📚 Year 8 SQA Philosophy: Formula & Theorem Quick Reference Guide | SQA 八年级哲学：公式定理速查手册
Philosophy might not have equations like mathematics, but it contains many powerful 'formulas' – concise statements of fundamental principles, logical rules, and ethical imperatives. This quick reference handbook gathers essential philosophical formulas and theorems that Year 8 SQA students should know, from Descartes' Cogito to Rawls' Veil of Ignorance. Understand these core ideas, and you will have a toolkit for clearer thinking, moral reasoning, and logical analysis.
哲学也许没有像数学那样的方程式，但它包含许多强有力的“公式”——基本准则、逻辑规则和道德律令的简洁陈述。这本速查手册汇集了SQA八年级学生需要了解的关键哲学公式与定理，从笛卡尔的我思到罗尔斯的无知之幕。理解这些核心思想，你将掌握清晰思考、道德推理和逻辑分析的工具包。
1. The Cogito Formula (Cogito, ergo sum) | 我思公式（我思，故我在）
"Cogito, ergo sum"
Descartes discovered this indubitable truth by doubting all his beliefs. He realised that even if an evil demon deceived him about the external world, the fact that he was being deceived required him to think, and thinking proves his existence.
笛卡尔通过怀疑所有信念发现了这一不容置疑的真理。他意识到，即使有一个邪恶的精灵在外部世界上欺骗他，他被欺骗这一事实也要求他进行思考，而思考证明了他的存在。
The Cogito is the first principle of Cartesian philosophy. It provides a secure foundation for knowledge, as one cannot coherently deny the self that is doing the denying.
我思是笛卡尔哲学的第一原理。它提供了一个安全的知识基础，因为一个人无法连贯地否认正在发出否认的那个自我。
2. The Categorical Imperative (Universal Law Formula) | 定言令式（普遍法则公式）
"Act only according to that maxim whereby you can, at the same time, will that it should become a universal law."
Immanuel Kant's formula for moral action: before you act, ask whether the principle behind your action could rationally be willed to apply to everyone without contradiction.
康德的道德行为公式：行动之前，请问自己，你行动背后的准则能否无矛盾地被理性地愿其成为一条普遍法则。
For example, making a false promise to borrow money fails the test, because if everyone made false promises, the institution of promising would collapse, making the maxim self-defeating.
例如，为了借钱而作出虚假承诺就无法通过检验，因为如果人人都这样做，承诺制度就会崩溃，该准则便自相矛盾。
3. The Greatest Happiness Principle (Utilitarian Formula) | 最大幸福原理（功利主义公式）
"Actions are right in proportion as they tend to promote happiness, wrong as they tend to produce the reverse of happiness."
Articulated by Jeremy Bentham and John Stuart Mill, this formula states that the moral worth of an action is determined by its contribution to overall utility, defined as pleasure minus pain.
由边沁和密尔阐发，这条公式指出一个行为的道德价值取决于它对总功利——定义为快乐减去痛苦——的贡献。
When faced with a moral dilemma, one should calculate the expected consequences for all affected and choose the action that maximises net happiness.
面对道德困境时，人们应当计算对所有相关者产生的预期后果，并选择能最大化净幸福的行为。
4. The Veil of Ignorance | 无知之幕
"Imagine you know nothing about your own position in society, then design the rules of justice."
John Rawls' formula for fairness: when choosing principles of justice, we should imagine we are behind a veil of ignorance, not knowing our own talents, social status, or circumstances. This ensures impartiality.
罗尔斯的公平公式：在选择正义原则时，我们应想象自己处于无知之幕背后，不知道自己的天赋、社会地位或处境。这确保了公正无私。
The outcome, Rawls argues, would be principles that protect basic liberties for all and only permit inequalities if they benefit the least advantaged.
罗尔斯论证说，结果将是保护所有人基本自由的原则，并且只有在对最不利者有利时才允许存在不平等。
5. The Law of Non-Contradiction | 不矛盾律
¬(P ∧ ¬P)
A statement cannot be both true and false at the same time and in the same respect. This law, first formulated by Aristotle, is a fundamental rule of thought and reality.
一个命题不能在同一时间、同一方面既为真又为假。这一定理最初由亚里士多德阐明，是思维与实在的根本规则。
Without the law of non-contradiction, rational discourse collapses, because any argument could be accepted together with its opposite.
没有不矛盾律，理性话语就会瓦解，因为任何论证都能与其反面同时被接受。
6. Modus Ponens (Affirming the Antecedent) | 肯定前件式
If P → Q, and P, then Q
This valid argument form states that if a conditional statement is true and its antecedent (the 'if' part) is true, then the consequent (the 'then' part) must be true.
这个有效论证形式指出，如果一个条件语句为真，且其前件（“如果”部分）为真，那么后件（“那么”部分）必然为真。
Example: If it rains, the ground will be wet. It is raining. Therefore, the ground is wet.
示例：如果下雨，地面会湿。天在下雨。所以，地面是湿的。
7. Modus Tollens (Denying the Consequent) | 否定后件式
If P → Q, and ¬Q, then ¬P
This valid logical formula works in reverse: if the consequent of a conditional is false, the antecedent must be false.
这个有效逻辑公式反向运作：如果条件语句的后件为假，那么前件必定为假。
Example: If the light bulb is working, the room will be lit. The room is not lit. Therefore, the light bulb is not working (or the power is off).
示例：如果灯泡正常工作，房间会亮。房间不亮。所以，灯泡没有正常工作（或停电了）。
8. The Socratic Method (Elenchus) | 苏格拉底式方法（问辩法）
Question → Cross‑examine → Refute → Admit ignorance (Aporia)
Socrates used this dialogical formula to uncover contradictions in beliefs. He asked for a definition, then used a series of questions to show that the definition leads to inconsistencies.
苏格拉底运用这一对话公式来揭示信念中的矛盾。他要求一个定义，然后用一连串问题表明该定义导致不一致。
The aim is not to win but to clear away false pretensions to knowledge, leading to a state of aporia (puzzlement) from which genuine inquiry can begin.
其目的不是取胜，而是清除虚假的知识自诩，达到一种无知之惑（aporia）的状态，从那里开始真正的探求。
9. Ockham's Razor (Principle of Parsimony) | 奥卡姆剃刀（简约原则）
"Entities should not be multiplied beyond necessity."
William of Ockham's rule advises that when we have competing explanations, we should choose the one that makes the fewest assumptions. Simpler theories are to be preferred, all else being equal.
奥卡姆的威廉的规则建议，当存在相互竞争的解释时，我们应选择假设最少的那个。在其他条件相同的情况下，更简单的理论应被优先考虑。
This razor cuts away unnecessary complications and guides reasoning in both science and philosophy, reminding us not to invent more causes than are needed.
这把剃刀削去不必要的复杂内容，引导科学和哲学中的推理，提醒我们不要发明超出所需的原因。
10. The Tabula Rasa (Blank Slate) Principle | 白板原理
"There is nothing in the intellect that was not first in the senses."
Empiricists like John Locke argued that the human mind at birth is a tabula rasa – a blank slate. All ideas come from experience and sensory input; there are no innate ideas.
洛克等经验主义者主张，人类心灵在出生时是一块白板（tabula rasa）。所有观念来自经验和感官输入；不存在天赋观念。
This formula underpins the idea that knowledge is built up through observation, reflection, and the combining of simple sense-data into complex concepts.
这条公式支撑了这样的观点：知识是通过观察、反思以及将简单感觉材料组合成复杂概念而建立起来的。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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