📚 Year 12 Edexcel Philosophy: Formula & Theorem Quick Reference Handbook | 爱德思Year 12哲学：公式定理速查手册
This handbook reframes core philosophical arguments, ethical principles and logical structures from the Year 12 Edexcel Philosophy specification as concise 'formulas' and 'theorems'. Each entry distils a key idea into a repeatable pattern—whether a deductive rule, a principled equation, or a schematic analogy—so you can rapidly recall, compare and apply them in essays and source-based questions. Think of it as your philosophical equation sheet for the examination hall.
本手册将爱德思Year 12哲学考纲中的核心论证、伦理原则和逻辑结构重新梳理为简洁的‘公式’与‘定理’。每一条目都将关键思想浓缩为一个可重复的模式——无论是演绎规则、原则方程式还是类比图示——帮助你快速回忆、对比并运用在论文和材料题中。把它当作考场上的哲学公式表来使用。
1. The Greatest Happiness Formula | 最大幸福公式
Bentham' c calculus: Rightness of an action = Σ (Pleasure₁ × Duration₁ + Pleasure₂ × Duration₂ ...) – The morally obligatory act is the one that maximises total net pleasure over pain for all sentient beings affected.
边沁的行为功利主义可表达为快乐主义演算：行为正当性 = Σ (快乐₁ × 持续时间₁ + 快乐₂ × 持续时间₂ ...) – Σ (痛苦₁ × 持续时间₁ ...)，其中每个快乐或痛苦都按强度、持续时间、确定性、邻近性、生产性、纯粹性和范围进行加权。道德上义务的行为，就是能为所有受影响的感性存在者带来最大净快乐总量的行为。
Mill refines this with a qualitative dimension: 'Better to be Socrates dissatisfied than a pig satisfied.' Higher pleasures (intellectual, moral) have greater inherent worth, so the formula is adjusted by a weighting factor Q for quality.
密尔用质的维度加以完善：‘宁做不满足的苏格拉底，不做满足的猪。’ 高等快乐（理智的、道德的）具有更高的内在价值，因此公式通过品质加权因子Q来修正。
2. Kant’s Categorical Imperative: Universal Law Formulation | 康德绝对命令：普遍法则公式
Formula: 'Act only according to that maxim whereby you can at the same time will that it should become a universal law.' In formal terms: An action is permissible iff the maxim M can be consistently conceived as a universal law without contradiction in conception, and can be willed without contradiction in will. Contradiction in conception yields a perfect duty; contradiction in will yields an imperfect duty.
公式：‘只按照你同时能够愿意它成为一条普遍法则的那个准则去行动。’ 形式化表达：一个行为是允许的，当且仅当准则M能够被无矛盾地设想为一条自然法则（概念矛盾），并且能够被无矛盾地意愿（意志矛盾）。概念矛盾产生完全义务；意志矛盾产生不完全义务。
Example for contradiction in conception: the maxim 'I will make a lying promise to get money' cannot be universalised without destroying the practice of promising, thus violating a perfect duty.
概念矛盾的例子：‘我要作出虚假承诺来获得金钱’这一准则若普遍化，将摧毁承诺制度本身，因而违反了完全义务。
3. The Humanity Formula | 人性公式
Kant's second formulation: '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.' The theorem: A rational being possesses dignity (inner worth) and must never be used solely as an instrument. Consent and shared ends are required for any instrumental use to be compatible with treating a person as an end in themselves.
康德的第二个表达式：‘你要如此行动，即无论在你的人格中还是在其他人的人格中，你始终把人当作目的，而绝不仅仅当作手段。’ 定理：理性存在者拥有尊严（内在价值），绝不能被仅仅当作工具使用。任何工具性的利用都必须以同意和共同目的为条件，才符合将人视为目的自身的要求。
4. Ontological Argument: Anselm’s Deductive Theorem | 本体论论证：安瑟伦的演绎定理
Anselm's logical structure can be presented as a reductio ad absurdum: (1) God is that than which nothing greater can be conceived (definition). (2) Suppose God exists only in the understanding and not in reality. (3) Then we can conceive of a greater being—one that exists both in understanding and in reality. (4) But this contradicts (1), because nothing greater can be conceived than God. (5) Therefore, God must exist in reality as well as in the understanding.
安瑟伦的逻辑结构可呈现为一个归谬推理：(1) 上帝是那无法设想比之更伟大者的存在者（定义）。(2) 假设上帝只存在于理智中，而不存在于现实中。(3) 那么我们就能设想一个更伟大的存在者——既存在于理智中，也存在于现实中。(4) 但这与(1)相矛盾，因为无法设想比上帝更伟大者。(5) 所以，上帝必然既存在于理智中，也存在于现实中。
Gaunilo's 'Lost Island' objection mirrors the formal structure to expose its flaw: the same reasoning could 'prove' the existence of a perfect island, showing that Anselm's definition alone cannot guarantee extra-mental existence.
高尼罗的‘迷失岛’反驳复制了相同的逻辑形式来揭示缺陷：同样的推理可以‘证明’一个完美的岛屿存在，这表明安瑟伦仅凭定义无法保证心外之物的存在。
5. Teleological Argument: The Analogy Formula | 目的论论证：类比公式
Paley's watchmaker analogy operates on a comparative formula: Artifact : Designer :: Nature : Divine Designer. The inference relies on the similarity of complex, functionally ordered systems. If a watch implies a watchmaker, then the eye, with its intricate adapted parts, implies an intelligent Creator.
佩利的钟表匠类比运作于一个对比公式：人造物 : 设计者 :: 自然物 : 神圣设计者。这一推论依赖于复杂且功能有序的系统的相似性。如果一块表意味着钟表匠，那么眼睛及其复杂而适应的部件，便意味着一位智慧的创造者。
Hume's counter-formula through Philo challenges the analogy: the universe is more like a vegetable or an animal than a machine, so the inference to a singular, perfect designer is underdetermined. Moreover, analogy weakens as dissimilarity increases: World ≠ Watch.
休谟借费罗之口提出反公式挑战该类比：宇宙更像一株植物或一只动物，而非一台机器，因此推出单一、完美的设计者是证据不足的。此外，类比随着不相似性的增加而减弱：世界 ≠ 钟表。
6. Cosmological Argument: The Causal Chain Theorem | 宇宙论论证：因果链定理
Aquinas's Second Way follows a causal dominion formula: (1) We observe an order of efficient causes. (2) Nothing can be the efficient cause of itself. (3) If there is no first cause, there would be no intermediate or ultimate effects. (4) But effects exist. (5) Therefore, there must be a first uncaused efficient cause, which everyone calls God.
阿奎那的第二路论证遵循因果统辖公式：(1) 我们观察到动力因的序列。(2) 没有任何东西能成为自身的动力因。(3) 若没有第一因，也就没有中间因和最后的结果。(4) 但结果确实存在。(5) 所以必然有一个最初的非受动的动力因，大家称之为上帝。
The Kalam version offers a temporalised formula: Everything that begins to exist has a cause; the universe began to exist; therefore, the universe has a cause. This cause is posited as a personal, timeless, immensely powerful creator.
卡拉姆论证版本提供了一个时间化公式：一切开始存在的事物都有其原因；宇宙开始存在；因此，宇宙有其原因。这一原因被设定为一个位格的、超越时间的、大能的创造者。
7. Plato’s Theory of Forms: Participation Equation | 柏拉图的理念论：分有公式
For any particular object x and property F, x is F iff x participates in the Form of F. The Form is the perfect, unchanging, non-spatial paradigm. The relationship can be written as: Particular x has property F because x μετέχει (metechei) in the Form F-itself. The Form–particular distinction explains the 'One Over Many' and 'Argument from Imperfection'.
对任意具体事物x和属性F，x是F当且仅当x分有了F的理型。理型是完美的、不变的、非时空的范式。这一关系可写作：具体事物x具有属性F，因为x分有了F-本身这一理型。理型与具体事物的区分解释了‘一在多之上’和‘不完善论证’。
8. Aristotle’s Four Causes: Explanatory Equation | 亚里士多德的四因说：解释方程
A complete explanation of any substance S requires stating: S' or purpose). Formula: Explain(S) = Matter + Form + Agency + Telos. The final cause is primary in nature: 'Nature does nothing in vain.'
对任何实体S的完整解释需要说明：S的质料因（由什么构成）、形式因（其本质或形式）、动力因（变化的最初来源）和目的因（它的telos或目的）。公式：解释(S) = 质料 + 形式 + 动因 + 目的。目的因在自然中居于首位：‘自然不做无用之事。’
9. Descartes’ Cogito: The Indubitable Theorem | 笛卡尔的我思：不可怀疑的定理
Descartes’ methodological doubt leads to a foundational truth: 'Cogito, ergo sum'—I think, therefore I am. In logical form: (1) I cannot doubt that I am thinking, for the very act of doubting is a mode of thinking. (2) If I am thinking, I must exist as a thinking thing. (3) Therefore, I am a res cogitans (thinking substance) whose existence is certain whenever I am thinking.
笛卡尔的方法论怀疑导引出一个基础真理：‘我思故我在’。逻辑形式为：(1) 我不能怀疑我正在思考，因为怀疑这一行为本身正是一种思想样式。(2) 如果我在思考，那么作为思考者的我就必然存在。(3) 因此，我是一个在思维的东西（res cogitans），每当我思考时，我的存在就是确定的。
The Cogito is not a syllogism but an intuitive insight: the very act of doubting confirms the existence of the self. This becomes the axiom for all further knowledge.
‘我思’并非三段论推理，而是一种直观洞见：怀疑这一行为本身确证了自我的存在。它成为所有进一步知识的公理。
10. Hume’s Fork: The Two Propositions Theorem | 休谟的叉子：两类命题定理
Hume's Fork divides all objects of human reason into two exclusive kinds: Relations of Ideas (a priori, necessarily true, known by pure thought; e.g., 'All bachelors are unmarried') and Matters of Fact (a posteriori, contingent, known by experience; e.g., 'The sun will rise tomorrow'). Any substantial philosophical claim that falls into neither category should be committed to the flames, for it contains nothing but sophistry and illusion.
休谟的叉子将人类理性的一切对象分为互斥的两类：观念关系（先天的、必然为真、通过纯粹思想认识；如‘所有单身汉都是未婚的’）和事实（后天的、偶然的、通过经验认识；如‘太阳明天会升起’）。任何既不属于前者也不属于后者的实体化哲学断言都应被投入烈火，因为它只包含诡辩和幻想。
This theorem underpins Hume's criticism of the cosmological argument: the causal principle 'every event has a cause' is neither a relation of ideas nor a provable matter of fact, so we cannot rationally infer a first cause.
这一定理奠定了休谟对宇宙论论证的批判基础：因果原则‘每一事件都有原因’既非观念关系，也非可证明的事实，因此我们不能理性地推出第一因。
11. The Logical Problem of Evil: The Inconsistent Triad | 恶的逻辑问题：不相容三元组
The classic formulation by J.L. Mackie presents a deductive inconsistency: (1) God is omnipotent. (2) God is wholly good. (3) Evil exists. The triad appears logically incompatible because an omnipotent, wholly good being would eliminate evil entirely. Since evil undoubtedly exists, the existence of such a God is logically impossible—unless one of the three propositions is revised or a new distinction (e.g., free will defence) is introduced.
麦克基的经典表述提出了一个演绎上的不一致：(1) 上帝是全能的。(2) 上帝是全善的。(3) 恶存在。这三者看似在逻辑上不相容，因为一个全能、全善的存在必会彻底消除恶。既然恶不容置疑地存在，那么这样一位上帝在逻辑上是不可能的——除非修正其中某个命题，或引入新的区分（如自由意志辩护）。
The free will defence counters that it is logically possible that God cannot create free beings who always choose good without contradiction; moral evil results from the misuse of free will, a greater good. Thus the triad is not strictly contradictory.
自由意志辩护反驳说，上帝不能既创造自由的存在者，又迫使其永远选择善，这在逻辑上是矛盾的；道德恶源于自由意志的误用，而自由意志是更大的善。因此三元组并非严格矛盾。
12. Divine Command Theory: Euthyphro’s Dilemma Formula | 神命论：尤西弗罗困境公式
Plato’s Euthyphro poses a disjunctive question: ‘Is the pious loved by the gods because it is pious, or is it pious because it is loved by the gods?’ Translated into monotheistic terms: Is an action right because God commands it (voluntarism), or does God command it because it is right (essentialism)? If the former, morality appears arbitrary and God’s goodness becomes tautologous; if the latter, morality is independent of God, threatening divine sovereignty.
柏拉图的《尤西弗罗》提出了一个二难问题：‘虔诚是因为被诸神所爱才为虔诚，还是因为它是虔诚的所以被诸神所爱？’ 转译为一神论语言：一个行为是正确的，是因为上帝命令它（意志主义），还是上帝命令它，因为它本身是正确的（本质主义）？若取前者，道德显得任意，上帝的良善沦为同义反复；若取后者，道德独立于上帝，威胁神的主权。
This dilemma remains a powerful logical tool to test the coherence of divine command meta-ethics.
这一困境仍然是检验神命元伦理学一致性的有力逻辑工具。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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