📚 Year 9 WJEC Philosophy: Key Philosophical Formulas & Theorems Cheat Sheet | WJEC九年级哲学：公式定理速查手册
Philosophy, like mathematics, has its own set of 'formulas' and 'theorems'. These are not calculations with numbers, but logical structures and principles that guide clear thinking and ethical decision-making. This cheat sheet presents essential philosophical formulas in a quick-reference format for Year 9 WJEC students.
哲学与数学一样，也有自己的“公式”和“定理”。它们不是数字运算，而是指导清晰思维和伦理决策的逻辑结构与原则。这份速查手册为 WJEC 九年级学生提供了基本的哲学公式，便于快速查阅。
1. What is an Argument? | 什么是论证？
A philosophical argument is a set of statements where some statements (premises) are offered as reasons to support another statement (conclusion). It is not a quarrel but a reasoned chain. The basic structure can be expressed as a simple formula.
哲学论证是一组陈述，其中一些陈述（前提）被提供作为支持另一个陈述（结论）的理由。它不是争吵，而是一个推理的链条。基本结构可以用一个简单的公式表达。
Premise 1 + Premise 2 + ... + Premise n → Conclusion
前提 1 + 前提 2 + ... + 前提 n → 结论
Example: (P1) All humans are mortal. (P2) Socrates is human. (C) Therefore, Socrates is mortal.
例子：(前提1) 所有人都会死。(前提2) 苏格拉底是人。(结论) 因此，苏格拉底会死。
2. Deductive Arguments: Modus Ponens and Modus Tollens | 演绎论证：肯定前件式与否定后件式
Deductive arguments aim to guarantee the truth of the conclusion if the premises are true. Two key valid forms act like foolproof logical equations.
演绎论证旨在保证如果前提为真，结论必然为真。两种关键有效形式就像可靠的逻辑方程式。
Modus Ponens: P → Q, P ∴ Q
肯定前件式：如果 P 则 Q，P，因此 Q。
Example: If it rains (P), the ground gets wet (Q). It rains. Therefore, the ground gets wet.
例如：如果下雨 (P)，地面会湿 (Q)。下雨了。因此，地面湿了。
Modus Tollens: P → Q, ¬Q ∴ ¬P
否定后件式：如果 P 则 Q，非 Q，因此非 P。
Example: If the cake is baked (P), the kitchen smells sweet (Q). The kitchen does not smell sweet (¬Q). Therefore, the cake is not baked (¬P).
例如：如果蛋糕烤好了 (P)，厨房闻起来香甜 (Q)。厨房没有闻起来香甜 (¬Q)。因此，蛋糕没有烤好 (¬P)。
3. Inductive Reasoning | 归纳推理
Induction draws probable conclusions from patterns in experience. The more evidence, the stronger the argument, but it never reaches absolute certainty. The inductive formula captures this generalising leap.
归纳法从经验模式中得出很可能成立的结论。证据越多，论证越强，但永远无法达到绝对的确定性。归纳公式呈现出这种概括性跃迁。
Many observed X have property Y → Probably all X have property Y
许多观察到的 X 具有属性 Y → 很可能所有 X 都具有属性 Y
Example: The sun has risen every day in recorded history. Therefore, the sun will probably rise tomorrow.
例子：有史以来太阳每天升起。因此，太阳明天很可能还会升起。
4. Analogical Arguments | 类比论证
Analogical reasoning argues that because two things are alike in some respects, they are probably alike in another respect. This formula highlights the comparative structure.
类比推理是这样一种论证：因为两个事物在某些方面相似，所以它们在另一个方面也可能相似。这个公式突出了比较的结构。
A has features X, Y, Z. B also has X, Y. Therefore, B probably has Z.
事物 A 具有特征 X, Y, Z。事物 B 也具有 X, Y。因此，B 很可能具有 Z。
Example: Earth and Mars both have an atmosphere and water. Earth has life. Therefore, Mars might have life.
例子：地球和火星都有大气层和水。地球有生命。因此，火星可能有生命。
5. Common Logical Fallacies | 常见逻辑谬误
Fallacies are errors in reasoning that weaken arguments. Recognising them is like knowing a false mathematical step. Here are four common fallacies expressed as faulty formulas.
谬误是推理中的错误，会削弱论证。识别它们就像识别错误的数学步骤。以下是四种常见谬误，表示为有缺陷的公式。
Ad Hominem: Attacking the person instead of the argument. Person A is flawed → Person A's argument is wrong.
人身攻击：攻击人而不是论点。人 A 有缺陷 → 人 A 的论证是错误的。
Straw Man: Misrepresenting an argument to make it easier to attack. X's view is distorted into Y → Y is then rejected.
稻草人谬误：歪曲对方论点使其更容易攻击。X 的观点被曲解为 Y → 然后拒绝 Y。
False Dilemma: Presenting only two options when more exist. Either A or B must be true (ignoring C, D…).
假两难推理：只呈现两个选项，而实际上有更多选项。要么 A 要么 B 必然为真（忽略 C、D……）。
Begging the Question: Assuming the conclusion in the premises. The premise contains the conclusion.
循环论证：前提中包含了结论。前提包含结论。
6. The Design Argument (Teleological Argument) | 设计论证（目的论论证）
The Teleological Argument claims that the complexity and order in the universe imply a designer. It can be structured as an analogical formula comparing the universe to a watch.
目的论论证声称宇宙中的复杂性和秩序意味着有位设计者。它可以被构造为一个将宇宙类比于钟表的类比公式。
→ A watch has a watchmaker. The universe has complex parts → The universe has a designer.
钟表有复杂部件 → 钟表有制表师。宇宙有复杂部件 → 宇宙有设计者。
Critics argue the analogy may be weak because we have never observed a universe-maker, unlike a watchmaker.
批评者认为这个类比可能薄弱，因为我们从未观察到宇宙的制造者，不像制表师。
7. The Cosmological Argument | 宇宙论论证
The Cosmological Argument reasons from the existence of the universe to a First Cause. The classic form follows a chain of causation that must stop at an uncaused cause.
宇宙论论证从宇宙的存在推理到第一因。经典形式遵循一个因果链条，该链条必须终结于一个无因的起因。
s a cause. The universe exists. → The universe must have a first cause (often called God).
一切存在的事物都有原因。宇宙存在。→ 宇宙必定有一个第一因（通常被称为上帝）。
A counter-question challenges: 'If everything has a cause, what caused God?' Proponents reply that the first cause is a necessary exception.
一个反问挑战：“如果一切都有原因，那是什么导致了上帝？”支持者回答第一因是一个必要的例外。
8. The Ontological Argument | 本体论论证
Anselm's Ontological Argument defines God as 'that than which nothing greater can be conceived' and argues that such a being must exist in reality, because existing in reality is greater than existing only in the mind. The logical structure is almost like a definitional equation.
安瑟伦的本体论论证将上帝定义为“无法设想比
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