Pre-U AQA Philosophy: Quick Reference Handbook of Logical Forms | Pre-U AQA 哲学：逻辑公式速查手册

📚 Pre-U AQA Philosophy: Quick Reference Handbook of Logical Forms | Pre-U AQA 哲学：逻辑公式速查手册

In Pre-U AQA Philosophy, structured reasoning is as essential as empirical evidence. Although the subject lacks mathematical equations, it relies on a rigorous set of argumentative schemas, logical principles, and conceptual frameworks that function like ‘theorems’ in philosophical analysis. This handbook gathers the most critical forms—from basic propositional logic to the formal structures of ethical theories and epistemological definitions—serving as a compact revision aid for students who need to recognise, apply, and evaluate philosophical reasoning under exam conditions.

在 Pre-U AQA 哲学课程中，结构化的推理与经验证据同等重要。尽管该学科没有数学公式，但它依赖一套严格的论证模式、逻辑原则和概念框架，它们在哲学分析中发挥着类似“定理”的作用。本手册汇集了最关键的逻辑形式——从基础命题逻辑到伦理学理论和认识论定义的形式结构——为需要在考试条件下识别、应用和评价哲学推理的学生，提供一本紧凑的复习指南。

1. Propositional Logic Basics | 命题逻辑基础

Atomic propositions are represented by letters such as P, Q, R. Connectives include negation (symbolised as ~ or ¬), conjunction (P & Q), disjunction (P ∨ Q), conditional (P → Q), and biconditional (P ↔ Q). Truth tables are used to determine the validity of arguments by exhaustively listing truth-value assignments.

原子命题用字母表示，如 P, Q, R。联结词包括否定（符号 ~ 或 ¬）、合取（P & Q）、析取（P ∨ Q）、条件（P → Q）以及双条件（P ↔ Q）。真值表通过穷尽罗列真值指派，来判断论证是否有效。

Negation: ~P is true iff P is false.
否定：~P 为真当且仅当 P 为假。
Conjunction: P & Q is true iff both are true.
合取：P & Q 为真当且仅当两者均为真。
Disjunction: P ∨ Q is true iff at least one is true.
析取：P ∨ Q 为真当且仅当至少一个为真。
Conditional: P → Q is false only when P is true and Q false.
条件句：P → Q 仅当 P 真而 Q 假时为假。
Biconditional: P ↔ Q is true when P and Q have the same truth value.
双条件：P ↔ Q 在 P 和 Q 真值相同时为真。

2. Valid Argument Forms | 有效论证形式

These deductively valid structures guarantee that if premises are true, the conclusion must be true. Recognising them is crucial for analysing and constructing philosophical arguments in essays, especially in the Philosophy of Religion and Epistemology units.

这些演绎有效的结构保证：如果前提为真，结论必为真。识别它们对于在论文中分析和构建哲学论证至关重要，尤其是在宗教哲学和认识论单元。

Modus Ponens (Affirming the Antecedent): P → Q, P, therefore Q.
肯定前件式： P → Q, P, 所以 Q。
Modus Tollens (Denying the Consequent): P → Q, ~Q, therefore ~P.
否定后件式： P → Q, ~Q, 所以 ~P。
Hypothetical Syllogism: P → Q, Q → R, therefore P → R.
假言三段论： P → Q, Q → R, 所以 P → R。
Disjunctive Syllogism: P ∨ Q, ~P, therefore Q.
选言三段论： P ∨ Q, ~P, 所以 Q。
Constructive Dilemma: (P → Q) & (R → S), P ∨ R, therefore Q ∨ S.
构造性二难： (P → Q) & (R → S), P ∨ R, 所以 Q ∨ S。

3. Common Formal Fallacies | 常见形式谬误

Fallacies are arguments that appear valid but contain a logical error. In timed essays, pointing out a fallacy can swiftly undermine an opponent’s position. The two most tested formal fallacies are affirming the consequent and denying the antecedent.

谬误是看似有效但包含逻辑错误的论证。在限时写作中，指出一个谬误可以迅速削弱对手的立场。考察最多的两个形式谬误是肯定后件和否定前件。

Affirming the Consequent: P → Q, Q, therefore P. (Invalid because Q could have other causes.)
肯定后件： P → Q, Q, 所以 P。（无效，因为 Q 可能由其他原因导致。）
Denying the Antecedent: P → Q, ~P, therefore ~Q. (Invalid because Q may occur without P.)
否定前件： P → Q, ~P, 因此 ~Q。（无效，因为即使没有 P，也可能出现 Q。）

A quick test for validity: if you can imagine a scenario where premises are true and the conclusion false, the argument is invalid. This ‘counterexample method’ works for both formal and informal reasoning.

一个快速检验有效性的方法：如果你能设想前提为真而结论为假的情景，那么该论证无效。这种“反例法”同时适用于形式和非形式推理。

4. The JTB Account of Knowledge | JTB 知识观

In epistemology, the classical analysis defines knowledge as Justified True Belief. It is often formalised as: S knows that P if and only if (i) P is true, (ii) S believes that P, and (iii) S is justified in believing that P. This triple condition serves as a baseline ‘formula’ against which all improvements and objections are measured.

在认识论中，古典分析将知识定义为被证成的真信念。它常被形式化为：S 知道 P，当且仅当 (i) P 为真，(ii) S 相信 P，并且 (iii) S 有证成地相信 P。这组三条件构成了一个基准“公式”，所有改进和反驳都以此为标准进行衡量。

K(S,P) ↔ [True(P) ∧ Believes(S,P) ∧ Justified(S,P)]

知识(S,P) ↔ [真(P) ∧ 相信(S,P) ∧ 证成(S,P)]

In exam responses, always state the three conditions explicitly before evaluating the JTB account. A common criticism is that the conditions are individually necessary but not jointly sufficient, as shown by Gettier.

在考试回答中，务必在评价 JTB 观之前明确陈述这三个条件。常见的批评是，这些条件各自必要但汇合起来并不充分，正如盖梯尔所示。

5. Gettier Cases & The Formula Revised | 盖梯尔案例与修订公式

Gettier cases demonstrate that J,T,B can co-occur accidentally, without genuine knowledge. The standard Gettier structure is: S has a justified false belief Q; from Q, S validly deduces a true proposition P; S’s belief in P is true and justified but only by luck. This reveals a gap in the JTB formula—a missing ‘no luck’ condition.

盖梯尔案例表明 J、T、B 可能偶然并存，而并非真正的知识。标准的盖梯尔结构是：S 有一个被证成的假信念 Q；S 由 Q 有效演绎出一个真命题 P；S 对 P 的信念既真又得到证成，但纯属运气。这揭示了 JTB 公式中的漏洞——缺少“无运气”条件。

Revised formula attempts: JTB + X (where X = no defeaters, reliable process, causal connection, etc.)
修订公式尝试：JTB + X（其中 X = 无否决因子、可靠过程、因果联系等。）
Reliabilism: S knows P iff S’s true belief is produced by a reliable cognitive process.
可靠主义： S 知道 P 当且仅当 S 的真信念由一个可靠的认知过程产生。
No False Lemmas: S knows P iff S’s justification does not rest on any false belief.
无假前提： S 知道 P 当且仅当 S 的证成不依赖于任何假信念。

When evaluating Gettier, always apply the original JTB formula to a classic case (e.g., Smith and Jones, the sheep in the field) to illustrate why it fails, then test whether a proposed revision succeeds.

在评价盖梯尔时，始终将原 JTB 公式应用于经典案例（例如，史密斯与琼斯、田野里的羊）来说明其为何失败，然后检验所提议的修订是否成功。

6. Utilitarian Calculus | 功利主义演算

Classical Utilitarianism, particularly Bentham’s act utilitarianism, can be seen as a hedonic calculus. The ‘formula’ for right action is: an act is right if and only if it produces the greatest net balance of pleasure over pain, considering all sentient beings affected. Bentham’s seven dimensions for measuring pleasure include intensity, duration, certainty, propinquity, fecundity, purity, and extent.

古典功利主义，尤其是边沁的行为功利主义，可被视作一种快乐演算。正确行为的“公式”为：一个行为是正确的，当且仅当它产生了最大的快乐对痛苦的净余额，将所有受影响的感性存在考虑在内。边沁衡量快乐的七个维度包括强度、持续时间、确定性、邻近性、丰度、纯度和范围。

Rightness = Max Σ (Pleasure − Pain) for all affected

正确性 = 对所有受影响者 max Σ (快乐 − 痛苦)

Mill’s qualitative hedonism layer integrates the notion of higher and lower pleasures, which complicates the simple additive model but retains the basic consequentialist structure. Exam questions often require evaluating whether the calculus is practical, or whether it justifies intuitively immoral acts.

密尔的质性快乐主义融入了高等快乐与低等快乐的概念，这使得简单的加总模型复杂化，但保留了基本的结果论结构。考题往往要求评价这个演算是否可行，或者它是否会为直观上不道德的行为提供辩护。

7. Kantian Ethics: The Categorical Imperative Formula | 康德伦理学：绝对命令公式

Kant’s moral philosophy offers a rationalist alternative to utilitarian calculation. The Categorical Imperative (CI) is expressed in several formulations, each functioning as a decision procedure for determining moral duties. The two most examined are the Formula of Universal Law and the Formula of Humanity.

康德的道德哲学提供了功利主义计算之外的理性主义选项。绝对命令以几种形式表述，每一种都充当了确定道德义务的决策程序。考察最多的两个是普遍法则公式和人性公式。

Formula of Universal Law (FUL): ‘Act only according to that maxim whereby you can at the same time will that it should become a universal law.’ Test: can the maxim be conceived without contradiction (conception) and consistently willed (volition)?
普遍法则公式 (FUL)：“只依照你同时愿意它成为一项普遍法则的准则去行动。” 检验：该准则能否毫无矛盾地被设想（概念矛盾）并被一贯地意愿（意愿矛盾）？
Formula of Humanity (FH): ‘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 simply as a means.’
人性公式 (FH)：“你要这样行动，永远都把你人格中的人性以及每个他人人格中的人性同时用作目的，而绝不只是用作手段。”

In application, FUL can be schematised: if everyone acted on maxim M, would the purpose of M be undermined? FH requires checking whether the action respects the rational agency of all persons involved. A strong essay will show how these two formulas are supposed to be equivalent and yield the same duties.

在实际应用中，FUL 可以图式化为：如果每个人都依照准则 M 行动，M 的目的会不会被破坏？FH 要求检验该行为是否尊重所有相关者的理性主体性。一篇有力的论文需要展示这两个公式如何被视为等价的，并得出相同的义务。

8. Aristotle’s Virtue Ethics: The Doctrine of the Mean | 亚里士多德德性伦理：中道学说

Aristotle’s ethical framework centres on character rather than rules or consequences. The ‘formula’ for virtue is that it lies in a mean relative to us, determined by practical wisdom (phronesis). Virtue (arete) is a disposition to choose the intermediate between excess and deficiency in actions and feelings.

亚里士多德的伦理框架以品格为核心，而非规则或后果。德性的“公式”在于相对于我们而言的中道，由实践智慧（phronesis）来确定。德性是一种在行为和情感中选择过度与不及之中间状态的品质。

A structured expression: Virtue V in domain D is the state between vice of excess E and vice of deficiency L, guided by right reason. For instance, courage is the mean between rashness and cowardice in the domain of fear. The mean is not arithmetic; it shifts with the context and the agent.

一个结构化的表达：领域 D 中的德性 V，是在理性的正确引导下，处于过度之恶 E 与不及之恶 L 之间的状态。例如，勇敢是在恐惧领域中鲁莽与懦弱之间的中道。中道并非算术均分，而是随着情境和行动者而变化。

In exams, always list a virtue table (e.g., courage – rashness/cowardice; temperance – self-indulgence/insensibility) and discuss how the doctrine avoids rigid rule-following. The key evaluative point is whether the doctrine provides sufficient action-guidance without lapsing into relativism.

考试中，始终列出一个德性表（如勇敢——鲁莽/懦弱；节制——放纵/麻木），并讨论该学说如何避免僵化的规则遵循。关键的评估要点在于，该学说是否提供了足够的行动指导而不至于滑入相对主义。

9. Mind-Brain Identity Theory Schema | 心脑同一论模式

Type identity theory claims that mental states are numerically identical to brain states. The formula is simple: for any mental state M, there exists a neural state N such that M = N. This identity is contingent, discoverable by science, much like Water = H₂O. The theory is a reductive physicalism that aims to preserve causal closure of the physical world.

类型同一论主张心理状态与大脑状态在数量上是同一的。公式很简单：对于任何心理状态 M，存在一个神经状态 N，使得 M = N。这种同一是后验的，可由科学发现，就像水 = H₂O 一样。该理论是一种还原的物理主义，旨在保持物理世界的因果闭合。

Schema: Pain ≡ C-fibre firing (or some specific neural event)
模式： 疼痛 ≡ C-纤维放电（或某种特定的神经事件）
Challenge of multiple realisability: If octopuses or aliens can feel pain without C-fibres, then type identity fails. Putnam’s argument forces a move to token identity or functionalism.
多重可实现性挑战： 如果章鱼或外星人能在没有 C-纤维的情况下感到疼痛，那么类型同一论就失效了。普特南的论证迫使人们转向个例同一论或功能主义。

10. Functionalist Multiple Realisability | 功能主义多重可实现性

Functionalism defines mental states by their causal roles: what they are caused by (input), what other mental states they interact with, and what behaviour they produce (output). Thus, pain is whatever state plays the pain-role. This is expressed as: M = the occupant of functional role F. Multiple realisability is built in because different physical substrates can occupy the same role.

功能主义通过因果角色来定义心理状态：它们由什么引起（输入）、它们与其他心理状态如何交互、以及它们产生什么行为（输出）。因此，疼痛就是任何扮演疼痛角色的状态。这表达为：M = 功能角色 F 的占据者。多重可实现性内嵌于此，因为不同的物理基质可以占据同一角色。

Pain = the state typically caused by tissue damage, causing distress and withdrawal behaviour

疼痛 = 通常由组织损伤引起、导致痛苦和退缩行为的状态

AQA questions may ask you to contrast functionalism with identity theory or behaviourism. Use the block diagram metaphor: mental states are defined by their place in a network, not by their physical constitution. The primary objection is the inverted spectrum/absent qualia argument, which suggests functionalism cannot account for the ‘what-it-is-likeness’ of conscious experience.

AQA 考题可能会要求你对比功能主义与同一论或行为主义。用方框图比喻：心理状态由其在一个网络中的位置定义，而非由其物理构成定义。主要反对意见是倒转光谱/感受质缺失论证，它表明功能主义无法解释意识经验的“它是什么样子”。

11. Logical Positivism & Verification Principle | 逻辑实证主义与证实原则

The Verification Principle, central to Ayer’s ‘Language, Truth and Logic’, asserts that a statement is meaningful if and only if it is either analytic or empirically verifiable. This operates as a ‘criterion of significance’ formula, used to dismiss metaphysics, theology, and ethics as literally nonsensical.

证实原则是艾耶尔《语言、真理与逻辑》的核心，它主张一个陈述是有意义的，当且仅当它是分析的或是经验上可证实的。这充当了一个“意义标准”公式，用于将形而上学、神学和伦理学斥为字面上无意义的。

Meaningful(S) ↔ Analytic(S) ∨ EmpiricallyVerifiable(S)

有意义(S) ↔ 分析的(S) ∨ 经验上可证实的(S)

Strong verification (conclusive verification) fails because it rules out universal laws and historical statements. Ayer moved to weak verification: S is meaningful if some sense-experience is relevant to determining its truth.
强证实（决定性证实）失败，因为它排除了普遍定律和历史陈述。艾耶尔转向弱证实：如果某些感觉经验与决定 S 的真假相关，那么 S 就是有意义的。

The principle’s self-refutation problem is a classic exam point: the verification principle itself is neither analytic nor empirically verifiable, thus by its own criterion it is meaningless. This paradox exposes the limits of reductive empiricism and paves the way for the holistic views of Quine and later philosophy of language.

该原则的自相反驳问题是经典的考点：证实原则本身既非分析的，也非经验上可证实的，因此根据它自身的标准，它是无意义的。这一悖论暴露了还原经验主义的局限，并为蒯因的整体论及后来的语言哲学铺平了道路。

12. Descartes’ Cogito Argument Form | 笛卡尔我思论证形式

Descartes’ ‘Cogito ergo sum’ is historically presented as a foundational certainty. Its argumentative form, however, can be reconstructed and tested for validity. The compact statement ‘I think, therefore I am’ is not a syllogism with a hidden major premise, as Descartes himself insisted. Rather, it is an intuition of the mind’s existence upon performing the act of doubting.

笛卡尔的“我思故我在”在历史上被呈现为一项基础性的确定性。然而，其论证形式可以被重构并检验有效性。简洁表述“我思，故我在”不是一个含隐藏大前提的三段论，正如笛卡尔本人所坚持的。相反，它是一种在施行怀疑行动时直觉到心灵存在的领悟。

Reconstruction as performative/self-verifying: The very act of doubting one’s own existence confirms that there must be a doubter.
作为施行性/自验证的重构： 怀疑自身存在这一行动本身就证实了必定有一个怀疑者存在。
Potential logical form: ∃x(I think(x)) → ∃x(I exist(x)). Simpler: If I am deceived, I exist. The premise is indubitable while acknowledging deception.
可能逻辑形式： ∃x(我思(x)) → ∃x(我存在(x))。更简单的：如果我被欺骗，那么我存在。该前提在承认欺骗时亦是不可置疑的。

Critics argue that the cogito delivers only momentary subjective certainty, not a permanent substance dualism. In AQA exams, use the cogito to illustrate foundationalist epistemology and the quest for an Archimedean point. Always link it to Descartes’ wider project of clear and distinct ideas and the Cartesian circle.

批评者认为，我思仅仅提供了瞬间的主观确定性，而非一种持久的实体二元论。在 AQA 考试中，用我思来例示基础主义认识论以及对阿基米德点的追求。始终将其与笛卡尔清晰分明观念的更广泛计划以及笛卡尔循环联系起来。

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Pre-U AQA Philosophy: Quick Reference Handbook of Logical Forms | Pre-U AQA 哲学：逻辑公式速查手册