📚 Year 8 Cambridge Philosophy: Formula & Theorem Quick Reference | 剑桥8年级哲学：公式定理速查手册
This quick reference guide collects the essential ‘formulas’ and ‘theorems’ of reasoning, logic, and philosophical argument for Year 8 Cambridge Philosophy students. Instead of equations with numbers, you will find patterns of valid reasoning, common fallacies, ethical principles, and conceptual tools that act just like formulas in mathematics — once you learn them, solving philosophical problems becomes much easier.
这份速查手册为剑桥8年级哲学学生整理了推理、逻辑和哲学论证的核心“公式”与“定理”。这里没有数字方程，取而代之的是有效推理模式、常见谬误、伦理原则以及概念工具，它们就像数学公式一样——一旦掌握，解决哲学问题会变得轻松许多。
1. Deductive Reasoning: The Certainty Formula | 演绎推理：确定性的公式
Deductive arguments aim to provide a guarantee of truth. The basic formula is: if the premises are true, the conclusion must be true. This is called a valid argument.
演绎论证旨在确保结论必然为真。基本公式是：如果前提为真，则结论必然为真。这称为有效论证。
One common valid form is Modus Ponens: If P then Q; P; therefore Q.
最常见的有效形式是肯定前件式：如果P则Q；P成立；因此Q成立。
Another is Modus Tollens: If P then Q; Not Q; therefore Not P.
还有否定后件式：如果P则Q；非Q；因此非P。
A deductive argument that is both valid and has all true premises is called sound.
一个演绎论证如果既有效且所有前提为真，则称为可靠的。
2. Inductive Reasoning: The Probability Formula | 归纳推理：概率的公式
Inductive arguments do not guarantee truth; they make the conclusion likely. The strength depends on the evidence.
归纳论证不保证结论必然为真，而是使结论很可能成立。其强度取决于证据。
A typical inductive formula: observed pattern X has held in all past cases; therefore X will likely hold in the next case.
典型的归纳公式：观察到的模式X在过去所有情况下都成立；因此X很可能在下一个情况中也成立。
The more representative and larger the sample, the stronger the inductive inference.
样本越具代表性且越大，归纳推理就越强。
Philosophers such as David Hume questioned whether inductive reasoning can ever be rationally justified — a problem known as the ‘Problem of Induction’.
像大卫·休谟这样的哲学家质疑归纳推理能否得到理性辩护——这被称为“归纳问题”。
3. Logical Validity and Soundness: The Quality Check | 逻辑有效性与可靠性：质量检验
Validity is about the form: an argument is valid if the conclusion follows logically from the premises. It does not require the premises to be true.
有效性关乎形式：如果结论在逻辑上从前提得出，论证就是有效的。这并不要求前提本身为真。
Soundness = validity + all true premises. A sound argument guarantees a true conclusion.
可靠性 = 有效性 + 所有前提为真。一个可靠的论证保证结论为真。
Many philosophical debates involve accepting the validity of an opponent's reasoning but challenging the truth of a premise. This is like checking a mathematical calculation and finding a wrong input value.
许多哲学辩论涉及承认对方推理的有效性，但质疑某个前提的真实性。这就像检查数学计算并发现输入值有误。
4. Common Fallacies: Error Patterns to Avoid | 常见谬误：需避免的错误模式
Fallacies are reasoning formulas that are invalid or misleading. Recognising them helps you avoid faulty arguments.
谬误是无效或误导性的推理公式。识别它们有助于避免错误论证。
Ad Hominem: attacking the person instead of the argument.
人身攻击：攻击人而非论点。
Straw Man: misrepresenting an opponent's view to make it easier to attack.
稻草人：歪曲对方观点以便更容易攻击。
False Dilemma: presenting only two options when more exist.
假两难：只给出两个选项，而实际上更多。
Slippery Slope: assuming a small step will lead to extreme consequences without justification.
滑坡谬误：假设一小步会导致极端后果而无合理依据。
Think of these as ‘error formulas’ — once memorised, they become easy to spot in everyday reasoning.
将它们视为“错误公式”——一旦记住，就能在日常推理中轻松发现。
5. Thought Experiment: The Imagination Laboratory | 思想实验：想象实验室
A thought experiment is a structured imaginative scenario used to test philosophical concepts. Its formula: ‘What if X happened? Would Y still be true?’
思想实验是用来检验哲学概念的结构化想象场景。其公式是：“如果X发生，Y还成立吗？”
Famous examples include the trolley problem (ethics), Plato’s cave (reality and knowledge), and the brain in a vat (scepticism).
著名例子包括电车难题（伦理学）、柏拉图的洞穴（实在与知识）和缸中之脑（怀疑论）。
When constructing or analysing a thought experiment, identify the variables being changed and the intuition being tested. It works like a controlled experiment, but in the mind.
在构建或分析思想实验时，要识别正在改变的变量和正在测试的直觉。它就像受控实验，只不过是在头脑中进行。
6. Ethical Theories: The Morality Formulas | 伦理学理论：道德公式
Ethical theories provide frameworks for deciding right and wrong. Each is like a different formula for calculating moral value.
伦理理论为判断对错提供了框架。每种理论都像计算道德价值的不同公式。
Utilitarianism: maximise overall happiness. Act so as to produce the greatest good for the greatest number.
功利主义：最大化总体幸福。行动以使最大多数人获得最大利益为标准。
Deontology: follow moral rules or duties regardless of consequences. The Categorical Imperative: Act only according to that maxim whereby you can at the same time will that it should become a universal law.
义务论：遵守道德规则或义务，不论后果。绝对命令：只按照你同时愿意它成为普遍法则的准则去行动。
Virtue Ethics: develop good character traits (virtues) such as courage, honesty, and kindness. Right action is what a virtuous person would do.
德性伦理：培养良好品格特征（德性），如勇敢、诚实和仁慈。正当的行为是有德之人会做的行为。
7. Epistemology: The Knowledge Formula | 知识论：知识的公式
The classic definition of knowledge is justified true belief (JTB): S knows that P if and only if (1) P is true, (2) S believes that P, and (3) S is justified in believing that P.
知识的经典定义是确证的真信念（JTB）：S知道P，当且仅当（1）P为真，（2）S相信P，并且（3）S有理由相信P。
Gettier cases challenged this formula by showing situations where someone has a justified true belief but still seems not to know. This shows that the formula might need extra conditions.
葛梯尔案例挑战了这个公式，展示了某人持有一个确证的真信念却似乎仍不算知道的情形。这表明该公式可能需要额外条件。
The sceptical formula: ‘Is it possible that I am dreaming / a brain in a vat? If so, I cannot be absolutely certain of anything.’ This pushes us to examine the limits of knowledge.
怀疑论的公式：“我是否可能在梦中/是缸中之脑？如果是，我就无法对任何事情绝对确定。”这促使我们审视知识的界限。
8. Metaphysics: The Reality Formulas | 形而上学：实在的公式
Metaphysics explores the nature of reality. Key formulas include the problem of identity over time: ‘If all parts of a ship are replaced, is it still the same ship?’ This is known as the Ship of Theseus.
形而上学探讨实在的本性。关键公式包括历时同一性问题：“如果一艘船的所有部件都被更换了，它还是同一艘船吗？”这被称为忒修斯之船。
Another formula is the mind-body problem: ‘How do mental states (thoughts, feelings) relate to physical states (brain processes)?’ Dualism and physicalism are two contrasting answers.
另一个公式是心身问题：“心理状态（思想、情感）与物理状态（大脑过程）如何关联？”二元论和物理主义是两种对立的回答。
Free will vs. determinism: ‘If every event has a cause, can we ever act freely?’ Compatibilists reformulate freedom to fit a deterministic world.
自由意志与决定论：“如果每个事件都有原因，我们还能自由行动吗？”相容论者重新表述自由以使其适应决定论的世界。
9. Philosophy of Religion: The God Arguments | 宗教哲学：关于上帝的论证
Arguments for God's existence often follow set patterns. The Teleological Argument (design argument): ‘The universe shows order and purpose; order implies a designer; therefore the universe has a designer.’
上帝存在的论证通常遵循固定模式。目的论论证（设计论证）：“宇宙显示出秩序与目的；秩序意味着设计者；因此宇宙有一个设计者。”
The Cosmological Argument: ‘Everything that begins to exist has a cause; the universe began to exist; therefore the universe has a cause.’ This cause is identified as God.
宇宙论论证：“凡开始存在的事物都有原因；宇宙开始存在；因此宇宙有一个原因。”这个原因被认定为上帝。
The Problem of Evil is a counter-formula: ‘If God is all-powerful and all-good, why does evil exist? Either God is not all-powerful, or not all-good, or does not exist.’
恶的问题是一个反公式：“如果上帝全能全善，为什么存在恶？要么上帝不全能，要么不全善，要么不存在。”
10. Philosophy of Science: Scientific Method Formulas | 科学哲学：科学方法公式
Science uses a blend of induction and deduction. The hypothetico-deductive method: (1) Form a hypothesis H; (2) Deduce observable consequence O: If H then O; (3) Test whether O occurs; (4) If O occurs, H is supported (not proven); if O does not occur, H is falsified.
科学运用归纳与演绎的结合。假说演绎法：（1）形成假说H；（2）推断可观察后果O：如果H则O；（3）检验O是否发生；（4）如果O发生，H得到支持（未被证明）；如果O不发生，H被证伪。
Falsifiability, proposed by Karl Popper, is the idea that for a theory to be scientific, there must be a possible observation that could prove it wrong.
可证伪性，由卡尔·波普尔提出，是指一个理论要成为科学的，必须存在可能的观察能证明它是错的。
11. Political Philosophy: The Social Contract Formulas | 政治哲学：社会契约公式
Social contract theories imagine life without government to justify political authority. Thomas Hobbes’ formula: In the state of nature, life is ‘solitary, poor, nasty, brutish, and short’; rational individuals agree to surrender freedom to a sovereign for security.
社会契约理论想象无政府状态下的生活以证成政治权威。托马斯·霍布斯的公式：在自然状态下，生活“孤独、贫困、卑污、残忍而短寿”；理性个体同意将自由交给主权者以换取安全。
John Locke’s formula: individuals have natural rights to life, liberty, and property; government is created to protect these rights; if it fails, people may resist.
约翰·洛克的公式：个体拥有生命、自由和财产的自然权利；政府为保护这些权利而建立；若政府失职，人民可以反抗。
John Rawls’ ‘veil of ignorance’ is a formula for justice: design society without knowing your own position in it, ensuring fairness for all.
约翰·罗尔斯的“无知之幕”是正义的公式：在不了解自己在社会中位置的情况下设计社会，确保对所有人公平。
12. Critical Thinking Toolkit: Analysis Formulas | 批判性思维工具包：分析公式
When evaluating any argument, apply the following checklist formula:
评估任何论证时，应用以下检查清单公式：
- Identify the conclusion. / 确定结论。
- List the premises. / 列出前提。
- Check for hidden assumptions. / 检查隐含假设。
- Test logical structure: is it valid/strong? / 检验逻辑结构：是否有效/强？
- Evaluate premise truth. / 评估前提的真假。
- Look out for fallacies. / 警惕谬误。
- Consider counterexamples. / 考虑反例。
This structured approach turns philosophical analysis into a repeatable procedure, much like solving an equation.
这种结构化的方法将哲学分析变成可重复的程序，就像解方程一样。
Published by TutorHao | Philosophy Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图