KS3 CIE Philosophy: Formulae and Theorems Quick Reference Handbook | KS3 CIE 哲学：公式定理速查手册

📚 KS3 CIE Philosophy: Formulae and Theorems Quick Reference Handbook | KS3 CIE 哲学：公式定理速查手册

Philosophy is not just a collection of abstract ideas; it is built upon rigorous structures of reasoning that function much like the formulae and theorems you encounter in mathematics and science. This handbook distils the core arguments and ethical frameworks from the KS3 CIE Philosophy syllabus into easy-to-remember ‘formulae’ and ‘theorems’, providing you with a powerful toolkit for analysis, evaluation, and debate.

哲学并非只是抽象思想的集合，它建立在严谨的推理结构之上，其运作方式与你在数学和科学中遇到的公式和定理非常相似。这本速查手册将 KS3 CIE 哲学课程的核心论证和伦理框架提炼成易于记忆的“公式”和“定理”，为你提供分析、评估和辩论的强大工具箱。

1. The Socratic Method Formula | 苏格拉底问答法公式

The Socratic Method is a dialectical process used to stimulate critical thinking and expose the weaknesses in commonly held beliefs. It functions as a formulaic loop: a statement is proposed, cross-examined through questions, contradictions are revealed, and the original statement is refined or rejected.

苏格拉底问答法是一种辩证过程，用于激发批判性思维并揭示普遍信念中的弱点。它像一个公式化的循环运作：提出一个陈述，通过提问来交叉检视，揭示矛盾，然后修正或摒弃最初的陈述。

Statement → Elenchus (Cross-examination) → Aporia (Puzzlement) → Re-evaluation

The key is never to accept a definition at face value. For example, if someone claims ‘Courage is never feeling fear,’ the Socratic questioner would ask if a soldier who feels fear but still acts to save a comrade is courageous. This process exposes that courage is more about right action in the face of fear.

关键在于永远不要接受一个定义的字面意思。例如，如果有人声称“勇气就是从不感到恐惧”，苏格拉底式的提问者会问，一个感到恐惧但仍旧行动去拯救战友的士兵是否勇敢。这个过程揭示了勇气更多是在恐惧面前做出正确行动。

2. The Golden Rule Ethical Formula | 黄金法则伦理学公式

The Golden Rule is a foundational ethical formula found in nearly every cultural and religious tradition. It provides a simple, universal test for moral actions by requiring you to imagine swapping places with those affected by your decision.

黄金法则是一个基础的伦理学公式，几乎出现在每一种文化和宗教传统中。它通过要求你想象与受你决策影响的人交换位置，为道德行为提供了一个简单、普遍性的检验标准。

Treat others as you would wish to be treated by them.

To apply this formula, one asks: ‘If I were in the other person’s position, would I want this action done to me?’ If the answer is no, the action is ethically unsound. This theorem does not require a sacred text or a complex calculation, making it a powerful, intuitive tool for students.

要应用这个公式，我们问自己：“如果我处在那个人的位置，我是否希望这个行动施加在我身上？”如果答案是否定的，那么这个行动在伦理上就是不合理的。这一定理不需要神圣经文或复杂的计算，使其成为学生的一个强大且直观的工具。

3. The Utilitarian Calculus | 功利主义计算公式

Jeremy Bentham proposed that the morality of an action is determined by its ability to produce the greatest happiness for the greatest number. This can be broken down into a hedonistic calculus that weighs pleasure against pain across all sentient beings affected.

杰里米·边沁提出，一个行动的道德性取决于它为最大多数人带来最大幸福的能力。这可以分解为一种幸福计算法，权衡所有受影响的有情众生的快乐与痛苦。

Net Utility = Σ (Intensity × Duration × Probability) of Pleasure − Σ (Intensity × Duration × Probability) of Pain

For a KS3 student, the core theorem is simpler: an action is right if it causes more overall happiness than any alternative. If you have to choose between giving £10 to one friend or £1 each to ten classmates, the utilitarian formula points to the latter, as it spreads more aggregate joy.

对于 KS3 学生，核心定理更简单：如果一个行动比任何替代方案能带来更多总体幸福，那它就是对的。比如你必须在给一个朋友 10 英镑和给十个同学每人 1 英镑之间选择，功利主义公式会指向后者，因为它分散了更多的总体快乐。

4. Kant’s Categorical Imperative: Formula of Universal Law | 康德定言令式：普遍法则公式

Immanuel Kant’s deontological ethics reject the calculation of consequences. Instead, he provides a logical test for maxims (personal rules of action): can you rationally will that your maxim become a universal law for everyone to follow without contradiction?

伊曼努尔·康德的义务论伦理学反对计算后果。相反，他为准则（个人行动规则）提供了一个逻辑检验：你能否理性地愿意让你的准则成为一条人人都可遵循、没有矛盾的普遍法则？

Act only according to that maxim whereby you can at the same time will that it should become a universal law.

Consider the maxim ‘It is acceptable to make a false promise to get money.’ If universalised, everyone would be making false promises, and the institution of promising would collapse. The maxim is self-defeating, thereby forbidden by the formula. This transforms morality into a question of logical consistency rather than emotional preference.

思考一下“做虚假承诺来获取金钱是可以接受的”这条准则。如果它被普遍化，每个人都会做虚假承诺，那么承诺这一制度就会崩溃。这条准则自相矛盾，因而被这一公式禁止。这使得道德成为了一个逻辑一致性的问题，而非情感偏好。

5. Descartes’ Cogito Theorem | 笛卡尔“我思”定理

René Descartes set out to doubt everything that could possibly be doubted in order to find a foundation for certain knowledge. His hyperbolic doubt stripped away sensory experience and even the existence of his own body, until he arrived at an indubitable truth.

勒内·笛卡尔试图怀疑一切可以被怀疑的东西，以便为确定的知识找到一个基础。他的极致怀疑剥离了感官经验甚至自己身体的存在，直到他抵达了一个毋庸置疑的真理。

Cogito, ergo sum. (I think, therefore I am.)

The theorem states that even if an evil demon is deceiving me about everything, I must exist in some form in order to be deceived. The very act of doubting proves the existence of the doubter. This formula is the bedrock of rationalist philosophy and a classic example of a self-verifying proposition.

这一定理指出，即使有一个邪恶的恶魔在一切事情上欺骗我，我为了能够被欺骗，也必定以某种形式存在。怀疑这一行为本身就证明了怀疑者的存在。这个公式是理性主义哲学的基石，也是自我验证命题的经典例子。

6. Plato’s Theory of Forms Formula | 柏拉图理型论公式

Plato distinguished between the ever-changing world of appearances that we perceive with our senses and an unchanging, eternal world of Forms (or Ideas). The relationship between a particular object and its Form can be mapped as a participation formula.

柏拉图区分了我们用感官感知到的不断变化的表象世界，和一个不变、永恒的理型（或理念）世界。一个具体物件与其理型之间的关系可以被映射为一个分有公式。

Particular (shadow/copy) ← Participates in → Form (perfect original)

A drawn circle on a whiteboard is never perfectly round; it is merely a poor copy of the true Form of Circularity. Knowledge, for Plato, is not about observing imperfect particulars but about using reason to recollect the perfect Forms that the soul knew before birth. This formula underlies his Allegory of the Cave.

白板上画的一个圆永远不会完美无缺；它只是真正的圆形之理型的拙劣摹本。对柏拉图而言，知识并非关于观察不完美的具体事物，而是关于运用理性去回忆灵魂出生前就认识了的完美理型。这一公式是他的洞穴比喻的基础。

7. Aristotle’s Four Causes Formula | 亚里士多德四因公式

Aristotle rejected Plato’s separate world of Forms and argued that to fully understand a thing, we must explain it in terms of four distinct causes. His formula provides a complete explanation of any object or being by answering four fundamental ‘why’ questions.

亚里士多德否定了柏拉图分离的理型世界，并主张要完全理解一个事物，我们必须用四种不同的原因来解释它。他的公式通过回答四个基本的“为什么”问题，为任何物体或生物提供了完整的解释。

Full Explanation = Material Cause + Formal Cause + Efficient Cause + Final Cause

Take a wooden dining table. The Material Cause is the wood; the Formal Cause is the blueprint or design ‘tableness’; the Efficient Cause is the carpenter who shaped it; and the Final Cause (telos) is to provide a surface for dining. For Aristotle, the Final Cause explains the ultimate purpose.

以一张木质餐桌为例。质料因是木头；形式因是蓝图或设计即“桌子性”；动力因是制作它的木匠；目的因则是提供一个用餐的表面。对亚里士多德而言，目的因解释了终极目的。

8. Hume’s Fork: The Analytic-Synthetic Divide | 休谟的叉子：分析-综合之分

David Hume proposed a powerful classification tool for all meaningful statements, often called ‘Hume’s Fork’. It cleaves knowledge into two distinct categories, providing a test for whether a claim is genuinely informative or merely definitional.

大卫·休谟为所有有意义的陈述提供了一个强大的分类工具，通常被称为“休谟的叉子”。它把知识劈成两个截然不同的类别，为判断一个主张是否真正提供信息，或者仅仅是定义性的，提供了一个检验标准。

Relations of Ideas (Analytic, a priori) vs. Matters of Fact (Synthetic, a posteriori)

A ‘Relation of Ideas’ is a statement like ‘All bachelors are unmarried’; it is true by definition and its denial is a contradiction. A ‘Matter of Fact’ is a statement like ‘The sun will rise tomorrow’; it is based on experience and its denial is conceivable. Hume’s theorem boldly states that any book containing neither abstract reasoning nor experimental reasoning should be committed to the flames, for it contains nothing but sophistry and illusion.

“观念的关系”是一类陈述，如“所有单身汉都未婚”；它在定义上为真，否定它就会产生矛盾。“事实”是一类陈述，如“太阳明天会升起”；它基于经验，而否定它是可以设想的。休谟的定理大胆地宣称，任何既不包含抽象推理也不包含实验推理的书都应被投入烈火，因为它除了诡辩和幻想之外别无他物。

9. The Logical Problem of Evil Formula | 恶的问题逻辑公式

The Problem of Evil presents a logical challenge to the traditional theistic concept of God. It argues that the joint claim that God is all-powerful, all-knowing, and all-good is logically incompatible with the existence of evil in the world. The formula is set out as a contradiction.

恶的问题向传统有神论的上帝概念提出了逻辑挑战。它论证说，上帝全能、全知、全善的联合主张与世间存在的恶在逻辑上是不相容的。该公式以一组矛盾的形式列出。

1. God is omnipotent, omniscient, and omnibenevolent.
2. Such a God would be able to prevent evil, know when it occurs, and desire to stop it.
3. Evil exists.
4. Therefore, such a God does not exist.

To resolve this theorem, one must show that the premises are not all simultaneously true. Some philosophers reject premise 1 by limiting God’s power, while others reject premise 3 by arguing that evil is an illusion or a necessary part of a greater good. This formula is a cornerstone of the philosophy of religion.

要化解这一定理，必须证明这些前提并非同时为真。一些哲学家通过限制上帝的能力来否定前提 1，另一些则通过论证恶是一种幻象或是更大善的必要部分来否定前提 3。这一公式是宗教哲学的基石。

10. The Trolley Problem Ethical Equation | 电车难题道德方程式

The Trolley Problem is a thought experiment that exposes the tension between utilitarian and deontological ethics. It sets up a moral equation where the death of one person can be weighed against the death of five, challenging our intuitive moral algorithms.

电车难题是一个思想实验，它暴露了功利主义和义务论伦理学之间的张力。它设立了一个道德方程式，将一个人的死亡与五个人的死亡放在天平上衡量，挑战我们直觉的道德算法。

Divert the trolley: 1 dead, 5 saved. (Utilitarian choice)
Do nothing: 5 dead, 1 saved. (Deontological constraint on directly harming)

Most people choose to divert the trolley. However, when the action changes from pulling a lever to physically pushing a large man off a bridge to stop the trolley, the utilitarian calculus often feels less acceptable. This reveals that our ethical reasoning involves both a consequence-based formula and an action-type constraint formula, forbidding using a person merely as a means.

大多数人选择改变电车方向。然而，当行动从拉动拉杆变成把一个胖子从桥上推下去以阻止电车时，功利主义的计算就常常让人觉得不那么可接受了。这揭示出我们的伦理推理同时包含基于结果的公式和行动类型约束公式，后者禁止仅仅把人当做手段来利用。

Published by TutorHao | Philosophy Revision Series | aleveler.com

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