📚 Year 7 AQA Philosophy: Quick Reference Handbook for Formulas and Theorems | 7年级 AQA 哲学：公式定理速查手册
Philosophers use clear logical patterns to test ideas, just like scientists use mathematical formulas. This quick reference handbook gathers essential philosophical ‘formulas’, ‘theorems’ and argument structures you are likely to encounter in Year 7 AQA Philosophy. Each entry is presented as a memorable rule or pattern, supported by a simple explanation and example. Use this to sharpen your reasoning skills, identify fallacies, and construct stronger arguments of your own.
哲学家使用清晰的逻辑模式来检验观点，就像科学家使用数学公式一样。这本速查手册汇集了你在 7 年级 AQA 哲学中可能遇到的基本哲学“公式”、“定理”和论证结构。每个条目都以一条好记的规则或模式呈现，并配有简单的解释和例子。用这本手册来提升你的推理能力、识别谬误并构建更有力的论证。
1. The Syllogism Formula | 三段论公式
A syllogism is a classic deductive argument using two premises to guarantee a conclusion. If the premises are true and the form is valid, the conclusion must be true. The basic pattern is: All A are B; All B are C; therefore, all A are C.
三段论是一种经典的演绎论证，它使用两个前提来保证结论。如果前提为真且形式有效，结论必然为真。基本模式是：所有 A 是 B；所有 B 是 C；因此，所有 A 是 C。
All M are P. All S are M. ∴ All S are P.
Example: All mammals are warm-blooded. All dogs are mammals. Therefore, all dogs are warm-blooded. When you encounter a three-line argument, try mapping it to this skeleton to check its validity.
例子：所有哺乳动物都是温血动物。所有狗都是哺乳动物。因此，所有狗都是温血动物。当你遇到一个三句话的论证时，试着把它套进这个骨架来检验其有效性。
2. Modus Ponens and Modus Tollens | 肯定前件与否定后件
These two conditional argument forms appear constantly in philosophical reasoning. Modus ponens affirms the antecedent, while modus tollens denies the consequent. They are easy to learn as ‘formulas’ for moving from an if-then statement to a conclusion.
这两个条件论证形式在哲学推理中频繁出现。肯定前件（Modus ponens）肯定条件句的前件，否定后件（Modus tollens）否定条件句的后件。它们可以轻松地作为从“如果……那么……”陈述推导结论的“公式”来学习。
If P, then Q. P. So, Q. (Modus Ponens)
If P, then Q. Not Q. So, not P. (Modus Tollens)
If it is raining, the ground is wet. It is raining. Therefore, the ground is wet (modus ponens). If it is raining, the ground is wet. The ground is not wet. Therefore, it is not raining (modus tollens). Notice that denying the antecedent or affirming the consequent are logical mistakes; avoid these hidden traps.
如果下雨，地面就是湿的。正在下雨。所以，地面是湿的（肯定前件）。如果下雨，地面就是湿的。地面不是湿的。所以，没有下雨（否定后件）。注意，否定前件或肯定后件都是逻辑错误；要避开这些隐藏的陷阱。
3. Cogito Ergo Sum (Descartes’ Theorem) | 我思故我在（笛卡尔定理）
René Descartes discovered one of philosophy’s most famous ‘theorems’ while trying to doubt absolutely everything. Even if an evil demon tricks him about the world, the very act of being tricked proves he exists as a thinking thing. This reasoning can be written as a chain: Doubt -> Thought -> Existence.
勒内·笛卡尔在试图怀疑一切时发现了哲学史上最著名的“定理”之一。即使有一个邪恶的魔鬼在世界的真相上欺骗他，被欺骗这一行为本身就证明了他作为一个思考者的存在。这个推理可以写成一个链条：怀疑 → 思考 → 存在。
I am doubting. → If I am doubting, I am thinking. → If I am thinking, I exist. ∴ I exist.
Descartes’ point is that the statement ‘I do not exist’ is self-defeating: to even think it requires a thinker. This formula teaches us that some truths are so foundational they survive the most extreme scepticism. Use it when you need to anchor knowledge against doubt.
笛卡尔的要点在于，“我不存在”这个陈述是自我推翻的：哪怕只是去想它，也需要一个思考者。这个公式告诉我们，有些真理如此基础，以至于它们经得起最极端的怀疑。当你需要用知识对抗怀疑时，就可以用这个定理。
4. Ockham’s Razor | 奥卡姆剃刀
Ockham’s Razor is not a physical blade but a principle of simplicity: when you have multiple explanations for the same thing, choose the one that makes the fewest new assumptions. It is often phrased as ‘Entities should not be multiplied beyond necessity’. Think of it as a cost-cutting rule for ideas.
奥卡姆剃刀不是一把真实的刀，而是一条简洁性原则：当对同一事物有多种解释时，选择那个需要最少新假设的解释。它常被表述为“若无必要，勿增实体”。可以把它看作一条给想法削减成本的原则。
Explanation A vs B: if A assumes less, prefer A until evidence forces more complexity.
If your lost homework could be explained by ‘a ghost ate it’ or ‘you left it on the bus’, Ockham’s razor slices away the ghost because that story adds an extra, unnecessary thing. Philosophers use this razor to debate the existence of abstract objects, God, and other minds.
如果你的作业丢了，可能的解释是“被幽灵吃掉了”或者“你把它落在了公交车上”，那么奥卡姆剃刀会切掉幽灵的说法，因为那个说法增添了一个不必要的额外事物。哲学家们用这把剃刀来辩论抽象对象、上帝和其他心灵的存在。
5. Hume’s Fork and the Is-Ought Gap | 休谟的叉子与“实然-应然”鸿沟
David Hume divided all knowledge into two prongs: relations of ideas (logical truths, like mathematics) and matters of fact (based on experience). He also spotted that you cannot logically jump from describing how things are (an ‘is’) to prescribing how they ought to be (an ‘ought’). This gap is a core formula in ethics.
大卫·休谟将所有知识分为两叉：观念的关系（如数学这类逻辑真理）与事实（基于经验）。他还发现，你无法从描述事物是怎样的（“实然”）直接跳到规定事物应当怎样（“应然”）。这种鸿沟是伦理学中的核心公式。
‘Is’ + no extra value premise ≠ ‘Ought’
For example, ‘Humans feel pain when hurt’ is an ‘is’ statement. It does not by itself give you ‘Therefore, you ought not to hurt others’. You must add a hidden value premise like ‘causing pain is wrong’. Whenever you hear a moral conclusion, check if someone has silently crossed the is-ought gap.
例如，“人受伤时会感到疼痛”是一个“实然”陈述。它本身并不能给你“因此，你不应当伤害他人”。你必须加上一个隐藏的价值前提，比如“造成痛苦是错误的”。每当你听到一个道德结论时，检查一下是否有人悄悄跨过了实然-应然鸿沟。
6. The Utilitarian Calculus | 功利主义计算公式
Utilitarianism, proposed by Jeremy Bentham and John Stuart Mill, judges actions by their consequences. The ‘formula’ is surprisingly mathematical: calculate the total pleasure (or happiness) an action produces and subtract the total pain; the action with the highest net utility wins. It is a balance sheet of well-being.
由杰里米·边沁和约翰·斯图尔特·密尔提出的功利主义根据后果来评判行为。其“公式”出奇地数学化：计算一个行为产生的总快乐（或幸福）并减去总痛苦；净效用最高的行为就是正确的选择。这是一张关于福祉的资产负债表。
Net Utility = Sum of Pleasure – Sum of Pain (for all affected)
In the famous trolley problem, pulling a lever to sacrifice one person and save five has a high positive net utility if we only weigh lives. But Bentham also considered intensity, duration, certainty and extent of pleasure. Always ask: whose happiness counts, and can suffering ever be cancelled out by others’ joy?
在著名的电车难题中，扳一下拉杆牺牲一人救五人，如果只计算生命数量，就会得出很高的正净效用。但边沁还考虑了快乐的强度、持续时间、确定性和范围。要永远追问：谁的幸福算数，而一个人的痛苦真的能被别人的快乐抵消吗？
7. Kant’s Categorical Imperative (Formula of Universal Law) | 康德的定言命令（普遍法则公式）
Immanuel Kant’s moral ‘formula’ tests whether a personal rule (maxim) can become a universal law without contradiction. Act only on that maxim which you can at the same time will that it should become a universal law. This shifts ethics from consequences to the rational structure of the rule itself.
伊曼努尔·康德的道德“公式”测试一个个人的行事准则（格准）能否不自相矛盾地成为一条普遍法则。你要只按照你同时能够意愿它成为一条普遍法则的那种格准去行动。这把伦理学从看重后果转向了规则本身的理性结构。
Maxim → Can it be universalised without contradiction? Yes: permissible; No: impermissible.
Consider the maxim ‘I will make a false promise when it suits me’. If everyone did that, the very practice of promising would collapse because nobody would trust a promise. A contradiction arises in the concept, so the maxim fails Kant’s test. This formula helps you distinguish right from duty, not from results.
考虑这个格准：“当对我有利时，我会做出虚假的承诺”。如果每个人都这么做，承诺这件事本身就会崩溃，因为没人会再相信承诺。在这个概念中就产生了矛盾，所以这个格准通不过康德的测试。这个公式帮助你从义务而非结果中辨别对错。
8. The Free Will Defence | 自由意志辩护
A pressing philosophical ‘equation’ appears in the problem of evil: if God is all-powerful and perfectly good, evil should not exist. The free will defence adds a term: morally significant free will is such a great good that it justifies allowing the possibility of evil. The formula becomes: God’s existence + free will → evil is possible.
在恶的问题中出现了一个紧迫的哲学“方程式”：如果上帝全能且全善，恶就不应该存在。自由意志辩护加入了一项内容：具有道德意义的自由意志是如此重大的善，以至于它为允许恶存在的可能性提供了理由。这个公式便成了：上帝存在 + 自由意志 → 恶是可能的。
Greater good (free will) morally outweighs the evil that creatures bring about.
If we were pre-programmed to always choose good, we would be like robots and not truly moral beings. The risk of evil is the price for genuine love and virtue. Many philosophers debate whether this defence works for natural evil like earthquakes, which do not result from human choices.
如果我们被预编程为始终选择善良，我们就会像机器人一样，而不是真正的道德存在者。恶的风险是为真正的爱与美德付出的代价。很多哲学家都在辩论这个辩护能否解释像地震这样的自然恶，这些恶并非由人的选择造成。
9. The Ontological Argument (Simplified) | 本体论论证（简化版）
Anselm of Canterbury proposed a daring ‘formula’ to prove God’s existence from the definition alone. He defined God as ‘that than which nothing greater can be conceived’. Then he argued that a being that exists in reality is greater than one that exists only in the mind, so God must exist in reality.
坎特伯雷的安瑟伦提出了一个大胆的“公式”，仅从定义出发来证明上帝存在。他将上帝定义为“那无法设想有比之更伟大的存在者”。然后他论证说，在现实中存在的存在者比只存在于心灵中的存在者更伟大，因此上帝必然在现实中存在。
God = the greatest conceivable being; existence is a greatness-making property; ∴ God exists.
Gaunilo cleverly countered by running the same formula on a ‘perfect island’: the greatest conceivable island must exist, or it wouldn’t be the greatest. This parody shows that the formula might license too much unless we can explain why the concept of God is special.
高尼罗巧妙地用同一个公式反怼了“完美岛屿”：那可以设想的最伟大的岛屿必须存在，否则它就不是最伟大的了。这个戏仿表明，这个公式可能允许太多的东西存在，除非我们能解释上帝的概念为何特殊。
10. The Trolley Problem Formula | 电车难题公式
The trolley problem is a thought experiment that reveals a conflict between two ethical formulas: the utilitarian calculus (save the greater number) and the deontological rule (do not use a person as mere means). It asks whether you should push a large man off a bridge to stop a runaway trolley from killing five.
电车难题是一个思想实验，它揭示了两条伦理公式之间的冲突：功利主义的计算（救更多的人）与道义论规则（不把人仅仅当作手段）。它问的是，你是否应该把一个胖子从桥上推下去，以阻止失控的电车撞死五个人。
Decision = (Utilitarian arithmetic) vs (Sacredness of direct harm)
Most people say it is permissible to pull a lever that diverts the trolley to kill one instead of five, but impermissible to push the man. The difference lies in the directness of physical force and treating a person as a tool. This puzzle trains us to look beyond raw numbers and consider the form of our actions.
大多数人认为，扳动拉杆让电车改道撞死一人来救五人，在道德上是允许的，但推人是不允许的。其区别在于体力的直接使用以及是否把人当作工具。这个难题训练我们超越纯粹的数字，去考虑我们行动的形式。
11. Logical Fallacy Spotter: Ad Hominem and Straw Man | 逻辑谬误识别器：人身攻击与稻草人
Philosophy guards against bad reasoning using fallacy formulas. An ad hominem attacks the person instead of the argument. Its structure is: ‘You are X, therefore your argument is wrong.’ A straw man misrepresents an opponent’s view to make it easier to knock down.
哲学用谬误公式来防范坏的推理。人身攻击谬误是攻击人而不是攻击论点。它的结构是：“因为你是什么样的人，所以你的论证是错的。”稻草人谬误则是歪曲对方的观点，让它更容易被击倒。
Ad Hominem: Speaker’s trait → Conclusion about argument’s truth (invalid)
Straw Man: Real argument A → distorted into B → B refuted → claim A is refuted (invalid)
During a class debate about homework, saying ‘You only say that because you are lazy’ is an ad hominem; it ignores the actual reasons. Claiming ‘You think we should never have any rules’ when someone simply suggests a later homework deadline is a straw man. Apply these detectors in every discussion.
在关于作业的课堂辩论中，说“你这么说只是因为你懒”就是一种人身攻击；它无视了真正的理由。当某人只是建议把作业截止时间延后，却被说成“你认为我们根本不需要任何规则”，这就是稻草人谬误。在每次讨论中都运用这些识别器吧。
12. The Zen Koan as a Philosophical Tool | 禅宗公案作为哲学工具
Philosophy extends beyond Western formulas. Zen koans short-circuit logical reasoning to provoke direct insight. A koan like ‘What is the sound of one hand clapping?’ does not have a correct rational answer; it is designed to break the mind’s attachment to tidy formulas and invite a different kind of understanding.
哲学并不仅仅局限于西方公式。禅宗公案通过短路逻辑推理来激发直接的洞见。像“只掌之声”这样的公案并没有一个正确的理性答案；它旨在打破心智对整齐公式的执着，并邀请一种不同的领悟。
Rational analysis → stuck → abandon formula → direct seeing
While Year 7 philosophy emphasises clear reasoning, remembering that not all wisdom fits a formula is itself a valuable theorem. After applying all the previous tools, ask yourself whether a question is genuinely analytical or whether it points toward an experiential truth that requires stillness rather than argument.
虽然 7 年级哲学强调的是清晰的推理，但记住并非所有智慧都能套用公式，这本身就是一条宝贵的定理。在运用了前面所有工具之后，问问自己，这个问题是真正分析性的，还是指向某种需要静观而非论证的体验性真理。
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