📚 Year 10 WJEC Philosophy: Quick Reference Handbook of Formulae & Theorems | Year 10 WJEC 哲学：公式定理速查手册
This handbook distils the core 'formulae' and 'theorems' you need for Year 10 WJEC Philosophy. Think of these not as mathematical equations but as condensed logical patterns, moral calculus rules, and argument schemas that underpin everything from the existence of God to how we make ethical decisions. Each entry gives you the key principle in a memorable symbolic form, followed by a clear explanation in both English and Chinese. Master these patterns, and you will have a powerful toolkit for your essays and exams.
这本手册提炼了 Year 10 WJEC 哲学所需的核心“公式”与“定理”。请不要将它们理解为数学方程式，而是浓缩的逻辑模式、道德演算规则和论证框架，它们支撑着从上帝存在到伦理决策的几乎所有主题。每个条目都用一个易记的符号形式呈现关键原则，并附有清晰的中英文解释。掌握这些模式，你就拥有了应对论文和考试的强大工具箱。
1. The JTB Formula for Knowledge | 知识的JTB公式
K ↔ (B ∧ J ∧ T)
The classic tripartite definition states that a subject S knows a proposition P if and only if S believes P, P is true, and S has justification for believing P. The symbol '↔' shows equivalence, while '∧' joins the three necessary conditions. This formula dominated epistemology until Edmund Gettier’s counterexamples revealed cases where a justified true belief still does not count as knowledge, prompting philosophers to add a fourth condition or replace JTB entirely.
经典的三要素定义指出，主体S知道命题P当且仅当S相信P、P为真，且S有理由相信P。符号“↔”表示等价，“∧”连接三个必要条件。这一公式一直统治着认识论，直到埃德蒙·葛梯尔的反例表明，即使拥有得到辩护的真信念，也未必等于知识，从而促使哲学家们增加第四个条件或彻底替换JTB结构。
2. Bentham’s Hedonic Calculus | 边沁的快乐计算法
U = I × D × C × R × E × P × S
Jeremy Bentham’s act utilitarianism evaluates any action by measuring the total pleasure it produces. The seven variables stand for Intensity, Duration, Certainty, Propinquity (how soon the pleasure will occur), Fecundity (chance it will be followed by more pleasure), Purity (chance it will be followed by pain) and Extent (number of people affected). A rational moral agent should calculate the net sum and choose the action that yields the highest utility, treating all pleasures as equal in kind.
杰里米·边沁的行为功利主义通过衡量行为所产生的总快乐来评价行为。这七个变量分别代表强度、持续时间、确定性、邻近性（快乐何时到来）、丰度（随之产生更多快乐的几率）、纯度（伴随痛苦的几率）和范围（受影响的人数）。理性道德主体应该计算净总和，并选择效用最高的行为，视所有快乐在本质上是等同的。
3. Kant’s Categorical Imperative (Formula of Universal Law) | 康德的定言令式（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.
can will this without contradiction in conception or in the will, the action is morally permissible. The formula can be expressed logically as: ∀M, [~Universalizable(M) → ~ e out false promises, suicide and neglect of talents as contradictory universal practices.
伊曼努尔·康德的义务论检验要求你想象将个人的行动准则（格律）变成人人都必须遵守的法则。如果你能够不陷入概念矛盾或意志矛盾地意愿这一点，该行为在道德上就是允许的。这个公式可以用逻辑表示为：∀M，[~可普遍化(M) → ~道德(M)]。康德用它来排除虚假承诺、自杀和荒废才能等行为，因为这些做法一旦普遍化就会自相矛盾。
4. The Design Argument’s Logical Structure | 设计论证的逻辑结构
(Complexity ∧ Purpose) → Designer
William Paley’s watchmaker analogy and other teleological arguments follow a simple inductive schema: if an object exhibits complex, ordered parts that serve a purpose, it probably had an intelligent designer. The universe exhibits such complexity and purpose (e.g., the eye, the laws of physics). Therefore, the universe probably had an intelligent designer, identified as God. Hume and Darwin challenged the analogy, pointing to the possibility of natural processes or a flawed designer.
威廉·佩利的手表匠类比及其他目的论论证遵循一个简单的归纳模式：如果一个物体展现出复杂、有序且服务于某种目的的部分，它很可能有一位智能设计者。宇宙展现出这样的复杂性和目的性（例如眼睛、物理法则）。因此，宇宙很可能有一位智能设计者，即上帝。休谟和达尔文对这一类比提出了挑战，指出了自然过程或一位有缺陷的设计者的可能性。
5. The Logical Problem of Evil (Inconsistent Triad) | 恶的逻辑问题（不一致三角）
(Omnipotent ∧ Omnibenevolent) → ¬Evil
J.L. Mackie formalised the classic argument against the existence of the God of classical theism. If God is all-powerful, He can prevent evil; if God is all-good, He would want to prevent evil. Therefore, evil should not exist. Since evil does exist, the two divine attributes cannot both be true. The theist must deny omnipotence, deny omnibenevolence, or find a logically sufficient reason why God allows evil — the task of theodicy.
J.L. 麦基将反对古典有神论上帝存在的经典论证形式化。如果上帝全能，祂就能阻止恶；如果上帝全善，祂就想要阻止恶。因此，恶不应该存在。既然恶确实存在，那么这两个神圣属性不能同时为真。有神论者必须否定全能，否定全善，或者找到一个逻辑上充分的理由说明上帝为何容许恶——这就是神正论的任务。
6. Divine Command Theory | 神命论公式
X is morally right ↔ God commands X
According to this meta‑ethical theory, moral goodness is entirely grounded in God’s will. If God commands an action, it becomes obligatory; if God forbids it, it becomes wrong — and there is no standard of rightness beyond God’s command. This immediately raises the Euthyphro dilemma: is an act right because God commands it, or does God command it because it is right? Supporters find strength in the absolute foundation it provides for moral objectivity.
根据这一元伦理理论，道德善完全建立在上帝意志的基础之上。如果上帝命令一个行为，它就变成义务；如果上帝禁止它，它就变成错误——在上帝的命令之外不存在任何道德标准。这立刻引发了游叙弗伦两难：一个行为是因为上帝命令它才正确，还是因为它正确上帝才命令它？支持者认为其优势在于为道德客观性提供了绝对的基础。
7. The Euthyphro Dilemma | 游叙弗伦两难
(DivineCom → Arbitrariness) ∨ (IndependentMorality)
Plato’s dialogue presents a fatal fork for divine command theory. If we take the first horn and say an act is right simply because God commands it, then morality becomes arbitrary — God could have commanded cruelty and that would become ‘good’. If we take the second horn and say God commands something because it is right, then morality exists independently of God, making God redundant as a moral foundation. The dilemma thus forces a choice between a capricious God and an irrelevant one.
柏拉图的对话为神命论呈现了一个致命的岔路。如果我们接受第一角，说一个行为正确仅仅因为上帝命令它，那么道德就变得任意——上帝本可以命令残忍，而那也会变成“善”。如果我们接受第二角，说上帝命令某事是因为它本来就是正确的，那么道德就独立于上帝而存在，上帝作为道德基础就变得多余。这一两难因此迫使人们在一位任性的上帝和一位无关的上帝之间做出选择。
8. The Free Will Defence | 自由意志辩护
Free Will → ◇Evil
Alvin Plantinga’s free will defence offers a logical response to Mackie’s problem of evil. It argues that a world containing creatures who are significantly free (and freely choose good) is more valuable than a world of automata. But if God creates significantly free beings, He cannot causally determine them to always choose good without destroying their freedom. Thus, the possibility of moral evil is logically inseparable from the gift of free will. If God had a morally sufficient reason to create such a world, the existence of evil is not logically incompatible with His goodness.
阿尔文·普兰丁格的自由意志辩护为麦基的恶之问题提供了一个逻辑回应。它论证说，一个包含具有重大自由的受造物（且它们自由地选择善）的世界，比一个机器人的世界更有价值。但如果上帝创造了具有重大自由的存有，祂就无法在不摧毁其自由的情况下因果性决定他们总是选择善。因此，道德恶的可能性与自由意志的赠礼在逻辑上不可分割。如果上帝有道德上充分的理由创造这样一个世界，恶的存在就与祂的善在逻辑上不矛盾。
9. The Ontological Argument’s Axiom | 本体论论证的公理
God = the greatest conceivable being → God must exist in reality
Anselm of Canterbury defines God as ‘that than which nothing greater can be conceived’. He then observes that existing in reality is greater than existing only in the understanding. If God existed only in the mind, we could conceive an even greater being — one that exists both in the mind and in reality. Hence, to avoid a contradiction, God must exist in reality. Critics like Gaunilo and Kant argue that existence is not a predicate that can add greatness.
坎特伯雷的安瑟伦将上帝定义为“不能设想有比之更伟大的东西”。然后他指出，实际存在比仅仅在理智中存在更伟大。如果上帝只存在于心灵中，我们就能设想出一个更伟大的存有——即同时存在于心灵和现实中的存有。因此，为避免矛盾，上帝必须在现实中存在。高尼罗和康德等批评者则认为，存在并不是一个可以增添伟大性的谓词。
10. Situation Ethics: Agape Calculus | 情境伦理学：圣爱计算
A is right ↔ A maximises agape (selfless love)
Joseph Fletcher’s Christian relativist theory holds that the only absolute rule is to do the most loving thing in every situation. Love is not mere emotion but an attitude of seeking the best for the neighbour, pragmatically calculated. There are no intrinsic moral rules except love; all other norms (e.g., ‘do not lie’) may be set aside if agape demands it. Thus the moral agent applies the formula by asking: which course of action will produce the greatest amount of selfless, caring love for those involved?
约瑟夫·弗莱彻的基督教相对主义理论认为，唯一绝对的法则就是在每一种处境中都做最具爱心的事。爱不仅是情绪，而是一种务实计算、为邻舍寻求最大益处的态度。除了爱之外，没有内在的道德规则；所有其他规范（例如“不可撒谎”）只要圣爱要求，都可以被搁置。因此，道德主体通过提问来应用这个公式：哪一条行动路线能给相关方带来最大量的无私关爱之爱？
Published by TutorHao | Philosophy Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图