📚 Year 10 Eduqas Philosophy: Formula & Theorem Quick Reference Handbook | Year 10 Eduqas 哲学：公式定理速查手册
In philosophy, arguments and ethical principles can be crystallised into clear logical structures, much like mathematical formulas. This quick-reference handbook presents the key 'theorems' required for the Year 10 Eduqas Philosophy specification. Each entry distills a classic argument or principle into a precise formula, helping you to master the logic behind the ideas and apply them effectively in revision and exams.
在哲学中，论证和伦理原则往往可以浓缩成清晰的逻辑结构，如同数学公式一般。本速查手册汇集了 Year 10 Eduqas 哲学课程所需的核心“定理”，将每一个经典论证或原则提炼为精确的公式，帮助你掌握观点背后的逻辑，并在复习与应试中灵活运用。
1. The Cosmological Argument: First Cause Formula | 宇宙论论证：第一因公式
Aquinas’ Cosmological Argument works like a logical chain: everything we observe is caused or moved by something else. This leads to a chain of causes stretching back in time, which Aquinas argues cannot be infinite. The only way to avoid an endless regress is to posit a first, uncaused cause.
阿奎那的宇宙论论证像一条逻辑链条：我们观察到的一切都是由他者引发或推动的。这就形成了一条回溯到过去的因果链，但阿奎那认为该链条不能是无限的。避免无限回溯的唯一方式就是设定一个不被推动的第一因。
P1: Every event has a cause. P2: An infinite causal chain is impossible. ∴ A first uncaused cause (God) exists.
前提1：每个事件皆有原因。 前提2：无限的因果链是不可能的。 ∴ 存在第一无因之因（上帝）。
This is a deductive structure: if both premises are true, the conclusion must follow with certainty. Critics often challenge the second premise, noting that some philosophers and scientists consider an infinite universe theoretically possible.
这是一种演绎结构：如果两个前提为真，结论必然成立。批评者常质疑第二个前提，指出一些哲学家和科学家认为无限宇宙在理论上是可能的。
2. The Kalam Cosmological Argument: Temporal Formula | 卡拉姆宇宙论论证：时间起始公式
The Kalam version focuses on the beginning of the universe itself. It uses two simple premises to conclude that the universe must have a transcendent cause, which many identify as God. This form is particularly influential in dialogue with modern cosmology.
卡拉姆版本聚焦于宇宙本身的起始。它用两个简单的前提得出结论：宇宙必定有一个超越的原因，许多人将此等同于上帝。这一形式在与现代宇宙学的对话中影响尤为深远。
P1: Everything that begins to exist has a cause. P2: The universe began to exist. ∴ The universe has a cause (God).
前提1：一切开始存在的事物皆有原因。 前提2：宇宙开始存在。 ∴ 宇宙有一个原因（上帝）。
Supporters point to the Big Bang as evidence that the universe did begin, while opponents argue that the notion of a cause might not apply to the universe as a whole or that 'nothingness' is illogical.
支持者以大爆炸作为宇宙有起始的证据，反对者则主张因果概念可能不适用于宇宙整体，或者“虚无”本身不合逻辑。
3. The Teleological Argument: Analogy Formula | 设计论证：类比公式
Paley's design argument hinges on an analogy: if you find a watch, you infer a watchmaker because of its complexity and purpose. The natural world displays far greater complexity and apparent purpose, so the argument infers a divine designer.
佩利的设计论证基于一个类比：如果你发现一块手表，你会因其复杂性和目的性推断出有制表师。自然界展现出更复杂的构造和明显的目的性，因此论证推断有一位神圣的设计者。
Watch : Watchmaker :: Nature’s complex order : Intelligent Designer (God).
手表 : 制表师 :: 自然的复杂秩序 : 智能设计者（上帝）。
The argument is inductive and analogical; it doesn't claim certainty but high probability. Its main challenge comes from evolutionary theory, which explains complexity through natural selection without needing a designer.
该论证是归纳性的和类比性的，并不宣称必然性，而是高概率。其主要挑战来自进化论——它通过自然选择解释了复杂性，而不需要设计者。
4. The Ontological Argument: Definitional Formula | 本体论论证：定义公式
Anselm’s argument begins not from observation but from the very definition of God as 'that than which nothing greater can be conceived'. If God exists only in the mind, a greater being could be thought of that also exists in reality. Therefore, God must exist in reality.
安瑟伦的论证并非从观察出发，而是从上帝的定义——“不可设想有比之更伟大者”——入手。若上帝仅存在于思想中，那便可设想一个也存在于现实中的更伟大者。因此，上帝必然存在于现实中。
ing → Existing in reality is greater than existing only in mind → ∴ God exists in reality.
上帝 = 可设想的最伟大者 → 存在于现实中比仅存在于思想中更伟大 → ∴ 上帝存在于现实中。
Gaunilo famously parodied this by applying the same logic to a 'perfect island', suggesting the argument would force absurd conclusions. Kant later argued that 'existence is not a predicate' and cannot be added to a definition like a property.
高尼罗以“完美海岛”作类比，指出同样的逻辑可得出荒诞结论。康德后来论证“存在不是谓词”，不能像属性一样添加到定义中。
5. The Problem of Evil: Inconsistent Triad Formula | 罪恶问题：不一致三元组公式
The logical problem of evil presents three claims about God that seem mutually incompatible. If God is all-powerful and all-loving, He would want to and be able to eliminate evil. Yet evil exists, casting doubt on the existence of such a God.
逻辑上的罪恶问题提出了关于上帝的三个似乎互不相容的声明。若上帝全能和全爱，他必然愿意并能够消除罪恶。但罪恶存在，这便质疑了这样一位上帝的存在。
1. God is omnipotent. 2. God is omnibenevolent. 3. Evil exists. ➔ These three cannot all be true.
1. 上帝全能。 2. 上帝全爱。 3. 罪恶存在。 ➔ 三者无法同时为真。
J. L. Mackie formalised this inconsistent triad, concluding that a theist must reject at least one of the three to restore logical consistency.
J. L. 麦凯将这不一致三元组形式化，指出有神论者必须至少放弃其中一项才能恢复逻辑一致性。
6. The Free Will Defence: Logical Formula | 自由意志辩护：逻辑公式
The free will defence argues that God could not have created a world where humans are genuinely free and yet never choose evil. Moral evil results from the misuse of free will, and the great good of freedom justifies a world in which evil is possible.
自由意志辩护提出，上帝不可能创造一个人类拥有真正自由却从不选择作恶的世界。道德上的恶源自对自由意志的误用，而自由的巨大善好使一个可能存在恶的世界得到辩护。
tails the possibility of evil → Therefore, evil is logically compatible with a loving God.
上帝渴望受造物拥有真正自由 → 真正自由包含作恶的可能 → 因此，罪恶在逻辑上与慈爱的上帝兼容。
This defence does not explain the amount or distribution of evil, but it aims to show that the existence of God and evil is not a logical contradiction.
这种辩护并未解释罪恶的数量与分布，但它旨在表明上帝与罪恶的存在并不在逻辑上矛盾。
7. The Argument from Religious Experience: Inductive Formula | 宗教体验论证：归纳公式
A large number of people across cultures claim to have experienced God or a divine reality. Swinburne’s principle of credulity suggests that we should accept what appears to be the case unless we have good evidence to doubt it. Applied to religious experiences, this inductively supports belief.
不同文化中大量人士声称体验过上帝或神圣实在。斯温伯恩的“轻信原则”主张，除非有充分证据怀疑，否则我们应接受呈现给我们的经验事实。将此应用于宗教体验，便构成对信仰的归纳支持。
xperience of X → In the absence of defeating evidence, it is rational to believe X exists.
众多主体报告对X的体验 → 若没有击倒性证据，相信X存在是合理的。
Challenges include the sheer variety of conflicting experiences and psychological or neurological explanations that reduce them to brain states rather than veridical perceptions.
挑战包括各种相互矛盾的体验之多，以及心理学或神经科学将之归结为大脑状态的解释，而非真实的感知。
8. Pascal’s Wager: Expected Value Formula | 帕斯卡的赌注：期望值公式
Pascal frames belief in God as a bet with infinite potential payoff. The wager relies on a decision matrix comparing the consequences of belief and disbelief under two possibilities: God exists or does not exist.
帕斯卡将对上帝的信仰框定为一场具有无限潜在回报的赌博。该赌注依赖一个决策矩阵，比较上帝存在与不存在两种可能下信与不信的后果。
| God exists / 上帝存在 | God does not exist / 上帝不存在 | |
| Believe / 信 | Infinite gain (Heaven) / 无限收益（天堂） | Minor loss (worldly pleasures) / 微小损失（世俗享乐） |
| Disbelieve / 不信 | Infinite loss (Hell) / 无限损失（地狱） | Minor gain / 微小收益 |
Expected value of belief = ∞ (infinite gain) − small finite cost → rational to believe.
信仰的期望值 = ∞（无限收益） − 微小有限成本 → 信是理性的。
Critics raise the 'many gods' objection: Pascal’s logic could be applied to any deity, and it also ignores that genuine belief cannot be willed on a purely calculative basis.
批评者提出“众多神灵”反对意见：帕斯卡的逻辑可应用于任何神祇，且忽视了真正的信仰不能仅凭计算而强加于意志。
9. Utilitarianism: Greatest Happiness Formula | 功利主义：最大幸福公式
Bentham’s utilitarianism puts forward a quantifiable principle: the right action is the one that produces the greatest happiness for the greatest number. His hedonic calculus attempts to measure pleasure and pain along several dimensions.
边沁的功利主义提出了一个可量化的原则：正确的行为是指能为最大多数人带来最大幸福的行为。他的快乐计算法试图从多个维度测量快乐与痛苦。
Greatest Happiness Principle: An action is right if Σ (Pleasure) − Σ (Pain) for all affected is maximised.
最大幸福原则：若对所有受影响者而言，快乐总量减去痛苦总量达到最大，行为即是正确的。
The hedonic calculus considers seven factors: intensity, duration, certainty, propinquity, fecundity, purity, and extent. This turns ethical decisions into a kind of moral arithmetic, though its feasibility is widely debated.
快乐计算法考量七个要素：强度、时长、确定性、远近、生殖性、纯度和范围。这把伦理决策转化为一种道德算术，但其可行性备受争议。
10. Kantian Ethics: Categorical Imperative Formula | 康德伦理学：绝对命令公式
Kant rejects utilitarian calculations, arguing that morality must be based on reason alone. His categorical imperative offers a universal formula to test whether an action is moral, independent of consequences.
康德拒绝功利主义计算，主张道德必须仅基于理性。他的绝对命令提供了一个不依赖于后果、检验行为是否道德的普遍公式。
