📚 Year 8 SQA Philosophy: Formula & Theorem Quick Reference Guide | Year 8 SQA 哲学：公式定理速查手册
Welcome to your quick reference philosophy handbook! Instead of memorising dates and names, we have turned the core ideas of philosophy into simple 'formulas' and 'theorems'. Each one captures a powerful way of thinking, arguing, or deciding what is right. Use this guide to lock in the logic behind the big questions — perfect for your SQA revision.
欢迎使用你的哲学速查手册！我们不再死记日期和名字，而是把哲学的核心思想转化成简单的“公式”和“定理”。每一个都抓住了一种有力的思考、论证或判断对错的方式。用这本指南锁定大问题背后的逻辑，非常适合你的 SQA 复习。
1. The Argument Formula: Premises + Conclusion = Reasoning | 论证公式：前提 + 结论 = 推理
In philosophy, an argument is not a fight. It is a carefully built chain of statements. The statements that give support are called premises, and the statement they support is the conclusion. The basic formula is straightforward: one or more premises work together, and an arrow points to the conclusion. If the premises are true and the logic is tight, the conclusion must be true — that is what we call a valid argument.
在哲学中，论证不是吵架。它是一条精心构建的陈述链。提供支持的陈述叫做前提，它们所支持的陈述是结论。基本公式很简单：一个或多个前提共同作用，用箭头指向结论。如果前提为真且逻辑紧密，结论就必然为真——这就是我们所说的有效论证。
Premise₁ + Premise₂ → Conclusion
2. The Cogito Theorem: 'I Think, Therefore I Am' | 我思定理：“我思故我在”
Rene Descartes wanted to find one absolutely certain truth. He doubted everything — his senses, his memories, even the existence of the physical world. But he realised that the very act of doubting proved something: he was thinking. And if he was thinking, he must exist. This became the foundation of modern philosophy: Cogito, ergo sum — 'I think, therefore I am.' It works like a self-proving theorem: the premise (I am thinking) guarantees the conclusion (I exist).
勒内·笛卡尔想找到一个绝对确定的真理。他怀疑一切——他的感官、他的记忆，甚至物理世界的存在。但他意识到，怀疑这个行为本身就证明了一件事：他正在思考。如果他在思考，他就必然存在。这成了现代哲学的基石：Cogito, ergo sum——“我思故我在”。它就像一个自我证明的定理：前提（我在思考）保证了结论（我存在）。
Doubt → Thinking → Existence
3. The Valid Argument Test: If Premises True, Conclusion Must Be True | 有效论证检验：前提真则结论必真
Not every argument that sounds good is valid. A valid argument has a special property: if we imagine all the premises are true, the conclusion cannot be false. We test this by asking a single question. Suppose the premises were true, could the conclusion still be false? If the answer is no, the argument passes the validity test. Truth of the premises is a different matter — an argument can be valid even with false premises, but a sound argument needs both true premises and valid structure.
不是每个听起来不错的论证都有效。有效论证有一个特殊性质：如果我们假设所有前提为真，结论就不能为假。我们通过一个问题来检验。假设前提为真，结论还可能为假吗？如果答案是否定的，论证就通过了有效性检验。前提的真假则是另一回事——哪怕前提为假，论证也可能有效，但一个好论证需要前提为真且结构有效。
Valid ⇔ (Premises True ⇒ Conclusion True)
4. Modus Ponens: The Direct Logic Formula | 肯定前件式：直接逻辑公式
Modus ponens is one of the most common valid argument forms. The Latin name means 'the way that affirms'. It has a conditional premise ('if p then q'), a second premise that affirms the 'p' part, and a conclusion that delivers 'q'. The formula is extremely reliable: whenever you spot this pattern, you are looking at a valid inference.
肯定前件式是最常见的有效论证形式之一。这个拉丁文名称意为“肯定的方式”。它有一个条件句前提（“如果 p 则 q”），第二个前提肯定“p”的部分，结论则推出“q”。这个公式极其可靠：一旦你认出这个模式，你看到的就是一个有效推理。
p → q, p ∴ q
- If it is raining, the ground is wet. (p → q)
- It is raining. (p)
- Therefore, the ground is wet. (q)
5. Modus Tollens: The Negative Logic Formula | 否定后件式：否定逻辑公式
Modus tollens is the mirror image of modus ponens. Its name means 'the way that denies'. Here the second premise denies the consequent (the 'q' part), which forces us to deny the antecedent ('p'). This form is equally valid and is often used in scientific testing: if a theory predicts a certain result, and we do not observe that result, the theory must be false.
否定后件式是肯定前件式的镜像。它的名称意为“否定的方式”。这里第二个前提否定了后件（'q' 部分），这迫使我们否定前件（'p'）。这个形式同样有效，并常用于科学检验：如果某个理论预测某种结果，而我们没有观测到该结果，这个理论就必定为假。
p → q, ¬q ∴ ¬p
- If I am in Edinburgh, I am in Scotland. (p → q)
- I am not in Scotland. (¬q)
- Therefore, I am not in Edinburgh. (¬p)
6. Utilitarian Calculus: Greatest Happiness Principle | 功利主义计算：最大幸福原则
Jeremy Bentham and John Stuart Mill proposed an ethical 'formula' for deciding right from wrong: the action that produces the greatest total happiness for the greatest number of people is the right action. This is often called the Greatest Happiness Principle. In theory, you could measure happiness in units called 'utils', adding up pleasure and subtracting pain. The moral choice is the one that maximises the final sum. While exact numbers are rarely used, the balancing act is a practical tool.
杰里米·边沁和约翰·斯图尔特·密尔提出了一个决定对错的伦理“公式”：能为最大多数人带来最大总幸福的行为就是正确的行为。这通常被称为最大幸福原则。理论上，你可以用叫做“效用”的单位衡量幸福，把快乐加起来，再减去痛苦。道德的选择就是最终总和最大的那一个。尽管很少用到精确数字，这种权衡却是一种实用的工具。
Right Action ⇔ Maximise Σ(Happiness) = Σ(Pleasure) – Σ(Pain)
7. Deontological Rule: The Categorical Imperative Theorem | 义务论规则：绝对命令定理
Immanuel Kant argued that morality is not about consequences but about duty. His central principle is the Categorical Imperative, which acts as a universal test for any action. 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 formula terms, if the rule behind your action can be applied to everyone without contradiction, then the action is morally permissible. If it leads to a contradiction or you would not want to live in such a world, the action is wrong.
伊曼努尔·康德主张，道德不在于后果而在于义务。他的核心原则是绝对命令，它作为任何行为的普遍检验。第一条表述说：“要只按照你同时能够愿意它成为一条普遍法则的那个准则去行动。”用公式来说，如果你行动背后的规则能毫无矛盾地适用于每一个人，那么这个行为就是道德上允许的。如果会导致矛盾，或者你不愿意生活在这样的世界里，这个行为就是错的。
Moral Action ⇔ Maxim can be universalised without contradiction
8. The Socratic Method Formula: Question → Define → Refine → Discover | 苏格拉底方法公式：提问→定义→精炼→发现
Socrates used a disciplined questioning process to help people uncover deeper truths. This method is not about winning an argument but about sharpening ideas. The step-by-step formula goes like this: ask a fundamental question, invite a definition, find counterexamples, refine the definition, and repeat until you reach a clearer understanding. The arrow flow captures the iterative nature of philosophical inquiry.
苏格拉底使用一套有纪律的提问流程，帮助人们发现更深的真理。这种方法不是为了赢得争论，而是为了磨砺思想。逐步公式如下：提出一个根本性问题，给出一个定义，找出反例，打磨定义，重复直到达到更清晰的理解。这个箭头流程抓住了哲学探究的迭代本质。
Question → Define → Challenge → Refine → (Back to Question) → Discovery
9. Fallacy Alert: Circular Reasoning Loop | 谬误警示：循环论证回路
A fallacy is a flaw in reasoning that makes an argument invalid or very weak. One of the simplest to spot is circular reasoning, sometimes called 'begging the question'. The formula is a closed loop: A because B, and B because A. No real evidence is offered, and the reasoning goes nowhere. Being able to identify this loop will sharpen your critical thinking in essays and debates.
谬误是推理中的缺陷，会让一个论证无效或极弱。最容易识别的一种谬误是循环论证，有时也叫“乞题”。它的公式是一个闭环：因为 B 所以 A，又因为 A 所以 B。没有提供真正的证据，推理原地打转。能够识别这种回路，会让你在论文和辩论中的批判性思维更加锋利。
A because B, B because A (invalid loop)
10. The Golden Rule Theorem: Treat Others as You Wish to Be Treated | 黄金法则定理：己所不欲勿施于人
Found in many cultures and religious traditions, the Golden Rule is a universal ethical touchstone. Its formula is both simple and profound: treat others as you would like to be treated in their situation. This principle can be used as a quick moral test. Before acting, ask: 'Would I want someone to do this to me?' If the answer is no, the action likely fails the Golden Rule test.
黄金法则见于许多文化和宗教传统，是一条普遍的伦理试金石。它的公式既简单又深刻：你希望别人怎样待你，你就怎样待人。这条原则可用作快速的道德检验。在行动之前，问自己：“我愿意别人这样对待我吗？”如果答案是否定的，这个行为很可能通不过黄金法则的检验。
Moral Action ⇔ I would will this treatment for myself
11. The Tabula Rasa Principle: Empiricist Starting Point | 白板原则：经验主义起点
Empiricist philosophers like John Locke argued against the idea of innate knowledge. Instead, they claimed the human mind at birth is a tabula rasa, a blank slate. All knowledge comes from experience, built up through sensation and reflection. The formula is additive: the mind starts empty, and every concept is written onto it by the senses. This principle underpins the scientific reliance on observation and experiment.
像约翰·洛克这样的经验主义哲学家反对天赋观念。相反，他们声称人类心智在出生时是一块白板（tabula rasa）。所有知识都来自经验，通过感觉和反省积累而成。这个公式是累加的：心智一开始是空的，每一个概念都由感官书写上去。这条原则奠定了科学对观察和实验的依赖。
Knowledge = Experience (Sensation + Reflection), Mind₀ = ∅
12. Occam's Razor: Simplicity Principle | 奥卡姆剃刀：简洁性原则
Occam's Razor is a guiding principle for choosing between competing explanations. It states: 'Entities should not be multiplied beyond necessity.' In everyday formula language, when you have two explanations that fit the facts equally well, prefer the simpler one — the one with fewer assumptions. This does not prove the simpler theory is true, but it keeps our reasoning clean and efficient, much like a mental razor that shaves away unnecessary complications.
奥卡姆剃刀是在相互竞争的解释之间进行选择的指导原则。它说：“如无必要，勿增实体。”用日常公式语言来说，当你有两个同样符合事实的解释时，优先选择更简单的那个——假设更少的那个。这并不证明简单理论为真，却能让我们的推理保持清爽高效，就像一把思想剃刀，剃去不必要的复杂。
If E₁ and E₂ explain data equally, choose the one with fewer assumptions
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