📚 AQA Year 7 Philosophy: Quick Reference Guide to Formulas and Theorems | AQA 七年级哲学：公式定理速查手册
Philosophy might not be full of mathematical formulas, but it has its own set of rules, patterns, and powerful ideas – we can call them 'philosophical formulas' or 'thought theorems'. This quick reference guide collects the key logic structures, ethical principles, and argument blueprints that Year 7 students encounter in the AQA syllabus. Use these to sharpen your reasoning and build stronger arguments.
哲学或许没有满纸的数学公式，但它自有规则、模式与强大的思想——我们可以称之为“哲学公式”或“思维定理”。这份速查手册汇集了七年级学生在 AQA 课程中会遇到的关键逻辑结构、伦理原则和论证蓝图。用它们来打磨推理能力，构建更有力的论证吧。
1. What is Philosophy? | 哲学是什么？
Philosophy is the activity of asking fundamental questions about existence, knowledge, values, reason, and language, and trying to answer them using careful reasoning rather than experiments or faith alone.
哲学是追问关于存在、知识、价值、理性与语言的根本问题，并努力用细致的推理而非仅仅实验或信仰来回答这些问题的活动。
The 'formula' of philosophical thinking can be simplified as: Question → Reason → Analyse → Conclude (tentatively).
哲学思维的“公式”可以简化为：提问 → 推理 → 分析 → （暂时地）得出结论。
2. The Formula of an Argument: Premises and Conclusion | 论证公式：前提与结论
Every philosophical argument has a basic structure: one or more premises (reasons) that support a conclusion (what you are trying to prove). The formula is Premise ₁ (P₁), Premise ₂ (P₂), ... therefore Conclusion (C).
每一个哲学论证都有一个基本结构：一个或多个前提（理由）来支持结论（你要证明的论点）。公式是 前提 ₁（P₁），前提 ₂（P₂），……因此结论（C）。
Example: P₁: All humans are mortal. P₂: Socrates is a human. Therefore, C: Socrates is mortal. This is a valid deductive argument.
例如：P₁：所有人都会死。P₂：苏格拉底是人。因此，C：苏格拉底会死。这是一个有效的演绎论证。
3. Deductive Logic Theorem: If...Then... | 演绎逻辑定理：如果……则……
Deductive arguments aim to guarantee the truth of the conclusion if the premises are true. The most common form is modus ponens: If P, then Q. P is true. Therefore, Q is true. The formula: (P → Q), P ⊢ Q.
演绎论证旨在保证：如果前提为真，结论必然为真。最常见的形式是肯定前件：如果 P 则 Q。P 为真。因此 Q 为真。公式：(P → Q)，P ⊢ Q。
Another valid form, modus tollens, works backwards: If P, then Q. Q is false. Therefore, P is false. (P → Q), ¬Q ⊢ ¬P.
另一有效形式否定后件则反向操作：如果 P 则 Q。Q 为假。因此 P 为假。(P → Q)，¬Q ⊢ ¬P。
4. Inductive Reasoning Formula: Pattern and Prediction | 归纳推理公式：模式与预测
Inductive reasoning moves from specific observations to general conclusions. The formula is: Observed pattern in sample → Generalisation to whole class → Prediction. It does not guarantee truth, only probability.
归纳推理从具体的观察走向一般结论。公式是：样本中的观察模式 → 推广到整个类别 → 预测。它不保证必然为真，只提供可能性。
Example: Every swan I have seen is white. Therefore, all swans are probably white. (A single black swan would falsify this.)
例如：我见过的所有天鹅都是白的。因此，大概所有天鹅都是白的。（只要出现一只黑天鹅，这个结论就被证伪。）
5. The Socratic Method: Question Everything | 苏格拉底方法：质疑一切
Socrates used a formula of systematic questioning to examine ideas and expose inconsistencies. The recipe: a definition → Test with counter-example → Refine definition → Repeat until clear or stuck.
苏格拉底运用系统提问的公式来检验观念并揭示矛盾。步骤是：要求一个定义 → 用反例检验 → 修正定义 → 重复，直至清晰或陷入困境。
This method shows that wisdom often begins with admitting what we do not know: 'I know that I am intelligent because I know that I know nothing.'
这一方法表明，智慧往往始于承认自己的无知：“我知道自己聪明，因为我知道自己一无所知。”
6. Ethics Formula: The Golden Rule | 伦理公式：黄金法则
One of the simplest ethical guidelines found across cultures: 'Treat others as you would like to be treated.' In philosophical form: Action A is permissible if you would rationally will that everyone acts in the same way towards you in similar circumstances.
各文化中共有的一条最简单的伦理准则：“你希望别人怎样对待你，你就怎样对待别人。” 用哲学语言表达：如果你理智地愿意所有人在相似情境下也以同样方式对待你，那么行动 A 就是许可的。
This reciprocity formula is a cornerstone of many moral and religious systems.
这种互惠公式是许多道德与宗教体系的基石。
7. Utilitarianism Theorem: The Greatest Happiness Principle | 功利主义定理：最大幸福原则
Jeremy Bentham and John Stuart Mill proposed a formula to decide right and wrong: An action is right if it produces the greatest amount of pleasure (or happiness) for the greatest number of people. Summarised as: Maximise utility = maximise pleasure minus pain.
边沁和密尔提出了一套决定对错的公式：如果一项行动能为最大多数人带来最大量的快乐（或幸福），它就是对的。概括为：最大化功利 = 最大化快乐减去痛苦。
Hedonic Calculus: When comparing possible actions, consider intensity, duration, certainty, propinquity (how near), fecundity (will it lead to more pleasure?), purity (free from pain?), and extent (how many people?).
快乐计算法：比较可能行动时，要考量强度、时长、确定性、邻近性（快慢）、多产性（会带来更多快乐吗？）、纯度（是否不含痛苦？）以及范围（影响多少人）。
8. Kant’s Categorical Imperative: Universal Law Formula | 康德绝对命令：普遍法则公式
Immanuel Kant offered a very different formula: Act only according to that maxim whereby you can at the same time will that it should become a universal law. Test your action: if everyone did it, would it still make sense, or would it lead to a contradiction?
康德给出了一个非常不同的公式：只按照你同时愿意它成为一条普遍法则的准则去行动。检验你的行动：如果每个人都这样做，它还能成立吗？还是会导致矛盾？
A second formulation: Always treat humanity, whether in yourself or in another, never simply as a means, but always at the same time as an end. This forbids using people merely as tools.
第二个表述：永远要把人性（无论是你自身还是他人身上的人性）不仅仅当作手段，同时也要当作目的。这禁止将人仅仅当作工具来利用。
9. The Mind-Body Problem: Dualism vs. Materialism | 心身问题：二元论与唯物论
Two competing formulas for the relationship between mind and body: Substance Dualism (Descartes): Mind and body are two fundamentally different substances; mind is non‑physical thinking stuff, body is physical extension in space. Materialism (modern science): Mental states are physical states of the brain; the mind is what the brain does.
关于心身关系，有两套对立的公式：实体二元论（笛卡尔）：心灵与身体是两种根本不同的实体；心灵是非物理的思维之物，身体是空间中延展的物理之物。唯物主义（现代科学）：心理状态是大脑的物理状态；心灵即大脑之所为。
Key puzzle: how can a non‑physical mind cause physical actions? This is the interaction problem, still debated.
关键难题：非物理的心灵如何引起物理行动？这就是交互问题，至今仍在争论。
10. Knowledge Formula: Justified True Belief | 知识公式：被证成的真信念
Since Plato, many philosophers have defined knowledge using a three‑part formula: K = JTB (Justified True Belief). To know that P, (1) P must be true, (2) you must believe that P, and (3) you must have good reasons (justification) for believing P.
自柏拉图以来，许多哲学家用一个三要素公式定义知识：K = JTB（被证成的真信念）。要知道命题 P，（1）P 必须为真，（2）你必须相信 P，且（3）你必须有好的理由（证成）来相信 P。
Gettier problems challenge this formula by showing cases where someone has a justified true belief but still seems not to know. The search for a fourth condition continues.
葛梯尔问题挑战了这一公式，表明有些情况下一个人拥有被证成的真信念，但似乎仍不算知道。对第四条件的探索仍在继续。
11. The Ontological Argument: A Logical Proof for God? | 本体论论证：上帝的逻辑证明？
Anselm’s formula attempts to prove God’s existence from the very definition of God: God is that than which nothing greater can be conceived. If God exists only in the mind, a greater being could be conceived (one that exists in reality too). Therefore, God must exist in reality.
安瑟伦的公式试图从上帝本身的定义出发证明上帝存在：上帝是被设想为无与伦比之伟大的存在。如果上帝只存在于心灵中，那么就能设想出一个更伟大的存在（同时也存在于现实中）。因此，上帝必然也存在于现实中。
Gaunilo’s reply used the perfect island parody, and Kant argued that existence is not a predicate – adding 'exists' to a definition does not add any real property. The debate continues.
高尼罗的回应用了完美岛屿的类比，康德则论证存在不是一个谓词——在定义中加上“存在”并没有增加任何实在的属性。争论仍在继续。
12. The Problem of Evil: A Logical Challenge | 恶的问题：逻辑挑战
For theists, the existence of evil and suffering seems to contradict the existence of an all‑powerful, all‑knowing, all‑good God. The logical formula is: If God is all‑powerful, He can prevent evil. If God is all‑good, He would want to prevent evil. Evil exists. Therefore, such a God does not exist.
对有神论者来说，恶与苦难的存在似乎与全知、全能、全善的上帝相矛盾。逻辑公式是：如果上帝全能，祂就能阻止恶。如果上帝全善，祂就愿意阻止恶。恶存在。因此，这样的上帝不存在。
Common responses include the free will defence (evil arises from misuse of free will, and free will is a greater good) and the soul‑making theodicy (suffering builds character and brings us closer to God).
常见的回应包括自由意志辩护（恶源于自由意志的误用，而自由意志是更大的善）和灵魂塑造神正论（苦难塑造品格，使人更接近上帝）。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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