KS3 OCR Philosophy: Formula & Theorem Quick Reference Handbook | KS3 OCR 哲学：公式定理速查手册

📚 KS3 OCR Philosophy: Formula & Theorem Quick Reference Handbook | KS3 OCR 哲学：公式定理速查手册

Welcome to your go-to quick reference for the logical ‘formulas’ and philosophical ‘theorems’ that shape critical thinking in KS3 OCR Philosophy. Just as maths uses equations to solve problems, philosophy uses argument structures and principles to test ideas. This handbook collects the core patterns of reasoning, foundational principles, and classic thought experiments you will encounter, all laid out like a cheat sheet for clear thinking. Keep it close when constructing arguments, spotting flaws, or unpacking big questions about reality, knowledge, and right and wrong.

欢迎使用这份专为 KS3 OCR 哲学设计的核心‘公式’与‘定理’速查手册。正如数学用方程解题，哲学用论证结构和原理来检验思想。本手册汇集了你将遇到的核心推理模式、基础原则和经典思想实验，像一份清晰思维的备忘单。在构建论证、发现漏洞或探讨关于现实、知识和是非的大问题时，请随时参考。

1. Modus Ponens (Affirming the Antecedent) | 肯定前件式

This is the most straightforward valid argument form. If you accept a conditional statement and its condition is met, the conclusion follows necessarily. The ‘formula’ locks together two premises to guarantee a true conclusion when the premises are true.

这是最直接的有效论证形式。如果你接受一个条件陈述，且其条件成立，结论必然得出。这个‘公式’将两个前提牢牢扣合，当前提为真时，结论必定为真。

Formula: P → Q, P ∴ Q

Example: If it is raining (P), the ground is wet (Q). It is raining (P). Therefore, the ground is wet (Q).

示例：如果下雨（P），那么地面湿（Q）。正在下雨（P）。因此，地面湿（Q）。

The structure is valid regardless of content. However, notice that the truth of the conclusion depends on the truth of the premises. A philosopher must always check whether the ‘if-then’ link is sound and whether P is actually the case.

无论内容如何，该结构总是有效的。但请注意，结论的真取决于前提的真。哲学家必须始终检查‘如果-那么’连接是否可靠，以及 P 是否确实成立。

---

2. Modus Tollens (Denying the Consequent) | 否定后件式

This valid form works by denying the second part of the conditional. If the expected outcome does not occur, the condition that would have caused it must be false. It is a powerful tool for eliminating hypotheses.

这种有效形式通过否定条件句的后半部分来运作。如果预期的结果没有出现，那么会导致它的条件必定为假。这是消除假说的有力工具。

Formula: P → Q, ¬Q ∴ ¬P

Example: If the battery is charged (P), the phone turns on (Q). The phone does not turn on (¬Q). Therefore, the battery is not charged (¬P).

示例：如果电池有电（P），手机就会开机（Q）。手机没有开机（¬Q）。因此，电池没有电（¬P）。

Be careful not to mix this up with denying the antecedent, which is a fallacy. Modus tollens relies on the absence of the consequence to rightly challenge the initial condition.

注意不要将其与否前件谬误混淆。否定后件式依靠结果的不存在来合理地质疑原初条件。

---

3. Hypothetical Syllogism (Chain Argument) | 假言三段论（连锁论证）

This formula chains two conditional statements together to form a new conditional. If A leads to B, and B leads to C, then A leads to C. It is the logical backbone of many extended arguments and causal explanations.

这个公式将两个条件陈述链接起来，形成一个新的条件句。如果 A 导致 B，且 B 导致 C，则 A 导致 C。这是许多扩展论证和因果解释的逻辑支柱。

Formula: P → Q, Q → R ∴ P → R

Example: If I study (P), I understand the material (Q). If I understand the material (Q), I pass the test (R). Therefore, if I study (P), I pass the test (R).

示例：如果我学习（P），我就能理解材料（Q）。如果我理解材料（Q），我就能通过考试（R）。因此，如果我学习（P），我就能通过考试（R）。

The chain is only as strong as each individual link. A philosopher examines whether each ‘if-then’ really holds in the real world.

这条链的强度取决于每个单独的环节。哲学家会检验每个‘如果-那么’在现实中是否真的成立。

---

4. Disjunctive Syllogism (Process of Elimination) | 选言三段论（排除法）

When you face a limited set of options, this formula allows you to conclude one option is true by eliminating the others. The ‘or’ must be inclusive (at least one is true) for the formula to work cleanly.

当你面对一组有限的选项时，这个公式允许你通过排除其他选项来推断某一选项为真。‘或’必须是包含性的（至少有一个为真），这个公式才能畅通无阻。

Formula: P ∨ Q, ¬P ∴ Q

Example: Either the door is locked (P) or the key is broken (Q). The door is not locked (¬P). Therefore, the key is broken (Q).

示例：要么门锁了（P），要么钥匙断了（Q）。门没锁（¬P）。因此，钥匙断了（Q）。

This pattern underlies Sherlock Holmes’s famous dictum: ‘When you have eliminated the impossible, whatever remains, however improbable, must be the truth.’ But careful—you must be sure the list of options really is complete.

这种模式是福尔摩斯名言的基础：‘排除所有不可能之后，剩下的无论多么不可思议，都必定是真相。’但要小心——你必须确保选项列表确实完整无缺。

---

5. Fallacy: Affirming the Consequent & Denying the Antecedent | 谬误：肯定后件与否前件

Not every pattern that looks like modus ponens or modus tollens is valid. The two most common logical fallacies arise from misusing the conditional. Recognizing these invalid ‘formulas’ is as important as knowing the valid ones.

并非每个看起来像肯定前件或否定后件的模式都是有效的。两个最常见的逻辑谬误源于对条件句的误用。识别这些无效‘公式’与掌握有效公式同样重要。

Invalid: P → Q, Q ∴ P (Affirming the Consequent)

Example: If it is a dog (P), it has four legs (Q). It has four legs (Q). Therefore, it is a dog (P). (A cat also has four legs.)

示例：如果它是狗（P），那么它有四条腿（Q）。它有四条腿（Q）。因此，它是狗（P）。（猫也有四条腿。）

Invalid: P → Q, ¬P ∴ ¬Q (Denying the Antecedent)

Example: If it is raining (P), the ground is wet (Q). It is not raining (¬P). Therefore, the ground is not wet (¬Q). (A sprinkler could make it wet.)

示例：如果下雨（P），地面湿（Q）。没下雨（¬P）。因此，地面不湿（¬Q）。（洒水器可以让地面变湿。）

---

6. Ockham’s Razor (Principle of Parsimony) | 奥卡姆剃刀（简约原则）

This is not a logical formula but a methodological theorem: ‘Entities should not be multiplied beyond necessity.’ In practice, when faced with competing explanations, prefer the one that makes the fewest assumptions. It shaves off unnecessary complexity.

这不是逻辑公式，而是一条方法论定理：‘如无必要，勿增实体。’在实践中，面对相互竞争的解释时，应选择假设最少的那一个。它剃除了不必要的复杂性。

If you hear hoofbeats, think horses, not zebras (unless you are on the savannah). The theorem guides scientific theory choice and everyday reasoning, though it does not guarantee truth—sometimes the more complex explanation is correct.

如果听到蹄声，先想马，而非斑马（除非你在热带草原）。该定理指导科学理论的选择和日常推理，尽管它不保证真理——有时更复杂的解释反而是正确的。

A classic application: ‘The kettle is boiling because I switched it on’ is simpler than ‘The kettle is boiling because invisible gremlins heated it after I switched it on.’ Ockham’s razor slices away the gremlins.

经典应用：‘水壶沸腾是因为我打开了开关’比‘水壶沸腾是因为我打开开关后，隐形小精灵加热了它’更简单。奥卡姆剃刀切掉了小精灵。

---

7. Hume’s Law (Is-Ought Gap) | 休谟法则（实然-应然鸿沟）

David Hume identified a critical philosophical theorem: you cannot logically derive an ‘ought’ statement (a value judgement) purely from ‘is’ statements (factual descriptions). A conclusion about what we should do requires at least one value premise.

大卫·休谟指出了一个关键的哲学定理：你不能纯粹从‘是’陈述（事实描述）中逻辑推导出‘应该’陈述（价值判断）。一个关于我们应当做什么的结论至少需要一个价值前提。

Formula: Is ≠ ∴ Ought

Example of a flawed argument: Animals suffer in factory farms (is). Therefore, we should not eat meat (ought). The missing piece is a normative claim, such as ‘We should avoid causing suffering.’ Always check if a moral argument has snuck in an unstated ought.

有缺陷的论证示例：动物在工厂化农场中受苦（实然）。因此，我们不应该吃肉（应然）。缺失的环节是一个规范性主张，例如‘我们应当避免造成痛苦。’始终检查一个道德论证是否偷偷带入了未明说的应然。

This theorem does not say moral arguments are weak; it merely reveals their hidden value assumptions, forcing us to debate those values openly rather than pretending they are raw facts.

这一定理并非说道德论证脆弱；它只是揭示了论证中隐藏的价值假设，迫使我们去公开讨论那些价值观，而不是假装它们是赤裸裸的事实。

---

8. Descartes’s Method of Doubt (The Cartesian Theorem) | 笛卡尔的怀疑方法（笛卡尔定理）

René Descartes proposed a systematic process for finding certainty: doubt everything that can possibly be doubted, even your senses and the existence of the physical world. If any belief survives this extreme scepticism, it counts as a foundation for knowledge.

勒内·笛卡尔提出了一个寻找确定性的系统过程：怀疑一切可能被怀疑的事物，甚至包括你的感觉和物理世界的存在。如果有任何信念能在这种极端怀疑主义下幸存，它就可以作为知识的基础。

The theorem’s core ‘formula’ is: If a belief can be doubted, set it aside. Through this, Descartes arrived at his famous foundational truth: ‘I think, therefore I am’ (Cogito, ergo sum). Even if an evil demon deceives me, I must exist to be deceived.

该定理的核心‘公式’是：如果一个信念可以被怀疑，就把它搁置一边。通过这个方法，笛卡尔得出了他著名的根基性真理：‘我思故我在。’即使有邪恶的魔鬼欺骗我，我也必须存在才能被欺骗。

For KS3, apply the method as a thought tool: question the reliability of your senses (optical illusions, dreams) and examine which beliefs remain standing. It teaches intellectual humility and resilience.

在 KS3 阶段，可将该方法用作思维工具：质疑感官的可靠性（视错觉、梦境），核查哪些信念能屹立不动。它教导智识上的谦逊与韧性。

---

9. The Trolley Problem (Utilitarian Calculus) | 电车难题（功利主义演算）

This thought experiment functions as a theorem in ethics, testing moral principles. A runaway trolley will kill five people on the track; you can pull a lever to divert it onto a side track with one person. Should you sacrifice one to save five?

这个思想实验在伦理学中相当于一个定理，用于检验道德原则。一辆失控的电车即将轧死主轨道上的五个人；你可以拉杆将车转向侧轨，但会轧死一个人。你应该牺牲一人来救五人吗？

A utilitarian ‘formula’ would compute the greatest happiness for the greatest number: 5 lives > 1 life, so pull the lever. But the problem deepens when we change the scenario: what if you have to push a large man off a bridge to stop the trolley? Many who pull the lever refuse to push.

功利主义的‘公式’会计算最大多数人的最大幸福：5 条命 > 1 条命，所以拉杆。但如果我们改变情景：你必须把一个胖子推下天桥来让电车停下呢？许多愿意拉杆的人拒绝推人。

The Trolley Problem reveals that our moral reasoning involves not just outcomes but also notions of action vs. omission, and personal involvement. Use it as a template to test other ethical ‘formulas’ like deontology (rules matter) or virtue ethics.

电车难题揭示出，我们的道德推理不仅涉及结果，还涉及作为与不作为、个人卷入等概念。用它作为模板来检验其他伦理‘公式’，如义务论（规则重要）或德性伦理学。

---

10. The Ship of Theseus (Identity Theorem) | 特修斯之船（同一性定理）

If every plank of a ship is gradually replaced, is it still the same ship? This ancient puzzle serves as a philosophical theorem about identity and change. It challenges the ‘formula’ that an object is simply the sum of its parts.

如果一艘船的所有木板都被逐渐替换，它还是同一艘船吗？这个古老的谜题充当了一条关于同一性与变化的哲学定理。它挑战了‘一个物体就是其各部分总和’的‘公式’。

Consider a stronger version: if you collect all the old planks and rebuild the original ship, which one is the true Ship of Theseus? The puzzle uncovers criteria for identity—is it the continuity of form, the material, or the history? This theorem applies to personal identity too: are you the same person after all your cells have been replaced?

考虑一个更强的版本：如果你把所有旧木板收集起来，重建了原来的船，哪一艘才是真正的特修斯之船？这个谜题揭示了同一性的标准——是形式的连续性、材料、还是历史？该定理也适用于人格同一性：在你的所有细胞都被替换后，你还是同一个人吗？

---

11. Plato’s Cave (The Allegory as Reality-Theorem) | 柏拉图的洞穴（作为实在定理的寓言）

Plato’s allegory is a profound theorem about knowledge and reality. Prisoners chained in a cave see only shadows on a wall and mistake them for the real world. When one prisoner breaks free and sees the sun outside, he realises the shadows were mere copies.

柏拉图的寓言是一条关于知识和实在的深刻定理。被锁在洞穴里的囚徒只能看到洞壁上的影子，并误以为那就是真实世界。当一个囚徒挣脱束缚，看到外面的太阳时，他意识到影子只是仿品。

The ‘formula’ suggests that what we perceive through our senses (shadows) is a flawed reflection of a higher reality (the Forms). For KS3, use it to ask: how do we know our experience isn’t just a shadow of something truer? It links directly to scientific inquiry seeking underlying truths beyond appearances.

这个‘公式’暗示，我们通过感官感知到的（影子）是更高实在（理型）的不完美映像。对 KS3 而言，用它来提问：我们如何知道自己的体验不是某种更真实之物的影子？它直接连向寻求表象之下真理的科学探究。

---

12. Brain in a Vat (Radical Scepticism Theorem) | 缸中之脑（激进怀疑论定理）

Imagine your brain has been removed, placed in a vat of nutrients, and connected to a supercomputer feeding you a perfect simulation of reality. How could you prove you are not a brain in a vat? This modern sceptical theorem updates Descartes’s demon.

想象你的大脑被取出，放在一个营养液缸中，并连接到一台超级计算机，它向你输入完美的现实模拟。你如何证明自己不是缸中之脑？这个现代怀疑论定理更新了笛卡尔的魔鬼。

The ‘formula’ of this thought experiment is: any evidence you appeal to (e.g., ‘I can feel my hands’) could itself be part of the simulation. Thus, a conclusive disproof seems impossible. The value lies not in despair, but in examining the foundations of knowledge and the limits of justification.

这个思想实验的‘公式’是：你所求助的任何证据（例如‘我能感觉到我的手’）本身可能就是模拟的一部分。因此，一个决定性的反驳似乎是不可能的。其价值不在于绝望，而在于审视知识的基础和辩护的限度。

Philosophers use this to refine theories of knowledge: perhaps we do not need absolute certainty to claim knowledge, as long as our beliefs are reliably formed. This theorem thus pushes us toward a more pragmatic, resilient epistemology.

哲学家利用这一点来完善知识论：也许我们不需要绝对确定性来主张知识，只要我们的信念是可靠形成的即可。该定理因此推动我们走向一种更务实、更具韧性的认识论。

Published by TutorHao | Philosophy Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）