📚 Year 13 Edexcel Philosophy: Formula & Theorem Quick-Reference Handbook | 爱德思 Year 13 哲学：公式定理速查手册
In the study of philosophy, there are no chemical equations or physical constants, yet the rigour of philosophical analysis often employs formal logical structures, clearly defined principles, and argument schemas that function much like formulas and theorems. This quick-reference handbook gathers the essential logical operators, valid inference patterns, and formalised versions of core philosophical arguments you will encounter in the Year 13 Edexcel A-level Philosophy course. It covers key formulas from epistemology, moral philosophy, philosophy of religion, and philosophy of mind, providing you with a concise toolkit for exam revision and essay writing.
在哲学学习中，虽然没有化学方程式或物理常数，但哲学分析的严谨性常常运用形式逻辑结构、明确定义的原则以及论证模式，它们的功能类似于公式和定理。本速查手册汇集了爱德思 A-level 哲学 Year 13 课程中必不可少的基本逻辑算子、有效推理模式以及核心哲学论证的形式化表述。它涵盖了认识论、道德哲学、宗教哲学和心灵哲学中的关键公式，为你提供一套简明扼要的复习与论文写作工具。
1. Propositional Logic: Operators & Truth Tables | 命题逻辑：联结词与真值表
Propositional logic provides the basic symbols for analysing philosophical arguments. The five standard logical operators are negation (¬), conjunction (∧), disjunction (∨), material implication (→), and biconditional (↔). Their truth-functional definitions can be summarised in truth tables. For any propositions P and Q, the expression P → Q is false only when P is true and Q is false; otherwise it is true. These operators allow us to represent deductive arguments symbolically.
命题逻辑为分析哲学论证提供基本符号。五个标准逻辑联结词为否定 (¬)、合取 (∧)、析取 (∨)、实质蕴涵 (→) 和双重条件 (↔)。它们的真值函项定义可用真值表概括。对于任意命题 P 和 Q，P → Q 只有在 P 真且 Q 假时为假，其余情况为真。这些联结词使我们能用符号表达演绎论证。
2. Valid Inferential Forms: Modus Ponens & Modus Tollens | 有效推理形式：肯定前件与否定后件
Two fundamental rules of inference are Modus Ponens and Modus Tollens. Modus Ponens has the form: If P then Q, P, therefore Q. Symbolically:
P → Q, P ⊢ Q
Modus Tollens denies the consequent: If P then Q, not Q, therefore not P. Symbolically:
P → Q, ¬Q ⊢ ¬P
Both are deductively valid. Philosophers often use these forms to test the logical structure of moral dilemmas, arguments for the existence of God, and mind-body theories. Recognising them is essential for evaluating the strength of any argument presented in your exam.
两种基本的推理规则是肯定前件和否定后件。肯定前件的形式为：如果 P 则 Q，P 成立，因此 Q 成立。其符号式为 P → Q, P ⊢ Q。否定后件通过否定后件来推理：如果 P 则 Q，非 Q 成立，因此非 P 成立，符号式为 P → Q, ¬Q ⊢ ¬P。二者均为演绎有效。哲学家常借助这些形式检验道德困境、上帝存在论证以及心身理论的逻辑结构。认出它们对你在考试中评价任何论证的强度至关重要。
3. The JTB Formula for Knowledge & the Gettier Challenge | 知识 JTB 公式与盖蒂尔挑战
Since Plato, knowledge has often been analysed as justified true belief (JTB). This can be expressed as a formula:
K(p) ↔ B(p) ∧ T(p) ∧ J(p)
where K stands for knowledge, B for belief, T for truth, and J for justification. However, Edmund Gettier demonstrated through counterexamples that there are cases satisfying JTB which we would not count as knowledge. Thus the formula represents a necessary but not sufficient condition. The post-Gettier project seeks to add a fourth condition, such as a ‘no false lemmas’ clause, aiming to repair the formula.
自柏拉图以来，知识常被分析为确证的真信念 (JTB)。这可以表示为公式：K(p) ↔ B(p) ∧ T(p) ∧ J(p)，其中 K 代表知识，B 代表信念，T 代表真，J 代表确证。然而，埃德蒙德·盖蒂尔通过反例证明，有些情形满足 JTB 却被视作不是知识。因此该公式仅代表必要而非充分条件。后盖蒂尔计划试图添加第四个条件，如“无虚假引理”条款，以期修补该公式。
4. Utilitarian Calculus: Bentham’s Hedonic Formula | 功利主义计算：边沁的快乐公式
Jeremy Bentham’s act utilitarianism proposes that the moral value of an action is determined by the total pleasure minus pain it produces for all affected. While Bentham did not write an actual equation, the principle can be represented as a decision function:
Utility = Σ (Pleasureᵢ − Painᵢ) over all individuals i
The right action is the one that maximises this sum. Bentham’s hedonic calculus further breaks down pleasure into seven dimensions: intensity, duration, certainty, propinquity, fecundity, purity, and extent. This quantitative approach treats ethics as a form of moral arithmetic, a ‘formula’ that students must be able to apply and criticise.
杰里米·边沁的行为功利主义主张，一个行为的道德价值取决于它为所有相关者带来的总快乐减去总痛苦。边沁并未写下真正的方程式，但该原理可表示为一个决策函数：效用 = Σ (快乐ᵢ − 痛苦ᵢ)，对所有个体 i 求和。正确的行为就是最大化此总和的行为。边沁的快乐计算进一步将快乐分解为七个维度：强度、持续时间、确定性、邻近性、丰富性、纯度和范围。这种量化方法将伦理学视为道德算术，是学生必须能够运用和批判的一种“公式”。
5. Kant’s Categorical Imperative: Formula of Universal Law | 康德绝对命令：普遍法则公式
Immanuel Kant’s moral philosophy centres on the categorical imperative. Its first formulation, the Formula of Universal Law, can be presented as:
Act only according to that maxim whereby you can at the same time will that it should become a universal law.
In logical terms, if the maxim’s universalisation leads to a contradiction in conception or in the will, the action is impermissible. This test functions as a formal procedure for testing moral rules, similar to a logical proof. For Kant, the formula yields perfect duties (e.g., not to lie) and imperfect duties (e.g., to develop talents).
康德的道德哲学以绝对命令为核心。其第一表述，即普遍法则公式，可表示为：只依据你能够同时愿意它成为一条普遍法则的那个准则去行动。在逻辑上，如果一个准则的普遍化导致概念上的矛盾或意志上的矛盾，则该行为不被允许。这一检验如同逻辑证明，用作检验道德规则的形式程序。对康德而言，该公式产生完全义务（如不说谎）和不完全义务（如发展才能）。
6. Ontological
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