# 線喻

## 描述

《理想國》 （509d–510a）中，柏拉图用这种方式描述了線喻：

Now take a line which has been cut into two unequal parts, and divide each of them again in the same proportion,[2] and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness, and you will find that the first section in the sphere of the visible consists of images. And by images I mean, in the first place, shadows, and in the second place, reflections in water and in solid, smooth and polished bodies and the like: Do you understand?

Yes, I understand.

Imagine, now, the other section, of which this is only the resemblance, to include the animals which we see, and everything that grows or is made.[3]

（翻譯：那麼請你畫一條線來表示它們，把這條線分成不等的兩部分，然後把它們按照同樣的比例再分別分成兩部分。假定原來的兩個部分中的一個部分相當於可見世界，另一部分相當於可知世界，然後我們再根據其清晰程度來比較第二次分成的部分，這樣你就會看到可見世界的一部分表示影像。所謂影像我指的首先是陰影，其次是在水裡或表面光滑的物體上反射出來的影子或其他類似的的東西。你懂我的意思嗎？

## 可理解的世界

There are two subdivisions, in the lower of which the soul uses the figures given by the former division as images; the enquiry can only be hypothetical, and instead of going upwards to a principle descends to the other end; in the higher of the two, the soul passes out of hypotheses, and goes up to a principle which is above hypotheses, making no use of images as in the former case, but proceeding only in and through the ideas themselves (510b).[3]

（翻譯：把這個世界分成兩部分，在一個部分中，人的靈魂被迫把可見世界中那些本身也有自己的影子的實際事物作為影像，從假設出發進行考察，但不是從假設上升到原則，而是從假設下降到結論；而另一個部分中，人的靈魂則朝著另一方面前進，從假設上升到非假設的原則，並且不用在前一部分中所使用的影像，而只用「類型」，完全依據「類型」來取得系統的進展。）

And when I speak of the other division of the intelligible, you will understand me to speak of that other sort of knowledge which reason herself attains by the power of dialectic, using the hypotheses not as first principles, but only as hypotheses – that is to say, as steps and points of departure into a world which is above hypotheses, in order that she may soar beyond them to the first principle of the whole (511b).[3]

（翻譯：至於可知世界的另一部分，你要明白，我指的是理性本身憑著辯證法的力量可以把握的東西。在這裡，假設不是被當作絕對的起點，而是僅僅被用作假設，也就是說假設是基礎、立足點和跳板，以便能從這個暫時的起點上升到一個不是假設的地方，在這個地方才是一切的起點，上升到這裡並且從中獲得第一原理。）

DE 理性 （ νόησις 知识（理解）：不限於可理解（ νοητόν ）的都能夠理解 這些觀念都是由善形式所賦予的真理（τὸαὐτὸἀγαθθν） 對於心靈的一切假設已不需使用辩证法驗證，完全使用理型，總是思考最初原理。 最高
CD 思想（διάνοια） 知识（思想）：认为知識不限于可理解的思想 對於几何和数的想法 從心靈上的假设，总是思考最终的结论
BC 信念（πίστις 观点（信念）：关于可见事物的本身 可见事物的本身（ὁρατά 眼睛观察可见物体的本身
AB 猜想（εikaκασία） 观点（想象力）：关于一切的猜想 可见事物的猜想（εἰκόνες 眼睛对观察可见事物之猜测 最低

## 參考文獻

1. "divided line," The Cambridge Dictionary of Philosophy, 2nd edition, Cambridge University Press, 1999, ISBN 0-521-63722-8, p. 239.
2. ^ Older Greek texts do not differentiate unequal from an equal (ανίσα, αν ίσα)
3. Plato, The Republic, Book 6, translated by Benjamin Jowett, online 互联网档案馆存檔，存档日期18 April 2009.
4. Desmond Lee and Rachana Kamtekar, The Republic, Notes to Book 6, Penguin, 1987, ISBN 0-14-044914-0.
5. ^ Let the length of AE be equal to ${\displaystyle \scriptstyle 1}$ and that of AC equal to ${\displaystyle \scriptstyle x}$, where ${\displaystyle \scriptstyle 0 (following Socrates, however, ${\displaystyle \scriptstyle 0; insofar as the equality of the lengths of BC and CD is concerned, the latter restriction is of no significance). The length of CE is thus equal to ${\displaystyle \scriptstyle 1-x}$. It follows that the length of BC must be equal to ${\displaystyle \scriptstyle x-x\times x\equiv (1-x)\times x}$, which is seen to be equal to the length of CD.
6. ^ Gail Fine, Knowledge and Belief in Republic V-VII, in G. Fine (ed.) Plato I (1990), also in S. Everson (ed.) Cambridge Companions to Ancient Thought I: Epistemology (Cambridge University Press: New York, 1990), pp. 85–115.
7. ^ Nicholas Denyer, Sun and line: the role of the Good, in G. R. F. Ferrari (ed.) The Cambridge Companion to Plato's Republic (Cambridge University Press: New York, 2007), pp. 284–309.
8. ^ Republic 520c页面存档备份，存于互联网档案馆）: "For once habituated ... you will know what each of the 'idols' is and whereof it is a semblance, because you have seen the reality of the beautiful, the just and the good."
9. ^ Rachel G.K. Singpurwalla, Plato’s Defense of Justice in the Republic页面存档备份，存于互联网档案馆） "justice is a virtue appropriate to both cities and individuals, and the nature or form of justice is the same in both (Republic, 435a)."
10. James Danaher, The Laws of Thought页面存档备份，存于互联网档案馆） "The restrictions Plato places on the laws of thought (i.e., "in the same respect," and "at the same time,") are an attempt to isolate the object of thought by removing it from all other time but the present and all respects but one." 引证错误：带有name属性“Danaher”的<ref>标签用不同内容定义了多次
11. ^ Cratylus 439d-e页面存档备份，存于互联网档案馆） "For if it is ever in the same state, then obviously at that time it is not changing (Plato's realism); and if it is always in the same state and is always the same, how can it ever change or move without relinquishing its own form (Aristotle's realism)"
12. ^ Republic 520c页面存档备份，存于互联网档案馆） "For once habituated you will discern them infinitely better than the dwellers there, and you will know what each of the 'idols' is and whereof it is a semblance, because you have seen the reality of the beautiful, the just and the good."
13. ^ Cratylus 439d-e页面存档备份，存于互联网档案馆） "How, then, can that which is never in the same state be anything? ... nor can it be known by anyone."
14. ^ Republic 4.436b页面存档备份，存于互联网档案馆） "It is obvious that the same thing will never do or suffer opposites in the same respect in relation to the same thing and at the same time"
15. ^ Republic 4.437a页面存档备份，存于互联网档案馆） "let us proceed on the hypothesis that this is so, with the understanding that, if it ever appear otherwise, everything that results from the assumption shall be invalidated"
16. ^ Also see the Timaeus 29c页面存档备份，存于互联网档案馆） on empirical "likelihood"
17. ^ It is interesting to note that modern logical analysis claims to prove that the potentially falsifiable "empirical content of a theory is exactly captured by ... axiomatization ... that uses axioms which are universal negations of conjunctions of atomic formulas" (C. Chambers, The Axiomatic Structure of Empirical Content) 互联网档案馆存檔，存档日期27 June 2010.
18. ^ Plato's Principle of Non-Contradiction (Republic, 4.436b) for the objective, physical world is presented with three axiomatic restrictions: The same thing ... cannot act or be acted upon ... in contrary ways ... (1) in the same part (2) in relation to the same thing (3) at the same time.