来源 / Source: Project Gutenberg

伦理学：第一部分 - 论神

本尼迪克特·德·斯宾诺莎 (Benedict de Spinoza) R.H.M. 埃尔威斯 (R.H.M. Elwes) 译

定义 (Definitions)

I. 自因 (causa sui)，我指的是这样的事物：其本质包含存在，或者说其本性只能被设想为存在。

II. 凡是可以被另一同性质的事物所限制的东西，就叫做同类有限 (finite after its kind)。例如，一个物体被称为有限，是因为我们总能设想另一个更大的物体。同样，一个思想被另一个思想所限制，但物体不被思想限制，思想也不被物体限制。

III. 实体 (substance)，我指的是在自身内并通过自身而被设想的东西：换言之，形成关于它的概念，不需要借助于关于其他东西的概念。

IV. 属性 (attribute)，我指的是理智将其知觉为构成实体本质的东西。

V. 样式 (mode)，我指的是实体的分殊 (affectiones)，亦即在别的事物内并通过别的事物而被设想的东西。

VI. 神 (God)，我指的是绝对无限的存在——也就是说，具有无限属性的实体，其中每一个属性都表现了永恒和无限的本质。

说明：我说它是绝对无限，而不是说它在同类中无限：因为仅在同类中无限的东西，我们可以否认它具有无限的属性；但是对于绝对无限者而言，凡是表示本质的，不包含任何否定的东西，都属于它的本质。

VII. 凡是仅仅由自身本性的必然性而存在，其行为仅仅由它自身决定的东西，就叫做自由 (free)。反之，凡是其存在或行为按某种固定的确定的方式为他物所决定者，就叫做必然，或者说受制 (constrained)。

VIII. 永恒 (eternity)，我指的是存在本身，就这存在被设想为必然只从永恒事物的定义推得而言。

说明：因为这样的存在被设想为一种永恒的真理，就像事物的本质那样，因此不能用延绵或时间来解释，即使延绵被设想为无始无终。

公理 (Axioms)

I. 凡存在者，或存在于自身内，或存在于他物内。

II. 凡不能通过他物而被设想者，必须通过自身而被设想。

III. 有确定的原因，必然有结果跟随；反之，若无确定的原因，绝不可能有结果跟随。

IV. 认识结果依赖于认识原因，且包含认识原因。 $$\text{知识}(结果) \implies \text{知识}(原因)$$

V. 凡相互间毫无共同之处的事物，不能借此一事物理解彼一事物；或者说，关于此一事物的概念不包含关于彼一事物的概念。 $$A \cap B = \emptyset \implies \text{概念}(A) \not\to \text{概念}(B)$$

VI. 真观念必须符合其对象（ideate）。

VII. 若一事物能被设想为不存在，则其本质不包含存在。

Source / 来源: Project Gutenberg

Ethics: Part I - Concerning God

Benedict de Spinoza Translated by R.H.M. Elwes

Definitions

I. By that which is self-caused (causa sui), I mean that of which the essence involves existence, or that of which the nature is only conceivable as existent.

II. A thing is called finite after its kind, when it can be limited by another thing of the same nature; for instance, a body is called finite because we always conceive another greater body. So, also, a thought is limited by another thought, but a body is not limited by thought, nor a thought by body.

III. By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception.

IV. By attribute, I mean that which the intellect perceives as constituting the essence of substance.

V. By mode, I mean the modifications (affectiones) of substance, or that which exists in, and is conceived through, something other than itself.

VI. By God, I mean a being absolutely infinite—that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality.

Explanation: I say absolutely infinite, not infinite after its kind: for, of a thing infinite only after its kind, infinite attributes may be denied; but that which is absolutely infinite, contains in its essence whatever expresses reality, and involves no negation.

VII. That thing is called free, which exists solely by the necessity of its own nature, and of which the action is determined by itself alone. On the other hand, that thing is necessary, or rather constrained, which is determined by something external to itself to a fixed and definite method of existence or action.

VIII. By eternity, I mean existence itself, in so far as it is conceived necessarily to follow solely from the definition of that which is eternal.

Explanation: Existence of this kind is conceived as an eternal truth, like the essence of a thing, and therefore cannot be explained by duration or time, even if the duration be conceived without beginning or end.

Axioms

I. Everything which exists, exists either in itself or in something else.

II. That which cannot be conceived through anything else must be conceived through itself.

III. From a given definite cause an effect necessarily follows; and, on the other hand, if no definite cause be granted, it is impossible that an effect can follow.

IV. The knowledge of an effect depends on and involves the knowledge of a cause. $$\text{Knowledge}(E) \implies \text{Knowledge}(C)$$

V. Things which have nothing in common cannot be understood, the one by means of the other; the conception of one does not involve the conception of the other. $$A \cap B = \emptyset \implies \text{Conception}(A) \not\to \text{Conception}(B)$$

VI. A true idea must agree with its ideate or object.

VII. If a thing can be conceived as non-existing, its essence does not involve existence.

来源 / Source: Project Gutenberg

几何原本：第一卷 (The Elements: Book I)

欧几里得 (Euclid) 托马斯·L·希思 (Thomas L. Heath) 译 (1908)

定义 (Definitions)

1. 点 (point) 是没有部分的。

2. 线 (line) 是无宽度的长度。

3. 线的端点是点。

4. 直线 (straight line) 是均匀地平放于其上诸点之线。

8. 平面角 (plane angle) 是平面内两条相交且不共一直线的线之间的倾斜度。 $$\angle \alpha$$

10. 当一条直线矗立在另一条直线上，使得邻角彼此相等时，这些相等的角每一个都是直角 (right)，而矗立在另一条上的直线叫做那条直线的垂线 (perpendicular)。 $$\text{若 } \angle \alpha = \angle \beta \implies \angle \alpha = 90^\circ$$

15. 圆 (circle) 是由一条线包围的平面图形，从图形内某一点向该线所作的所有直线彼此相等。

23. 平行 (parallel) 直线是在同一平面内，向两个方向无限延长而在任何方向都不相交的直线。 $$L_1 \parallel L_2 \iff L_1 \cap L_2 = \emptyset$$

公设 (Postulates)

提出以下公设：

1. 从任一点到任一点作一条直线。

2. 将有限直线连续地沿直线延长。

3. 以任意中心和距离（半径）画圆。

4. 凡直角都彼此相等。

5. 若一条直线与另外两条直线相交，使同侧的内角和小于两个直角，则这两条直线若无限延长，必在内角和小于两直角的一侧相交。

注： 这就是著名的平行公设 (Parallel Postulate)。用现代符号表示： 若 $\alpha + \beta < 180^\circ$，则两直线相交。

公理 / 一般概念 (Common Notions)

1. 等于同量的量彼此相等。 $$A = C \land B = C \implies A = B$$

2. 等量加等量，其和相等。 $$A = B \implies A + C = B + C$$

3. 等量减等量，其差相等。

4. 彼此重合的东西彼此相等。

5. 整体大于部分。 $$\forall x \in S, S > x$$

Source / 来源: Project Gutenberg

The Elements: Book I

Euclid Translated by Thomas L. Heath (1908)

Definitions

1. A point is that which has no part.

2. A line is breadthless length.

3. The extremities of a line are points.

4. A straight line is a line which lies evenly with the points on itself.

8. A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line. $$\angle \alpha$$

10. When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands. $$\text{If } \angle \alpha = \angle \beta \implies \angle \alpha = 90^\circ$$

15. A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another.

23. Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction. $$L_1 \parallel L_2 \iff L_1 \cap L_2 = \emptyset$$

Postulates

Let the following be postulated:

1. To draw a straight line from any point to any point.

2. To produce a finite straight line continuously in a straight line.

3. To describe a circle with any centre and distance.

4. That all right angles are equal to one another.

5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Note: This is the famous Parallel Postulate. In modern notation: If $\alpha + \beta < 180^\circ$, then the lines intersect.

Common Notions

1. Things which are equal to the same thing are also equal to one another. $$A = C \land B = C \implies A = B$$

2. If equals be added to equals, the wholes are equal. $$A = B \implies A + C = B + C$$

3. If equals be subtracted from equals, the remainders are equal.

4. Things which coincide with one another are equal to one another.

5. The whole is greater than the part. $$\forall x \in S, S > x$$

来源 / Source: Wikisource

新工具：四种假象 (Novum Organum: The Four Idols)

弗朗西斯·培根 (Francis Bacon) Spedding, Ellis, and Heath 译 (1863)

假象学说

XXXVIII (38). 现今占据人类理智并深植其中的假象和错误观念，不仅如此围困人类的心灵以致真理很难找到进入的途径，而且即使真理得以进入，它们也会在科学的复兴（instauration）中再次遭遇并困扰我们，除非人们预先得到警告，并尽可能地武装自己以防备它们的侵袭。

XXXIX (39). 困扰人类心灵的假象有四类。为了区别起见，我给它们起了名字。

1.  种族假象 (Idola Tribus) 2.  洞穴假象 (Idola Specus) 3.  市场假象 (Idola Fori) 4.  剧场假象 (Idola Theatri)

假象分析

I. 种族假象 (Idola Tribus)

XLI (41). 种族假象植根于人类本性之中，植根于人类这一种族或族类之中。

因为断言人的感官是事物的尺度，这是一种错误的说法。

相反，所有的知觉，无论是感官的还是心灵的，都是根据个人的尺度，而不是根据宇宙的尺度。人类的理智就像一面不平整的镜子，它不规则地接收光线，把自己的性质掺杂到事物的性质中，从而使事物的性质变形和变色。

$$ P_{erception} \neq T_{ruth} \ P_{erception} = f(T_{ruth} + \text{Human Nature}) $$ (感知 \neq 真理 \ 感知 = f(真理 + 人类本性))

II. 洞穴假象 (Idola Specus)

XLII (42). 洞穴假象是个人的假象。因为每个人（除了人类本性普遍共有的错误之外）都有一个属于他自己的洞穴或巢穴，它折射并改变了自然之光；这或者是由于他自己独特的本性；或者是由于他的教育和与他人的交谈；或者是由于阅读书籍，以及对他所尊敬和仰慕的人的权威。

因此，人类的精神（正如它在不同个体中的分布那样）实际上是一个多变且充满扰动的东西，仿佛受偶然性的支配。

III. 市场假象 (Idola Fori)

XLIII (43). 还有一种假象是由人们相互间的交往和联系形成的，鉴于人们在市场上的往来和聚会，我称之为市场假象。因为人们靠言语进行交往，而语词的制定是根据俗人的理解能力的。因此，糟糕和不恰当的语词选择奇特地阻碍了理解力。

• 语词强迫理解力。
• 语词把一切都搞得混乱不堪。
• 语词把人们引向无数空洞的争论和无聊的幻想。

IV. 剧场假象 (Idola Theatri)

XLIV (44). 最后，还有一种假象是从各种哲学的教条以及错误的论证法则中移入人心的。我称之为剧场假象；因为在我看来，所有已被接受的体系都不过是许多舞台剧，以一种不真实的、戏剧性的方式表现着它们自己创造的世界。

我所说的不仅指目前流行的体系，也不仅指古代的派别和哲学；因为同样类型的许多剧本还可以被创作出来，并以同样人为的方式上演；既然即使最广泛不同的错误，其原因在很大程度上也是相同的。

Source / 来源: Wikisource

Novum Organum: The Four Idols

Francis Bacon Translated by Spedding, Ellis, and Heath (1863)

The Doctrine of Idols

XXXVIII. The idols and false notions which are now in possession of the human understanding, and have taken deep root therein, not only so beset men's minds that truth can hardly find entrance, but even after entrance is obtained, they will again in the very instauration of the sciences meet and trouble us, unless men being forewarned of the danger fortify themselves as far as may be against their assaults.

XXXIX. There are four classes of Idols which beset men's minds. To these for distinction's sake I have assigned names.

1. Idols of the Tribe (Idola Tribus)
2. Idols of the Cave (Idola Specus)
3. Idols of the Market-place (Idola Fori)
4. Idols of the Theatre (Idola Theatri)

Analysis of the Idols

I. Idols of the Tribe (Idola Tribus)

XLI. The Idols of the Tribe have their foundation in human nature itself, and in the tribe or race of men.

For it is a false assertion that the sense of man is the measure of things.

On the contrary, all perceptions as well of the sense as of the mind are according to the measure of the individual and not according to the measure of the universe. And the human understanding is like a false mirror, which, receiving rays irregularly, distorts and discolours the nature of things by mingling its own nature with it.

$$ P_{erception} \neq T_{ruth} \ P_{erception} = f(T_{ruth} + \text{Human Nature}) $$

II. Idols of the Cave (Idola Specus)

XLII. The Idols of the Cave are the idols of the individual man. For every one (besides the errors common to human nature in general) has a cave or den of his own, which refracts and discolours the light of nature; owing either to his own proper and peculiar nature; or to his education and conversation with others; or to the reading of books, and the authority of those whom he esteems and admires.

So that the spirit of man (according as it is meted out to different individuals) is in fact a thing variable and full of perturbation, and governed as it were by chance.

III. Idols of the Market-place (Idola Fori)

XLIII. There are also Idols formed by the intercourse and association of men with each other, which I call Idols of the Market-place, on account of the commerce and consort of men there. For it is by discourse that men associate, and words are imposed according to the apprehension of the vulgar. And therefore the ill and unfit choice of words wonderfully obstructs the understanding.

• Words force the understanding.
• Words throw all into confusion.
• Words lead men away into numberless empty controversies and idle fancies.

IV. Idols of the Theatre (Idola Theatri)

XLIV. Lastly, there are Idols which have immigrated into men's minds from the various dogmas of philosophies, and also from wrong laws of demonstration. These I call Idols of the Theatre; because in my judgment all the received systems are but so many stage-plays, representing worlds of their own creation after an unreal and scenic fashion.

Nor is it only of the systems now in vogue, or only of the ancient sects and philosophies, that I speak; for many more plays of the same kind may yet be composed and in like artificial manner set forth; seeing that errors the most widely different have nevertheless causes for the most part alike.

来源 / Source: Project Gutenberg

逻辑哲学论 (Tractatus Logico-Philosophicus)

路德维希·维特根斯坦 (Ludwig Wittgenstein) C.K. 奥格登 (C.K. Ogden) 译 (1922)

1. 世界 (The World)

1 世界是所发生的一切。

1.1 世界是事实的总体，而不是事物的总体。

1.11 世界由事实决定，并由它们是全部事实这一点所决定。

1.12 因为事实的总体决定了什么是所发生的，也决定了所有什么不是所发生的。

1.13 逻辑空间中的事实就是世界。

1.2 世界分解为事实。

1.21 任何一件事情都可以发生或不发生，而其余的一切则保持不变。

2. 原子事实 (Atomic Facts)

2 所发生的事，即事实，就是原子事实的存在。

2.01 原子事实是对象（实体，事物）的结合。

2.011 事物的本质在于它能够成为原子事实的组成部分。

2.012 在逻辑中没有什么是偶然的：如果一个事物能够出现在一个原子事实中，那么该原子事实的可能性必然已经预含于该事物之中。

2.0121 如果对于一个原本能够独自存在的事物，随后却有一个事态去适合它，这看起来就像是一种偶然。 如果事物能够出现在原子事实中，这种可能性必然已经存在于它们之中。 $$(逻辑实体不能只是可能的。逻辑处理每一种可能性，而一切可能性都是它的事实。)$$

2.013 每一个事物都好似在一个可能的原子事实的空间里。我可以设想这个空间是空的，但我无法设想没有这个空间的事物。

2.014 对象包含了一切事态的可能性。

2.0141 它出现在原子事实中的可能性就是对象的形式。

2.02 对象是简单的。

2.0201 每一个关于复合物的陈述都可以分析为关于其组成部分的陈述，并分析为那些完全描述了该复合物的命题。

2.021 对象构成了世界的实体。因此它们不能是复合的。

2.022 很明显，无论一个想象的世界与真实的世界有多么不同，它必然与真实世界有着某种共同的东西——即一种形式。

2.023 这种固定的形式由对象组成。

2.024 实体是独立于所发生的事而存在的。

2.025 它是形式和内容。

2.0251 空间、时间和颜色（有色性）是对象的形式。

2.027 固定的、持存的和对象是同一个东西。

2.0271 对象是固定的、存在的；配置是变动的、可变的。

2.0272 对象的配置构成了原子事实。

2.03 在原子事实中，对象相互咬合，就像链条的环节一样。

2.031 在原子事实中，对象以确定的方式结合在一起。

2.032 对象在原子事实中相互咬合的方式就是原子事实的结构。

2.033 形式是结构的可能性。

2.034 事实的结构由原子事实的结构组成。

2.04 存在的原子事实的总体就是世界。

2.05 存在的原子事实的总体也决定了哪些原子事实不存在。

2.06 原子事实的存在我们亦称之为正面的事实，它们的不存在称为负面的事实。

Source / 来源: Project Gutenberg

Tractatus Logico-Philosophicus

Ludwig Wittgenstein Translated by C.K. Ogden (1922)

1. The World

1 The world is everything that is the case.

1.1 The world is the totality of facts, not of things.

1.11 The world is determined by the facts, and by these being all the facts.

1.12 For the totality of facts determines both what is the case, and also all that is not the case.

1.13 The facts in logical space are the world.

1.2 The world divides into facts.

1.21 Any one can either be the case or not be the case, and everything else remain the same.

2. Atomic Facts

2 What is the case, the fact, is the existence of atomic facts.

2.01 An atomic fact is a combination of objects (entities, things).

2.011 It is essential to a thing that it can be a constituent part of an atomic fact.

2.012 In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing.

2.0121 It would, so to speak, appear as an accident, when to a thing that could exist alone on its own account, subsequently a state of affairs could be made to fit. If things can occur in atomic facts, this possibility must already lie in them. $$(A \text{ logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.})$$

2.013 Each thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.

2.014 Objects contain the possibility of all states of affairs.

2.0141 The possibility of its occurrence in atomic facts is the form of the object.

2.02 The object is simple.

2.0201 Every statement about complexes can be analysed into a statement about their constituent parts, and into those propositions which completely describe the complexes.

2.021 Objects form the substance of the world. Therefore they cannot be compound.

2.022 It is clear that however different from the real one an imagined world may be, it must have something—a form—in common with the real world.

2.023 This fixed form consists of the objects.

2.024 Substance is what exists independently of what is the case.

2.025 It is form and content.

2.0251 Space, time and colour (colouredness) are forms of objects.

2.027 The fixed, the subsistent and the object are one.

2.0271 The object is the fixed, the existent; the configuration is the changing, the variable.

2.0272 The configuration of the objects forms the atomic fact.

2.03 In the atomic fact objects hang one in another, like the links of a chain.

2.031 In the atomic fact the objects are combined in a definite way.

2.032 The way in which objects hang together in the atomic fact is the structure of the atomic fact.

2.033 The form is the possibility of the structure.

2.034 The structure of the fact consists of the structures of the atomic facts.

2.04 The totality of existent atomic facts is the world.

2.05 The totality of existent atomic facts also determines which atomic facts do not exist.

2.06 The existence of atomic facts we also call a positive fact, their non-existence a negative fact.