📚 Year 7 SQA Philosophy: Formula & Theorem Quick Reference Handbook | 七年级 SQA 哲学：公式定理速查手册
Welcome to your handy quick reference guide for Year 7 SQA Philosophy! While philosophy may not have mathematical formulas in the strict sense, it does possess powerful ‘formulas’ for clear thinking — logical patterns, ethical principles, and knowledge structures that work much like theorems. This handbook presents them in easy-to-remember formats, helping you reason with precision, spot fallacies, and reflect on life’s big questions. Treat it like a cheat sheet for your mind, and let these philosophical formulas guide you through debates, written tasks, and everyday decisions.
欢迎使用这本七年级 SQA 哲学的速查手册！虽然哲学没有传统意义上的数学公式，但它拥有强大的思维“公式”——逻辑模式、伦理法则和知识结构，如同定理一般发挥作用。本手册以易于记忆的形式将它们总结出来，帮助你精准推理、识别谬误，并思考人生的大问题。把它当作头脑的“小抄”，让这些哲学公式在辩论、书面作业和日常选择中指引你。
1. The Socratic Formula: Question → Examine → Refine | 苏格拉底公式：提问→审视→改进
The Socratic method is a cornerstone of Western philosophy. Its core process can be captured by a simple chain: Q → E → R where Q stands for Questioning assumptions, E for Examining answers with evidence and logic, and R for Refining your understanding. Instead of accepting opinions at face value, you keep digging deeper until beliefs become sturdy or are justly abandoned.
苏格拉底方法是西方哲学的一块基石。其核心过程可用一条简单链条表示：Q → E → R，其中 Q 代表质疑假设，E 代表用证据和逻辑审视回答，R 代表提炼自己的理解。不要轻信表面观点，而要持续深挖，直到信念变得牢固或被合理放弃。
For example, if someone says ‘stealing is always wrong’, apply Q: ‘Why must it always be wrong?’ E: ‘What if a starving child steals bread?’ R: ‘Perhaps absolute rules need context.’ This habit turns passive learners into active philosophers.
例如，如果有人声称“偷窃永远是错的”，运用 Q：“为什么它必须永远是错的？” E：“如果一个挨饿的孩子偷了面包呢？” R：“也许绝对规则需要结合情境。”这种习惯将被动的学习者转变为积极的哲人。
2. The Golden Rule Theorem: Treat Others as You Wish to Be Treated | 黄金法则定理：对待他人如同你期望被对待
Found across cultures and religions, the Golden Rule functions as a universal ethical principle. You can phrase it as a conditional formula: If action A towards person B, then would I wish to receive A? ⇒ Moral if Yes, Immoral if No. This simple test encourages empathy and consistency. When you consider spreading a rumour, shouting at a sibling, or helping a friend, run the Golden Rule check.
黄金法则横跨文化与宗教，发挥着普遍伦理原则的作用。可用条件公式表述：若对乙作出的行为甲，我是否乐意接受行为甲？⇒ 若是则道德，若否则不道德。这一简易检验鼓励共情与一致性。当你考虑散播谣言、对兄弟姐妹吼叫或帮助朋友时，运用黄金法则检验一下。
Philosophers like Confucius and Kant explored similar ideas, but for Year 7, the key takeaway is that ethics begins with putting yourself in someone else’s shoes. The theorem also has a positive version: do for others what you would appreciate them doing for you.
儒家和康德等哲学家探讨过类似理念，但对七年级学生而言，关键在于：伦理始于换位思考。这条定理还有一个积极版本：主动为他人做你希望别人为你做的事。
3. The Logic Formula: Premise₁ + Premise₂ = Conclusion | 逻辑公式：前提₁ + 前提₂ = 结论
Basic deductive logic often takes the form of a syllogism. Its formula can be represented as: P₁: A → B, P₂: B → C, ∴ C: A → C This is the classic Barbara syllogism. If the structure is valid and the premises are true, the conclusion must be true. For instance: P₁: All mammals are warm-blooded. P₂: All dogs are mammals. Therefore, all dogs are warm-blooded.
基础演绎逻辑常采用三段论形式，其公式可表示为：P₁: A → B，P₂: B → C，∴ C: A → C 这就是经典的 Barbara 三段论。如果结构有效且前提为真，结论必然为真。例如：P₁：所有哺乳动物是温血动物。P₂：所有狗是哺乳动物。因此，所有狗是温血动物。
Learning this formula helps you build strong arguments and spot shaky reasoning. If either premise is dubious or the structure is flawed (e.g., P₁: All cats are animals. P₂: Some animals are fluffy. Conclusion: All cats are fluffy. — invalid), the argument collapses. Always check both the premises and the logical shape.
学习这一公式有助于你建构有力的论证并发现薄弱的推理。只要有一项前提可疑，或结构有瑕疵（例如 P₁：所有猫是动物。P₂：有些动物毛茸茸。结论：所有猫都毛茸茸。— 无效），论证就会崩塌。务必同时检验前提和逻辑结构。
4. The Validity vs. Truth Distinction: Structure ≠ Content | 有效性与真实性区分：结构 ≠ 内容
A fundamental insight in logic is that validity and truth are not the same. A formula to remember: Validity concerns IF the premises were true, would the conclusion follow? Truth concerns whether the premises ARE actually true. An argument can be valid but have false premises, or have true premises but be invalid. The two properties are independent.
逻辑学的一个基本洞见是有效性与真实性并不相同。记住这条公式：有效性关心“假如前提为真，结论是否必然推出？”真实性关心“前提实际上是否为真”。一个论证可以有效但前提虚假，也可以前提真实却无效。这两个性质是独立的。
Use this table for clarity:
| Valid? | True premises? | Sound? | Example (English) | 示例（中文） |
|---|---|---|---|---|
| Yes | Yes | Yes (sound) | All birds have feathers. Eagles are birds. So eagles have feathers. | 所有鸟有羽毛。鹰是鸟。所以鹰有羽毛。（可靠） |
| Yes | No | No | All cats can fly. Fluffy is a cat. So Fluffy can fly. (valid but false premises) | 所有猫会飞。Fluffy是猫。所以Fluffy会飞。（有效但前提假） |
| No | Yes | No | Some teenagers are students. Some students enjoy music. So some teenagers enjoy music. (true premises, invalid) | 有些青少年是学生。有些学生喜欢音乐。所以有些青少年喜欢音乐。（前提真但无效） |
Mastering this distinction shields you from being tricked by clever-sounding nonsense.
掌握这种区分，能让你不被听起来巧妙的无稽之谈所蒙骗。
5. The Knowledge Equation: Justified True Belief = Knowledge? | 知识方程：确证的真信念 = 知识？
Since Plato, philosophers have defined knowledge with a classic equation: Knowledge = Justified True Belief (JTB) That is, you know something if (1) you believe it, (2) it is actually true, and (3) you have good reasons or evidence for your belief. For example, you know that Paris is the capital of France because you believe it, it is true, and you can justify it with a reliable source.
自柏拉图以来，哲学家用一个经典方程定义知识：知识 = 确证的真信念（JTB） 也就是说，当你（1）相信某事，（2）它确实为真，（3）你有充分理由或证据支持这一信念时，你便知道它。例如，你知道巴黎是法国的首都，因为你相信它，它为真，且你能用可靠来源加以确证。
However, note that in 1963 philosopher Edmund Gettier showed cases where JTB might not be enough — the so-called Gettier problem. For Year 7, simply remember the JTB framework as a starting point and remain curious about what makes beliefs truly ‘knowledge’. The formula is a helpful baseline, not the final word.
不过请注意，1963年哲学家埃德蒙·葛梯尔提出了反例，表明 JTB 可能还不够——这就是所谓的葛梯尔问题。对七年级学生而言，只需将 JTB 框架作为起点，并对“什么使信念真正成为知识”保持好奇。这个公式是一个有用的基础，而非定论。
6. The Utility Calculus: Greatest Happiness = Sum of Pleasures − Sum of Pains | 功利计算：最大幸福 = 快乐总和 − 痛苦总和
Utilitarianism, developed by Jeremy Bentham and John Stuart Mill, suggests that the morally right action is the one that produces the greatest happiness for the greatest number. This can be expressed as a hedonistic equation: Net Happiness = ∑ Pleasures − ∑ Pains When facing a decision, list all the people affected, estimate the pleasures and pains each action would cause, and choose the one with the highest net score.
由杰里米·边沁和约翰·斯图尔特·密尔发展的功利主义主张，道德上正确的行为是能为最大多数人带来最大幸福的行为。这可用一个享乐主义方程来表达：净幸福 = ∑ 快乐 − ∑ 痛苦 面对抉择时，列出所有受影响者，估算每一行为将产生的快乐与痛苦，并选择净分值最高的选项。
While the ‘felicific calculus’ is not literally computed, the principle encourages you to weigh consequences impartially. Questions you can ask: ‘Who benefits? Who suffers? For how long? How intense is the effect?’ This formula trains you to think beyond your own preferences.
虽然“幸福微积分”并非真的要数值计算，但这一原则鼓励你公正地权衡后果。你可以问：“谁受益？谁受苦？持续多久？影响强度如何？”这一公式训练你超越自身偏好去思考。
7. The Fallacy Detection Theorem: If Personal Attack, Then Invalid | 谬误侦测定理：若人身攻击，则无效
Logical fallacies are errors in reasoning that weaken arguments. One of the most common is the ad hominem fallacy. Its theorem is straightforward: If the arguer attacks the person instead of the argument, the reasoning is fallacious. Example: ‘You can’t trust her views on climate change because she’s not a scientist.’ The merits of her argument should be evaluated on evidence, not her credentials or character.
逻辑谬误是削弱论证的推理错误。其中最常见的一种是人身攻击谬误，其定理简单明了：若论证者攻击的是人而非论点，则推理为谬误。例如：“你不能相信她对气候变化的看法，因为她不是科学家。”她的论点优劣应根据证据来评判，而非其资历或品格。
Other fallacies you can spot with similar ‘if… then’ structures:
| Fallacy Name (English) | 谬误名（中文） | Detection Formula | 侦测公式 |
|---|---|---|---|
| Straw Man | 稻草人 | If you misrepresent an opponent’s view, the argument is fallacious. | 若你歪曲对方观点，则论证为谬误。 |
| False Dilemma | 假两难 | If only two options are presented when more exist, the argument is fallacious. | 若仅呈现两个选项而实际存在更多，则论证为谬误。 |
Practising fallacy detection makes you a sharper thinker and a fairer debater.
练习谬误侦测，能让你思维更敏锐，辩论更公正。
8. The Deontological Principle: Act Only on Rules That Can Be Universalised | 义务论原则：只按可普遍化的规则行动
Immanuel Kant’s ethics revolve around the Categorical Imperative, which can be simplified into a universalisability test: Act only according to that maxim which you can at the same time will to become a universal law. In formula terms: If everyone followed rule R, would the purpose of my action be achievable? ⇒ If No, the action is morally impermissible.
康德的伦理学围绕绝对命令展开，可简化为一个普遍化检验：只按照你同时愿意其成为一条普遍法则的准则去行动。以公式表示：若人人遵守规则 R，我的行为目的还能实现吗？⇒ 若否，该行为在道德上不允许。
For instance, imagine you consider lying to get out of trouble. Can you will that ‘everyone may lie when it benefits them’ become a universal law? If everyone lied constantly, trust would collapse and the very purpose of lying (being believed) would disappear. Hence, the maxim fails the test and lying is generally prohibited. This theorem respects human dignity and consistency.
例如，假设你想撒谎摆脱麻烦。你是否愿意“人人皆可在有利时撒谎”成为普遍法则？如果每个人不断撒谎，信任将崩塌，撒谎的目的（让人相信）也会消失。因此，该准则未能通过检验，撒谎普遍被禁止。该定理尊重人的尊严与一致性。
9. The Mind-Body Connection Formula: Mental State → Physical Action | 心身连接公式：心理状态 → 身体行动
Philosophy of mind explores how thoughts and feelings relate to the physical body. A simplified formula for illustrating the interaction is: Intention or Emotion (Mental) → Brain Activity → Bodily Action For example, the desire for ice cream (mental) triggers neural signals, leading to your hand reaching for the freezer.
心灵哲学探讨思想、感受与身体的关系。一个简化的公式用以说明这种互动：意念或情感（心理） → 大脑活动 → 身体动作 例如，想吃冰激凌的欲望（心理）激发神经信号，导致你的手伸向冰箱。
Philosophers debate whether the mind and body are distinct substances (dualism) or whether mental states are entirely physical (physicalism). For Year 7, the key takeaway is that our inner world has observable effects, and studying this connection raises deep questions about personal identity, free will, and responsibility. The formula reminds us that our choices are not detached from our physical existence.
哲学家们争论心灵与身体是不同的实体（二元论），还是心理状态完全是物理的（物理主义）。对七年级而言，关键认识在于：我们的内在世界会产生可观测的效果，研究这一连接会引发关于人格同一性、自由意志与责任的深刻问题。这个公式提醒我们，选择并非脱离物理存在。
10. The Empathy Equation: Understanding = Listening + Perspective-Taking | 共情方程：理解 = 倾听 + 换位思考
Empathy is crucial for moral philosophy and constructive dialogue. You can visualise it as an additive formula: Genuine Understanding = Active Listening + Perspective-Taking + Suspending Judgment Active listening involves paraphrasing and asking clarifying questions. Perspective-taking means imagining the world from another’s standpoint — their background, emotions, and reasoning. Suspending judgment allows you to remain open before reaching conclusions.
共情对道德哲学和建设性对话至关重要。可视作一个加法公式：真正理解 = 积极倾听 + 换位思考 + 暂缓评判 积极倾听包括复述和提出澄清性问题。换位思考意味着从他人的立场想象世界——他们的背景、情感和推理。暂缓批判让你在得出结论前保持开放。
Practise this equation during classroom debates or disagreements with friends. It does not mean you must agree with everyone; it means you commit to understanding before evaluating. Philosophers from Hume to contemporary care ethicists have emphasised that rationality is enriched, not weakened, by empathy.
在课堂辩论或与朋友意见分歧时练习这一方程。这并不意味着你必须同意每个人；而是承诺先理解再评估。从休谟到当代关怀伦理学家都强调，理性因共情而丰满，并非被削弱。
11. The Relativism vs. Objectivism Balance: Truth = Perspective × Critical Inquiry | 相对主义与客观主义的平衡：真理 = 视角 × 批判性探究
In ethics and even in everyday knowledge, we encounter the tension between ‘it’s true for me’ (relativism) and ‘it’s true for everyone’ (objectivism). A helpful philosophical product formula is: Warranted Belief = Personal Perspective × Critical Inquiry This acknowledges that our cultural and individual lenses shape our starting points, but through questioning, comparing, and testing, we can move closer to shared, well-supported truths.
在伦理学甚至日常知识中，我们都会遇到“对我而言是真理”（相对主义）与“对所有人都是真理”（客观主义）之间的张力。一个有用的哲学乘积公式是：有保证的信念 = 个人视角 × 批判性探究 这承认文化与个人视角塑造了我们的出发点，但通过提问、比较和检验，我们可以更接近共同且证据充分的真理。
For example, different cultures have different food customs — a relativist would say both are ‘right’ within their contexts. But if we add critical inquiry — examining nutritional science or the Golden Rule — we can evaluate customs beyond mere preference. This balance prevents arrogance and nihilism, keeping philosophy an open conversation.
例如，不同文化有不同的饮食习俗——相对主义者会说两者在各自情境中都是“对的”。但如果我们加入批判性探究——考察营养科学或黄金法则——便能超越纯粹偏好来评估习俗。这一平衡防止了傲慢与虚无主义，使哲学保持为一门开放的对话。
12. The Socratic Wisdom Theorem: Wisdom = Knowing That You Do Not Know | 苏格拉底智慧定理：智慧 = 知道自己不知道
Socrates famously claimed that his only wisdom lay in recognising his own ignorance. We can frame this as a reflexive theorem: Wisdom ∝ 1 / Certainty (when certainty is unwarranted) More simply: True wisdom begins when you realise the limits of your knowledge. This intellectual humility drives you to keep asking questions, researching, and revising your views.
苏格拉底有一句名言：他唯一的智慧在于认识到自己的无知。我们可以将其表述为一条反思性定理：智慧 ∝ 1 / 确定性（当确定性缺乏根据时） 更简洁地说：真正的智慧始于认识到自己知识的局限。这种智识上的谦逊驱动你不断提问、探究和修正观点。
For a Year 7 student, this theorem is liberating. You do not need to have all the answers; the willingness to admit ‘I don’t know, but I want to find out’ is a mark of a mature thinker. It is also an antidote to closed-mindedness and intellectual arrogance.
对七年级学生而言，这条定理令人解放。你不必拥有所有答案；愿意承认“我不知道，但我想寻找答案”是成熟思考者的标志。这也是治疗思维封闭和智识傲慢的良方。
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