📚 Year 9 CIE Philosophy: Quick Reference Handbook of Formulas and Principles | Year 9 CIE 哲学：公式定理速查手册
Philosophy may not have equations in the mathematical sense, but it certainly possesses its own 'formulas' – structured ways of reasoning, evaluating arguments, and applying ethical principles. This quick reference handbook brings together the essential logical patterns, conceptual frameworks, and argument templates that every Year 9 CIE Philosophy student needs to master. Think of each entry as a reliable tool for dissecting complex ideas and constructing clear, persuasive philosophical responses.
哲学或许没有数学意义上的方程式，但它绝对拥有自己的“公式”——结构化的推理方式、评估论证的模式以及应用伦理原则的方法。这本速查手册汇集了每一位 Year 9 CIE 哲学学生都需要掌握的基本逻辑模式、概念框架和论证模板。你可以将每一条目视为剖析复杂思想、构建清晰且有说服力的哲学回应的可靠工具。
1. The Basic Argument Structure | 基本论证结构
nt offered as a reason to accept another statement. The conclusion is the statement that the premises are intended to support. When you read a philosopher's work, your first task is always to identify these components. For example, ' al (premise 1); Socrates is human (premise 2); therefore, Socrates is mortal (conclusion).' Practise separating premises from conclusions by looking for indicator words: 'since', 'because', 'given that' signal premises; 'therefore', 'hence', 'so', 'thus' signal conclusions.
每一个哲学论证都可以简化为一个简单的公式：前提 → 结论。前提是为接受另一个陈述而提供的理由。结论则是前提所意图支持的陈述。当你阅读哲学家的作品时，首要任务始终是识别这些组成部分。例如，“所有人都会死（前提1）；苏格拉底是人（前提2）；因此，苏格拉底会死（结论）。”通过寻找指示词来练习区分前提与结论：“既然”“因为”“鉴于”提示前提；“因此”“所以”“由此可见”提示结论。
2. Validity and Soundness: The Quality Test | 有效性与可靠性：质量检验
is measured by two qualities: validity and soundness. Validity is about logical structure – ires both validity and true premises. The formula is: Sound Argument = Valid Form + True Premises. When evaluating a philosophical argument, always ask two separate questions: 'Does the conclusion follow logically from the premises?' and 'Are all the premises actually true?' An argument can be valid but unsound, like 'All birds can fly; penguins are birds; therefore, penguins can fly.' The logic is valid, but the first premise is false, making the argument unsound.
一个论证的强度由两个品质衡量：有效性与可靠性。有效性关乎逻辑结构——如果前提为真，结论必然为真。前提实际是否为真并不重要。然而，可靠性要求同时具备有效性和真实的前提。公式是：可靠论证 = 有效形式 + 真实前提。在评估哲学论证时，始终要提出两个独立的问题：“结论是否从前提中逻辑地推出？”以及“所有前提实际上是否为真？”一个论证可以有效但不可靠，例如“所有鸟都会飞；企鹅是鸟；因此，企鹅会飞。”逻辑有效，但第一个前提为假，使得该论证不可靠。
3. Deductive vs. Inductive Reasoning | 演绎推理与归纳推理
Philosophy uses two main families of reasoning. Deductive reasoning aims for certainty: if the premises are true, the conclusion must be true, without exception. It moves from general principles to specific instances. Inductive reasoning aims for probability: the premises provide good reasons to believe the conclusion, but do not guarantee it. It often moves from specific observations to general claims. The deductive formula goes 'All X are Y; A is X; therefore, A is Y'. The inductive formula is 'In all observed cases, X leads to Y; therefore, probably X always leads to Y'. Knowing which type of reasoning is being used helps you set the correct standard of evaluation – absolute proof for deduction, high likelihood for induction.
哲学使用两大类推理。演绎推理旨在达到确定性：如果前提为真，结论必然为真，毫无例外。它从普遍原理走向具体事例。归纳推理旨在达到概率性：前提提供了充分的理由去相信结论，但并不保证结论为真。它通常从具体观察走向普遍主张。演绎公式为“所有X都是Y；A是X；因此，A是Y”。归纳公式为“在所有观察到的情况中，X导致Y；因此，很可能X总是导致Y”。了解正在使用哪一类推理，有助于你设定正确的评价标准——演绎要求绝对证明，归纳要求高度可能性。
4. Common Logical Fallacies: Patterns to Avoid | 常见逻辑谬误：需避免的模式
A fallacy is a flaw in reasoning that weakens an argument. Recognising fallacies is like having a diagnostic manual for poor thinking. Key fallacies include: Ad hominem – attacking the person instead of the argument ('You can't trust her view on climate change because she isn't a scientist'). Straw man – misrepresenting an opponent's position to make it easier to attack. False dilemma – presenting only two options when more exist. Slippery slope – claiming that one small step will inevitably lead to a chain of extreme events without justification. Begging the question – assuming the truth of the conclusion within a premise. Spot these patterns in your own writing and in the texts you analyse.
谬误是推理中的缺陷，会削弱论证。识别谬误就像拥有一本不良思维的诊断手册。主要谬误包括：人身攻击——攻击人而不是论证（“你不能相信她对气候变化的看法，因为她不是科学家”）。稻草人——歪曲对手的立场，使其更容易被攻击。假两难——在存在更多选项时只呈现两种选择。滑坡谬误——在没有根据的情况下声称一小步将不可避免地导致一连串极端事件。乞题——在前提中假设了结论为真。在你自己的写作和分析的文本中识别这些模式。
5. The Principle of Utility: Bentham's Hedonic Calculus | 功利原则：边沁的快乐计算
In ethics, utilitarianism offers a decision-making formula: choose the action that produces the greatest happiness for the greatest number. Jeremy Bentham proposed a 'hedonic calculus' to quantify pleasure and pain using criteria like intensity, duration, certainty, propinquity, fecundity, purity, and extent. While you do not need to assign numbers, the mental checklist is: For each possible action, consider how much pleasure and pain it will cause, to how many people, for how long, and how likely each outcome is. The morally right action is the one that maximises the total net balance of pleasure over pain. This formula turns ethics into a kind of cost-benefit analysis focused on well-being.
在伦理学中，功利主义提供了一个决策公式：选择能为最多人带来最大幸福的行为。杰里米·边沁提出了一种“快乐计算法”，使用强度、持续时间、确定性、临近性、衍生性、纯度和范围等标准来量化快乐和痛苦。虽然你不需要真的赋予数值，但心理清单是：针对每个可能的行为，考虑它会产生多少快乐与痛苦，影响多少人，持续多久，以及每种结果的可能性有多大。道德上正确的行为是能使快乐减去痛苦的总净余额最大化的行为。这一公式将伦理学转变为一种聚焦于福祉的成本效益分析。
6. Kant's Categorical Imperative: The Universal Law Formula | 康德的定言令式：普遍法则公式
Immanuel Kant’s deontological ethics rests on the categorical imperative, which functions as a test for moral rules. The first formulation states: 'Act only according to that maxim whereby you can at the same time will that it should become a universal law.' In practice, this means: 1. Identify the maxim (the personal rule) behind your intended action. 2. Imagine a world where everyone followed that maxim. 3. Ask: does this universalised maxim lead to a contradiction, either in conception (the action becomes impossible) or in will (you could not rationally will such a world)? If yes, the action is morally forbidden. The formula is a tool for exposing inconsistencies and testing whether you are making a special exception for yourself.
伊曼努尔·康德的义务论伦理学建立在定言令式之上，它充当道德规则的检验标准。第一个表述是：“只按照你同时能够愿意它成为一条普遍法则的那个准则去行动。”在实践中，这意味着：1. 识别你意图行为背后的准则（个人规则）。2. 想象一个每个人都遵循该准则的世界。3. 询问：这个普遍化了的准则是否会导致矛盾——无论是概念上的矛盾（行为变得不可能）还是意志上的矛盾（你无法理性地意愿这样一个世界）？如果答案是肯定的，该行为在道德上就是被禁止的。这一公式是用来揭露不一致性和检验你是否在为自己制造特例的工具。
7. Aristotle's Virtue Ethics: The Doctrine of the Mean | 亚里士多德的美德伦理：中道学说
vices (excess and deficiency). For example, courage is the mean between cowardice (deficiency of confidence) and recklessness (excess of confidence). Generosity lies between stinginess and wastefulness. To determine the right action, ask: 'What would a virtuous person do in this situation?' l average but a flexible target relative to the situation and the individual. This provides a framework for moral development rather than a rule-based decision algorithm.
美德伦理将焦点从行为转向品格。核心公式是：美德 = 两个恶（过度与不足）之间的中道。例如，勇敢是怯懦（自信不足）与鲁莽（自信过度）之间的中道。慷慨位于吝啬与挥霍之间。要确定正确的行为，就问：“一个有美德的人在这种情况下会怎么做？”然后，通过练习击中中道来培养相关的品格特质——中道并非刻板的数学平均值，而是相对于情境和个体而言的灵活目标。这为道德培养提供了一个框架，而非基于规则的决策算法。
8. The Socratic Method: A Formula for Questioning | 苏格拉底式方法：提问的公式
The Socratic method is a cooperative argumentative dialogue that uses probing questions to examine beliefs and uncover assumptions. Its structure can be remembered as: 1. Elicit a claim or definition from your partner. 2. Ask questions to clarify and test the boundaries of that claim. 3. Present a counterexample or a case that challenges the claim. 4. Help the partner revise the claim to accommodate the new insight. 5. Repeat until a more robust understanding is achieved. This process is not about winning but about refining ideas. In written philosophy, emulate Socrates by anticipating objections to your own view and responding to them.
苏格拉底式方法是一种合作性的辩论式对话，使用探索性问题来检验信念并揭示假设。其结构可以记作：1. 从对话伙伴那里引出一个主张或定义。2. 提出澄清性问题，测试该主张的边界。3. 提供一个反例或挑战该主张的情境。4. 帮助伙伴修正主张以容纳新的洞见。5. 重复，直至达成更坚实的理解。这一过程不是为了取胜，而是为了完善思想。在书面哲学中，通过预想他人对自己观点的反驳并加以回应，来效法苏格拉底。
9. The Philosophical Essay Structure: PEEL | 哲学论文结构：PEEL
A well-organised philosophical paragraph often follows the PEEL formula: Point, Evidence/Example, Explanation, Link. Point: State clearly the idea you are defending. Evidence/Example: Use a philosopher’s claim, a thought experiment, or a real-world analogy to support it. Explanation: Analyse how your evidence supports the point; unpack the reasoning. Link: Tie the paragraph back to the main question or transition to the next argument. For instance, in discussing utilitarianism: P – Utilitarianism avoids personal bias. E – A utilitarian would calculate the happiness of all affected parties equally, just as a judge should. E – This ensures moral decisions are public and impartial, based on observable consequences rather than private feelings. L – Therefore, it meets the demand for moral objectivity, unlike subjectivism.
组织良好的哲学段落通常遵循 PEEL 公式：Point（观点）、Evidence/Example（证据/例子）、Explanation（解释）、Link（连接）。观点：清晰陈述你所捍卫的想法。证据/例子：使用哲学家的主张、思想实验或现实世界的类比来支持它。解释：分析你的证据如何支持该观点；拆解推理过程。连接：将该段落与主要问题联系起来，或过渡到下一个论证。例如，在讨论功利主义时：观点——功利主义避免了个人偏见。证据/例子——一个功利主义者会平等计算所有受影响方的幸福，正如一位法官应该做的那样。解释——这确保了道德决定是公开且不偏不倚的，基于可观察的结果而非私人感受。连接——因此，它满足了道德客观性的要求，不同于主观主义。
10. Analysing Thought Experiments: A Step-by-Step Formula | 分析思想实验：逐步公式
Philosophy is rich with thought experiments like the trolley problem, the experience machine, or the ring of Gyges. Use this procedure to break them down: 1. Scenario: Describe the imaginary situation clearly and concisely. 2. Intuition pump: Identify the immediate moral intuition the experiment aims to evoke. 3. Target theory: Determine which philosophical theory or claim the experiment is designed to support or challenge. 4. Analogy check: Ask whether the scenario is sufficiently analogous to real-life cases to carry weight. 5. Alternative responses: Consider how a defender of the challenged theory might reinterpret the scenario or deny the intuition. This formula ensures you engage with thought experiments critically rather than simply accepting their punchlines.
哲学中充满了思想实验，如电车难题、体验机器或盖吉斯之戒。使用以下步骤来拆解它们：1. 情境：清晰、简洁地描述想象中的情境。2. 直觉泵：识别该实验旨在激发的直接道德直觉。3. 目标理论：确定该实验旨在支持或挑战的是哪个哲学理论或主张。4. 类比检验：询问该情境是否与现实生活中的案例足够类似，从而具有分量。5. 替代回应：思考被挑战理论的捍卫者可能如何重新诠释该情境或否认该直觉。这一公式确保你批判性地参与思想实验，而非简单地接受其结论。
11. Truth Tables for Logical Connectives | 逻辑连接词的真值表
Basic propositional logic helps you analyse complex claims. The key connectives and their truth-functional definitions are:
| Connective | Symbol | Truth condition | Example |
|---|---|---|---|
| Conjunction (AND) | ∧ | True only if both parts are true | P ∧ Q |
| Disjunction (OR) | ∨ | True if at least one part is true | P ∨ Q |
| Conditional (IF...THEN) | → | False only if antecedent true and consequent false | P → Q |
| Negation (NOT) | ¬ | Reverses truth value | ¬P |
基本命题逻辑帮助你分析复杂的陈述。主要的连接词及其真值函项定义如下：
| 连接词 | 符号 | 真值条件 | 例句 |
|---|---|---|---|
| 合取（且） | ∧ | 仅当两部分都为真时为真 | P ∧ Q |
| 析取（或） | ∨ | 只要至少一部分为真即为真 | P ∨ Q |
| 条件（如果...那么） | → | 仅在前件真且后件假时为假 | P → Q |
| 否定（非） | ¬ | 逆转真值 | ¬P |
12. The S.E.E.D. Formula for Evaluating Ethical Arguments | 评估伦理论证的 S.E.E.D. 公式
When faced with an ethical argument, quickly apply the S.E.E.D. checklist: Stakeholders – Who is affected, and whose interests are being considered or ignored? Empirical claims – What factual assertions about the world is the argument relying on, and are they true? Ethical principle – Which moral theory or principle is the argument implicitly or explicitly using (utility, rights, virtue)? Decision test – If we universalised the recommended action or principle, would the results be acceptable and consistent? This formula integrates many of the previous tools into a single, practical method for dissecting any moral argument you encounter in exams or class discussions.
当面对一个伦理论证时，快速应用 S.E.E.D. 检查清单：Stakaholders（利益相关者）——谁受到影响，哪些人的利益被考虑或被忽略？Empirical claims（经验性主张）——该论证依赖哪些关于世界的事实性断言，它们是真的吗？Ethical principle（伦理原则）——该论证隐含或明确使用了哪种道德理论或原则（功利、权利、美德）？Decision test（决策检验）——如果我们将所建议的行动或原则普遍化，其结果是否可接受且一致？这一公式将之前许多工具整合为一个单一且实用的方法，助你剖析在考试或课堂讨论中遇到的任何道德论证。
Published by TutorHao | Philosophy Revision Series | aleveler.com
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