📚 Year 7 CCEA Philosophy: Formulas and Theorems Quick Reference Handbook | Year 7 CCEA 哲学：公式定理速查手册
This quick reference guide offers Year 7 students a handy collection of essential ‘formulas’ and ‘theorems’ in philosophy – from logical structures to ethical principles. Use it to revise key concepts, practise clear reasoning, and sharpen your thinking skills.
这份速查手册为 Year 7 学生整理了一组哲学中必备的“公式”和“定理”——从逻辑结构到伦理学原则。用它来复习关键概念，练习清晰推理，磨砺你的思维技能。
1. What is Philosophy? | 什么是哲学？
Philosophy comes from the Greek words philo (love) and sophia (wisdom). It means ‘love of wisdom’ and is an activity of asking big questions about existence, knowledge, values and reason.
哲学源于希腊语 philo（爱）和 sophia（智慧），意为“爱智慧”。它是一种追问关于存在、知识、价值与理性等大问题的活动。
The main branches of philosophy include logic (rules of correct thinking), ethics (how we should live), epistemology (what we can know) and metaphysics (what is ultimately real).
哲学的主要分支包括逻辑学（正确思维的规则）、伦理学（我们应如何生活）、认识论（我们能知道什么）以及形而上学（什么是终极实在）。
Philosophers do not just collect opinions; they build arguments supported by reasons. The philosopher’s ‘formula’ is: question assumptions, examine evidence, and follow the strongest argument.
哲学家并不只是收集意见；他们会用理由来构建论证。哲学家的“公式”是：质疑假设，检视证据，并追随最强的论证。
Philosophy helps us think critically about everyday life, science, law and art. It is a toolkit for exploring the world with curiosity and rigour.
哲学帮助我们批判性地思考日常生活、科学、法律和艺术。它是一个凭借好奇心和严谨性去探索世界的工具箱。
2. The Anatomy of an Argument | 论证的剖析
An argument in philosophy is a set of statements where some (premises) are offered as reasons to support another statement (the conclusion). The basic formula is: Premise₁, Premise₂, … → Conclusion.
在哲学中，一个论证是一组陈述，其中一些陈述（前提）作为理由被提出来支持另一个陈述（结论）。基本公式是：前提₁、前提₂…… → 结论。
A valid argument is one where, if the premises are true, the conclusion must be true. For example: ‘All cats are mammals; Felix is a cat; therefore, Felix is a mammal.’ The structure guarantees the conclusion.
一个有效的论证是指如果前提为真，则结论必然为真的论证。例如：“所有猫都是哺乳动物；菲利克斯是猫；因此，菲利克斯是哺乳动物。”其结构保证了结论。
A sound argument is a valid argument with all true premises. Soundness is the gold standard: we want arguments that are both logically strong and factually correct.
一个可靠的论证是一个所有前提都为真的有效论证。可靠性是黄金标准：我们想要的论证既要在逻辑上强而有力，又要在事实上正确。
When evaluating an argument, always ask two questions: (1) Are the premises true? (2) Does the conclusion follow logically? This is your argument-checking formula.
评价一个论证时，始终问两个问题：（1）前提为真吗？（2）结论在逻辑上能必然推出吗？这就是你的论证检验公式。
3. Logical Connectives | 逻辑连接词
In propositional logic, simple statements can be combined using special symbols called connectives. These act like mathematical operators, letting us build complex formulas.
在命题逻辑中，简单的陈述可以用被称为连接词的特殊符号组合起来。它们就像数学运算符一样，让我们能构建复杂的公式。
| Symbol | Name / 名称 | Meaning / 意义 | Example / 例子 |
|---|---|---|---|
| ∧ | Conjunction (and) / 合取 | Both parts true / 两部分都真 | P ∧ Q: ‘It rains’ ∧ ‘It is cold’ / “下雨”且“天冷” |
| ∨ | Disjunction (or) / 析取 | At least one part true / 至少一部分为真 | P ∨ Q: ‘You can have tea’ ∨ ‘You can have coffee’ / “你可以喝茶”或“你可以喝咖啡” |
| ¬ | Negation (not) / 否定 | Reverses truth value / 反转真值 | ¬P: ‘It is not raining’ / “并非下雨” |
| → | Conditional (if…then) / 条件 | If antecedent true, consequent true / 如果前件真，则后件真 | P → Q: ‘If it rains, then the ground is wet’ / “如果下雨，那么地面湿” |
| ↔ | Biconditional (iff) / 双条件 | Both parts have same truth value / 两部分同真或同假 | P ↔ Q: ‘A shape is a square iff it has four equal sides and four right angles’ / “一个图形是正方形当且仅当它有四条等边和四个直角” |
Remember, the conditional P → Q does not assert that P causes Q; it only means that if P is true, Q cannot be false. This is the truth-functional view of ‘if’.
请记住，条件式 P → Q 并不断言 P 导致 Q；它仅仅意味着如果 P 为真，则 Q 不会为假。这就是“如果”的真值函项观点。
You can use truth tables to test whether a complex formula is always true (a tautology). The table systematically checks all possible truth values of the simple statements.
你可以用真值表来检验一个复合公式是否恒真（重言式）。真值表系统地核查简单陈述所有可能的真值组合。
4. The Syllogism | 三段论
A syllogism is a classic form of deductive reasoning consisting of two premises and a conclusion, each expressing a relationship between categories. It was formalised by Aristotle.
三段论是一种经典的演绎推理形式，由两个前提和一个结论组成，每个陈述都表达了类别之间的关系。它由亚里士多德形式化。
All M are P
All S are M
∴ All S are P
This is the most famous valid syllogism form, often called Barbara. For example: ‘All humans are mortal; all Athenians are humans; ∴ all Athenians are mortal.’
这是最著名的有效三段论形式，常被称为 Barbara。例如：“所有人都会死；所有雅典人都是人；∴ 所有雅典人都会死。”
A syllogism is valid solely because of its logical form, not its content. Replace the terms with any categories, and if the premises are true, the conclusion must be true.
三段论仅因其逻辑形式而有效，与内容无关。将词项替换为任何类别，只要前提为真，结论就必然为真。
Watch out for common mistakes: undistributed middle (the middle term must refer to all members in at least one premise) and illicit major or minor terms. These break the syllogism’s validity.
当心常见错误：中项不周延（中项必须在至少一个前提中指称该类的所有成员），以及大项或小项非法周延。这些都会破坏三段论的有效性。
5. Common Logical Fallacies | 常见逻辑谬误
A fallacy is a mistake in reasoning that makes an argument unsound. Fallacies often look persuasive, so recognising them is like having a ‘logic safety check’.
谬误是推理中的错误，它使论证不可靠。谬误常常看起来很有说服力，因此识别它们就如同拥有一个“逻辑安全检查”。
The Straw Man fallacy misrepresents an opponent’s argument to make it easier to attack. Formula: Twist argument A into B, attack B, then claim you have refuted A.
稻草人谬误歪曲对方的论点，使之更易攻击。其公式为：把论点 A 扭曲成 B，攻击 B，然后声称驳倒了 A。
Ad Hominem (‘against the person’) attacks the person making the argument rather than the argument itself. Example: ‘You can’t believe Tom’s opinion on healthy eating – he is overweight.’
人身攻击谬误攻击的是提出论证的人，而非论证本身。例如：“你不能相信汤姆关于健康饮食的看法——他超重了。”
The False Dilemma presents only two options when more exist. It forces a choice between black and white, ignoring shades of grey. Formula: ‘Either you agree with me, or you are against progress.’
虚假两难谬误在存在更多选项时只给出两个选项。它迫使人们在黑白之间选择，忽略了灰色地带。公式为：“要么你同意我，要么你反对进步。”
Slippery Slope assumes that a first step will inevitably lead to a chain of extreme, bad consequences without evidence. Always ask: Is each step really bound to happen?
滑坡谬误假定第一步将不可避免地导致一连串极端的糟糕后果，却不提供证据。始终要问：每一步真的必然会发生吗？
6. The Golden Rule | 黄金法则
The Golden Rule is a foundational ethical principle found in many cultures and religions. Its simplest formula is: treat others as you would like to be treated.
黄金法则是在众多文化与宗教中都能找到的一条基础伦理原则。它最简单的公式是：你希望别人怎样对待你，你就怎样对待别人。
In its negative form, it says: do not do to others what you would not want done to yourself. This encourages empathy and serves as a quick moral compass.
其否定形式说：己所不欲，勿施于人。这鼓励同理心，并充当一个快速的道德指南针。
Philosophers see the Golden Rule as a principle of consistency: you should not make an exception of yourself. If you think it is wrong for others to lie, then you should also not lie.
哲学家将黄金法则视为一项一致性原则：你不应把自己当作例外。如果你认为他人说谎是错误的，那么你也不应该说谎。
While the Golden Rule is helpful, it assumes everyone wants the same treatment. A refined ‘formula’ is: treat others as they would rationally want to be treated, considering their interests.
尽管黄金法则很有帮助，但它假定每个人想要的对待都一样。一个经过提炼的“公式”是：考虑他人的利益，按照他们合理希望被对待的方式去对待他们。
7. The Utilitarian Principle | 功利主义原理
Utilitarianism is an ethical theory that judges actions by their consequences. The central formula, proposed by Jeremy Bentham, is: the right action produces the greatest happiness for the greatest number.
功利主义是一种根据后果来评判行为的伦理学理论。其由边沁提出的中心公式是：正确的行为能为最大多数人带来最大幸福。
Happiness is understood as pleasure and the absence of pain. Bentham even proposed a ‘felicific calculus’ to measure pleasure using factors like intensity, duration and certainty.
幸福被理解为快乐以及痛苦的缺失。边沁甚至提出了一个“幸福计算法”，通过强度、持续时间和确定性等因素来度量快乐。
John Stuart Mill refined the theory by distinguishing higher pleasures (intellectual, moral) from lower pleasures (purely physical). He argued it is ‘better to be Socrates dissatisfied than a fool satisfied’.
约翰·斯图尔特·密尔通过区分高级快乐（智力、道德）与低级快乐（纯肉体）来改进这个理论。他主张“宁愿做不满足的苏格拉底，也不做满足的傻瓜”。
When applying the utilitarian formula, always ask: who is affected, how much pleasure or pain will likely result, and are there any long-term effects? This keeps the calculus practical.
应用功利主义公式时，始终要问：谁会受到影响，可能产生多少快乐或痛苦，以及是否有长期效应？这使计算保持实际可行。
8. Knowledge as Justified True Belief | 知识即经过辩护的真信念 (JTB)
In epistemology, the traditional ‘formula’ for knowledge is JTB: Knowledge = Justified True Belief. A person S knows that P if and only if S believes P, P is true, and S has justification for believing P.
在认识论中，传统的知识“公式”是 JTB：知识 = 经过辩护的真信念。一个人 S 知道命题 P，当且仅当 S 相信 P，P 为真，并且 S 有相信 P 的辩护理由。
Belief alone is not enough – you might believe a lucky guess. Truth is needed so that knowledge reflects reality. Justification ensures your belief is not merely accidental.
仅有信念是不够的——你可能只是侥幸猜中。需要真理来让知识反映实在。辩护则确保你的信念不是偶然的。
Philosopher Edmund Gettier challenged the JTB model by constructing cases where someone has a justified true belief that still seems not to be knowledge. These are called Gettier problems.
哲学家埃德蒙·盖梯尔通过构建某人拥有经过辩护的真信念却似乎仍不构成知识的案例，挑战了 JTB 模型。这些被称为盖梯尔问题。
Because of Gettier cases, many philosophers now add a fourth condition, such as ‘no false lemmas’ or ‘the belief is reliably formed’. The quest for a perfect knowledge formula continues!
由于盖梯尔案例，许多哲学家现在添加了第四个条件，比如“没有虚假引理”或“信念是可靠地形成的”。对完美知识公式的追寻仍在继续！
9. Descartes’ Cogito | 笛卡尔的“我思故我在”
René Descartes set out to find something absolutely certain. He used the method of radical doubt, asking: what can I know if a powerful evil demon is deceiving me about everything?
勒内·笛卡尔试图找到某种绝对确定的东西。他使用了彻底怀疑的方法，追问：如果一个强大的恶魔在一切事情上欺骗我，我还能知道什么？
His breakthrough ‘formula’ is Cogito, ergo sum – ‘I think, therefore I am’ (or more precisely, ‘I am thinking, therefore I exist’). Even if I am being deceived, I must exist to be deceived.
他的突破性“公式”是 Cogito, ergo sum——“我思故我在”（更确切地说，“我正在思考
Published by TutorHao | Year 7 哲学 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