数学·编程·诗词·音乐·人思维方式极简的数学(数学的极简美学)

The importance of logic for phil

2015-11-03  本文已影响159人  朱小虎XiaohuZhu

逻辑对哲学的重要性

译者按这是奎因(1908—2000) 1947年12月2日在哈佛大学哲学俱乐部的讲演的文字稿,收入W. V. Quine, Confessions of a Confirmed Extensionalist and Other Essays(一个坚定的外延主义者的自白及其他论文), Dagfinn Føllesdal奎因的学生and Douglas B. Quine奎因的儿子(eds.), Harvard University Press, 2008.,在这之前未曾公开发表过平时在与同事和学生的交流中,我一直觉得有必要讲清楚逻辑在哲学中的作用到底是什么下个学期我要为哲学系的部分研究生开设数理逻辑课程在备课过程中,我看到了奎因的这篇文章,真有一种说不出来的酒逢知己千杯少的感激心情在这篇文章中,他讲述了现代逻辑在消解哲学伪问题(比如无或非存在的本性的问题),在澄清真正的哲学问题(比如经验主义提出的关于知识和感觉经验之间的关系问题,关于逻辑和数学知识的本性的问题)并将它们引向更精确更深入的研究中的极端重要性这对于许多长于玄想疏于论证的中国哲学工作者和学生是很有启发的在这篇文章中,我们还看到一个真正的哲学家对待哲学研究的一丝不苟不断进取的精神这篇文章所呈现的绝不是奎因的最终哲学观点,他也没有对别人(包括他在哲学上所尊敬的人)的观点采取盲从的态度,而是无论对自己还是对他人的观点都采取了一个开放的态度正是这种求真的精神和开放的态度,使得他的哲学观点能不断地得到发展,直至他生命的尽头

为了方便大家的理解,我将文章的具体内容的摘要置于前面,并对正文中个别难解之处作了有节制的注释欢迎各位老师和同学对我的译文和讲解提出批评,也欢迎对文章内容展开讨论和交流

内容摘要和评论

1—2:开场白,引出主题:逻辑对哲学的重要性

3—8:‘nothing’的逻辑分析:‘nothing’在日常语法中的名词性地位曾诱导在古往今来的很多哲学家追问所谓无的本性,但实际上,任何包含这个词的句子都可以改写成另外一个与之等值的句子,而新句子不包含与‘nothing’对应的词,从而上面的那种诱惑就自然消失了

9—15:罗素的摹状词理论:罗素通过对包含摹状词的语境的系统改写,向我们表明:单称词项的使用并不必然以这个词项有对应的超语言实体为前提,这就解开了从巴门尼德和柏拉图以来的所谓非存在之谜(据说,因为不存在的东西也是一个东西,所以我们不能自圆其说地声称某个东西不存在)

16—29:经验主义的演变:经验主义在洛克和休谟那里的最初表述是:我们的一切观念都来自于感觉印象;美国哲学家图克对这个表述进行了语言学的转向,他建议对观念和印象之间关系的研究应该让位于词项和感觉词项之间关系的研究;边沁和罗素则倡导语境定义,即不再拘泥于寻找词项的根据感觉词项的直接定义,而转向寻找词项的语境定义,即寻求对词项出现的语境的整体的翻译而间接给出词项的定义由于直接定义可以看成语境定义的特殊情形,因此句子(而不是词项)成了意义的基本单位这是经验主义的又一次发展但通过卡尔纳普的工作,人们看清了并不是所有语句都可以翻译为基本语句,这就表明即使是语境定义也仍是有局限性的,奎因正是通过对这一难局的思考提出了他的整体主义,即科学语句和常识语句单个地看,并不能蕴含任何基本语句,只有一个充分大的语句系统才能做到这一点奎因的观点可视为经验主义的第三次发展经验主义的每一次发展都离不开逻辑技术的运用

30—35:分析真理的本性:康德对真理实行了两个两分法,一是所谓分析真理和综合真理的区分,二是所谓先天真理和经验真理的区分关于这两个两分之间的关系,康德之前的莱布尼兹和休谟都认为它们是重合的,即分析真理同时也是先天真理,先天真理同时也是分析真理(莱布尼兹称为“理性真理”,休谟则称为“观念的关系”)康德同意前半句,但不同意后半句,他认为有些先天真理并不是分析真理,而是综合真理根据康德的见解,算术真理就是这样的先天综合真理数理逻辑的创始人弗雷格和罗素的工作都直接针对了康德(罗素和怀特海的数学原理一书的最初目的就是为了反驳康德这个“强词夺理的庸人”的),他们指出算术可以还原为逻辑;如果逻辑是分析的,那么算术也是分析的对这个结论,康德的信徒当然仍有回旋的空间但正反两方的交锋如果不想沦为毫无成果的吵架,了解和正视现代逻辑的发展就成为必要

36—46: 哥德尔定理和分析/综合真理的划界:根据哥德尔不完全性定理,包含集合论在内的广义逻辑系统不可能证明每一个该系统里的真理这对分析性的概念是一个很大的冲击,因为一向被认为是分析真理的逻辑真理,居然也有无法被证明的情形奎因在这篇文章提出了一个解决方案,即在不违背分析真理可以得到证明这一经验主义直觉的前提下,将逻辑一分为二,前者为基本逻辑,有完全性的证明程序,它的真理都是分析真理;另一部分为集合论,没有完全性的证明程序,它的真理是先天综合真理与这个二分相重合的是,基本逻辑是本体论上中立的,而集合论则承认了抽象实体的存在应该说,哥德尔的不完全性定理确实揭示了量化理论和作为数学基础的高阶逻辑之间的深刻差异,奎因本人所指出的两者对共相问题的不同态度也是真实的但奎因这时仍没有走出康德认识论的框架,他仍在使用康德哲学的术语来标示这两者之间的同异(同:两者都是先天真理;异:基本逻辑真理为分析真理而集合论真理为综合真理)实际上,基本逻辑和数学的分界,和分析和综合的分界,是两个完全不同的问题他后来的研究表明,分析/综合之间的区别最后蜕变为自明真理和不自明的真理之间的区别,但这个区别从认识论的角度看并不是一个有任何重要性的区别,真理之间只有自明性程度的差别,这种差别是因人而异的和因时因地而异的,并没有任何一刀切的标准;而承认先天真理则更是完全违背了经验主义的根本原则

48—52: 本体论承诺:要弄清楚某个理论有着什么样的本体论,只消弄清楚它的量化结构和量词相联系的变项所指的范围就是它的本体论显然,逻辑对于弄清楚量化结构,特别是复杂理论的量化结构是非常重要的奎因在这里为了澄清人们对他的误解,强调了弄清楚一个理论的本体论承诺是什么和这个理论的本体论承诺正确与否这两者的区别这是他并不同意全部哲学问题都是语词问题的证据之一遗憾的是,这样的混淆和误解在六十年后的中国仍然普遍存在

53—58:数学为什么对自然科学不可或缺:一方面,数学陈述没有经验意义,但另一方面,数学对自然科学却不可缺少对这个矛盾,奎因此时仍没有找到答案他此时想到的是能建立不预设抽象对象的数学;这样的新数学也许会因为对抽象对象的免疫力,进而摆脱不完全性的梦魇其实,即使做到了这一点,上面的矛盾也仍旧没有解决因为上面这个矛盾对于本体论上中立的基本逻辑也是成立的:一方面,逻辑陈述没有经验意义(和数学不同的是它的绝对可证明性),但另一方面,逻辑对科学同样不可缺少解决这个矛盾的钥匙是他后来提出的整体主义:一般地说,单个的陈述,不论是自然科学里的陈述,还是逻辑数学里的陈述,都无法独自与经验发生联系,它们都只能从它们参与其中的充分大的陈述系统与经验的联系中获得间接的意义数学和逻辑恰恰因为它们对科学预测系统的不可或缺而分享了全部科学的经验意义至此,它们终于不再被看成是与经验没有关系的先天真理了

正文+汉译

1. The little group of skeptics who run this club have asked me to explain why in the world anybody who is intent on philosophy should allow himself to be sidetracked into taking a course in logic. I know better than to try to satisfy these people by suggesting that a logic course might help a student pass the prelims. For, being philosophers, these skeptics will pursue the issue to its fundamentals, and ask: Why should there be a preliminary exam in logic? The doubt implicit in such a question could never be a genuine doubt, of course; it must be a purely methodological doubt, a Cartesian doubt of the most fanciful order; but the inquisitors in question are quite capable, I believe, of Cartesian doubt.

有那么几个参加这个俱乐部的怀疑论者让我解释一下:为什么在这个世界上任何一个专心于哲学的人,要偏离正题,去学习一门逻辑课程?我很清楚,如果我对这些人说,逻辑课能帮助学生通过预备考试,这样的回答是不能满足他们的要知道,这些怀疑论者是哲学家,他们一定会向根本处追问:为什么在预备考试中要有逻辑这门课呢?当然,包含在这样一个问题里的怀疑不可能是真正的怀疑;它肯定只是笛卡尔式的方法论上的怀疑,而且是这类怀疑中离奇性级别最高的,当然我相信发问者完全具有纯正的笛卡尔式怀疑的能力

2. This gives me no cause for complaint. If it is difficult and unnatural to doubt the value of logic, it should be correspondingly easy and natural to establish the value of logic. I’m grateful for having been assigned an easier task than any I might have taken on if left to my own devices.

这样一来,我便没有什么好抱怨的了如果怀疑逻辑的价值既困难又不自然,那么,相应地,确认逻辑的价值就是既容易又自然的了这个分派给我的话题,甚至都要比任我自便的话题还要来得容易,我对此表示感激

3. To illustrate one important way in which logic contributes to philosophy, let me begin with an over-simple instance of philosophical confusion: “If an event has a cause at all, it must have something as its cause, rather than nothing, for nothing cannot be a cause. But if an event has no cause, nothing causes it. Therefore it is impossible for an event to have no cause”. This, substantially, is the unsympathetic version which Hume gives to an argument in Locke. Whether it is an argument that Locke or any other sensible person could have intended, at least it will help me to begin schematizing one of the uses of logic.

为了说明逻辑有益于哲学的一个重要方式,让我先举一个超级简单的哲学混乱的例子:“如果某个事件有原因,那么它就以某物而不是无物作为其原因,因为无物不可能是一个原因但是如果某个事件没有原因,无物引起了它所以,一个事件没有原因是不可能的”这在实质上便是休谟对洛克的一个论证所作的无同情心的改写不论这个改写版的内容是不是洛克或任何可理喻的人物所意指的,它都有助于我说明逻辑的一项用途

4. This argument makes use of the fact that the word ‘nothing’ behaves in ordinary language like a noun. “A causes the event” means that something, viz., this A, is the cause. Analogously it is argued that “nothing causes the event” means that something, viz., this nothing, is the cause.

这个论证利用了下面这个事实:在日常语言中,“无物”(‘nothing’)这个词表现得就像一个名词一样“A引起了这个事件”意味着:某物,也就是A,是原因类似地,也可以作出下面的论证“无物引起了这个事件”意味着:某物,也就是无物,是原因

Something similar seems to have been going on in Heidegger’s mind when he asked ‘What about Nothing? What does Nothing do?’ and decided that Nothing nothings, and that we have a special way of sensing nothing, this sense being anguish.

海德格尔曾追问“无物怎么样?无物做什么?”,他最后得出结论:无物无着,并且我们有感知无物的一种特殊的方式,这种感觉的名字叫“烦恼”海德格尔的这个思路与上面的思路看起来是相似的远在两千多年前的中国哲学家老子曾声称:“天下之物生于有,有生于无”,他显然也是将“有”和“无”名词化了

5. Such treatment of the word ‘nothing’ can lead to ridiculous results, as Lewis Carroll has shown; and similar fallacies can be devised with ‘something’ and ‘everything’.

对“无物”这个词这样的处理可以带来很可笑的结果,正如刘易斯·卡罗尔所表明的那样;对“某物”和“每物”也可以设计出类似的谬误

6. Now, returning to the first example, let’s see how it fares in logical symbols:

Nothing causes x

(y)~(y causes x)

‘Whatever y may be, y does not cause x’. Here there is no term, no substantive corresponding to ‘nothing’, and so no opportunity to draw the false inferences that depend on handling ‘nothing’ like a name. In logical notation the same thing happens also to the false substantives ‘everything’ and ‘something’; they disappear.

现在让我们回到第一个例子,看看用逻辑符号是如何处理它的:

无物引起x

(y)~(y引起x)

“不管y是什么,y不引起x”这里不存在与“无物”对应的词项或实词,所以我们将不再有机会作出那些有赖于对“无物”进行名词性处理的错误推理同样地,假实词“某物”和“每物”在逻辑记号法中也将消失

7. Now let’s see what this sort of therapeutic translation really comes down to. A troublesome or misleading part of ordinary language has been translated into another part which is well-behaved. Another part still of ordinary language:

Whatever you select, it does not cause x.

(Symbols are inessential.) All the serious and proper uses of ‘nothing’ can be translated, sentence by sentence, into this well-behaved part of language. But the translation operates only on the sentences as wholes; the word ‘nothing’ has no translation by itself; and hence this part of language contains no misleading substantive, simple or complex, corresponding the misleading substantive ‘nothing’. Therefore, the perplexities and fallacies attaching to the word ‘nothing’ are by-products of a dispensable part of our language; and in this sense they may be said to be purely linguistic confusions.

现在让我们看看这种翻译为什么会有治疗的功效日常语言中某个引起麻烦或误导人的部分被翻译成了表现好的另一部分这另一部分仍属于日常语言:

无论你选择什么,它都不引起x

(符号化并不是这里的实质问题)“无物”的所有严肃和正当的使用方式都可以逐句逐句地被翻译为语言中表现良好的部分但是,翻译所针对的是作为整体的句子;“无物”这个词本身并不能被翻译;所以在这个表现良好的部分中并不包含与误导人的实词“无物”相对应的误导人的(简单或复杂的)实词与“无物”这个词联系在一起的困惑和谬误只是语言中某个可以省去的部分的副产品;从这个意义上说,那些困惑和谬误可谓纯粹的语言上的混乱

8. The so-called quantification idiom used in modern logic is prompted by technical counteractions of efficient manipulation and deduction. Its efficacy in eliminating the fallacies of ‘nothing’, and the similar fallacies of ‘everything’ and ‘something’, is incidental. But it illustrates the first point which I want to make this evening: the logical analysis resolves certain confusions and philosophical perplexities by showing how to paraphrase language into peculiarly clear and straightforward subsections of language. It resolves the perplexities by showing them to be purely verbal: products of gratuitous idioms.

现代逻辑对所谓量化习语的使用,是为了从技术的角度对运算和推理进行更有效的处理至于它也能用来消除“无物”“某物”和“每物”等词引起的谬误,只是一个附带的功用但是这个附带的功用说明了我今晚想要阐明的第一个观点:逻辑分析可以消除某些混乱和哲学困惑,方法是将语言改写为它的特别清楚和平实的某个子集它可以表明这些困惑只是纯粹语词上的困惑,是一些不必要的习语所引起的混乱

9. I don’t maintain, as Wittgenstein does, that all philosophical problems are verbal in that sense. But some are. I’ve illustrated the point with a trivial type of example; a more serious example is afforded by Russell’s theory of descriptions, in its bearing on perplexities of non-existence. The perplexity, briefly, is this: How can we consistently say there is no such thing as Pegasus, if there is no Pegasus about whom to say it? Or that there is no such thing as the King of France? How can any such statement of non-existence be true?

我并不像维特根斯坦那样声称所有哲学问题都是像上面那样的语词问题但有些哲学问题确实是语词问题我已经举了一个微不足道的例子来加以说明;而罗素的摹状词理论提供了更加严肃的例子,这些例子都与非存在的困惑有关这个困惑简单说来便是:如果我们所要谈的帕格索斯并不存在,我们又如何能自圆其说地说帕格索斯不存在呢?同样地,如果我们所要谈的法国国王并不存在,我们又如何能自圆其说地说他并不存在呢?一句话,关于非存在的任何陈述怎么可能是正确的陈述呢?

10. One answer sometimes resorted to is this: there are such things as Pegasus and the king of France after all; they merely happen not to be actual. Actuality, like redness, is merely one special quality of things.

一个有时候会诉诸的答案是这样的:帕格索斯和法国国王毕竟还是存在的,只是它们不具有现实性而已现实性,就像红一样,也可以是事物的一种特殊性质非存在之谜最早可以追溯到古希腊哲学家巴门尼德他声称思维与存在具有同一性,即任何我们能想到的东西都是存在的如果我们能想到帕格索斯,那么帕格索斯一定是存在的;如果帕格索斯不存在,我们就不会想到它,因此说帕格索斯不存在是自相矛盾的我们通常认为不存在的事物一定在某种更深刻的意义上是存在的

11. Two reasons why some of us find this unsatisfactory: one, the recognition of a realm of unactualized possibles offends our taste for a tidy, economical ontology; two, the method still avails us nothing if we change the example and speak not of Pegasus or the king of France but of the round square. To accommodate such cases as this we should have, analogously, to recognize not only a realm of unactualized possibles but a realm of impossibles. Few of us, certainly, have so little taste for tidiness as not to be offended by an ontology of this kind. Various awkward problems arise, moreover, apart from mere questions of taste.

有两个理由,使我们中的一些人认为这个答案不能令人满意第一,承认未被现实化的可能对象败坏了对本体论的整洁和俭约的口味第二,当我们把例子从帕格索斯和法国国王转向方圆时,这个方法仍是无济于事正如要容纳帕格索斯和法国国王需要承认未被现实化的可能对象一样,要容纳方圆,则要进一步承认不可能的对象但不在乎整洁不为这种本体论所冒犯的的人肯定是很少的这种处理问题的方法会带来很多棘手的问题,不只是口味问题

12. Russell goes back to the beginning of the trouble and protests that when we say there is no such thing as Pegasus, or the king of France, there need be no Pegasus or king of France about whom to say it. He first paraphrases all statements containing so-called singular descriptions: the king of France, the author of Waverley: idioms using ‘the’ in the singular. He does not paraphrase these descriptions themselves, but the statements as wholes which contain them; and the statements into which he paraphrases them contain such words as ‘author’ and ‘Waverley’, or ‘king’ and ‘France’, scattered through them, but no single phrase that can be equated with ‘the king of France’ or ‘the author of Waverley’. Thus these translations are statements still about France and perhaps kingship, or perhaps Waverley and perhaps authorship, but there is nothing in them that would tempt us to say that they are about the king of France or the author of Waverley.

罗素回到了这个难题的最初形式;他指出,当我们说不存在帕格索斯或法国国王这样的事物时,所谈到的帕格索斯或法国国王的存在并不是必要条件他首先对包含所谓单称摹状词的陈述进行解释单称摹状词是使用定冠词“这个”的单称词组,“这个法国国王”“这个瓦弗利的作者”就是这样的词组他并不直接解释这些摹状词,而是解释包含摹状词的陈述;原摹状词的成分,如“作者”和“瓦弗利”,或“国王”和“法国”,仍散布在经过解释而形成的新陈述中,但新陈述中不再包含与“这个法国国王”或“这个瓦弗利的作者”这些摹状词本身相对应的单一短语所以经过翻译得到的新陈述也许仍是关于法国或王位的陈述,或关于瓦弗利和作者身份的陈述,但不再包含可能会诱惑我们认为它谈到了这个法国国王或这个瓦弗利的作者的任何成分作为语境翻译的一个例子,我们看罗素是如何翻译“这个法国国王是个秃子”这个陈述的:“存在着这样一个对象x,这个对象是法国国王,而且如果任何对象y是法国国王的话,那么y就是x,而且这个对象是秃子”原来的主谓句变成了一个存在句,原来的主词“这个法国国王”在翻译句中不再有对应的单一成分,因此我们不必在事先就认为,要使我们作出的陈述有意义(真假且不论),必须有一个和“这个法国国王”相对应的实体存在

13. ‘Pegasus’ can be handled similarly if we read it as short for a description: ‘the winged horse captured by Bellerophon’. So for all proper names.

“帕格索斯”也可进行类似的处理,如果我们将它视为“柏勒洛丰捕获的那匹有翼的马”这个摹状词的缩写的话以上处理也适用于所有的专名

14. The same process is at work here as in the treatment of words like ‘nothing’: paraphrase the context so that no single segment survives answerable to the troublesome substantive in question. The substantive ‘nothing’ itself received no translation, but simply disappeared on translation of the contexts as wholes; and similarly now for the substantive ‘Pegasus’ or ‘the king of France’ or ‘the author of Waverley’. The terms surviving in the translations are terms not giving rise to the perplexities that prompted the analysis; and those perplexity are thereby shown to be by-products of gratuitous, avoidable portions of language.

罗素对摹状词的处理和我们上面对“无物”的处理是类似的:改写包含这些成问题的实词的语境,使新语境中不再包含与它们相应的单一成分实词“无物”本身并没有被翻译,但在对包含它的整个语境的翻译中消失了;同样地,实词“帕格索斯”“这个法国国王”和“这个瓦弗利的作者”在翻译中也消失了翻译所得的新语境中的词项不会引发要求分析的那些困惑;因此,那些困惑只是语言中的可以避免的不必要的部分的副产品

15. Logic is needed to guide such paraphrasing; and the suppler and subtler our logic is, the farther it can carry us in philosophical enterprises of this type.

逻辑对于指引这类翻译是必需的,而且我们对逻辑越是精通和敏感,我们在这类哲学事业中就会走得越远

16. Now there is also another conspicuous domain of philosophy in which such logical paraphrasing plays a central role. This is in the empiricistic program of constructing the world from experience.

逻辑解释发挥核心作用的还有另一个引人注目的哲学领域,这便是从经验中构造出世界的经验主义纲领

17. Hume’s notion was that all our ideas are composite of so-called simple ideas, each of which is a straight copy of some simple sense datum. Essentially this was also Locke’s point of view. According to the doctrine, every meaningful word—meaningful in the sense of expressing an idea—evidently ought to be translatable into a complex of words each of which, individually, names a simple sense impression.

休谟主张,我们的全部观念都是所谓的简单观念的复合,而每一个简单观念都只是某个简单的感觉材料的摹本这实际上也是洛克的观点根据这个学说,每一个有意义的词—即每一个能够表达观念的词—明显地应该翻译为简单的词的组合,而每一个简单的词,都命名了一个独一无二的简单的感觉印象

18. But this is an intolerably strict standard of meaningfulness, as becomes apparent the minute you try to put it into practice at all. Whatever our own criterion of a simple impression may be, certainly a mere roster of names of simple impressions isn’t going to be enough. By merely putting such names together, and taking new words as abbreviations of the compounds, we can’t begin to build a serious language; and men like Hume and Locke can scarcely have thought we could.

但是,我们如果当真实施这个方案,将会清楚地看到,这个意义标准的严格性是令人无法容忍的不管我们关于简单印象的标准是什么,这些简单印象的单纯的花名册肯定是不管用的仅仅把这些名字堆在一起,并引入作为它们缩写的新词,我们是无法开始构建真正像样子的语言的,即使是休谟和洛克这样的人大概也不会认为我们能够吧

19. At the very least we are going to need various auxiliary connectives; and in fact we shall need much more.

除了表示简单印象的名字,我们最起码还需要很多辅助性的联结词;事实上,我们需要的要比这些多得多

20. Without trying to decide what Hume and Locke wanted, I expect we can agree among ourselves that the most the empiricist can reasonably demand is definition of words in context, sentence by sentence. We suppose a basic language which talks, in specified ways, about direct sense data; and then all further meaningful sentences are to be translatable as wholes into sentences of that basic language. Individual words of the derivative language need not go over directly into complexes of words of the basic language. The word ‘nothing’ did not go over into any continuous segment of quantification notation, but the sentences containing that word were translated systematically as wholes; similarly for descriptions; and the same may be expected when we undertake constructions upon a basic language of empiricism.

我们先不管休谟和洛克是怎么想的,但我希望在我们之间能达成共识:经验主义者能够合理要求的,最多不过是对词的逐句逐句的语境定义我们假定有某个基本语言,它可以用来具体地谈论这样那样的直接感觉材料;然后所有其他有意义的句子都可以翻译为基本语言中的句子派生语言中的单个的词不必直译为基本语言中的词的组合“无物”这个词,还有所有的摹状词,在量化记号系统中并没有对应的连续性成分,但包含它们的句子却可以得到整体上的翻译当我们试图将全部语言翻译为经验主义的基本语言时,也可以提出同样的要求,即逐句逐句翻译的要求

21. This being the case, there is full scope again for all the resources of the supplest and subtlest logic we can contrive; the better we are at logic, the farther we can hope to get in our constructions, and the more of everyday and scientific language we can hope to reduce to that basic language, whatever it may be, which empiricism allows us as a starting point. For, a surprising amount can be done through contextual definition if one has techniques for finding his way through the mazes.

在语境翻译的前提下,我们还要充分运用逻辑的资源,我们对逻辑越是擅长和敏感,我们的逻辑构造就会走得越远,日常语言和科学语言能被翻译为作为经验主义起点的基本语言(且不管这个基本语言的具体内容)的部分也就越多如果我们有穿越迷宫的逻辑技术,语境翻译就能推展到许多令人乍舌的角落

22. This is strikingly brought out by reading Carnap’s rare and little known Der Logische Aufbau der Welt. Although Carnap by no means succeeds in reducing the whole of everyday or scientific discourse to the very meager basic language of experience which he allows himself, he does get startlingly far along the way. Many of his constructions are complex and ingenious and few of them could have been achieved without high proficiency in modern logic.

卡尔纳普的世界的逻辑构造一书就达到了这样一个令人乍舌的地步尽管卡尔纳普并没有实现将全部日常语言和科学语言都还原为他所期许的那种表达经验的贫乏的基本语言,但他确实达到了一个令人吃惊的水平他的许多构造既复杂又巧妙,如果没有对现代逻辑的娴熟的运用,这些构造基本上是作不出来的

23. Much had been said in an empiricistic vein in recent centuries, but the Aufbau is so far as I know the first serious effort to put the program of epistemological reduction rigorously into effect. The problem couldn’t even have been seriously tackled without the benefit of modern advances in mathematical logic. As Professor Sheffer remarked an hour ago, the importance of logic to philosophy is simply the importance of basic experience.

在最近几个世纪里,我们听到了很多经验主义的言论,但就我所知,构造一书却是把认识论还原方案严格地付诸实施的第一次严肃的尝试如果不是受惠于数理逻辑的最新进展,这个问题根本就无法予以严肃的对待正如 谢弗教授一小时前所评论的那样,逻辑对哲学的重要性就是基本经验的重要性

24. Even so, there is reason to suppose that the program of straight reduction to a basic language of experience can never be carried through in completion—not even granted all the liberality of contextual definition and all the earnestness of modern logic. I expect that empiricists are bound, eventually—as most, including Carnap, already have done—to relax their demand of translatability, and to require only that every meaningful statement be related to the basic language, in some way short of out and out translatability.

尽管如此,我们仍有理由认为,即使用上比较开明的语境定义的方法和现代逻辑的全部看家本领,直接还原为描述经验的基本语言的方案仍不会完全成功我希望经验主义者最终会放松他们对可翻译性的要求,转而只要求每一个有意义的陈述与基本语言以某种方式发生关系,这种关系不再是彻底的翻译关系而事实上,包括卡尔纳普在内的多数经验主义者已经在这样做了

25. Just what the basic language should be is itself a question, but this I shall pass over. Another question is: what relations should we demand between the statements of science and the basic language, if full translatability in not to be insisted on?

基本语言应该是个什么样子,这本身其实也是个问题,不过我在这里将略而不论另一个问题是,如果我们不再坚持完全的可翻译性,那么我们应该要求科学中的陈述与基本语言有着怎样一种关系呢?

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