Year 12 SQA Philosophy: Formula & Theorem Quick Reference Handbook | SQA 哲学公式定理速查手册

📚 Year 12 SQA Philosophy: Formula & Theorem Quick Reference Handbook | SQA 哲学公式定理速查手册

This quick reference handbook distils the essential arguments, principles and reasoning patterns from the Year 12 SQA Philosophy syllabus into clear, formula-like structures. By mastering these conceptual ‘formulae’, you will be better equipped to analyse classic texts, evaluate philosophical positions and construct rigorous, exam-ready essays.

本速查手册将 12 年级 SQA 哲学课程中的核心论证、原理与推理模式提炼为清晰的公式化结构。掌握这些概念“公式”，能帮助你更有效地分析经典文本、评估哲学立场并构建严谨的考试作文。

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1. Descartes’ Method of Doubt | 笛卡尔的怀疑方法

In the Meditations on First Philosophy, Descartes employs the Method of Doubt in order to discover a foundation of absolute certainty. He resolves to reject any belief that admits the slightest possibility of doubt, treating it as if it were false, until he finds something indubitable.

在《第一哲学沉思集》中，笛卡尔运用怀疑方法来寻找绝对确定的基础。他决心把任何容许丝毫怀疑的信念都当作虚假的一样抛弃，直到发现某种不可怀疑的东西为止。

Step 1 – Sensory Doubt: Descartes notes that the senses sometimes deceive us concerning distant or small objects. Therefore, it is not prudent to trust them completely for certain knowledge.

步骤一——感官怀疑：笛卡尔指出，感官在远距离或微小对象上有时会欺骗我们。因此，完全信赖感官来获取确定性知识是不明智的。

Step 2 – The Dream Argument: He then considers the possibility that he might be dreaming. There are no definitive signs to distinguish waking experiences from dreams; thus, any sensory belief could be part of a dream and is dubitable.

步骤二——梦的论证：他进而考虑自己可能正在做梦。没有明确的标志能区分清醒经验与梦境，因此任何感官信念都可能属于梦境，都是可怀疑的。

Step 3 – The Evil Demon Hypothesis: To push doubt to its extreme, Descartes imagines a powerful, malicious demon who deceives him about even the simplest rational truths, such as arithmetic and geometry. This scenario renders all a priori beliefs dubitable as well.

步骤三——恶魔假设：为了将怀疑推向极致，笛卡尔设想有一个强大而邪恶的恶魔，甚至在最简单的理性真理（如算术与几何）上也欺骗他。这一情形使得所有先验信念也变得可怀疑。

Central formula of the method:

这一方法的核心公式：

For any belief B: if it is possible that B is false or generated by deception, then B is not a foundationally certain truth.

∃ possible doubt for B → B is rejected as foundational knowledge

This systematic doubt clears away all uncertain beliefs until the thinker arrives at the one truth that resists even the evil demon.

这种系统怀疑清除了所有不确定的信念，直到思考者抵达那条连恶魔也无法动摇的真理。

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2. The Cogito: ‘I think, therefore I am’ as Certainty | 我思：作为确定性的“我思故我在”

After applying thoroughgoing doubt, Descartes discovers that the very act of doubting confirms his own existence. Even if a demon deceives him about everything else, he must exist in order to be deceived.

在进行彻底怀疑之后，笛卡尔发现，怀疑活动本身就证实了他自己的存在。即使恶魔在其他一切事情上欺骗他，他为了能够受骗也必须存在。

Whenever I am thinking, I cannot coherently deny my own existence as a thinking thing. This proposition is not derived from a deductive argument in the traditional sense but is experienced as a clear and distinct self-evident truth.

每当我思考时，我无法在逻辑上一致地否定自己作为一个思维者的存在。这一命题并非来自传统意义上的演绎论证，而是被体验为清晰分明、自明的真理。

The core certainty formula: Cogito, ergo sum – I think, therefore I am. In logical terms:

核心确定性公式：我思，故我在。用逻辑语言表示：

I am thinking → I exist (as a thinking substance)

Descartes then treats this ‘I’ as a res cogitans, a thinking thing whose essence is thought, and uses it as the indubitable foundation on which to rebuild knowledge.

笛卡尔随后将这个“我”视为res cogitans（思维实体），其本质是思维，并用它作为重建知识大厦的不可怀疑的基石。

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3. Hume’s Fork: A Priori vs A Posteriori | 休谟的叉子：先验与后验

David Hume divides all objects of human reason into two exclusive categories, known as ‘Hume’s Fork’: relations of ideas and matters of fact.

大卫·休谟将人类理性的全部对象划分为两个互斥的范畴，即著名的“休谟的叉子”：观念的关系和事实。

Relations of ideas are a priori, necessarily true (their denial implies a contradiction) and discoverable by pure thought. Examples include mathematical truths and logical tautologies.

观念的关系是先验的、必然为真（否认它们会导致矛盾），并且纯粹通过思维即可发现。例子包括数学真理和逻辑重言式。

Matters of fact, by contrast, are a posteriori, contingent (their denial is possible without contradiction) and known only through experience. ‘The sun will rise tomorrow’ is a matter of fact because its contrary is conceivable.

与之相反，事实是后验的、偶然的（否认它们并不导致矛盾），只有通过经验才能认识。“太阳明天会升起”是一个事实，因为设想其相反情况并不矛盾。

The fork can be expressed as a rule: any meaningful proposition that is not a relation of ideas must be a matter of fact; otherwise, it is mere sophistry and illusion.

这一叉子可表达为一条规则：任何有意义的命题，如果不是观念的关系，就必定是事实；否则不过是在玩弄辞藻和幻觉。

∀ proposition P: P ∈ Relations of Ideas (a priori, necessary) ∨ P ∈ Matters of Fact (a posteriori, contingent)

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4. Hume’s Problem of Induction | 休谟的归纳问题

Hume challenges the rational justification of inductive reasoning: our inference from past regularities to future events. All inductive arguments rely on the assumption that nature is uniform, that the future will resemble the past.

休谟对归纳推理的理性辩护提出了挑战：我们从过去的恒常联系推断未来的事件。一切归纳论证都依赖于“自然齐一性”这一假设，即未来与过去相像。

But how can the Principle of the Uniformity of Nature be justified? It cannot be proved a priori, because its denial is conceivable. It cannot be proved by experience either, because any appeal to past experience presupposes the very uniformity we are trying to establish. The argument becomes circular.

但是，自然齐一性原则本身如何得到辩护？它无法通过先验证明，因为它的反面是可以设想的。它也无法通过经验证明，因为任何诉诸过去经验的尝试都已经预设了我们试图建立的齐一性，从而陷入循环。

The sceptical formula captures this circle:

怀疑论的公式抓住了这个循环：

Inductive inference: (Swans₁, Swans₂, … Swansₙ were white) → (All swans are white) relies on (Nature is uniform),
but (Nature is uniform) is itself an inductive generalisation from past experience.

Hume concludes that induction is not rationally justified but is a habit or custom of the mind. This remains one of the most powerful challenges in epistemology.

休谟的结论是：归纳推理并非基于理性，而是心灵的一种习惯或习俗。这至今仍是认识论中最强有力的挑战之一。

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5. Bentham’s Hedonic Calculus | 边沁的快乐计算法

In utilitarian moral philosophy, Jeremy Bentham proposes that the rightness of an action depends on the amount of pleasure or pain it produces. To measure this, he devises the Hedonic Calculus, which evaluates pleasures across seven dimensions.

在功利主义道德哲学中，边沁提出，一个行为的对错取决于它所产生的快乐或痛苦的总量。为了衡量这个总量，他设计了快乐计算法，从七个维度来评估快乐。

The seven criteria allow us to compare different actions and choose the one that maximises overall utility. The calculus can be seen as a decision-making formula:

这七个标准让我们能够比较不同的行为，并选择能最大化总体功利的行为。该计算法可视为一种决策公式：

Utility(Action) = Σ (Intensity + Duration + Certainty + Propinquity + Fecundity + Purity) × Extent

Criterion (English)	标准（中文）	Explanation (说明)
Intensity	强度	How strong is the pleasure? 快乐有多强？
Duration	持续时间	How long will it last? 它会持续多久？
Certainty	确定性	How likely is it to occur? 它发生的可能性多大？
Propinquity	远近	How soon will it happen? 它多久后会发生？
Fecundity	丰度	Will it lead to further pleasures? 它会带来更多快乐吗？
Purity	纯度	Is it mixed with pain? 它是否夹杂痛苦？
Extent	广度	How many beings are affected? 有多少个体受到影响？

While Bentham treats all pleasures as qualitatively equal, his calculus provides a systematic method for aggregating consequences. Criticisms include the difficulty of precise measurement and the neglect of justice or rights.

虽然边沁认为所有快乐在性质上相等，但他的计算法提供了一个系统化的后果加总方法。批评包括难以精确测量以及忽视了正义或权利。

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6. Kant’s Categorical Imperative (Formula of Universal Law) | 康德的定言命令（普遍法则公式）

Immanuel Kant holds that moral obligations are derived from pure practical reason. The supreme principle of morality is the Categorical Imperative, which commands unconditionally, unlike hypothetical imperatives that depend on desires.

康德主张，道德义务源于纯粹实践理性。道德的最高原则是定言命令，它无条件地发出指令，不同于依赖于欲望的假言命令。

The first formulation, the Formula of Universal Law, states: ‘Act only according to that maxim whereby you can, at the same time, will that it should become a universal law.’

第一个表达——普遍法则公式——要求：“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。”

To apply this formula, identify the maxim of your proposed action and ask whether it can be consistently universalised. If willing the maxim as a universal law leads to a contradiction in conception (the action becomes impossible) or a contradiction in will (you cannot rationally will such a world), then the action is forbidden.

应用该公式时，首先要确定你打算采取行动的准则，然后追问：如果它被普遍化，是否依然自洽。如果愿意该准则成为普遍法则会导致构想中的矛盾（行为本身变得不可能）或意愿中的矛盾（你不能合乎理性地意愿这样一个世界），那么该行动就是被禁止的。

Action A is morally permissible iff the maxim M of A can be consistently universalised without contradiction in conception or in will.

∀ maxim M: Permissible(M) ↔ Universalising(M) is consistent

For example, making a false promise cannot be universalised because the institution of promising would break down; therefore, it violates duty.

例如，做虚假承诺无法被普遍化，因为那样承诺制度将崩溃；因此它违反了义务。

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7. Anselm’s Ontological Argument as a Modal Formula | 安瑟伦的本体论论证（模态公式）

Anselm of Canterbury defines God as ‘that than which nothing greater can be conceived’ (TTWNGCBC). He argues that if God exists only in the mind, we could conceive of a greater being that also exists in reality. Thus, God must exist in reality to be the greatest conceivable being.

安瑟伦将上帝定义为“那无法设想有比之更伟大者”。他论证说，如果上帝只存在于心灵中，我们就能设想一个更伟大的、也存在于现实中的存在者。因此，上帝必须在现实中存在，才能成为可设想的最伟大者。

The logical structure can be presented as a reductio ad absurdum:

其逻辑结构可以呈现为归谬法：

Premise 1: God = TTWNGCBC
Premise 2: Suppose God exists only in the understanding and not in reality.
Premise 3: A being that exists both in the understanding and in reality is greater than one that exists only in the understanding.
Conclusion: Then we can conceive of a being greater than God (contradiction).
Therefore, God must exist in reality.

Anselm’s argument treats existence as a perfection, a property that makes a thing greater. Kant later objects that existence is not a real predicate, but the formula remains a cornerstone of the Philosophy of Religion module.

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