📚 AS Eduqas Philosophy: Formula & Theorem Quick Reference Handbook | AS Eduqas 哲学：公式定理速查手册
Welcome to your essential quick reference for AS Eduqas Philosophy. In this guide, key arguments, definitions, and logical structures are presented as compact ‘formulas’ and ‘theorems’ to help you memorise and apply philosophical ideas with precision. Each section breaks down a core concept into its logical skeleton, making revision faster and exam answers sharper.
欢迎使用 AS Eduqas 哲学的必备速查手册。本指南将关键论证、定义和逻辑结构整理成紧凑的“公式”与“定理”，帮助你准确记忆并运用哲学思想。每一节都将一个核心概念拆解为逻辑骨架，让复习更高效，答题更犀利。
1. The JTB Formula for Knowledge | 知识的 JTB 定义
The classical tripartite definition of knowledge can be expressed as: Subject S knows proposition p if and only if (i) p is true, (ii) S believes that p, and (iii) S is justified in believing that p. This is often abbreviated as K=JTB (Justified True Belief).
经典的知识三元定义可表述为：主体 S 知道命题 p，当且仅当 (i) p 为真、(ii) S 相信 p 且 (iii) S 有理由相信 p。这常简写为 K=JTB（真确信念）。
Symbolically: K(S,p) ↔ (B(S,p) ∧ T(p) ∧ J(S,p))
符号形式：K(S,p) ↔ (B(S,p) ∧ T(p) ∧ J(S,p))
This formula sets the standard for knowledge in epistemology, though Gettier later showed it is not sufficient.
这个公式设定了认识论中知识的标准，尽管盖梯尔后来证明它并不充分。
2. Gettier Counterexamples as Logical Disproofs | 盖梯尔反例作为逻辑反证
Gettier cases demonstrate that JTB is not sufficient for knowledge. Their common structure: S has a justified true belief that p, but the justification relies on a false lemma q, and p is only true by luck. Therefore, S does not know p.
盖梯尔案例证明 JTB 不足以构成知识。它们的一般结构是：S 有一个真确信念 p，但其理由依赖于一个假命题 q，并且 p 为真只是碰巧。因此 S 并不真正知道 p。
Logical pattern: (1) B(S,p) ∧ T(p) ∧ J(S,p) ← thanks to false q. (2) S’s belief is merely accidentally true. (3) Hence ¬K(S,p). Hence JTB is not sufficient for knowledge; a fourth condition is needed to rule out epistemic luck.
逻辑模式：(1) B(S,p) ∧ T(p) ∧ J(S,p) ← 因假 q 所致。(2) S 的信念只是偶真。(3) 因此 ¬K(S,p)。 所以 JTB 不足以承载知识，需要第四个条件来排除认知运气。
3. Direct Realism and the Argument from Illusion | 直接实在论与幻觉论证
Direct Realism (DR) says we perceive mind-independent physical objects directly. The Argument from Illusion can be formalised: (1) If DR is true, then in normal and illusory cases we perceive physical objects directly. (2) In illusion, the object appears to have a property F it does not actually possess. (3) The perceived F is either a physical object or a sense-datum. (4) Since the physical object lacks F, we are aware of a sense-datum. (5) Thus, in illusion we do not perceive physical objects directly. (6) Therefore, DR is false.
直接实在论主张我们直接感知独立于心灵的物理对象。幻觉论证可形式化为：(1) 如果直接实在论为真，那么在正常和幻觉情形中我们都直接感知物理对象。(2) 在幻觉中，对象表现出它并不实际拥有的性质 F。(3) 被感知的 F 要么是物理对象，要么是感觉材料。(4) 由于物理对象并不具有 F，我们所意识到的乃是感觉材料。(5) 因而在幻觉中我们并非直接感知物理对象。(6) 所以直接实在论为假。
Key formula: Illusion → ¬DirectAccess(Physical Object). The sense-datum becomes the immediate object of awareness, leading to indirect realism.
关键公式：幻觉 → ¬直接通过(物理对象)。感觉材料成为意识的直接对象，从而导向间接实在论。
4. Act Utilitarianism’s Happiness Calculus | 行为功利主义的幸福计算
Act Utilitarianism holds that an action is right if and only if it maximises utility, where utility is defined as pleasure minus pain. The formula: for any action A, Right(A) ↔ ∀ alternatives A’, U(A) ≥ U(A’), where U(A) = Σ (pleasure – pain) for all sentient beings affected.
行为功利主义主张，一个行为是正当的，当且仅当它能最大化功利，功利被定义为快乐减去痛苦。公式为：对任何行为 A，正当(A) ↔ 对所有替代行为 A’，U(A) ≥ U(A’)，其中 U(A) = 对所有受影响的众生(快乐 – 痛苦)求和。
Bentham’s hedonic calculus further considers intensity, duration, certainty, propinquity, fecundity, purity, and extent. The basic theorem: Moral goodness ⇔ Maximised net pleasure. Criticisms include the problem of measuring pleasure and the potential to justify injustice.
边沁的幸福计算进一步考量强度、持续期、确定性、临近性、衍生性、纯净性和范围。基本定理：道德善 ⇔ 最大化净快乐。常见批评包括快乐难以衡量，以及可能为不义辩护。
5. Kant’s Categorical Imperative Formulations | 康德的绝对命令公式化
The first formulation (Formula of Universal Law): “Act only according to that maxim whereby you can at the same time will that it should become a universal law.” If the maxim leads to a contradiction in conception or in will when universalised, it is morally impermissible.
第一公式（普遍法则公式）：“仅按照你能同时意愿它成为一条普遍法则的准则去行动。” 如果一条准则在普遍化时导致概念上的矛盾或意志上的矛盾，那么它就在道德上不被允许。
The second formulation (Formula of Humanity): “Act in such a way that you treat humanity, whether in your own person or in the person of another, always at the same time as an end and never merely as a means.” This forbids using rational agents solely as tools.
第二公式（人性公式）：“如此行动，即你总是将人性——无论是你自己人格中的人性还是任何他人人格中的人性——同时当作目的，而绝不仅仅当作手段。” 这禁止仅仅将理性存在者当作工具使用。
These two formulations are claimed to be equivalent. Together they form a rationalist ethical system independent of consequences.
这两个公式据称是等价的。它们共同构成了一个不依赖后果的理性主义伦理体系。
6. Aristotle’s Doctrine of the Mean | 亚里士多德的中道学说
Every moral virtue is a mean between two corresponding vices: one of excess and one of deficiency. The formula: Virtue X = Mean between excess X+ and deficiency X-, determined by practical wisdom (phronēsis) relative to the agent.
每种道德德性都是两种对应恶习的中道：一种过度，一种不及。公式：德性 X = 在过度 X+ 与不及 X- 之间的中道，由实践智慧相对于行动者而确定。
For example, courage is the mean between rashness (excess) and cowardice (deficiency); generosity lies between prodigality and meanness. The mean is not an arithmetic average but a relative equilibrium appropriate to the context.
例如，勇敢是鲁莽（过度）与怯懦（不及）之间的中道；慷慨介于挥霍和吝啬之间。这个中道不是算术平均，而是针对情境的适当平衡。
Formula for action: Do the right thing, to the right person, at the right time, for the right reason, in the right way——this constitutes the virtuous act.
行动的公式：在正确的时间、针对正确的人、出于正确的理由、以正确的方式做正确的事——这构成了有德性的行为。
7. The Teleological Argument’s Logical Structure | 目的论论证的逻辑结构
The design argument uses an analogy: watch is to watchmaker as universe is to universe maker. Its logical form: (1) Complex order and purpose seen in the world cannot arise by chance. (2) The best explanation for such order is an intelligent designer. (3) Therefore, an intelligent designer (God) exists.
设计论证使用类比：手表之于制表匠，如同宇宙之于宇宙创造者。其逻辑形式为：(1) 世界中所见的复杂秩序和目的不可能偶然产生。(2) 这类秩序的最佳解释是一位理智的设计者。(3) 因此，一位理智的设计者（上帝）存在。
Paley’s version: if you find a watch on a heath, you infer a watchmaker; likewise, the eye’s intricate arrangement points to a divine designer. Hume’s critique: the analogy is weak and the universe might be more like a vegetable than a machine.
佩利的版本：如果你在荒野上发现一只手表，你会推断有位制表匠；同样，眼睛的精妙结构指向一位神圣的设计者。休谟的批评：类比牵强，宇宙可能更像一株植物而非机器。
8. The Cosmological Argument and the Principle of Sufficient Reason | 宇宙论论证与充足理由原则
The cosmological argument can be condensed: (1) Everything that exists has a cause or reason for its existence. (Principle of Sufficient Reason) (2) The universe exists. (3) The universe cannot be self-caused or have an infinite causal chain. (4) Therefore, a first cause (God) exists.
宇宙论论证可浓缩为：(1) 任何存在的东西都有其原因或存在理由。（充足理由原则）(2) 宇宙存在。(3) 宇宙不可能自因，也不可能有无限的因果链。(4) 因此，第一因（上帝）存在。
Aquinas’ Third Way adds contingency: Contingent beings → Necessary Being. If everything were contingent, eventually there would be nothing. Since something exists now, a necessary being must exist to ground all contingents.
阿奎那的第三路论证加入了偶然性：偶然存在 → 必然存在。如果一切都是偶然的，终将一无所有；既然现在有物存在，必有一个必然存在者为一切偶然提供根基。
9. The Logical Problem of Evil | 恶的逻辑问题
The deductive problem of evil challenges the consistency of God’s attributes: (1) If God exists, then God is omnipotent, omniscient, and omnibenevolent. (2) An OOO God would prevent all evil. (3) Evil exists. (4) Therefore, God does not exist.
恶的演绎问题挑战上帝属性的相容性：(1) 如果上帝存在，则上帝是全知、全能、全善的。(2) 一个全知全能全善的上帝会阻止一切恶。(3) 恶存在。(4) 因此上帝不存在。
In logical notation: G → ¬E; E; ∴ ¬G. J.L. Mackie argues that the theist cannot consistently hold all three propositions; if evil is real, then the classical God is logically impossible.
逻辑符号表示：G → ¬E; E; ∴ ¬G。J.L. 麦基主张，有神论者无法同时持守这三项命题；如果恶是真实的，那么古典上帝概念在逻辑上不可能。
10. Free Will Defence and Theodicy | 自由意志辩护与神正论
The Free Will Defence counters the logical problem by inserting a premise: God may permit evil because free will is a greater good, and even an omnipotent God cannot force free beings to choose only good without contradiction. Thus, evil is logically possible in a God-governed world.
自由意志辩护通过插入一项前提来回应逻辑问题：上帝允许恶，是因为自由意志是更高层级的善，而即使是全能的上帝也不可能在不出现矛盾的情况下强迫自由生物只选择善。 因此，恶在上帝治理的世界中在逻辑上是可能的。
Alvin Plantinga’s formula: It is possible that God creates a world containing moral good and cannot eliminate moral evil without removing free will. Theodicies like soul-making (Hick) give further positive reasons: evil is necessary for spiritual growth.
阿尔文·普兰丁格的公式：上帝有可能创造一个包含道德善的世界，但若消除道德恶就必然取消自由意志。 灵魂塑造神正论（希克）进一步给出正面理由：恶是灵性成长所必需的。
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