KS3 AQA Philosophy: Formula & Theorem Quick Reference Handbook | KS3 AQA 哲学：公式定理速查手册

📚 KS3 AQA Philosophy: Formula & Theorem Quick Reference Handbook | KS3 AQA 哲学：公式定理速查手册

Philosophy can feel like a vast ocean of ideas, but beneath the surface there are logical structures – formulas and theorems – that help you navigate. This quick-reference handbook presents key philosophical principles in a concise, memorable format. Each entry captures a core philosophical insight as a simple expression you can apply to arguments, ethical dilemmas, and big questions. Use these tools to sharpen your thinking and ace your KS3 AQA Philosophy studies.

哲学有时像一片广阔的思想海洋，但在表面之下，隐藏着许多逻辑结构——就像公式和定理一样——它们能帮你航行自如。这本速查手册以简洁、好记的形式呈现关键的哲学原理。每个条目都把核心的哲学洞见浓缩成一个简单的表达式，你可以把它运用到论证、伦理困境和大问题中。使用这些工具来磨砺你的思维，在 KS3 AQA 哲学课程中取得优异成绩。

1. The Knowledge Formula | 知识公式

Knowledge = Justified True Belief (JTB)
According to Plato, to say “I know X” you must tick three boxes: you believe X; X is actually true; and you have good reasons (justification) for your belief. Without all three, it’s just lucky guesswork, not real knowledge.

知识 = 被证成的真信念（JTB）
根据柏拉图，当你说“我知道X”时，必须满足三个条件：你相信X；X确实是真的；并且你有充分的理由（证成）支持你的信念。缺少任何一项，那都只是侥幸的猜测，而不是真正的知识。

Analogy: Think of a courtroom. The jury must believe the defendant is guilty, the defendant really must be guilty, and the evidence must justify that belief. If the jury believes it but the evidence is flimsy, we don’t call that knowledge.

类比：想象一个法庭。陪审团必须相信被告有罪，被告确实有罪，而且证据必须能证明那个信念。如果陪审团相信了，但证据站不住脚，我们就不能说那是一种知识。

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2. Descartes’ Certainty Theorem | 笛卡尔的确定性定理

“I think, therefore I am” → Certainty
In his search for a foundation of knowledge that cannot be doubted, Descartes arrived at one indubitable truth: even if an evil demon is deceiving me about everything, I must exist in order to be deceived. The very act of doubting proves my existence as a thinking thing. This became the bedrock for his rationalist project.

“我思，故我在” → 确定性
在寻找不可怀疑的知识基础时，笛卡尔到达了一个无可置疑的真理：即使一个邪恶的恶魔在欺骗我关于一切，我为了被欺骗也必须要存在。怀疑的行为本身就证明了我作为一个思维者的存在。这成为他理性主义体系的基石。

Logical form: If I doubt, then I think. If I think, then I exist. ∴ I exist. Use this “Archimedean point” to challenge scepticism.

逻辑形式：如果我在怀疑，那么我在思考。如果我在思考，那么我存在。故我存在。用这个“阿基米德点”来挑战怀疑论。

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3. The Socratic Elenchus Loop | 苏格拉底反诘法循环

Question → Definition → Counterexample → Improved Definition (repeat)
Socrates did not lecture; he questioned. To test a claim like “courage is endurance of the soul,” he would produce a counterexample (e.g., foolish endurance isn’t courage). The interlocutor then revises the definition. This dialectical loop refines concepts until they withstand scrutiny. It’s philosophy’s debugging algorithm.

提问 → 定义 → 反例 → 改进定义（重复）
苏格拉底不训诲；他提问。为了检验像“勇敢是灵魂的忍耐”这样的主张，他会举出反例（比如愚蠢的忍耐并非勇敢）。对话者随之修正定义。这种辩证循环不断提炼概念，直到它们经受住检验。这是哲学的“除错算法”。

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4. Utilitarian Happiness Calculus | 功利主义幸福计算

Right action = max Σ (pleasure − pain) across all affected
Jeremy Bentham proposed that the moral worth of an action is measured by its utility – the balance of pleasure over pain. To decide what to do, imagine a scale: add up all the pleasure the action would produce and subtract all the pain. The option with the greatest net happiness for the greatest number wins. Simplified formula: Hij = ∑(P − Q) for each person i, action j.

正确的行动 = 最大化所有受影响者的 Σ（快乐 − 痛苦）
边沁提出，一个行动的道德价值取决于它的效用——即快乐与痛苦的差额。做决定时想象一架天平：把所有产生的快乐加起来，再减去所有的痛苦。能给最多人带来最大净幸福的那个选项就是正确的。简式：Hij = ∑(P − Q) 对每个人 i，行动 j。

• Unit of measurement: “utils” (a hypothetical unit of happiness)
• 测量单位：“效用子”（一个假想的幸福单位）
• Bentham’s dimensions: intensity, duration, certainty, propinquity, fecundity, purity, extent (the “felicific calculus”).
• 边沁的维度：强度、持续时间、确定性、远近程度、繁殖性、纯度、范围（“幸福计算法”）。

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5. Kant’s Categorical Imperative Test | 康德的定言令式检验

Act only according to that maxim whereby you can at the same time will that it should become a universal law.
For Kant, morality is not about consequences but about the principle behind your action. Before you act, ask: “Could I rationally want everyone to follow the same rule?” If the answer is no – if universalizing the maxim would lead to a contradiction in conception or in will – the act is morally forbidden. This is like a logical consistency check for ethics.

只依据那些你同时愿意它成为普遍法则的准则去行动。
在康德看来，道德不在于后果，而在于你行动背后的原则。在行动之前，先问自己：“我能理性地愿意让每个人都遵循同样的规则吗？”如果答案是否定的——如果普遍化这条准则会导致概念上的矛盾或意愿上的矛盾——那么该行动就是道德上禁止的。这就像伦理学的逻辑一致性检查。

Formula of Humanity version: “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.” Always respect rational agency.

人性公式版本：“你的行动，要把你自己人身中的人性，和其他人身中的人性，在任何时候都同样看作是目的，永远不能只看作是手段。”始终尊重理性行动者。

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6. Aristotle’s Golden Mean | 亚里士多德的中庸之道

Virtue = (Excess + Deficiency) ÷ 2, relative to us, determined by reason.
Aristotle held that moral virtue lies in finding the intermediate between two vices: one of excess and one of deficiency. Courage, for example, is the mean between cowardice (deficiency) and rashness (excess). But it’s not arithmetic; the mean depends on the situation and the individual. Practical wisdom (phronesis) helps us hit the target.

德性 =（过度 + 不足）÷ 2，相对于我们自身，由理性决定。
亚里士多德认为，道德德性在于在两个恶之间找到中道：一个是过度，一个是不足。例如，勇敢是怯懦（不足）与鲁莽（过度）之间的中道。但这不是算术平均值；中道取决于情境和个体。实践智慧（phronesis）帮助我们命中目标。

Sphere of action	Deficiency	Virtue (Mean)	Excess
Fear	Cowardice	Courage	Rashness
Pleasure	Insensibility	Temperance	Licentiousness
Giving money	Stinginess	Generosity	Prodigality

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7. Hobbes’ Social Contract Equation | 霍布斯的社会契约方程

State = individuals surrender natural rights → sovereign provides security
In Hobbes’ state of nature, life is “solitary, poor, nasty, brutish, and short” because everyone has a right to everything. To escape this war of all against all, rational individuals agree to give up certain freedoms and transfer power to a sovereign (Leviathan). The equation: Liberty sacrificed = security gained. The sovereign’s job is to keep the peace.

国家 = 个体交出自然权利 → 主权者提供安全保障
在霍布斯的自然状态中，生活是“孤独、贫困、卑污、残忍而短寿”的，因为每个人对一切都有权利。为了逃离这场一切人对一切人的战争，理性的个体同意放弃某些自由，把权力交给一个主权者（利维坦）。方程式：牺牲的自由 = 获得的安全。主权者的职责是维护和平。

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8. Mill’s Harm Principle | 穆勒的伤害原则

Your liberty ends where harm to others begins.
John Stuart Mill argued that the only justification for restricting an individual’s freedom is to prevent harm to others. You are sovereign over your own body and mind, but the moment your actions risk harming someone else, society may intervene. Think of it as a boundary line: self-regarding actions are free; other-regarding actions that cause harm are not.

你的自由止于对他人的伤害之处。
约翰·斯图亚特·穆勒主张，限制个人自由的唯一理由就是防止对他人造成伤害。你对自己的身体和思想拥有主权，但一旦你的行为可能伤害他人，社会就有权干预。可以把它想象成一条边界线：只关涉自己的行为是自由的；关涉他人且造成伤害的行为则不受保护。

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9. Cultural Relativism Formula | 文化相对主义公式

Truth and morality = f(culture) → No universal standard
Relativists argue that what counts as true or morally right depends on the cultural or individual context. There is no viewpoint-independent fact of the matter. If culture A says X is wrong and culture B says X is right, there is no further fact that settles the dispute. This formula highlights the variability, but also invites critique: if all truth is relative, is that statement itself absolutely true?

真理与道德 = f(文化) → 没有普遍标准
相对主义者主张，什么是真的、什么是道德上正确的，取决于文化或个人的背景。不存在独立于观点的客观事实。如果文化A说X是错的，文化B说X是对的，那就没有更高一层的事实来解决这个争议。这个公式凸显了差异性，但也引来了批评：如果一切真理都是相对的，那么这个命题本身是绝对真理吗？

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10. The Evil Demon Sceptical Challenge | 邪恶恶魔怀疑论挑战

If an all-powerful deceiver is possible → all sensory beliefs could be false → suspend judgment
Descartes imagined a malicious demon with complete control over his sensory experiences. This “hyperbolic doubt” calls into question the entire external world. The theorem: P (knowledge of external world) = 0, unless we can rule out the demon scenario. Modern versions use the brain-in-a-vat or simulation hypothesis. The recipe for scepticism: doubt everything that is not absolutely certain.

如果存在一个全能的欺骗者 → 所有感官信念都可能为假 → 中止判断
笛卡尔设想了一个邪恶的恶魔，完全掌控他的感官经验。这种“夸张的怀疑”质疑了整个外部世界。定理：P（关于外部世界的知识）= 0，除非我们能排除恶魔情景。现代版本使用了“缸中之脑”或模拟假说。怀疑论的配方是：怀疑一切不是绝对确定的事物。

Knowledge → Justified True Belief + No Defeaters (No Evil Demon)

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11. The Mind–Body Problem as a Dualist Equation | 心身问题的二元论方程

Mental state ≠ physical state (according to dualism)
Substance dualism (Descartes) claims that mind and body are two fundamentally different substances: the mind is non-physical, thinking; the body is extended, non-thinking. The interaction problem asks: how can an immaterial mind cause physical movements? This tension generates philosophical puzzles, and it’s often expressed as: M (mind) ←?→ B (body). Materialists reply that mental states are just brain states, collapsing the equation.

心理状态 ≠ 物理状态（根据二元论）
实体二元论（笛卡尔）声称，心灵与身体是两种根本不同的实体：心灵是非物质的、能思考的；身体是广延的、不思考的。交互问题随之而来：非物质的灵魂如何引起身体的运动？这种张力产生了哲学谜题，常被表示为：M（心）←?→ B（身）。唯物主义者则回应说心理状态就是大脑状态，从而消解了这个方程。

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12. The Abductive Principle (Inference to the Best Explanation) | 溯因原则（最佳解释推理）

Best hypothesis = the simplest, most comprehensive explanation of the evidence (Ockham’s Razor: do not multiply entities beyond necessity)
When competing theories explain the same data, choose the one that is simplest, makes the fewest unsupported assumptions, and covers the widest range of phenomena. Philosophers use this principle to compare worldviews, from the existence of God to the nature of reality. Simplicity is not proof, but a guiding norm in rational inquiry.

最佳假说 = 对证据最简单、最全面的解释（奥卡姆剃刀：如无必要，勿增实体）
当相互竞争的理论都能解释同一批数据时，选择那个最简单、依赖最少未经证实的假定、能涵盖最广泛现象的理论。哲学家使用这一原则来比较各种世界观，从上帝是否存在到实在的本性。简单性不是证明，但它是理性探究中的一个指导性规范。

If theory A explains data D with fewer assumptions than theory B, prefer A.

如果理论A 比理论B 用更少的假设解释了数据D，就偏好A。

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Published by TutorHao | Philosophy Revision Series | aleveler.com

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