📚 Year 7 WJEC Philosophy: Formulas & Theorems Quick Reference | Year 7 WJEC 哲学：公式定理速查手册
In philosophy, we don't use mathematical formulas but we do have powerful 'formulas' and 'theorems' — these are key principles, arguments, and thought experiments that help us reason about the world. This handbook collects the essential philosophical formulas every Year 7 WJEC student should know, from logic to ethics.
在哲学中，我们不使用数学公式，但我们确实拥有强大的“公式”和“定理”——这些是帮助我们思考世界的关键原则、论证和思想实验。本手册汇集了每个 WJEC 七年级学生都应掌握的基本哲学公式，涵盖逻辑到伦理学。
1. The Socratic Formula: Question Everything | 苏格拉底公式：质疑一切
The Socratic formula is a method of inquiry that uses continuous questioning to test beliefs and uncover deeper truths. Instead of accepting ideas at face value, we ask 'What does this really mean?' and 'Why do we think that?' until we reach the most basic assumptions.
苏格拉底公式是一种通过不断提问来检验信念、揭示更深层真理的探究方法。我们不是直接接受表面的观点，而是问“这到底是什么意思？”“我们为什么这样想？”，直到触及最基本的假设。
This formula works as a cooperative dialogue where each answer leads to another question. Socrates used it to show that many people hold contradictory opinions without realising it. For Year 7 students, the Socratic formula is a tool to think critically about everyday concepts like fairness, courage, and friendship.
这个公式以合作对话的形式运作，每个答案都会引出下一个问题。苏格拉底用它来表明，许多人持有矛盾的观点却没有意识到。对于七年级学生来说，苏格拉底公式是批判性思考公平、勇气、友谊等日常概念的工具。
2. The Cartesian Theorem: I Think, Therefore I Am | 笛卡尔定理：我思故我在
Rene Descartes arrived at one of the most famous philosophical theorems: "I think, therefore I am" (Cogito, ergo sum). After doubting everything — his senses, the physical world, even his own body — he realised that the act of doubting itself proved that he must exist. A doubt is a thought, and a thought requires a thinker.
勒内·笛卡尔得出了最著名的哲学定理之一：“我思故我在”。在怀疑了一切——他的感官、物质世界，甚至他自己的身体——之后，他意识到怀疑行为本身就证明了他必然存在。怀疑是一种思想，有思想就必然有思想者。
This theorem works like a foundational axiom in mathematics: it is self-evident and provides a secure starting point for building knowledge. For Year 7 learners, it introduces the difference between knowledge that depends on the senses and knowledge that comes from pure reasoning.
这条定理就像数学中的基础公理：它不证自明，为建立知识提供了一个可靠的起点。对七年级学生而言，它介绍了依赖感官的知识与来自纯推理的知识之间的区别。
3. The Platonic Formula of Forms | 柏拉图的理型公式
Plato's formula states that beyond the physical objects we see, there exist perfect, unchanging 'Forms' or Ideas. Every circle we draw is imperfect, yet we all recognise what a perfect circle is — that is because we are accessing the Form of the Circle, which exists in a non-physical realm of reality.
柏拉图的公式指出，在我们看到的物理对象之外，存在着完美、不变的“理型”或“理念”。我们画出的每个圆都不完美，但我们都认得完美的圆是什么——这是因为我们触及了圆的理型，它存在于非物理的实在领域。
This formula applies to concepts like justice, beauty, and equality. We can recognise injustice because we have an innate grasp of the Form of Justice. The world of Forms gives us standards against which we measure ordinary life. In class, you might use this formula to ask: What is the perfect example of friendship?
这个公式适用于正义、美、平等这些概念。我们能认出不正义，是因为我们天生就把握了正义的理型。理型世界为我们提供了衡量日常生活的标准。在课堂上，你可以用这个公式来问：友谊的完美实例是什么？
4. The Aristotelian Four Causes Theorem | 亚里士多德四因说定理
Aristotle offered a theorem to explain why any object exists or any event occurs: everything has four causes. The material cause is what it is made of; the formal cause is its shape or blueprint; the efficient cause is the agent that brought it into being; and the final cause is its purpose or function — what it is for.
亚里士多德提出了一个定理来解释任何物体为何存在或任何事件为何发生：一切事物都有四因。质料因是它由什么构成；形式因是它的形状或蓝图；动力因是使它产生的作用者；目的因是它的目的或功能——它是为了什么。
For a wooden desk, the material cause is wood, the formal cause is the desk's design, the efficient cause is the carpenter, and the final cause is to provide a surface for writing. This theorem trains Year 7 students to think beyond simple explanations and look for purpose and structure in the world around them.
以一张木桌为例，质料因是木头，形式因是桌子的设计，动力因是木匠，目的因是提供一个写字的面板。这个定理训练七年级学生超越简单的解释，在周围世界中寻找目的和结构。
5. The Empiricist Formula: All Knowledge Comes from Experience | 经验主义公式：一切知识来源于经验
The empiricist formula, championed by John Locke, holds that the mind at birth is a tabula rasa — a blank slate — and all concepts are built from sensory experience. There are no innate ideas; what we know is a collection of impressions received through seeing, hearing, touching, and so on.
由约翰·洛克倡导的经验主义公式认为，心灵在出生时是一块 tabula rasa（白板），所有概念都是从感官经验中建立起来的。不存在天赋观念；我们所知的只是通过看、听、触摸等接收到的印象的集合。
According to this formula, simple ideas combine to form complex ideas. A 'unicorn' is not something we have experienced directly, but we combine the simple ideas of 'horse' and 'horn'. This approach encourages Year 7 students to trace the origins of their beliefs back to evidence from the senses.
根据这个公式，简单观念组合成复杂观念。“独角兽”并非我们直接经验过的东西，但我们组合了“马”和“角”这两个简单观念。这种方法鼓励七年级学生追溯自己信念的起源，回到感官证据上。
6. The Categorical Imperative Formula: Act Only on That Maxim… | 绝对命令公式：只按照你同时愿意它成为普遍法则的准则去行动
Immanuel Kant's categorical imperative is a moral formula that does not depend on consequences. The first formulation says: "Act only according to that maxim whereby you can, at the same time, will that it should become a universal law." In other words, before you act, ask yourself: What if everyone did this?
伊曼努尔·康德的绝对命令是一条不依赖于后果的道德公式。第一个表述是：“只按照你同时能够愿意它成为一条普遍法则的准则去行动。”换句话说，在你行动之前，问自己：如果每个人都这样做会怎样？
If you are thinking about breaking a promise, imagine a world where everyone broke promises. In that world, the practice of promising would collapse, and your own action would become impossible or self-defeating. This formula helps Year 7 students test the fairness of rules by checking whether they can be consistently applied to all people.
如果你正在考虑违背承诺，想象一个人人都违背承诺的世界。在那个世界里，承诺的做法将会崩溃，你的行为本身也就变得不可能或自相矛盾。这个公式帮助七年级学生通过检验一条规则是否能够一致地适用于所有人，来判断它的公平性。
7. The Greatest Happiness Principle: Utilitarian Calculus | 最大幸福原则：功利计算
Jeremy Bentham and John Stuart Mill proposed a formula for making moral decisions: the right action is the one that produces the greatest happiness for the greatest number of people. This is often called the principle of utility, and it treats pleasure and pain as measurable units that can be added and subtracted.
杰里米·边沁和约翰·斯图尔特·密尔提出了一个作道德决定的公式：正确的行动就是能为最大多数人带来最大幸福的那个行动。这通常被称为功利原则，它把快乐和痛苦当作可以加减的可测量单位。
When faced with a dilemma, the utilitarian formula instructs you to consider everyone affected, estimate the pleasure and pain each option would cause, and choose the one with the highest net happiness. For Year 7 students, this formula explains why we sometimes allow small harms to prevent greater ones, but it also raises the question: Can all values really be measured?
面对两难局面时，功利主义公式指示你考虑所有受影响的人，估算每个选项会带来的快乐和痛苦，然后选择净幸福值最高的那个。对七年级学生来说，这个公式解释了为什么我们有时允许小的伤害来防止更大的伤害，但它也引出了一个问题：所有价值真的都能测量吗？
8. The Social Contract Theorem: Agreement Creates Authority | 社会契约定理：同意创造权威
The social contract theorem states that legitimate political authority arises not from divine right or force, but from the consent of the governed. Thinkers like Thomas Hobbes, John Locke, and Jean-Jacques Rousseau imagined a 'state of nature' without government and argued that people voluntarily agreed to form societies for mutual protection and benefit.
社会契约定理指出，合法的政治权威并非来自神授权力或武力，而是来自被统治者的同意。霍布斯、洛克和卢梭等思想家设想了一种没有政府的“自然状态”，并主张人们自愿同意组成社会，以获得相互保护和利益。
Even though we never signed an actual contract, by living in a community and accepting its protections, we give implicit consent to its rules. This theorem is a powerful tool for Year 7 discussions about why we should obey laws, what makes a government fair, and when it is right to challenge authority.
尽管我们从未签署过实际的契约，但通过生活在一个社群中并接受其保护，我们对其规则给予了默示同意。这个定理是七年级讨论为什么我们应该遵守法律、什么使政府公平、以及何时挑战权威是正当的强有力工具。
9. The Golden Rule Formula: Treat Others As You Want to Be Treated | 黄金法则公式：你想别人怎样对待你，你就要怎样对待别人
The Golden Rule is a universal ethical formula found in many world religions and philosophical traditions. In its simplest form, it states: 'Treat others as you would like to be treated.' This principle promotes empathy by asking you to imagine yourself in the other person's situation before acting.
黄金法则是一条普遍的伦理公式，存在于许多世界宗教和哲学传统中。其最简单的形式是：“你想别人怎样对待你，你就要怎样对待别人。”这条原则通过要求你在行动前想象自己处在对方的处境中，来促进同理心。
Unlike complex ethical theories, this formula is concrete and testable in everyday life. When Year 7 students face decisions about sharing, exclusion, or honesty, the Golden Rule offers a quick reflective test: How would I feel if this were done to me? It forms the foundation of mutual respect in classroom communities.
与复杂的伦理理论不同，这个公式在日常生活中是具体且可检验的。当七年级学生面对分享、排斥或诚实方面的决定时，黄金法则提供了一个快速的反思检验：如果这件事发生在我身上，我会有什么感受？它构成了课堂社群中相互尊重的基础。
10. The Turing Test Theorem: Can Machines Think? | 图灵测试定理：机器能思考吗？
Alan Turing proposed a practical test to answer the philosophical question of whether machines can think. The Turing Test theorem replaces the vague concept of 'thinking' with an operational definition: if a human interrogator cannot distinguish a machine's responses from a human's through text-based conversation, the machine should be considered intelligent.
阿兰·图灵提出了一个实际测试来回答机器能否思考这个哲学问题。图灵测试定理用一种操作性定义取代了“思考”这个模糊的概念：如果人类提问者通过文字对话无法区分机器的回答和人类的回答，那么这台机器就应该被认为是智能的。
This theorem does not require the machine to have feelings or consciousness — it only requires the ability to produce human-like linguistic output. For young philosophers, it opens up vital questions about what it means to have a mind, whether thinking is just information processing, and how we treat entities that behave intelligently.
这个定理并不要求机器拥有感受或意识——它只要求能够产生像人类一样的语言输出。对年轻的哲学家来说，它开启了关于拥有心智意味着什么、思考是否只是信息处理，以及我们如何对待表现出智能行为的实体等重要问题。
11. The Principle of Charity: Interpret Others in the Strongest Way | 宽容原则：用最有力的方式解读他人
The principle of charity is a logical formula for engaging with arguments: when you encounter someone else's claim, you should interpret it in the most reasonable, coherent, and persuasive way possible before responding. This avoids attacking weak versions of an argument (straw man fallacies) and promotes genuine understanding.
宽容原则是参与论证的一个逻辑公式：当你遇到他人的主张时，你应该先以最合理、最连贯、最有说服力的方式来解读它，然后再回应。这避免了攻击论证的弱化版本（稻草人谬误），并促进真正的理解。
Applying this formula means you assume the other person is rational unless proven otherwise. In Year 7 philosophy discussions, this builds a culture of respectful disagreement. You learn to say, 'If I understand your strongest point correctly, you are saying that...' before offering a counterargument.
应用这个公式意味着除非被证明相反，否则你假定对方是理性的。在七年级的哲学讨论中，这营造了一种尊重分歧的文化。你学会在提出反驳之前先说：“如果我对你最强有力的观点理解正确的话，你是在说……”
12. The Formula of Infinite Regress: Why Explanations Need Foundations | 无限回溯公式：为什么解释需要基础
Philosophical questioning often risks an infinite regress, where every explanation requires a further explanation, going on forever. The formula of infinite regress shows that any complete system of knowledge or ethics must arrive at a foundational stopping point — something that is self-evident or accepted without needing further justification.
哲学追问常常面临无限回溯的风险，即每一个解释都需要更进一步的解释，永无止境。无限回溯公式表明，任何完备的知识或伦理体系都必须到达一个基础的终止点——某种不证自明，或无需进一步辩护就被接受的东西。
We see this formula at work in Aristotle's uncaused cause, Descartes' cogito, and even in the foundations of mathematics. For Year 7 students, it explains why in any philosophical conversation, we eventually hit a point where we simply have to say, 'This is where our reasoning begins.' Understanding this pattern helps learners identify the core assumptions in any argument.
我们在亚里士多德的不动的推动者、笛卡尔的“我思”，甚至在数学的基础中都看到了这个公式的作用。对七年级学生来说，它解释了为什么在任何哲学对话中，我们最终都会到达一个点，在那里我们只能简单地说：“这就是我们推理的起点”。理解这个模式有助于学习者在任何论证中识别出核心假设。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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