📚 Quick-Reference Guide to Philosophical Formulas and Theorems | 七年级爱德思哲学：公式定理速查手册
Welcome to your quick-reference guide for philosophical formulas and key principles. This guide compiles logical rules, ethical principles, and epistemological formulas that are essential for Year 7 Edexcel Philosophy. Use it to sharpen your reasoning, evaluate arguments, and make well-founded ethical decisions. Each entry is presented as a concise 'formula' you can learn and apply.
欢迎使用哲学公式与核心原理速查手册。本手册汇编了七年级爱德思哲学中必备的逻辑规则、伦理原则和认识论公式。你可以利用它来提升推理能力、评估论证并做出有理有据的伦理决策。每一条都以简明的“公式”形式呈现，方便记忆与应用。
1. Propositional Logic Symbols | 命题逻辑符号
These symbols are the building blocks of logical formulas. Each connects simple statements (P, Q) into complex arguments.
这些符号是逻辑公式的基石，每个都能将简单陈述（P, Q）组合成复杂的论证。
| Symbol | Meaning | Example |
|---|---|---|
| ¬ | Not / negation | ¬P (It is not raining) |
| ∧ | And / conjunction | P ∧ Q (It is raining and cold) |
| ∨ | Or / disjunction | P ∨ Q (Either it rains or it snows) |
| → | If...then / implication | P → Q (If it rains, the ground is wet) |
| ↔ | If and only if / biconditional | P ↔ Q (You pass iff you score above 50%) |
Learning these symbols is like learning the alphabet of philosophical reasoning. They will appear in many formulas throughout this guide.
学会这些符号就像学会了哲学推理的字母表。它们将出现在本手册的许多公式中。
2. Modus Ponens (MP) | 肯定前件式
Modus Ponens is a valid argument form: if a conditional is true and its antecedent is true, then the consequent must be true.
肯定前件式是一种有效论证形式：若条件句为真且其前件为真，则后件必然为真。
P → Q, P ∴ Q
Example: If Socrates is a human (P), then he is mortal (Q). Socrates is a human. Therefore, Socrates is mortal.
示例：如果苏格拉底是人（P），那么他会死（Q）。苏格拉底是人。因此，苏格拉底会死。
3. Modus Tollens (MT) | 否定后件式
Modus Tollens is another valid pattern: if the conditional is true and the consequent is false, the antecedent must be false.
否定后件式是另一种有效形式：若条件句为真且后件为假，则前件必定为假。
P → Q, ¬Q ∴ ¬P
Example: If the lamp had been plugged in (P), it would light (Q). The lamp does not light (¬Q). Therefore, it is not plugged in (¬P).
示例：如果台灯插上电了（P），它就会亮（Q）。台灯不亮（¬Q）。因此，它没插电（¬P）。
4. Hypothetical Syllogism (HS) | 假言三段论
This rule chains two conditionals: if the first leads to the second, and the second leads to the third, then the first leads to the third.
这条规则将两个条件句串联起来：若第一个推出第二个，第二个推出第三个，则第一个推出第三个。
P → Q, Q → R ∴ P → R
Example: If it rains (P), the picnic is cancelled (Q). If the picnic is cancelled (Q), we will go to the cinema (R). Therefore, if it rains, we will go to the cinema.
示例：如果下雨（P），野餐取消（Q）。如果野餐取消（Q），我们就去看电影（R）。因此，如果下雨，我们就去看电影。
5. Disjunctive Syllogism (DS) | 选言三段论
When you have an 'or' statement and you know one option is false, the other must be true.
当你有一个“或”陈述，并且知道其中一项为假时，另一项必然为真。
P ∨ Q, ¬P ∴ Q
Example: Either the keys are on the table (P) or in the bag (Q). They are not on the table (¬P). Therefore, they are in the bag.
示例：钥匙要么在桌上（P），要么在包里（Q）。钥匙不在桌上（¬P）。因此，钥匙在包里。
6. Double Negation (DN) | 双重否定律
Double negation states that a statement and its double negation are logically equivalent. It allows you to add or remove a pair of negations.
双重否定律指出，一个陈述与其双重否定在逻辑上等价。你可以添加或移除一对否定符号。
¬¬P ↔ P
Example: 'It is not true that I do not like pizza' (¬¬P) means the same as 'I like pizza' (P).
示例：“不是我不喜欢披萨”（¬¬P）与“我喜欢披萨”（P）意思相同。
7. Laws of Thought | 思维三定律
These three classical laws form the bedrock of rational thinking. They are often treated as foundational axioms in philosophy.
这三条经典定律构成了理性思考的基石，在哲学中常被视作基础公理。
Law of Identity (同一律): P = P. A thing is what it is. A tree is a tree.
同一律: P = P。事物就是其自身。树就是树。
Law of Noncontradiction (矛盾律): ¬(P ∧ ¬P). Nothing can both be and not be at the same time and in the same respect.
矛盾律: ¬(P ∧ ¬P)。在同一时间、同一方面，任何东西都不能既存在又不存在。
Law of Excluded Middle (排中律): P ∨ ¬P. Every statement must be either true or false; there is no middle ground.
排中律: P ∨ ¬P。每个陈述非真即假，没有中间状态。
8. Utilitarian Formula: The Greatest Happiness Principle | 功利主义公式：最大幸福原则
Jeremy Bentham' produces the greatest happiness for the greatest number. Happiness = pleasure minus pain.
边沁的功利主义可表达为一个决策公式：如果一种行为能为最大多数人带来最大幸福，它就是正确的。幸福 = 快乐 - 痛苦。
Moral worth = ∑(Pleasure) - ∑(Pain) evaluated for all affected
When choosing between actions, calculate the total net happiness for everyone involved. Choose the action with the highest net happiness.
在不同行动之间选择时，计算所有相关者的净幸福总和。选择能产生最高净幸福的行为。
9. Kant's Formula of Universal Law | 康德的普遍法则公式
Kant's categorical imperative provides a logical test for moral principles: act only according to that maxim whereby you can at the same time will that it should become a universal law.
康德的定言令式提供了一种对道德原则的逻辑检验：只按照你同时愿意它成为普遍法则的准则去行动。
If the maxim 'I will do X' can be universalised without contradiction, then X is permissible.
Example: Is it acceptable to make a false promise? Imagine a world where everyone made false promises. Promises would cease to exist – a contradiction. Therefore, false promises are impermissible.
示例：许假诺可以接受吗？想象一个所有人都许假诺的世界，承诺本身将不复存在——这是一个矛盾。因此，许假诺是不被允许的。
10. Descartes' Cogito Formula | 笛卡尔的“我思故我在”公式
Descartes' foundational principle of knowledge is 'Cogito, ergo sum' – I think, therefore I am. He used this as the first indubitable truth after doubting everything.
笛卡尔的知识根基原则是“Cogito, ergo sum”——我思故我在。他在怀疑一切之后，将这一点当作第一个无可置疑的真理。
If I am doubting (thinking), then I must exist. D → E, D ∴ E
The act of doubting proves the existence of a thinking self. Even if an evil demon deceives me, I must exist to be deceived.
怀疑的行为证明了一个思考着的自我的存在。即便有邪恶的魔鬼在欺骗我，我也必须存在才能被欺骗。
11. The Hypothetico-Deductive Method | 假设演绎法
This is the formula of scientific reasoning proposed by Karl Popper and others. A hypothesis is tested by deducing an observable prediction and then checking if it is true.
这是卡尔·波普尔等人提出的科学推理公式。通过从假说演绎出可观察的预测，再检验其真伪来进行验证。
If hypothesis H is true, then prediction P will occur. ¬P occurs. ∴ H is false. (Modus Tollens)
A genuine scientific theory must be falsifiable. We can never prove a hypothesis, only fail to falsify it – it stands as tentatively accepted.
一个真正的科学理论必须具有可证伪性。我们永远无法证明一个假说，只能未能否证它——它只是暂时被接受。
12. Common Logical Fallacy Formulas | 常见逻辑谬误公式
Logical fallacies are errors in reasoning that can make an argument invalid. Recognising their patterns helps you avoid being misled.
逻辑谬误是推理中的错误，会让论证无效。识别它们的模式有助于你避免被误导。
Ad Hominem (诉诸人身): Rejecting an argument by attacking the person, not the claim. Form: Person A says X, Person A is bad, therefore X is false. (Invalid)
诉诸人身: 通过攻击人来否定其主张。形式：甲说X，甲有缺点，因此X为假。（无效）
Straw Man (稻草人): Misrepresenting an opponent's position to make it easier to attack. Form: Person A says X, you distort it to Y, then attack Y, claiming you have refuted X.
稻草人: 歪曲对方的立场以便更容易攻击。形式：甲说X，你把它歪曲成Y，攻击Y，然后声称驳倒了X。
False Dilemma (假两难): Presenting only two options when more exist. Form: Either A or B must be true; A is false, so B is true – ignoring C, D, etc.
假两难: 只给出两个选项，而实际存在更多。形式：要么A成立，要么B成立；A不成立，因此B成立——忽略C、D等。
Every time you analyse an argument, scan it for these fallacy formulas to check if the reasoning is sound.
每次分析一个论证时，扫一眼这些谬误公式，看看推理是否可靠。
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