一个无可置疑的真理：即使有一个邪恶的恶魔在一切事情上欺骗他，为了受骗，他也必须存在。这给了他那个著名的确定性公式：“我思故我在”。从这一坚如磐石的起点出发，他重新构建了知识。对年轻的哲学家来说，这个公式的启示在于基础确定性：在你建立庞大的信念体系之前，先找到一个你绝对确信的东西，然后从那里向外构建。
4. Knowledge Formula (JTB) | 知识公式（JTB）
Knowledge = Justified True Belief (K = J + T + B).
For centuries, philosophers defined knowledge as justified true belief. You don’t really know something if it’s just a lucky guess. The belief must be true, and you must have good reasons – justification – for holding it. For instance, you know it’s raining outside only if (a) you believe it is raining, (b) it is actually raining, and (c) you have good evidence, such as seeing rain through the window or hearing it on the roof. Even though later thinkers found tricky counter-examples (the Gettier problem), JTB remains the classic starting point for any discussion about what it means to know something.
几个世纪以来，哲学家们将知识定义为被证成的真信念。如果只是侥幸猜对，那就不算真正知道某事。信念必须是真的，而且你必须拥有正当的理由——即证成——来持有它。例如，你之所以知道外面在下雨，仅当（a）你相信在下雨，（b）实际上确实在下雨，且（c）你有充分的证据，比如透过窗户看到雨或听到雨打在屋顶上。虽然后来的思想家找到了一些棘手的反例（盖梯尔问题），但 JTB 仍然是任何关于“知道某事意味着什么”的讨论的经典起点。
5. Utilitarian Calculus | 功利主义计算式
Greatest Happiness = Σ Pleasure – Σ Pain for all affected.
Utilitarianism, developed by Jeremy Bentham and John Stuart Mill, offers a simple formula for moral decisions: choose the action that produces the greatest net happiness for the greatest number of people. Happiness is understood as pleasure and the absence of pain. When you face a dilemma, you can ‘calculate’ by adding up the pleasure points and subtracting the pain points for everyone involved. The action with the highest score is the right one. This ‘hedonic calculus’ encourages impartiality – your own happiness counts no more than anyone else’s. It sounds straightforward, but measuring pleasure and comparing different kinds of happiness remains a big philosophical puzzle.
由杰里米·边沁和约翰·斯图尔特·密尔发展起来的功利主义，为道德决策提供了一个简单的公式：选择那个能为最大多数人带来最大净幸福的行为。幸福被理解为快乐以及痛苦的缺席。当你面临两难时，你可以通过加总所有相关者的快乐分值并减去痛苦分值来进行“计算”。得分最高的行为就是正确的。这种“快乐计算”鼓励了公正无私——你自己的幸福并不比其他任何人的更重要。它听起来很直接，但如何衡量快乐、如何比较不同种类的幸福，依然是一个巨大的哲学难题。
6. Categorical Imperative Test | 绝对命令检验式
CI Test: Can I will that my maxim become a universal law? If yes → permissible; if no → forbidden.
Immanuel Kant proposed a completely different moral formula. Instead of looking at consequences, think about the rule (maxim) behind your action. Ask yourself: ‘Could I rationally want everyone in the world to follow this same rule?’ If that would lead to a contradiction or a world you couldn’t possibly will, then the action is morally wrong. For example, if you consider telling a lie to get out of trouble, imagine a world where everyone lies whenever it suits them. In such a world, trust would collapse and lying itself would become pointless. Kant’s test forces you to treat humanity, in yourself and others, always as an end in itself, never merely as a means.
伊曼努尔·康德提出了一个完全不同的道德公式。他不是看后果，而是审视你行为背后的准则（ maxim ）。问问自己：“我能否理性地希望世界上的每个人都遵循这同一个准则？”如果这会导致矛盾，或导致一个你不可能意愿的世界，那么该行为在道德上就是错误的。例如，如果你考虑为了摆脱麻烦而说谎，就想象一个所有人只要合适就说谎的世界。在那个世界，信任将崩溃，说谎本身也失去了意义。康德的检验式迫使你总是将人——无论是自身还是他人——视为目的本身，而绝不仅仅当成手段。
7. Golden Mean Formula | 中庸之道公式
Virtue = the midpoint between excess and deficiency (courage = mean between rashness and cowardice).
Aristotle’s ethical formula was not a set of fixed rules but a balance point. Every virtue, he argued, lies at the golden mean between two vices – one of excess and one of deficiency. Courage, for instance, is the mean between rashness (too much confidence) and cowardice (too little confidence). Generosity is the mean between wastefulness and stinginess. This formula reminds us that morality isn’t about blindly following rules but about finding the right response in each situation. It requires practical wisdom (phronesis) to judge where the mean lies in specific circumstances. For a Year 7 student, it’s a tool for self-reflection: ‘Am I being too extreme, or is there a better, more balanced way to act?’
亚里士多德的伦理学公式并不是一套固定的规则，而是一个平衡点。他认为，每一种美德都位于两个极端之间的黄金中点上——一端是过度，另一端是不及。例如，勇敢就是鲁莽（过度的信心）和怯懦（缺乏信心）之间的中道。慷慨则是浪费与吝啬之间的中道。这个公式提醒我们，道德不是盲目地遵从规则，而是在每个具体情境中找到恰当的回应。这需要实践智慧（phronesis）来判断中道在特定环境中的位置。对一名 Year 7 学生而言，它是一个自我反省的工具：“我是不是太极端了？有没有更好、更平衡的行事方式？”
8. Ockham’s Razor | 奥卡姆剃刀原则
Entities should not be multiplied beyond necessity. (Simpler explanations are to be preferred.)
William of Ockham gave philosophy a powerful tool for cutting away unnecessary complications. His ‘razor’ is a principle of explanation: when you have two theories that explain the same facts equally well, choose the simpler one – the one that makes fewer assumptions. This does not mean the simpler theory is always true; it means we shouldn’t add extra things (entities, causes, forces) without good reason. In everyday thinking, it helps you resist overcomplicated excuses. If you didn’t do your homework, ‘I forgot’ is a simpler explanation than ‘Aliens took my notebook, erased my memory, but then returned it.’ Ockham’s razor shaves off the extra story and keeps you focused on what genuinely needs explanation.
奥卡姆的威廉为哲学提供了一件切除不必要复杂性的利器。他的“剃刀”是一条解释原则：当你有两个理论能够同样好地解释相同事实时，选择更简单的那个——也就是做出较少假设的那个。这并不意味着更简单的理论总是真实的，而是说我们不应在没有充分理由的情况下增添额外的事物（实体、原因、力量）。在日常思考中，这能帮你抵制那些过分复杂的借口。如果你没做家庭作业，“我忘了”就是一个比“外星人拿走了我的笔记本，抹掉了我的记忆，然后又还回来了”更简单的解释。奥卡姆剃刀刮去了额前多余的叙述，让你专注于真正需要解释的部分。
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