📚 Year 11 Eduqas Philosophy: Formula & Theorem Quick Reference | 哲学公式定理速查手册
In philosophy, a ‘formula’ or ‘theorem’ is not a string of algebraic symbols but a compact logical structure that captures the essence of an argument or principle. This quick reference manual distills the key philosophical moves in the Eduqas Year 11 syllabus into formula-like statements that expose their inner machinery. Use these as mental shortcuts for revision, essay planning, and in‑depth understanding.
在哲学中，“公式”或“定理”不是代数符号串，而是一种紧凑的逻辑结构，浓缩了论证或原则的精髓。这本速查手册将 Eduqas 十一年级课程中的核心哲学构式提炼成类似公式的表述，揭示其内在机制。可将它们用作复习、论文构思和深度理解的心智快捷键。
1. Anselm’s Ontological Formula | 安瑟伦本体论公式
If we define God as ‘that than which nothing greater can be conceived’, then God must exist in reality, because existing in reality is greater than existing only in the mind. The formula runs: Definition of God → existence in understanding → necessity of existence in reality (reductio ad absurdum).
如果我们把上帝定义为“无法设想有比之更伟大的存在者”，那么上帝必然实际存在，因为实际存在比只存在于心灵中更伟大。该公式的结构是：上帝的定义 → 存在于理解中 → 必须实际存在（归谬法）。
The formal logical skeleton: Goddefinition ≡ (∀x)(x is not greater than God) → God exists in mind → (∃y)(y = God in reality) greater than (God in mind) → contradiction if God does not exist in reality → ∴ God exists.
形式逻辑骨架：定义上帝 ≡（∀x）（x 不大于上帝）→ 上帝存在于心中 →（∃y）（y = 实际中的上帝）更伟大 → 如果上帝不实际存在则矛盾 → ∴ 上帝存在。
2. Aquinas’ First Cause Formula | 阿奎那第一因公式
Aquinas’ Cosmological Argument can be reduced to an infinite regress blocker: If every event has a cause, the chain of causes cannot go back infinitely; therefore, there must be a first uncaused cause, which is God. Formula: (∀e)(e has cause) ∧ ¬(infinite causal chain possible) → ∃!Cuncaused = God.
阿奎那的宇宙论论证可归结为一个无限回溯阻断器：如果每一事件都有原因，因果链条不能无限回溯；因此必须有一个第一因，即不受他物推动的推动者——上帝。公式：（∀e）（e 有原因）∧ ¬（无限因果链可能）→ ∃!第一因 = 上帝。
The core move is the rejection of an actual infinite series in per se causal chains: a per se chain needs a first member that is pure act, otherwise no intermediate causation can be sustained. In symbols: per se series: A1 ← A2 ← … ← An requires A1 as absolute initiator.
关键举措是拒绝在“自因”因果链中出现实际无限序列：自因链需要一个纯粹现实的第一项，否则任何中间因果都无法传递。用符号表示：自因序列 A₁ ← A₂ ← … ← Aₙ 需要 A₁ 作为绝对启动者。
3. Paley’s Design Formula | 佩利设计论证公式
William Paley’s watchmaker analogy yields this inductive formula: Complex, purpose‑ordered object (watch) → implies an intelligent designer. The universe exhibits far greater complexity and order → implies a cosmic Designer (God). Formally: (Oordered ∧ Ccomplex) → Ddesigner; Universe ≫ watch in O&C → ∴ God exists.
威廉·佩利的钟表匠类比得出如下归纳公式：复杂、目的有序的物体（钟表）→ 意味着一位智慧的设计者。宇宙展现出远比钟表更复杂的秩序 → 意味着一位宇宙设计者（上帝）。形式化：（O 有序 ∧ C 复杂）→ D 设计者；宇宙在 O 和 C 上远大于钟表 → ∴ 上帝存在。
The formula’s strength lies in analogy, but Hume’s criticism targets the inference: limited to machine‑like complexity, multiple designers, or even a world‑making apprentice are equally plausible. The modal claim – design → designer – is not a deductive certainty.
该公式的优势在于类比，但休谟的批评瞄准了此推理：仅限于机器式的复杂，多个设计者或一个宇宙学徒同样可能。模态断言“设计 → 设计者”并非演绎必然。
4. Logical Problem of Evil Formula | 恶的逻辑问题公式
The classic inconsistency triad is: God is omnipotent, God is wholly good, yet evil exists. If the first two are true, evil should not exist; if evil exists, at least one attribute is false. Formula: (Omnipotence ∧ Omnibenevolence) → ¬Evil; Evil → ¬(Omnipotence ∧ Omnibenevolence). The set is logically inconsistent.
经典的不一致三角是：上帝全能，上帝全善，但恶存在。如果前两者真，恶就不应存在；如果恶存在，至少一个属性为假。公式：（全能 ∧ 全善）→ ¬恶；恶 → ¬（全能 ∧ 全善）。这组命题在逻辑上不相容。
Mackie formalised this as a three‑statement contradiction: (1) God is omnipotent. (2) God is wholly good. (3) Evil exists. Add the unstated premise (4) A good omnipotent being eliminates evil as far as it can, and inconsistency is proved. Thus the theist must deny at least one.
麦基将此形式化为三个陈述的矛盾：（1）上帝全能。（2）上帝全善。（3）恶存在。加上未明言的前提（4）一个全善全能的存有会尽其所能消除恶，即证不一致。因此有神论者必须否认至少一条。
5. Free Will Defence Theodicy Formula | 自由意志辩护神正论公式
A theodicy attempts to break the inconsistency by inserting a third value that makes evil a necessary by‑product of a greater good. Plantinga’s free will defence: God maximises creaturely freedom; moral evil results from misuse of freedom, but a world with free beings is better than one with only robots. Formula: Greater good (free will) > necessary risk of evil → evil is permitted not caused by God.
神正论试图通过插入第三种价值来打破不一致，使恶成为更伟大善的必然副产品。普兰丁格的自由意志辩护：上帝最大化受造物的自由；道德恶来自自由的误用，但有自由的存在世界比只有机器人的世界更好。公式：更大的善（自由意志）> 恶的必然风险 → 恶被允许，而非上帝所造。
The logical form: God creates a world W with significant freedom. Any such world contains the possibility of moral evil. It is possible that every essence suffers from transworld depravity, yet God is not culpable because He creates the best feasible world.
逻辑形式：上帝创造了一个具有显著自由的世界 W。任何此类世界都包含道德恶的可能性。可能每个本质都遭受跨世界堕落，但上帝不承担责任，因为祂创造了最好的可行世界。
6. Hume’s Is–Ought Gap Formula | 休谟“是—应当”鸿沟公式
Hume observed that many moral arguments move from descriptive premises (what is) to normative conclusions (what ought to be) without justification. The formula alerts: From ‘is’ statements alone, no ‘ought’ statement logically follows. In notation: Σis ⊬ Ought. An additional evaluative premise is always required.
休谟观察到，许多道德论证从描述性前提（是）跳跃到规范性结论（应当）而缺乏正当理由。该公式警告：单从“是”陈述中，逻辑上推不出任何“应当”陈述。用符号表示：Σ_is ⊬ 应当。总是需要一个额外的评价性前提。
Example: From ‘Infertile intercourse does not produce children’ one cannot deduce ‘Therefore, such intercourse is morally wrong’ without an implicit premise like ‘Acts that do not produce offspring are wrong’. The gap exposes naturalism’s logical flaw.
例子：从“不导致生育的性行为不产生孩子”无法推导出“因此，这种行为在道德上是错误的”，除非隐含前提如“不产生后代的行为是错误的”。鸿沟揭示了自然主义的逻辑缺陷。
7. Bentham’s Utility Calculus Formula | 边沁功利计算式
For Bentham, the right action is the one that maximises the sum of pleasure over pain for all affected. The felicific calculus evaluates each action by seven dimensions: intensity, duration, certainty, propinquity, fecundity, purity, extent. Formula: Uact = Σi (Pleasurei × factors) − Σj (Painj × factors). Maximise U.
对边沁而言，正确的行为是能为所有受影响者产生最大快乐减痛苦总和的行为。快乐计算通过七个维度评估每一行为：强度、持续时间、确定性、邻近性、丰产性、纯度、范围。公式：行为 U = Σᵢ（快乐ᵢ × 因素）− Σⱼ（痛苦ⱼ × 因素）。最大化 U。
This formula treats all pleasures as commensurable – pushpin is as good as poetry. Mill refined it by introducing higher and lower pleasures, but the basic quantitative framework remains: Utility = net pleasure balance across all sentient beings involved.
这一公式将所有快乐视为可以通约——针戏与诗等值。密尔通过引入高级与低级快乐加以改良，但基本的量化框架仍是：功利 = 所有涉事有感知者的净快乐余额。
8. Kant’s Categorical Imperative Formula | 康德绝对命令公式
Kant supplies the rational rule: ‘Act only according to that maxim whereby you can at the same time will that it should become a universal law.’ The first formulation test: Can your maxim be universalised without contradiction? Formula: Max → Universal Law cannot entail contradiction in conception or in will → permissible; otherwise, duty not to act.
康德提供了理性规则：“只按照你同时能够愿意它成为一个普遍法则的那个准则去行动。”第一公式测试：你的准则能否无矛盾地普遍化？公式：准则 → 普遍法则不能在概念上或意愿上导致矛盾 → 允许；否则，有义务不行动。
The practical test: take the maxim ‘To lie to secure an advantage’. Universalise: everyone lies when convenient → the institution of promise‑making collapses → the maxim contradicts itself (cannot will the fraud while willing the practice). Therefore, lying is strictly impermissible.
实践检验：取准则“为获利益而说谎”。普遍化：人人方便时说谎 → 许诺的制度崩溃 → 准则自相矛盾（不能既意愿欺诈又意愿该实践）。因此，说谎被严格禁止。
9. Determinism–Free Will Tension Formula | 决定论与自由意志张力公式
The incompatibilist formula states: If determinism is true, every event is the necessary result of prior causes and laws → no alternative possibilities exist → no free will (no moral responsibility). Concisely: Determinism → (∼φ) [no ability to do otherwise] → ∼Moral Responsibility. Compatibilists redefine freedom to avoid the conclusion.
不相容论公式陈述：如果决定论为真，每一事件都是先前原因和规律的必然结果 → 没有别的可能性存在 → 没有自由意志（无道德责任）。简洁地：决定论 → （∼φ）[无他途能力] → ∼道德责任。相容论者重新定义自由以避免这一结论。
Hard determinists accept the conditional and deny free will. Libertarians accept the conditional but deny determinism, often invoking agent causation or quantum indeterminacy. The formula clarifies exactly where each philosopher inserts their premise.
强硬决定论者接受该条件句并否认自由意志。自由意志论者接受条件句但否认决定论，常诉诸行为者因果或量子不确定性。该公式精确标明了每位哲学家放置其前提的位置。
10. Locke’s Memory Criterion for Personal Identity | 洛克个人同一性记忆准则公式
For Locke, person P at time t2 is identical with person Q at time t1 if and only if P can remember (is conscious of) the experiences of Q. Formula: Pt2 = Qt1 ↔ P has episodic memory chains extending back to Q’s first‑person actions/thoughts. Identity is a forensic concept tied to accountability.
对洛克而言，时间 t₂ 的人 P 与时间 t₁ 的人 Q 同一，当且仅当 P 能够回忆（意识到）Q 的经验。公式：P_t2 = Q_t1 ↔ P 拥有可回溯到 Q 的第一人称行为/思想的情景记忆链。同一性是一个与问责相联的法权概念。
Objections like Reid’s brave officer paradox (memory transitivity fails) prompted refinements. Psychological continuity theories still retain the Lockean core: identity consists in overlapping memory and psychological connectedness. Simple formula: Continuity → identity.
里德的勇敢军官悖论（记忆传递性失效）等反驳促成了改进。心理连续性理论仍保留了洛克内核：同一性由重叠的记忆和心理联系构成。简单公式：连续性 → 同一性。
11. Religious Experience Validity Formula | 宗教体验有效性公式
The argument from religious experience can be cast as: A person S has an experience E that seems subjectively to be of God → without defeaters, S is justified in believing that God exists. In formula: E with phenomenological content X (numinous, self‑authenticating) → prima facie justification for belief in X’s reality, unless undercut by naturalistic explanation.
宗教体验论证可表述为：某人 S 拥有一个主观上似乎是上帝的体验 E → 在没有败因的情况下，S 有理由相信上帝存在。公式：带有现象学内容 X（神圣、自证实）的 E → X 为真的初步理由，除非被自然主义解释所削弱。
Swinburne’s principle of credulity (things being as they seem) and principle of testimony (others’ reports provide evidence) give a cumulative framework: ΣEi + testimony → strengthened theistic case. The formula highlights reliance on experiential evidence.
斯温伯恩的轻信原则（事物如其所现）与见证原则（他人的报告提供证据）给出了累积框架：ΣEᵢ + 见证 → 增强的有神论论证。该公式凸显了对经验证据的依赖。
12. Pascal’s Wager Decision Formula | 帕斯卡赌注决策矩阵公式
Pascal frames belief as a rational bet under uncertainty: If God exists and you believe, infinite reward (heaven); if God does not exist, finite loss (worldly pleasures forgone). The expected utility overwhelmingly favours belief. Formula: EUbelieve = ∞ × p + (−f) × (1−p); EUnot believe = (−∞) × p + g × (1−p). Since ∞ dominates, believe.
帕斯卡将信仰框定为不确定条件下的理性打赌：如果上帝存在且你信仰，无限奖赏（天堂）；如果上帝不存在，有限损失（放弃世俗快乐）。期望效用极大偏向信仰。公式：EU_信 = ∞ × p + (−f) × (1−p)；EU_不信 = (−∞) × p + g × (1−p)。由于∞主导，选择信。
Objections include the many‑gods problem (which deity to wager on?), the genuineness of belief arrived at by calculation, and the moral illegitimacy of pragmatic belief. Yet the formula remains a vivid model of decision theory applied to religious commitment.
反驳包括多神问题（该赌哪位神？）、计算得来的信仰是否真实，以及实用主义信仰的道德不正当性。但该公式仍然是决策理论应用于宗教委身的生动模型。
Published by TutorHao | Philosophy Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply