📚 KS3 Edexcel Philosophy: Formula & Theorem Quick Reference Handbook | KS3 Edexcel 哲学：公式定理速查手册
In philosophy, ideas often follow clear logical structures — like formulas in mathematics or science. This handbook collects the essential "formulas" and "theorems" you need for KS3 Edexcel Philosophy, presenting them as easy‑to‑remember patterns. Each entry includes the core statement, a breakdown of its meaning, and a simple example to help you apply it in your revision and exam answers.
在哲学中，思想往往遵循清晰的逻辑结构——就像数学或科学中的公式一样。这本手册汇集了 KS3 Edexcel 哲学课程所需的基本“公式”和“定理”，以易于记忆的模式呈现。每一条都包含核心表述、含义分解以及简单示例，帮助你在复习和考试答题中灵活运用。
1. The Cogito Formula: Descartes' Starting Point | “我思”公式：笛卡尔的起点
The Cogito is often written as: "I think, therefore I am." Its logical form can be summarised as a conditional proof: if I am doubting, then I must exist to do the doubting. The formula is:
“我思”常表述为：“我思故我在。”其逻辑形式可以概括为一个条件证明：如果我在怀疑，那么我必然存在以进行怀疑。公式为：
Doubt → Thinking → Existence
Descartes realised that even if an evil demon deceived him about everything, the very act of being deceived guarantees that he is a thinking thing. This formula is the foundation of rationalist epistemology.
笛卡尔意识到，即使有一个邪恶的恶魔在一切事情上欺骗他，被欺骗这一行为本身就保证了他是一个思维的东西。这个公式是理性主义认识论的基础。
2. The Principle of Non‑Contradiction | 不矛盾律
Aristotle's most fundamental logical theorem states: a statement cannot be both true and false at the same time and in the same respect. The formula is:
亚里士多德最基本的逻辑定理指出：一个命题在同一时间和同一方面不可能既真又假。公式为：
¬(P ∧ ¬P)
It is not the case that P and not‑P. This "law of thought" underpins all coherent reasoning. If someone says "the door is open" and "the door is not open", at least one must be false.
并非 P 且非 P。这条“思维律”是一切连贯推理的基础。如果有人说“门是开的”和“门不是开的”，至少有一个必为假。
3. The Problem of Evil: The Inconsistent Triad | 罪恶问题：不一致三元组
The logical problem of evil shows a tension between three claims about God. The classic formula, often called the inconsistent triad, is:
逻辑上的罪恶问题展示了关于神的三个主张之间的张力。这个经典公式常被称为不一致三元组：
God is omnipotent ∧ God is wholly good ∧ Evil exists → Contradiction
If God is all‑powerful, He could prevent evil; if He is perfectly good, He would want to. Yet evil exists. Therefore, at least one of the premises must be false, or we must refine our understanding of God's attributes.
如果神是全能的，他就能阻止罪恶；如果他是全善的，他就会想要阻止罪恶。然而罪恶存在。因此，至少有一个前提为假，或者我们必须重新理解神的属性。
4. The Euthyphro Dilemma Formula | 游叙弗伦两难公式
Plato’s Euthyphro asks: is something holy because the gods love it, or do the gods love it because it is holy? The formula captures the dilemma for divine command theory:
柏拉图的《游叙弗伦》问道：事物是神圣的因为众神喜爱它，还是众神喜爱它因为它是神圣的？这个公式捕捉了神圣命令理论的两难：
X is good because God commands X ⇌ God commands X because X is good
If goodness depends solely on God's will, morality seems arbitrary. If God commands things because they are independently good, then morality does not depend on God after all.
如果善仅仅取决于神的意志，道德就显得任意；如果神因为事物独立地是善的而命令它们，那么道德最终并不依赖于神。
5. The Principle of Sufficient Reason | 充足理由律
Leibniz claimed that nothing happens without a sufficient reason why it is so and not otherwise. The formula is:
莱布尼茨主张，没有任何事情的发生是没有充足理由的，即为什么是这样而不是那样。公式为：
∀x ∃y (y is the sufficient reason for x)
For every fact or event x, there must be a reason y that fully explains it. This principle leads to the cosmological argument: the universe itself requires a sufficient reason, which many call God.
对于每一个事实或事件 x，必须有一个理由 y 充分解释它。这一原则引出了宇宙论论证：宇宙本身需要一个充足理由，许多人称之为神。
6. Utilitarian Calculus: Bentham's Hedonic Formula | 功利主义计算：边沁的快乐公式
Jeremy Bentham proposed that moral actions can be evaluated by measuring pleasure and pain. The core formula weighs seven factors of a pleasure or pain:
杰里米·边沁提出，道德行为可以通过衡量快乐和痛苦来评判。其核心公式权衡了一种快乐或痛苦的七个因素：
Utility = Σ (Intensity × Duration × Certainty × Propinquity × Fecundity × Purity × Extent)
Add up the total pleasure an action produces and subtract the total pain. The right action maximises net happiness for all affected. This is the "Greatest Happiness Principle" in mathematical form.
将行动产生的总快乐相加，减去总痛苦。正确的行为为所有受影响者带来最大的净幸福。这是“最大幸福原则”的数学化表达。
7. Kant's Categorical Imperative: The Universal Law Formula | 康德的绝对命令：普遍法则公式
Kant’s first formulation of the categorical imperative provides a test for moral actions. The formula is:
康德对绝对命令的第一个表述提供了检验道德行为的方法。公式为：
Act only according to that maxim whereby you can at the same time will that it should become a universal law.
If your reason for acting (the maxim) cannot be consistently willed as a law for everyone, the action is morally forbidden. For instance, making a lying promise fails because a world where everyone lied would destroy trust, making promises impossible.
如果你行动的依据（准则）不能被一贯地意愿成为所有人的法则，该行为在道德上就是被禁止的。例如，作出虚假承诺就不能通过检验，因为在一个人人说谎的世界里信任会崩溃，承诺本身变得不可能。
8. Aristotle's Doctrine of the Mean: The Virtue Formula | 亚里士多德的中庸之道：德性公式
For Aristotle, moral virtue lies between two extremes. The formula for a specific virtue can be written as:
对亚里士多德而言，道德德性处于两个极端之间。特定德性的公式可以写作：
Virtue = Defect → Mean ← Excess
Courage is the mean between cowardice (defect) and rashness (excess). Generosity is the mean between stinginess and wastefulness. The mean is not arithmetic but relative to the person and situation.
勇敢是怯懦（不及）和鲁莽（过度）之间的中道。慷慨是小气和挥霍之间的中道。中道不是算术上的，而是因人因情况而异的。
9. The Ship of Theseus: Identity Through Change | 忒修斯之船：变化中的同一性
This ancient puzzle asks: if all the planks of a ship are gradually replaced, is it still the same ship? The theorem of identity can be expressed as:
这个古老难题问道：如果一艘船的所有木板都被逐渐更换，它还是同一艘船吗？同一性定理可以表达为：
If A(t₁) = A(t₂) despite all parts replaced, what constitutes identity?
Philosophical solutions include: identity lies in the continuous form (Aristotle), in the causal chain linking stages (four‑dimensionalism), or that there is no fact of the matter. This puzzle tests material constitution and personal identity.
哲学解答包括：同一性在于连续的形式（亚里士多德），在于连接阶段的因果链（四维主义），或者根本没有事实可言。这个谜题考验了物质构成和人格同一性。
10. Pascal’s Wager: The Decision Matrix | 帕斯卡的赌注：决策矩阵
Pascal argued that believing in God is the rational choice when we weigh the possible outcomes. The wager can be presented as a decision table:
帕斯卡主张，当我们权衡可能的结果时，信仰神是理性的选择。这个赌注可以呈现为决策表：
| God exists | 神存在 | God does not exist | 神不存在 | |
|---|---|---|
| Believe | 信仰 | Infinite gain (heaven) | 无限收益（天堂） | Minor loss (worldly pleasures) | 微小损失（世俗享乐） |
| Not believe | 不信仰 | Infinite loss (hell) | 无限损失（地狱） | Minor gain | 微小收益 |
The expected value calculation heavily favours belief, making non‑belief an irrational gamble according to Pascal.
根据期望值计算，信仰极度有利，因此按照帕斯卡的观点，不信仰是非理性的赌博。
11. Plato’s Tripartite Soul: The Chariot Analogy | 柏拉图的三分灵魂：战车比喻
Plato divided the soul into three parts, each with its own desire. The formula for a just soul mirrors the just city:
柏拉图将灵魂分为三个部分，各有其欲望。正义灵魂的公式映射了正义城邦：
Reason (charioteer) → guides ← Spirit (white horse) & Appetite (black horse)
Reason must rule with the help of spirited emotion, keeping appetites in check. When each part does its proper job, the person is psychologically harmonious.
理性（御者）必须在激情（白马）的帮助下进行统治，约束欲望（黑马）。当每个部分各司其职时，人便在心理上达到和谐。
12. The Allegory of the Cave: The Formula of Enlightenment | 洞穴寓言：启蒙公式
Plato’s cave illustrates the journey from ignorance to knowledge. The process can be summarised as:
柏拉图的洞穴寓言阐释了从无知到知识的旅程。这一过程可以概括为：
Shadows (opinion) → Objects (belief) → Outside world (reason) → The Sun (Form of the Good)
A prisoner escapes, sees the fire, then the real world outside, and finally the sun — the ultimate source of truth. This formula underpins Plato’s theory of Forms and his epistemology.
囚徒挣脱束缚，看到火光，然后是外面的真实世界，最终看到太阳——真理的终极源头。这个公式支撑着柏拉图的理论论和认识论。
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