📚 Philosophy Formula & Theorem Quick Reference Guide | 哲学公式定理速查手册
This handbook distills the most essential ideas in Year 8 CAIE Philosophy into clear, formula-like statements. Think of each entry as a mental tool a key theorem, a logical structure, or an ethical principle that you can instantly recall and apply. From the Cogito to the Greatest Happiness Principle, each section offers a quick-reference version of a major philosophical move, followed by a concise explanation.
这本手册将Year 8 CAIE哲学中最关键的思想提炼为清晰的、类似公式的陈述。你可以把每一个条目视为一个思维工具：一则关键定理、一个逻辑结构或一条伦理原则，能够随时回忆和运用。从“我思”到“最大幸福原则”，每个小节都提供一个重要哲学思维的速查版本，并附上简洁的说明。
1. What is Philosophy? | 什么是哲学？
wisdom through reason, argument, and questioning. Its core branches are metaphysics (What is real?), epistemology (How do we know?), ethics (What should we do?), and logic (What makes reasoning good?).
哲学 = 通过理性、论证和提问追求智慧的活动。其核心分支包括形而上学（什么是真实的？）、认识论（我们如何知道？）、伦理学（我们应当做什么？）和逻辑学（什么使得推理有效？）。
The philosophical mindset demands that we never simply accept a claim, but always ask "What reasons support it?" and "Could it be otherwise?"
哲学思维要求我们从不简单地接受某个主张，而总是追问“有哪些理由支持它？”以及“是否有其他可能？”。
2. Logical Arguments: Deduction & Induction | 逻辑论证：演绎与归纳
Deduction Formula: If premises are true → conclusion MUST be true.
A deductive argument aims for certainty. Example: All humans are mortal. Socrates is human. Therefore, Socrates is mortal. If the premises hold, the conclusion cannot be false.
演绎论证追求确定性。例子：所有人都会死。苏格拉底是人。所以苏格拉底会死。如果前提为真，结论不可能为假。
Induction Formula: Premises raise probability of conclusion, but do not guarantee it.
Inductive arguments support their conclusions with evidence from experience. The classic form: The sun has risen every day in recorded history, so it will probably rise tomorrow. The conclusion is likely true, but not logically necessary.
归纳论证用经验证据支持结论。经典形式：有记录以来太阳每天都升起，所以明天太阳很可能会升起。结论很可能为真，但在逻辑上并非必然。
3. Validity, Soundness & Fallacies | 有效性、健全性与谬误
Validity: IF premises true, THEN conclusion must be true.
Validity concerns the structural connection between premises and conclusion; it says nothing about whether the premises are actually true. A valid argument can have false premises.
有效性关注的是前提与结论之间的结构联系；它不关心前提实际上是否为真。一个有效的论证也可能含有假的前提。
Soundness = Validity + All premises are actually true.
A sound argument gives you a guaranteed true conclusion. It is the philosophical gold standard of proof.
健全论证保证你得到一个真实的结论。它是哲学证明的黄金标准。
Common Fallacy Quick Check:
- Affirming the consequent: If P then Q; Q is true, therefore P. (Invalid form.)
- Denying the antecedent: If P then Q; P is false, therefore ¬Q. (Invalid.)
- Ad hominem: Attacking the person, not the argument.
- Straw man: Misrepresenting an opponent’s view to make it easier to attack.
- 肯定后件：如果P则Q；Q为真，因此P。（无效形式。）
- 否定前件：如果P则Q；P为假，因此非Q。（无效。）
- 人身攻击：攻击人而不是论证。
- 稻草人谬误：歪曲对方观点以使其更容易攻击。
4. The Cogito: "I Think, Therefore I Am" | 我思故我在
Cogito ergo sum: The act of doubting proves the existence of the doubter.
Descartes resolved to doubt everything that could possibly be doubted, including his senses, his body, and even mathematical truths (via an evil demon hypothesis). He found he could not doubt that he was doubting. This act of thinking necessarily implies a thinker. "I think, therefore I am" becomes the first indubitable truth, the foundational axiom of his philosophy.
笛卡尔决定怀疑一切可能被怀疑的东西，包括他的感官、身体，甚至数学真理（借助邪恶恶魔的假设）。他发现，他无法怀疑自己正在怀疑这一事实。思考的行为必然意味着一个思考者的存在。“我思，故我在”成为第一个不容置疑的真理，是其哲学的公理基础。
5. The Problem of Evil: Logical Form | 恶的问题：逻辑形式
The inconsistent triad: God is omnipotent, God is omnibenevolent, Evil exists. At most two can be true.
If God is all-powerful, He can prevent evil; if He is all-good, He would want to prevent evil. Since evil undeniably exists, the existence of such a God seems logically impossible. This deductive form of the argument forces the theist to deny one of the three claims.
如果上帝是全能的，祂能阻止恶；如果祂是全善的，祂会想要阻止恶。既然恶无可否认地存在，这样一种上帝的存在似乎在逻辑上是不可能的。这个演绎形式的论证迫使人必须否定三个命题中的一个。
6. Utilitarianism: The Greatest Happiness Principle | 功利主义：最大幸福原则
Utility = Total pleasure produced - Total pain produced.
Jeremy Bentham and John Stuart Mill hold that the right action is the one that maximises utility for all affected. Consequences alone matter; every person's happiness counts equally. The "hedonic calculus" attempts to measure intensity, duration, certainty, and extent of pleasure.
杰里米·边沁和约翰·斯图亚特·密尔主张，正确的行为是能为所有相关者带来最大功用的行为。只有后果才是重要的；每个人的幸福同等重要。“快乐计算”试图衡量快乐的强度、持续时间、确定性和范围。
Act Utilitarianism: Choose the specific act that yields the highest net utility.
Rule Utilitarianism: Choose the rule that, if generally followed, would maximise utility.
行为功利主义：选择能产生最大净功用的具体行为。
规则功利主义：选择如果被普遍遵守将会最大化功用的规则。
7. Kant's Categorical Imperative: Universalizability Formula | 康德的定言命令：可普遍化公式
"Act only according to that maxim whereby you can at the same time will that it should become a universal law."
Kant’s test for moral action does not look at consequences but at the principle behind the action. Ask: Could I rationally want everyone to act on this maxim? If universalising the maxim leads to a contradiction in conception or in the will, the act is forbidden. This formula makes dignity and respect for persons fundamental.
康德的道德行为检验不关注后果，而关注行为背后的原则。试问：我能理性地希望每个人都按照这条准则行动吗？如果将该准则普遍化导致概念上的矛盾或意志上的矛盾，那么该行为就是被禁止的。这一公式将尊严和对人的尊重作为根本。
8. Virtue Ethics: The Golden Mean | 美德伦理：中庸之道
ue = a stable disposition to choose the mean between excess and deficiency relative to us.
Aristotle argues that moral goodness is not about following rules but about cultivating character. Each virtue lies at a midpoint between two vices. Courage is the mean between cowardice (deficiency) and rashness (excess). Practical wisdom (phronesis) is the intellectual virtue needed to identify the mean in a given situation.
亚里士多德认为，道德上的善不在于遵守规则，而在于培养品格。每一种美德都处于两种恶习之间的中点。勇气是怯懦（不足）与鲁莽（过度）之间的中道。实践智慧（phronesis）是识别特定情境下中道所需的理智德性。
9. The JTB Account of Knowledge | 知识的JTB解释
Knowledge = Justified True Belief (JTB).
Traditionally, if S knows that P, then (1) P is true, (2) S believes that P, and (3) S has adequate justification for P. This analysis was accepted until Edmund Gettier presented counterexamples in which someone has a justified true belief but intuitively lacks knowledge (e.g., a stopped clock that happens to show the right time).
传统上，如果S知道P，那么（1）P是真的，（2）S相信P，并且（3）S对P有充分的辩护。这个分析一直被人们接受，直到埃德蒙·盖梯尔提出了反例：某人拥有被辩护的真信念，但直觉上却缺乏知识（例如，一只恰好显示正确时间的坏钟）。
10. Hume's Problem of Induction | 休谟的归纳问题
Inductive inference assumes the Uniformity of Nature, but this cannot be justified without circularity.
Hume points out that all our inductive reasoning rests on the belief that the future will resemble the past. But we can only justify this belief by appealing to past experience—which is itself an inductive argument. Thus, induction cannot be rationally justified. We rely on it out of custom or habit, not logical necessity.
休谟指出，我们所有的归纳推理都基于“未来会与过去相似”的信念。但我们只能通过诉诸过去的经验来为这个信念辩护——而这本身就是一个归纳论证。因此，归纳无法得到理性的辩护。我们依赖归纳是出于习俗或习惯，而非逻辑必然。
11. Determinism vs Free Will: Key Arguments | 决定论与自由意志：关键论证
Hard Determinism: If every event is caused, then no free will; responsibility is an illusion.
Determinism claims that the state of the universe at any moment, plus the laws of nature, fixes all future events. Hard determinism accepts this and denies free will entirely. Libertarianism denies determinism, insisting that genuine free choices exist. Compatibilism holds that free will is compatible with determinism if “freedom” simply means acting on one’s own desires without external coercion.
决定论声称，宇宙在任意时刻的状态加上自然法则就决定了所有未来事件。强硬决定论接受这一点并完全否认自由意志。自由意志论否认决定论，坚称存在真正的自由选择。相容论则认为，如果“自由”仅仅意味着按照自己的欲望行动而没有外部强制，那么自由意志与决定论是相容的。
12. Ockham's Razor | 奥卡姆剃刀
"Do not multiply entities beyond necessity."
When comparing two explanations that account for the same evidence, the simpler one—with fewer assumptions—should be preferred. William of Ockham used this principle to argue against unnecessary abstractions. In modern philosophy, it serves as a methodological tool: shave away superfluous hypotheses.
当比较两个能解释同一现象的理论时，应当选择更简单的、假设更少的那个。奥卡姆的威廉运用这一原则来反对不必要的抽象。在现代哲学中，它作为一种方法论工具：剃掉多余的假设。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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