📚 Year 7 Cambridge Philosophy: Quick Reference Handbook of Formulas & Theorems | 剑桥七年级哲学：公式定理速查手册
Welcome to your Year 7 Philosophy quick reference handbook. Think of this as a toolbox filled with powerful ‘formulas’ and ‘theorems’ that help you think clearly, argue fairly, and explore big questions about knowledge, reality, and right and wrong. Unlike maths or science, philosophy’s formulas are patterns of reasoning and ethical principles. Each one is a shortcut to deeper thinking.
欢迎来到你的七年级哲学速查手册。你可以把这看作一个装满强大“公式”和“定理”的工具箱，它们能帮你清晰地思考、公平地辩论，并探索关于知识、现实与对错的大问题。与数学或科学不同，哲学的公式是推理的模式与伦理原则。每一条都是通往深层思考的捷径。
1. The Knowledge Formula | 知识公式
For centuries, philosophers have tried to define what it means to truly know something. The classic formula, often called the ‘justified true belief’ theory, breaks knowledge down into three essential parts.
几个世纪以来，哲学家一直试图定义真正认识某件事意味着什么。这个经典公式常被称为“被证成的真信念”理论，将知识分解为三个必要部分。
K = JTB (Knowledge = Justified True Belief)
知识 = 证成 + 真 + 信念 (K = JTB)
- Belief (B): You must believe the claim. If you don’t believe it, you can’t know it.
- 信念 (B): 你必须相信这个主张。如果你不信，你就无法知道它。
- Truth (T): The claim must actually be true. You cannot know something that is false.
- 真 (T): 这个主张必须是真的。你不可能知道一件虚假的事情。
- Justification (J): You must have good reasons or evidence for your belief. A lucky guess is not knowledge.
- 证成 (J): 你必须有充分的理由或证据支持你的信念。侥幸猜中不是知识。
Example: You know it is raining outside because you see water falling from the sky (justification), it is actually raining (truth), and you believe it is raining (belief).
例如：你知道外面在下雨，因为你看到水从天空落下（证成），天确实在下雨（真），并且你相信在下雨（信念）。
2. The Argument Structure Formula | 论证结构公式
A philosophical argument is not a fight. It is a structured set of reasons leading to a conclusion. The basic formula ensures your reasoning is clear and testable.
哲学论证不是争吵。它是一组支撑结论的、结构化的理由。这个基本公式能确保你的推理清晰且可检验。
Premise 1 + Premise 2 → Conclusion
前提1 + 前提2 → 结论
If the premises are true, and the reasoning is valid, the conclusion must be true. This is a deductive argument.
如果前提为真，且推理有效，那么结论必然为真。这就是演绎论证。
- Premise 1: All humans are mortal.
- 前提1： 所有人都会死。
- Premise 2: Socrates is a human.
- 前提2： 苏格拉底是人。
- Conclusion: Therefore, Socrates is mortal.
- 结论： 所以，苏格拉底会死。
Always check: Are the premises actually true? Does the conclusion logically follow? This formula helps you spot weak reasoning.
切记要检查：前提确实为真吗？结论在逻辑上能必然推出吗？这个公式有助你发现薄弱的推理。
3. The Greatest Happiness Principle | 最大幸福原则
This is the core ethical formula of utilitarianism, proposed by Jeremy Bentham and John Stuart Mill. It asks us to measure the moral worth of an action by its outcome.
这是边沁和密尔提出的功利主义核心伦理公式。它要求我们通过后果来衡量一个行为的道德价值。
Right action = Maximises overall happiness and Minimises overall suffering
正确行动 = 最大化总体幸福，最小化总体痛苦
When facing a choice, calculate which option creates the greatest balance of pleasure over pain for everyone affected. Think of it as a happiness equation.
面对选择时，算一算哪个选项能给所有受影响的人带来最大程度的快乐多于痛苦。你可以把它想象成一道幸福算式。
Example: If you have two sweets and three friends, sharing brings more total happiness than eating them all yourself, even though your own pleasure is reduced.
例如：如果你有两颗糖和三个朋友，分享比独吞能带来更多的总幸福，即使你个人的快乐减少了。
4. The Categorical Imperative Simplified | 简化的绝对命令
Immanuel Kant gave us a completely different ethical formula. It does not look at consequences but at the principle behind the action. The most famous version is the ‘universal law’ test.
康德给了我们一套截然不同的伦理公式。它不看后果，而看行为背后的原则。最著名的版本是“普遍法则”检验。
Act only according to that rule which you could will to become a universal law for everyone.
只按照你同时愿意它成为一条普遍法则的准则去行动。
Before you act, ask yourself: ‘What if everyone did this?’ If the action would become pointless or the world chaotic if everyone copied it, then the action is morally wrong.
在行动之前，问一问自己：“要是人人都这样做呢？” 如果人人都模仿这一行为会导致这个行为本身变得无效或世界混乱，那么这一行为在道德上就是错误的。
Example: You want to break a promise. If everyone lied and broke promises all the time, the very idea of promising would collapse. Therefore, breaking a promise is wrong, according to Kant.
例如：你想违背诺言。如果人人都撒谎、随时背弃承诺，“承诺”这个概念本身就会崩溃。因此，根据康德的说法，违背诺言是错误的。
5. The Virtue Formula | 美德公式
Aristotle’s ethical formula focuses not on individual actions or consequences, but on the character of the person. The goal is to become a virtuous person who naturally does the right thing.
亚里士多德的伦理公式不关注个别行为或后果，而关注人的品格。目标是成为一个有美德的人，自然而然地做出正确的事。
Virtue = The Golden Mean between two extremes
美德 = 两个极端之间的黄金中道
Every virtue is a midpoint between a vice of excess and a vice of deficiency. Courage is the mean between cowardice (too little fear) and recklessness (too much boldness).
每一种美德都是一个过度之恶与不足之恶之间的中点。勇气是怯懦（恐惧不足）与鲁莽（胆量过度）之间的中道。
| Sphere of action | Vice of Deficiency | Virtue (Golden Mean) | Vice of Excess |
|---|---|---|---|
| Fear and confidence | Cowardice | Courage | Recklessness |
| Pleasure and pain | Insensibility | Temperance | Overindulgence |
| Giving and taking money | Stinginess | Generosity | Wastefulness |
By practising virtue, we shape our character, and the right actions flow naturally from who we are.
通过践行美德，我们塑造自身的品格，于是正确的行动便从我们的为人中自然流露。
6. The Brain in a Vat Doubt Formula | 缸中之脑怀疑公式
This famous thought experiment updates the ancient idea of scepticism into a modern setting. It gives us a formula for radical doubt about the external world.
这个著名的思想实验将古代的怀疑论思想升级到了现代场景。它为我们提供了一个彻底怀疑外部世界的公式。
If you cannot rule out that all your experiences are an illusion created by a supercomputer, then you cannot be completely certain about the physical world.
如果你无法排除“你所有的体验不过是超级电脑制造的幻象”这种可能，那么你就无法彻底确定物理世界的真实存在。
Imagine your brain is kept alive in a vat of nutrients, wired to a computer that simulates everything you see, hear, and touch. The experience of reading this sentence right now could be part of that simulation. The formula challenges us to find one certain truth that even the brain-in-a-vat story cannot destroy.
想象你的大脑被保存在一缸营养液里，连接着一台电脑，这台电脑模拟了你所看到、听到和触摸到的一切。你现在读这句话的体验也可能只是那个模拟的一部分。这个公式挑战我们找到一条连“缸中之脑”故事都无法摧毁的确定真理。
Descartes’ famous answer: ‘I think, therefore I am.’ Even if deception is total, the fact that you are being deceived proves your existence as a thinking thing.
笛卡尔著名的回答是：“我思故我在。” 即使欺骗是彻底的，你正被欺骗这一事实本身也证明了作为思考者的你的存在。
7. The Identity Formula (Ship of Theseus) | 同一性公式（忒修斯之船）
Identity over time is a deep puzzle. This formula helps us think about what makes something the same thing even after all its parts have changed.
同一性随时间的变化是一个深奥的谜题。这个公式帮助我们思考：是什么让某个事物在所有零件都更换后，仍然是同一个事物。
If all the parts of X are gradually replaced, does X remain the same object?
如果X的所有部件都逐渐被替换，X仍然是同一个物体吗？
According to the legend, the ship of Theseus was kept as a memorial. Over time, every plank of wood was replaced. Is the restored ship the original? And what if someone collected the old planks and rebuilt the ship? Which one is the true Ship of Theseus?
相传，忒修斯的船被保存为纪念舰。随时间流逝，每一块木板都被替换了。这艘修复后的船是原来的那艘吗？如果有人收集了所有旧木板，重新造了一艘船，哪一艘才是真正的忒修斯之船？
This formula asks you to consider whether identity depends on physical continuity, the pattern or structure, or something else entirely.
这个公式要求你思考，同一性到底是依赖于物理的连续性，还是依赖于模式或结构，抑或是其他完全不同的东西。
8. The Free Will Equation | 自由意志方程
The debate over free will can be expressed as a tension between two fundamental beliefs. The equation helps you map the positions.
围绕自由意志的辩论可以被表达为两个根本信念之间的拉扯。这个方程能帮你梳理不同立场。
Determinism + Responsibility = Compatibilism (or incompatibilism)
决定论 + 道德责任 = 相容论（或不兼容论）
- Determinism says every event is caused by prior events and the laws of nature, so future states are inevitable.
- 决定论认为每个事件都由之前的事件和自然法则所决定，因此未来状态是不可避免的。
- Free will claims we could have chosen differently in exactly the same situation.
- 自由意志主张在完全相同的处境下，我们本可以做出不同的选择。
The equation shows the puzzle: If determinism is true, and the universe is like a clockwork, do we still have the freedom needed to hold people morally responsible? Compatibilists argue ‘yes’, while hard determinists argue ‘no’.
这个方程展示了困惑：如果决定论是正确的，宇宙如同钟表机械，我们是否还拥有道德责任所需的那种自由？相容论者说“有”，而强决定论者说“没有”。
9. The Ethical Dilemma Weighing Scale | 伦理困境天平
When abstract formulas clash in real life, you need a method for balancing competing values. This scale helps you weigh reasons in an ethical dilemma.
当抽象的公式在现实生活中冲突时，你需要一个方法来权衡相互竞争的价值。这架天平能帮你衡量伦理困境中的理由。
Moral Decision = Weighing Duties vs. Consequences vs. Virtues
道德决定 = 权衡义务 vs. 后果 vs. 美德
Imagine a classic dilemma: A friend is hiding from someone who intends to harm them. The attacker asks you where your friend is. Your weighing scale might include:
想象一个经典的困境：一位朋友正躲避一个意图伤害他的人。行凶者询问你朋友在哪里。你的天平上可能包括：
- Duty (Kant): You have a duty never to lie. Lying would violate the universal law.
- 义务（康德）: 你有永不撒谎的义务。撒谎会违背普遍法则。
- Consequences (Utilitarianism): Saving a life produces far more happiness and less suffering than telling the truth to a murderer.
- 后果（功利主义）: 对一个杀人犯说真话，与拯救生命相比，救人能带来更大的幸福和更少的痛苦。
- Virtue (Aristotle): A compassionate and loyal person would protect their friend. What would a brave and kind person do?
- 美德（亚里士多德）: 一个有同情心且忠诚的人会保护朋友。一个勇敢仁慈的人会怎么做？
The formula doesn’t give a pre-calculated answer; it forces you to articulate which reasons carry the most weight for you.
这个公式不会给出一个预设的答案，它迫使你说清楚，在你看来哪些理由分量最重。
10. The Socratic Method Formula | 苏格拉底法公式
Socrates taught us that true wisdom begins with admitting one’s ignorance. The Socratic method is a formula for uncovering truth through collaborative questioning.
苏格拉底教会我们，真正的智慧始于承认自己的无知。苏格拉底法是通过合作式提问来揭示真理的公式。
Claim → Cross-Examination → Refinement or Rejection → Deeper Understanding
主张 → 盘问 → 修正或放弃 → 更深的理解
Step 1: Someone makes a bold claim, such as ‘Justice means helping your friends and harming your enemies.’ Step 2: You ask testing questions: ‘What if your friend is doing evil?’ Step 3: The definition is shown to be incomplete or contradictory. Step 4: Together, you search for a better definition.
第一步：某人提出一个大胆的主张，比如“正义就是帮助朋友、伤害敌人。” 第二步：你提出考验性的问题：“如果你的朋友在做坏事呢？” 第三步：那个定义会被证明不完善或自相矛盾。第四步：你们一起探寻更好的定义。
This formula is not about winning a debate but about sharpening ideas until they withstand all scrutiny. The outcome is intellectual humility and closer approximation of truth.
这个公式不是为了赢得辩论，而是打磨观点，直到它能经得起所有审问。结果是智识上的谦卑和对真理更接近的认知。
11. The Mind–Body Problem Formula | 身心问题公式
What is the relationship between our physical brain and our conscious mind? This formula sets up the central puzzle of philosophy of mind.
我们的物质大脑和我们的意识心理之间是什么关系？这个公式建立了心灵哲学的核心难题。
Mental states (beliefs, pains) ≠ Brain states (neurons firing) ?
心理状态（信念、疼痛） ≠ 脑状态（神经元放电）？
If you feel sad, we can observe chemical changes in the brain. But is the feeling of sadness identical to those chemical changes, or is it something extra? Dualists believe the mind is a non-physical substance, while physicalists argue the mind just is the brain.
当你感到悲伤时，我们可以观察到大脑中的化学变化。但悲伤的感觉和那些化学变化是完全等同的，还是额外的某种东西？二元论者认为心灵是非物质的实体，而物理主义者认为心灵就是大脑。
The formula encourages you to reflect: Can science ever fully describe what it is like to be a bat having a bat experience, or are there subjective truths that escape objective measurement?
这个公式促使你反思：科学是否永远无法完全描述作为一只蝙蝠拥有蝙蝠体验是什么感觉，还是说存在着逃避客观测量的主观真理？
12. The Just State Formula | 正义国家公式
Political philosophy asks how we should organise society. This formula, inspired by John Rawls, gives a tool for designing fair rules.
政治哲学探讨我们应如何组织社会。这个受罗尔斯启发的公式提供了一个设计公平规则的工具。
Just principles = Rules chosen from behind the Veil of Ignorance
正义原则 = 在“无知之幕”背后选择的规则
Imagine you are about to be born into a society. You do not know your future wealth, talents, gender, or health status. You are behind a ‘veil of ignorance’. The rules you would design from that original position are likely to be fair, because you would want to protect the least well-off, just in case you end up among them.
想象你即将诞生于某个社会。你不知道自己未来的财富、才智、性别或健康状况。你处于一张“无知之幕”背后。你从那个原初位置设计出的规则很可能是公平的，因为你会想要保护最弱势的群体，以防自己恰好落入其中。
From this position, principles like equal basic liberties, fair equality of opportunity, and the difference principle (inequalities must benefit the least advantaged) naturally emerge.
从这一位置出发，像基本自由平等、公平的机会平等以及差异原则（不平等必须利于最不利者）等原则就自然出现了。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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