📚 A-Level Eduqas Philosophy: Quick Reference Handbook of Formulae and Theorems | A-Level Eduqas 哲学：公式定理速查手册
This handbook condenses the essential logical structures, core principles, and argument forms that appear throughout the Eduqas A-Level Philosophy specification into a clear and accessible format. By treating arguments like theorems and key definitions like formulae, you can sharpen your analytical precision and write more rigorous essays. Use these pages to refresh your memory before exams, to check the validity of a line of reasoning, or to anchor abstract ideas in concrete symbolic form.
本手册将Eduqas A-Level哲学课程中涉及的关键逻辑结构、核心原则和论证形式浓缩为清晰易用的公式化速查。把论证视作定理、把关键定义视作公式，能够提升分析精度，让论文更加严谨。无论是考前回顾、检验推理的有效性，还是用简洁的符号固定抽象概念，你都可以随时查阅这些速查页。
1. Propositional Logic Symbols and Truth Tables | 命题逻辑符号与真值表
In Philosophy, much of our analysis depends on propositional logic. You must know how basic connectives work. Here are the core symbols and their truth-functional meanings.
在哲学中，分析常常依赖命题逻辑。必须掌握基本联结词的意义。以下是核心符号及其真值功能。
- Negation (¬): ¬P is true when P is false.
否定 (¬)：¬P为真，当P为假。 - Conjunction (∧): P ∧ Q is true only when both P and Q are true.
合取 (∧)：P ∧ Q仅当P与Q同真时为真。 - Disjunction (∨): P ∨ Q is true when at least one of P, Q is true.
析取 (∨)：P ∨ Q为真，只要P或Q至少一个为真。 - Material conditional (→): P → Q is false only when P is true and Q is false.
实质条件 (→)：P → Q仅在P真且Q假时为假。 - Biconditional (↔): P ↔ Q is true when P and Q share the same truth value.
双条件 (↔)：P ↔ Q为真，当P与Q真值相同。
Truth tables help you test validity. Always remember: a valid deductive argument is one where it is impossible for all premises to be true and the conclusion false.
真值表可用于检验有效性。牢牢记住：一个演绎论证是有效的，当且仅当不可能所有前提为真而结论为假。
2. Valid Rules of Inference in Propositional Logic | 命题逻辑中的有效推理规则
These inference rules function like algebraic theorems. You can apply them to deduce conclusions from premises. Learn them as ready-made building blocks for any philosophical argument.
这些推理规则犹如代数定理。你可以用它们从前提演绎出结论，把它们当作构建哲学论证的现成积木。
- Modus Ponens (MP): From P → Q and P, infer Q.
肯定前件 (MP)：由P → Q和P，推出Q。 - Modus Tollens (MT): From P → Q and ¬Q, infer ¬P.
否定后件 (MT)：由P → Q和¬Q，推出¬P。 - Hypothetical Syllogism (HS): From P → Q and Q → R, infer P → R.
假言三段论 (HS)：由P → Q和Q → R，推出P → R。 - Disjunctive Syllogism (DS): From P ∨ Q and ¬P, infer Q.
选言三段论 (DS)：由P ∨ Q和¬P，推出Q。 - Constructive Dilemma (CD): From (P → Q) ∧ (R → S) and P ∨ R, infer Q ∨ S.
二难推理建设式 (CD)：由(P → Q) ∧ (R → S)和P ∨ R，推出Q ∨ S。
Recognising these forms in extended prose is essential for evaluating the arguments of Plato, Descartes, Hume, and others. Tagging a passage with 'this is modus tollens' instantly highlights its logical force or exposes a flaw.
在长文阅读中识别这些推理形式，对于评价柏拉图、笛卡尔、休谟等人的论证至关重要。标记“此段为否定后件式”可以立即揭示其逻辑力度或暴露缺陷。
3. Predicate Logic Quick Reference | 谓词逻辑速查
Predicate logic (first-order logic) introduces quantifiers and predicates, allowing us to formalise statements about 'all', 'some', and 'none'. This is indispensable for unpacking ontological and metaphysical arguments.
谓词逻辑（一阶逻辑）引入量词和谓词，让我们能够形式化“所有”“有些”“没有”等陈述，是拆解本体论和形而上学论证的必备工具。
- Universal quantifier (∀): ∀x Fx means 'All x are F'.
全称量词 (∀)：∀x Fx 表示“所有x都是F”。 - Existential quantifier (∃): ∃x Fx means 'There exists at least one x such that x is F'.
存在量词 (∃)：∃x Fx 表示“至少存在一个x，使得x是F”。 - Relations: You can use capital letters for relations, e.g., Lxy for 'x loves y'.
关系：用大写字母表示关系，如Lxy表示“x爱y”。
Typical translations help you decipher Anselm's ontological argument or the move from 'God is that than which nothing greater can be conceived'.
典型的符号互译有助于解读安瑟伦的本体论论证，或者“上帝是可设想的无与伦比之伟大存在”这一思路。
4. Epistemology: The JTB Formula and Gettier Cases | 认识论：JTB公式与盖梯尔案例
The classical analysis of knowledge can be expressed as: K = JTB . A subject S knows that P if and only if: (1) P is true, (2) S believes that P, and (3) S is justified in believing that P.
知识经典分析可表述为：知识 = JTB（被证成的真信念）。主体S知道P，当且仅当：(1) P为真；(2) S相信P；(3) S有正当理由相信P。
S knows that P ↔ (P is true ∧ S believes that P ∧ S has justification for P)
Gettier's counterexamples show that JTB is not sufficient for knowledge. The 'Gettier formula' can be understood as: there exist cases where JTB holds but knowledge is absent due to luck or defeaters.
盖梯尔的反例表明JTB对知识来说并不充分。“盖梯尔公式”可以理解为：存在JTB成立但因运气或否决因子而缺乏知识的情形。
5. Metaphysics: Identity, Persistence, and Causation | 形而上学：同一性、持存与因果关系
Several central metaphysical issues can be compressed into memorable schemata. Begin with Leibniz's Law (the indiscernibility of identicals):
若干核心形而上学议题可被压缩为易记的公式。首先看莱布尼茨律（同一者不可分辨）：
∀x ∀y [x = y → (Fx ↔ Fy)]
This is used in discussions of personal identity, the mind-body relation, and time travel. If two supposed entities differ in any property, they are not identical.
该律被用于人格同一性、心身关系和时间旅行的讨论。如果两个假定实体在任何属性上不同，它们就不是同一的。
For causation, Hume's regularity theory can be summarised as: event C causes event E if and only if C precedes E, C and E are contiguous, and all events similar to C are regularly followed by events similar to E.
对于因果关系，休谟的恒常联结理论可总结为：事件C导致事件E，当且仅当C先于E发生，C与E邻近，且所有与C相似的事件都规律性地被与E相似的事件跟随。
6. Ethical Theories: Formulae of Right Action | 伦理学理论：正确行动公式
Normative ethical theories can be expressed as precise decision procedures. Here are three formulae for right action according to different traditions.
规范伦理学理论可用精确的决策程序加以表达。以下是不同传统下的三个正确行动公式。
- Act Utilitarianism ces the greatest happiness for the greatest number, where happiness = pleasure minus pain.
行为功利主义：行动A是对的，当且仅当A为最大多数人产生最大幸福，其中幸福 = 快乐 − 痛苦。 - Kantian Deontology (First Categorical Imperative Formulation): Act only on that maxim whereby you can at the same time will that it should become a universal law.
康德义务论（定言命令第一公式）：只按照你同时能够意愿它成为一条普遍法则的准则去行动。 - Virtue Ethics (Aristotle's Doctrine of the Mean): A virtuous action is one that lies in a mean between excess and deficiency relative to us, determined by reason.
美德伦理学（亚里士多德中庸之道）：有德性的行动是处于相对于我们而言的过度与不及之间的中道，由理性来确定。
When answering essay questions, explicitly stating the relevant formula and then applying it to a scenario demonstrates top-level understanding.
在回答论文题时，明确陈述相关公式，然后将其应用到情境中，能够展示出最高水平的理解。
7. Philosophy of Mind: Core Positions and Reductive Arguments | 心灵哲学：核心立场与还原论证
The main positions in philosophy of mind can be expressed through the relationship between mental states (M) and physical states (P).
心灵哲学的主要立场可以通过心理状态(M)与物理状态(P)之间的关系来表达。
- Substance Dualism (Descartes): M and P are two fundamentally distinct substances. Mental events do not equal physical events.
实体二元论（笛卡尔）：M与P是两种根本不同的实体。心理事件不等于物理事件。 - Identity Theory (Physicalism type): M = P. Every mental state is numerically identical to some brain state.
同一论（类型物理主义）：M = P。每一种心理状态都等于某一种大脑状态。 - Functionalism: Mental states are defined by their causal roles: M is a functional state that mediates input, other mental states, and output.
功能主义：心理状态由其因果角色定义：M是调节输入、其他心理状态和输出的功能状态。
The 'irreducibility formula' often appears in arguments against physicalism: if there are qualitative feels (qualia) that cannot be captured by physical description, then M ≠ P.
“不可还原性公式”常见于反对物理主义的论证：如果存在无法被物理描述捕捉的质的感受（感质），那么M ≠ P。
8. Arguments for the Existence of God: Logical Structures | 上帝存在的论证：逻辑结构
These arguments appear frequently and benefit from being broken down into premise-conclusion form. Treat each as a logical proof you can analyse for validity and soundness.
这些论证频繁出现，拆解为前提-结论形式将大有裨益。将每个论证视作一个逻辑证明，分析其有效性与可靠性。
Ontological Argument (Anselm's version):
本体论论证（安瑟伦版）：
- God is that than which nothing greater can be conceived. (Definition)
上帝是可设想的无与伦比之伟大存在。（定义） - That which cannot be conceived not to exist is greater than that which can be conceived not to exist. (Premise)
不能被设想为不存在的东西，比能被设想为不存在的东西更伟大。（前提） - Therefore, God cannot be conceived not to exist.
因此，上帝不能被设想为不存在。 - So, God exists in reality. (Conclusion)
故而，上帝在现实中存在。（结论）
Cosmological Argument (Aquinas' Second Way):
宇宙论论证（阿奎那第二路）：
- We observe a series of efficient causes. (Empirical premise)
我们观察到一系列动力因。（经验前提） - Nothing can cause itself. (Premise)
无物能自为原因。（前提） - An infinite regress of causes is impossible because then there would be no first cause, and so no subsequent causes. (Premise)
无穷回溯是不可能的，因为那样就没有第一因，进而不会有后续原因。（前提） - Therefore, there must be a first uncaused cause, which we call God.
因此，必有一个第一非受动因，我们称之为上帝。
Teleological Argument (Paley's Watch): best expressed as an analogical argument: the universe resembles a watch; a watch requires a designer; thus the universe requires a Designer.
目的论论证（培理的表）：最好表现为类比论证：宇宙像一块表；表需要设计者；因此宇宙需要一位设计者。
9. Free Will and Determinism: Positions as Conditional Claims | 自由意志与决定论：立场作为条件句
The debate can be distilled into logical relations between determinism (D) and free will (F). Use these definitions to navigate essay questions.
这一争论可以蒸馏为决定论(D)与自由意志(F)之间的逻辑关系。利用这些定义驾驭论文题目。
- Hard Determinism: D is true → F is impossible. (D rules out free will)
强硬决定论：D为真→ F不可能。（D排除了自由意志） - Compatibilism: D is true ∧ F is possible if F means acting according to one's desires without coercion.
相容论：D为真且F是可能的，只要F意指在没有强制的情况下按照自己的欲望行动。 - Libertarianism: D is false (
¬D) ∧ humans have F. Free will requires a break in the causal chain.
自由意志论：D为假（¬D）且人类拥有F。自由意志要求因果链条出现断裂。
The Consequence Argument formalises the incompatibilist intuition: if we have no choice about the past or the laws of nature, and our actions follow from them, then we have no choice about our actions.
后果论证将不相容直觉形式化：如果我们对过去和自然规律没有选择，而我们的行动又由它们推出，那么我们对自己的行动也没有选择。
10. Philosophical Methodology: Thought Experiments and Dialectics | 哲学方法：思想实验与辩证法
Finally, the 'formulae' of philosophical method itself are essential for constructing and deconstructing arguments. Two key patterns dominate Eduqas assessments.
最后，哲学方法本身的“公式”对于构建和解构论证至关重要。两个关键模式主导着Eduqas评估。
The Thought Experiment Pattern: (1) Describe a scenario that isolates a variable or intuition. (2) Test the implications of a theory in that scenario. (3) If the implications clash with our considered judgement, the theory is challenged.
思想实验模式：(1) 描述一个隔离变量或直觉的情景。(2) 测试某一理论在该情景中的蕴涵。(3) 若蕴涵与我们深思后的判断冲突，该理论便受到挑战。
The Dialectical Triad: often seen around cosmological arguments. Start with a thesis (e.g., infinite regress is possible), encounter an antithesis (a criticism showing it is impossible), and work towards a synthesis that refines the original position.
辩证三段式：常见于宇宙论论证周围。由正题（如无限回溯是可能的）始，遭遇反题（表明其不可能的批评），进而努力达成一个精炼原初立场的合题。
Using these method-formulae helps you structure answers, moving from 'some say' through 'others object' to a defended conclusion.
运用这些方法公式有助于组织答案，从“有人说”到“另有人反对”，再到有辩护的结论。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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