📚 Year 10 CCEA Philosophy: Formula & Theorem Quick Reference Handbook | CCEA Year 10 哲学公式定理速查手册
This quick reference handbook collects the most essential "formulas" and "theorems" from the Year 10 CCEA Philosophy syllabus – logical structures, key arguments, ethical principles and critical definitions – into a practical revision tool. Treat it as a cheat sheet for philosophical reasoning and a handy companion for essay writing.
本速查手册将 CCEA Year 10 哲学课程中最核心的“公式”和“定理”——逻辑结构、关键论证、伦理原则与重要定义——汇编成一份实用的复习工具。您可以把它当作哲学推理的备忘录，也适合答题时快速调用。
1. The Structure of an Argument | 论证的结构
In philosophy, an argument is a set of statements in which some statements (premises) are intended to provide support for another statement (the conclusion). Not every collection of sentences is an argument; there must be an inferential link.
在哲学中，一个论证是一组陈述，其中某些陈述（前提）旨在为另一个陈述（结论）提供支持。并非随意几句话就能构成论证；必须存在推理的关联。
- Premise indicator words: since, because, for, given that. | 前提指示词：因为、由于、鉴于。
- Conclusion indicator words: therefore, thus, so, consequently. | 结论指示词：所以、因此、因而、由此。
A standard form displays the premises first, each on a new line, followed by a line and the conclusion. For example: P₁ All humans are mortal. P₂ Socrates is a human. C Therefore, Socrates is mortal.
标准形式先列出前提，每行一个，然后在分隔线后写出结论。例如： P₁ 所有人都会死。P₂ 苏格拉底是人。C 所以，苏格拉底会死。
2. Validity and Soundness | 有效性与可靠性
A deductive argument is valid if and only if the truth of the premises guarantees the truth of the conclusion. Validity is about the logical structure, not about whether the premises are actually true.
一个演绎论证是有效的，当且仅当前提的真能保证结论的真。有效性只关心逻辑结构，不关心前提在现实中是否为真。
An argument is sound if and only if it is valid and all of its premises are actually true. Soundness is the gold standard for a deductive argument: a sound argument always has a true conclusion.
一个论证是可靠的，当且仅当它既是有效的，而且所有前提事实上为真。可靠性是演绎论证的黄金标准：可靠的论证总能得出真结论。
Validity + True Premises = Soundness
有效性 + 真前提 = 可靠性
3. Common Deductive Argument Forms | 常见演绎论证形式
These patterns appear frequently in philosophical reasoning. If you recognise the form and know it is valid, you can quickly assess an argument's logic.
以下模式在哲学推理中频繁出现。认准这些形式并知道它们是有效的，就能快速判断论证的逻辑。
| Name | 名称 | Logical Form | 逻辑形式 | Quick Check | 速查 |
|---|---|---|
| Modus Ponens 肯定前件式 |
If P then Q P ∴ Q |
Valid |
| Modus Tollens 否定后件式 |
If P then Q Not Q ∴ Not P |
Valid |
| Hypothetical Syllogism 假言三段论 |
If P then Q If Q then R ∴ If P then R |
Valid |
| Disjunctive Syllogism 选言三段论 |
P or Q Not P ∴ Q |
Valid |
| Affirming the Consequent 肯定后件 |
If P then Q Q ∴ P |
Invalid fallacy |
| Denying the Antecedent 否定前件 |
If P then Q Not P ∴ Not Q |
Invalid fallacy |
Understanding why the last two are invalid is just as important as memorising the valid forms. They show that truth can be accidentally preserved even when the reasoning is broken.
理解最后两种形式为何无效，与记住有效形式同样重要。它们说明，即使推理本身有缺陷，结论也可能碰巧为真。
4. Inductive Reasoning and Analogies | 归纳推理与类比
Unlike deduction, inductive arguments aim to make the conclusion probable, not certain. A strong inductive argument gives good reasons to accept the conclusion, while a weak one does not. Cogency adds the requirement that the premises are actually true.
与演绎不同，归纳论证旨在使结论具有可能性，而非必然性。强的归纳论证为接受结论提供了充分理由，弱的则不然。“有说服力”还要求前提本身为真。
Induction often moves from observed cases to general rules: 'The sun has risen every day in recorded history; therefore, the sun will rise tomorrow.' Analogical reasoning compares two things: 'A and B share properties x, y, and z; A also has property w; therefore, B probably has property w.'
归纳常从观察到的个案推出普遍规则：“自有记载以来太阳每天都升起；因此，明天太阳也会升起。”类比推理则比较两事物：“A与B共享属性x、y、z；A还具有属性w；因此，B可能也具有属性w。”
Strength + True Premises = Cogency
强度 + 真前提 = 有说服力
5. Common Logical Fallacies | 常见逻辑谬误
A fallacy is a mistake in reasoning that undermines the argument. Recognising fallacies helps you to critique weak arguments and avoid them in your own writing.
谬误是推理中的错误，会削弱论证。识别谬误有助于批判薄弱的论证，并避免自己犯错。
- Ad hominem (attack on the person) – rejecting a claim based on who says it, not the evidence. | 诉诸人身——根据说话者是谁来拒绝主张，而非依据证据。
- False dilemma – presenting only two options when more exist. | 假两难——只给出两种选项，实际还有更多可能。
- Straw man – misrepresenting an opponent's view to make it easier to attack. | 稻草人——歪曲对方观点，使其更容易被攻击。
- Begging the question – assuming the conclusion within a premise. | 乞题——在前提中预设了结论。
- Slippery slope – arguing that a small step will inevitably lead to a chain of extreme events without justification. | 滑坡谬误——无证据地声称一小步必然导致一系列极端后果。
- Post hoc ergo propter hoc – assuming that because B happened after A, A caused B. | 后此谬误——因为B在A之后发生，就认为A导致了B。
6. The Nature of God: Key Attributes | 上帝的本质：核心属性
In the philosophy of religion, the classical theistic God is defined by three 'omni-' attributes. These attributes generate much philosophical debate, especially when combined with the existence of evil.
在宗教哲学中，古典有神论的上帝由三个“全”属性定义。这些属性引发了大量哲学争论，尤其是当与恶的存在结合时。
- Omnipotence – God is all-powerful; able to do anything that is logically possible. | 全能——上帝无所不能，能做任何逻辑上可能的事。
- Omniscience – God is all-knowing; knows everything past, present and future, including free human choices. | 全知——上帝无所不知，知晓过去、现在和未来的一切，包括人的自由选择。
- Omnibenevolence – God is perfectly good and all-loving. | 全善——上帝具有完美的善，是全然慈爱的。
Philosophers ask whether these attributes are internally consistent. For example: if God knows the future, can humans still have free will? And how can an omnibenevolent and omnipotent God permit suffering?
哲学家追问这些属性是否内在一致。例如：若上帝预知未来，人类还能有自由意志吗？全能全善的上帝又怎能容许苦难呢？
7. Arguments for God's Existence | 上帝存在的论证
Three classical arguments attempt to prove God's existence through reason alone. Each has a distinctive logical "formula".
三种经典论证试图仅凭理性证明上帝存在。每一种都有独特的逻辑“公式”。
Cosmological Argument (First Cause) – Everything that begins to exist has a cause; the universe began to exist; therefore, the universe has a cause. Aquinas developed the 'unmoved mover' and 'first cause' versions.
宇宙论论证（第一因）——凡开始存在之物皆有原因；宇宙开始存在；因此，宇宙有一个原因。托马斯·阿奎那提出了“不动的推动者”和“第一因”版本。
∀x (B(x) → C(x)), B(u) ⊢ C(u)
Teleological Argument (Design) – The universe exhibits complexity and purpose that resembles intelligent design; design implies a designer; therefore, the universe has an intelligent designer. Paley's watchmaker analogy is the classic example.
设计论论证（目的论）——宇宙展现出的复杂性和目的性类似于智能设计；设计意味着设计者；因此，宇宙有一位智能设计者。佩利的钟表匠类比是经典例子。
Ontological Argument – Anselm defines God as 'that than which nothing greater can be conceived'. If God exists only in the mind, we can conceive of something greater (the same being existing in reality too). So God must exist in reality. This argument proceeds from the definition of God alone.
本体论论证——安瑟尔谟将上帝定义为“无法设想有比之更伟大者”。若上帝仅存在于心灵中，我们还能设想更伟大者（即同一位也在现实中存在）。因此上帝必须在现实中存在。该论证从定义上帝本身出发。
8. The Problem of Evil | 恶的问题
The logical problem of evil challenges the coherence of an omnipotent, omnibenevolent God in a world that contains evil. The core "formula" is a reductio ad absurdum.
恶的逻辑问题挑战全能全善的上帝与一个包含恶的世界是否相容。其核心“公式”是一种归谬法。
1. If God exists, God is omnipotent, omniscient and omnibenevolent.
2. An omnibenevolent being would want to prevent all evil.
3. An omnipotent being could prevent all evil.
4. Yet evil exists.
∴ An omnipotent, omnibenevolent God does not exist.
1. 如果上帝存在，上帝就是全能、全知且全善的。
2. 一个全善的存在会想要阻止一切恶。
3. 一个全能的存在能够阻止一切恶。
4. 但恶却存在。
∴ 一个全能全善的上帝并不存在。
Theists respond with theodicies, such as the free will defence: moral evil results from the misuse of free will, and free will is a greater good that justifies God allowing evil. The evidential problem of evil shifts from logical impossibility to the sheer quantity and distribution of suffering.
有神论者以神义论回应，比如自由意志辩护：道德恶源于对自由意志的误用，而自由意志是一种更大的善，足以让上帝允许恶存在。恶的证据问题则从逻辑不可能性转向苦难的巨大量级与分布。
9. Religious Experience as Evidence | 作为证据的宗教经验
Religious experiences are often presented as inductive evidence for God's existence. William James argued that such experiences have 'noetic quality', giving the experiencer direct knowledge of a transcendent reality.
宗教经验常被当作上帝存在的归纳证据。威廉·詹姆斯认为这类经验具有“认识性”，让经验者获得对超越现实的直接知识。
The argument form: If a person has a direct experience that seems to be of God, then, in the absence of defeaters, that person is justified in believing that God exists. The principle of credulity (Swinburne) suggests we should trust our experiences unless we have good reason to doubt them.
论证形式：若某人有了似乎来自上帝的直接经验，且没有推翻该经验的理由，则该人有理由相信上帝存在。斯温伯恩的“轻信原则”提出，除非有好理由怀疑，否则我们应相信自己的经验。
Challenges include the diversity of conflicting experiences, psychological explanations (wish fulfilment, neurotheology) and the problem of testing private experiences.
挑战包括相互矛盾的体验的多样性、心理学的解释（愿望满足、神经神学），以及私人经验难以检验的问题。
10. Ethical Theories: Utilitarianism | 伦理学理论：功利主义
Utilitarianism is a consequentialist theory: the right action is the one that produces the greatest good for the greatest number. The fundamental "formula" is known as the principle of utility.
功利主义是一种后果论理论：正确的行为就是能为最大多数人带来最大幸福的行为。其基本“公式”即功利原则。
Right action = maximises overall happiness (pleasure minus pain)
正确行为 = 能最大化总体幸福（快乐减去痛苦）
Bentham proposed a 'hedonic calculus' measuring intensity, duration, certainty, propinquity, fecundity, purity and extent. Mill distinguished higher and lower pleasures, arguing that 'it is better to be a human being dissatisfied than a pig satisfied'.
边沁提出“快乐计算法”，衡量强度、持续期、确定性、邻近性、生产力、纯度和范围。密尔区分了高级快乐与低级快乐，主张“做不满意的人，好过做满意的猪”。
Act utilitarianism applies the principle to each individual act; rule utilitarianism applies it to general rules. Key criticisms: crushing individual rights, ignoring justice, and the demandingness objection.
行为功利主义将原则应用于每一具体行为；规则功利主义将其应用于普遍规则。主要批评：践踏个人权利、忽视正义，以及要求过高的问题。
11. Ethical Theories: Kantian Ethics | 伦理学理论：康德伦理学
Kant's deontological ethics judges actions by their adherence to duty and the categorical imperative, not by consequences. The first formulation of the categorical imperative works like a universalisability test.
康德的义务论伦理学根据行为是否遵守义务和定言命令来判断，而非依据后果。定言命令的第一公式就像一种可普遍化的检验。
Act only on that maxim through which you can at the same time will that it should become a universal law.
只按照你同时能够愿意它成为一条普遍法则的准则去行动。
Another formulation: 'Act in such a way that you treat humanity, whether in your own person or in the person of another, always as an end and never merely as a means.' These principles ground human dignity and forbid lying, breaking promises and using others.
另一表述：“总是把人当作目的，无论是对自己还是他人，而绝不仅仅当作手段。”这些原则奠定了人的尊严，禁止说谎、背弃承诺和利用他人。
Critics point to the problem of conflicting duties (e.g., lying to save a life) and the rigidity of absolute rules.
批评者指出义务冲突的问题（如为救人而说谎）以及绝对规则的僵化。
12. Ethical Theories: Virtue Ethics | 伦理学理论：美德伦理学
Virtue ethics, rooted in Aristotle, focuses on character rather than rules or consequences. The central "formula" is the doctrine of the mean: virtue lies at a mean between two vices – one of excess and one of deficiency.
美德伦理学植根于亚里士多德，关注的是品格而非规则或后果。其核心“公式”是中道学说：德性处于两种恶的中间——过度与不及。
Virtue = the mean relative to us, determined by practical wisdom (phronesis)
德性 = 由实践智慧（phronesis）确定的相对于我们的中间
Examples: courage is the mean between rashness and cowardice; generosity is the mean between prodigality and stinginess. For Aristotle, the ultimate goal is eudaimonia – human flourishing or living well.
例：勇敢是鲁莽与怯懦的中道；慷慨是挥霍与吝啬的中道。在亚里士多德看来，最终目标是eudaimonia（幸福或盛放的人生）。
A common criticism is that virtue ethics does not give clear action guidance in a dilemma, and that what counts as a virtue may vary across cultures.
常见的批评是，美德伦理学在困境中无法提供明确的行动指南，而且什么算作美德可能因文化而异。
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