📚 Philosophy Formula & Theorem Quick Reference Handbook | 哲学公式定理速查手册
Philosophy may not have equations like maths or physics, but it does contain structured arguments, logical rules, and ethical 'formulas' that help us reason clearly. This handbook presents essential philosophical principles, logical forms, and ethical theories as concise formulas and theorems, designed for Year 9 SQA Philosophy. Each entry is a tool for thinking: use it to analyse dilemmas, construct arguments, or evaluate claims.
哲学或许不像数学或物理那样有方程式，但它确实包含结构化的论证、逻辑规则和伦理“公式”，能帮助我们清晰地推理。这本速查手册将基本的哲学原理、逻辑形式和伦理学理论浓缩为简洁的公式和定理，专为 Year 9 SQA 哲学课程而设计。每一个条目都是一个思考工具：用它来分析两难问题、建构论证或评价主张。
1. The Principle of Non-Contradiction | 不矛盾律
The most fundamental law of thought: a proposition cannot be both true and false at the same time and in the same respect. Formally, for any statement P, it is not the case that (P ∧ ¬P).
思维最根本的定律：一个命题不可能在同一时间和同一方面既真又假。形式上，对于任意陈述 P，并非 (P 且 非P)。
When someone claims 'It is raining and it is not raining in this exact spot right now,' they violate this principle. Recognising contradictions is the first step in critical analysis.
当某人声称“此刻此地正在下雨且没有下雨”时，就违背了这一原则。识别矛盾是进行批判性分析的第一步。
2. The Law of Excluded Middle | 排中律
Every proposition is either true or false; there is no middle ground. Symbolised as: P ∨ ¬P (P or not-P).
任一命题要么为真，要么为假；没有中间状态。符号表示为：P ∨ ¬P (P 或 非P)。
This law reminds us that when facing a clear yes/no question, waffling is not a truth value. In philosophical debate, equivocation often tries to hide between the two, but logic demands a decision.
这条定律提醒我们，面对明确的是非问题时，含糊其辞不是真值。在哲学辩论中，模棱两可往往试图躲在二者之间，但逻辑要求做出抉择。
3. Modus Ponens (Affirming the Antecedent) | 肯定前件式
A valid argument form: If P then Q; P is true; therefore Q is true. Formula: [(P → Q) ∧ P] → Q.
一种有效的论证形式：如果 P 那么 Q；P 为真；因此 Q 为真。公式：[(P → Q) ∧ P] → Q。
Example: If it is a dog, then it is a mammal. It is a dog. Therefore, it is a mammal. If the premises are true, the conclusion must be true — this is deductive validity.
示例：如果它是狗，那么它是哺乳动物。它是狗。因此，它是哺乳动物。如果前提为真，结论必然为真——这就是演绎有效性。
4. Modus Tollens (Denying the Consequent) | 否定后件式
Another valid form: If P then Q; Q is false; therefore P is false. Formula: [(P → Q) ∧ ¬Q] → ¬P.
另一种有效的形式：如果 P 那么 Q；Q 为假；因此 P 为假。公式：[(P → Q) ∧ ¬Q] → ¬P。
Example: If the battery is charged, the phone turns on. The phone does not turn on. Therefore, the battery is not charged. This is how we falsify hypotheses in science and philosophy.
示例：如果电池有电，手机就会开机。手机没有开机。因此，电池没电。这就是我们在科学和哲学中证伪假设的方式。
5. Hypothetical Syllogism | 假言三段论
hains of conditionals: If P then Q; if Q then R; therefore, if P then R. Formula: [(P → Q) ∧ (Q → R)] → (P → R).
条件链：如果 P 那么 Q；如果 Q 那么 R；因此，如果 P 那么 R。公式：[(P → Q) ∧ (Q → R)] → (P → R)。
This form allows us to build extended arguments, linking causes and effects. In ethics, it can connect a principle to a distant consequence, forcing us to examine the whole chain.
这种形式允许我们构建扩展论证，将原因与结果联系起来。在伦理学中，它可以将一个原则与遥远的后果相连，迫使我们审视整个因果链。
6. Kant's Categorical Imperative (First Formulation) | 康德的定言令式（第一公式）
'Act only according to that maxim whereby you can at the same time will that it should become a universal law.' This can be seen as a logical test: Can the rule behind your action be consistently willed for everyone?
“只依据你同时能够愿意它成为一条普遍法则的那个准则而行动。”这可以看作一个逻辑检验：你行动背后的规则能否一贯地愿意所有人都遵循？
If the maxim fails the test (leads to a contradiction in conception or in will), the action is morally impermissible. Example: Lying to get money — if everyone lied, trust would collapse, making lying pointless; this is a contradiction in conception.
如果准则未能通过检验（导致概念上的矛盾或意志上的矛盾），该行为在道德上就是不允许的。示例：为了得钱而撒谎——如果人人撒谎，信任就会崩溃，撒谎便毫无意义；这就是概念上的矛盾。
7. The Greatest Happiness Principle (Utilitarianism) | 最大幸福原则（功利主义）
ne that maximises overall happiness (pleasure minus pain) for all affected. Jeremy Bentham's classic statement: 'the greatest happiness of the greatest number.'
公式：正当行为 = 能为所有受影响者带来最大总体幸福（快乐减去痛苦）的行为。边沁的经典表述：“最大多数人的最大幸福”。
This is a consequentialist 'calculation': sum up all pleasures and pains resulting from each possible action; the action with the highest net total is the morally right one. In practice, Bentham proposed a 'hedonic calculus' measuring intensity, duration, certainty, etc.
这是一种结果论的“计算”：将每种可能行动所产生的所有快乐和痛苦加总；净总和最高的行动就是道德上正确的。在实践中，边沁提出了一种衡量强度、持续时间、确定性等的“快乐计算法”。
8. Aristotle's Doctrine of the Mean | 亚里士多德的中庸之道
Virtue is a mean between two vices — eficiency) ÷ 2, but it is relative to the person and situation, not an arithmetic average.
德性是两种恶之间的中道——一个是过度，一个是不及。公式：德性 = (过度 + 不及) ÷ 2，但这是相对于人和情境而言的，不是算术平均值。
Example: Courage is the mean between cowardice (deficiency) and recklessness (excess). The mean is determined by practical wisdom (phronesis), not a rigid formula. This is a guideline for character development.
示例：勇敢是怯懦（不及）与鲁莽（过度）之间的中道。中道要通过实践智慧来确定，而非死板的公式。这是品格培养的指南。
9. The Socratic Method: Elenchus | 苏格拉底方法：反诘法
ross-examination to test consistency → Refinement or abandonment of the initial claim. The 'formula' is: If claim C implies contradiction, then C must be revised.
一种合作式的论证对话：提问 → 回答 → 交叉检验一致性 → 修正或放弃初始主张。其“公式”是：如果主张 C 蕴含矛盾，则必须修改 C。
Socrates used this to uncover ignorance and lead people to aporia (puzzlement), the first step towards wisdom. In modern classrooms, this is the root of critical thinking pedagogy.
苏格拉底用此法揭示无知，引导人们到达“疑难”（困惑），这是走向智慧的第一步。在现代课堂中，这是批判性思维教学法的根源。
10. Occam's Razor | 奥卡姆剃刀
Principle of parsimony: Do not multiply entities beyond necessity. Formulated as: Among competing hypotheses, the one with the fewest assumptions should be selected — all else being equal. Symbolically, minimise the number of unobserved entities or principles.
简洁性原则：如无必要，勿增实体。可表述为：在相互竞争的假设中，应选择假设最少的那一个——在其他条件相同的情况下。用符号表示，即尽量减少不可观察实体或原理的数目。
This is not a proof but a heuristic. In philosophy of mind, the debate between dualism (mind and body are separate) and physicalism (only physical stuff exists) often invokes Occam's Razor: if we can explain consciousness without an immaterial soul, we should.
这不是证明，而是一种启发法。在心灵哲学中，二元论（心物分离）与物理主义（只存在物理事物）之间的争论常援引奥卡姆剃刀：如果我们无需非物质灵魂就能解释意识，我们就应当那样做。
11. The Is–Ought Gap (Hume's Law) | 实然–应然鸿沟（休谟法则）
You cannot logically derive an 'ought' from an 'is'. That is, no set of purely descriptive statements (facts about the world) entails a prescriptive moral conclusion without at least one evaluative premise.
你不能从“是”逻辑地推出“应当”。也就是说，没有一组纯粹描述性的陈述（关于世界的事实）能在缺乏至少一个评价性前提的情况下，推出规定性的道德结论。
Example: 'Species evolve through natural selection' (is) does not directly imply 'we ought to let the weak perish' (ought). The gap alerts us to hidden value assumptions in arguments that claim to be purely factual.
示例：“物种通过自然选择进化”（是）并不直接蕴涵“我们应当让弱者消亡”（应当）。这一鸿沟提醒我们注意那些声称纯粹基于事实的论证中隐含的价值假设。
12. Descartes' Cogito | 笛卡尔的“我思”
The indubitable foundation: 'I think, therefore I am' f doubting proves my existence as a thinking thing. Formula: Doubt → Thinking → Existence.
不可怀疑的基础：“我思故我在”。即便我怀疑一切，怀疑这一行为本身就证明了我作为一个思维着的存在者而存在。公式：怀疑 → 思维 → 存在。
This is not an argument with premises but a self-evident intuition: the performance of thinking guarantees the thinker's reality. It is the starting point of modern epistemology.
这并不是一个包含前提的论证，而是一个自明的直觉：思考的施行确保了思考者的实在性。这是现代认识论的起点。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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