On the Mechanical Performance of Logical Inference, §§ 1–8

1. It is an interesting subject for reflection that from the earliest times mechanical assistance has been required in mental operations. The word calculation at once reminds us of the employment of pebbles for marking units, and it is asserted that the word ἀριθμός is also derived from the like notion of a pebble or material sign. Even in the time of Aristotle the wide extension of the decimal system of numeration had been remarked and referred to the use of the fingers in reckoning; and there can be no doubt that the form of the most available arithmetical instrument, the human hand, has reacted upon the mind and moulded our numerical system into a form which we should not otherwise have selected as the best.

1. 有一件事值得深思：从最早的时代起，心智活动就需要机械的辅助。“计算”（calculation）这个词立刻让我们想到用小石子标记单位的做法；据说希腊文 ἀριθμός（数）一词，也源于小石子或某种实物记号的概念。早在亚里士多德的时代，人们就已注意到十进制记数法流传之广，并把它归因于用手指计数；毫无疑问，最方便的算术工具——人的手——的形状，反过来影响了心智，把我们的记数系统塑造成一种我们本来未必会选为最佳的形式。

2. From early times, too, distinct mechanical instruments were devised to facilitate computation. The Greeks and Romans habitually employed the abacus or arithmetical board, consisting, in its most convenient form, of an oblong frame with a series of cross wires, each bearing ten sliding beads. The abacus thus supplied, as it were, an unlimited series of fingers, which furnished marks for successive higher units and allowed of the representation of any number. The Russians employ the abacus at the present day under the name of the shtshob, and the Chinese have from time immemorial made use of an almost exactly similar instrument called the schwanpan.

2. 同样从很早的时候起，人们就设计出各种专门的机械工具来帮助计算。希腊人和罗马人习惯使用算盘，也就是计算板，它最方便的形式是一个长方形的框子，框里横着一排金属丝，每根丝上穿着十颗可以滑动的珠子。这样，算盘就仿佛提供了一列无穷无尽的手指，为一级级更高的单位提供标记，可以表示任何数目。俄国人至今仍在使用算盘，称之为 shtshob；中国人自古以来就使用一种几乎完全相同的工具，叫作 schwanpan（算盘）。

3. The introduction into Europe of the Arabic system of numeration caused the abacus to be generally superseded by a far more convenient system of written signs; but mathematicians are well aware that their science, however much it may advance, always requires a corresponding development of material symbols for relieving the memory and guiding the thoughts. Almost every step accomplished in the progress of the arts and sciences has produced some mechanical device for facilitating calculation or representing its result. I may mention astronomical clocks, mechanical globes, planetariums, slide rules, &c. The ingenious rods known as Napier's Bones, from the name of their inventor, or the Promptuarium Multiplicationis of the same celebrated mathematician, are curious examples of the tendency to the use of material instruments.

3. 阿拉伯记数法传入欧洲后，算盘大体上被一套方便得多的书写符号所取代；但数学家们都清楚，他们的学科无论怎样进步，总是需要相应地发展出各种实物符号，来减轻记忆的负担、引导思路。艺术和科学进步的几乎每一步，都产生了某种便于计算或表示计算结果的机械装置。我可以举出天文钟、机械地球仪、天象仪、计算尺等等。以发明者命名的精巧算筹“纳皮尔骨筹”，以及这位著名数学家的“乘法速算器”，都是人们倾向于使用实物工具的奇特例证。

4. As early as the 17th century we find that machinery was made to perform actual arithmetical calculation. The arithmetical machine of Pascal was constructed in the years 1642-45, and was an invention worthy of that great genius. Into the peculiarities of the machines subsequently proposed or constructed by the Marquis of Worcester, Sir Samuel Morland, Leibnitz, Gersten, Scheutz, Donkin, and others we need not inquire; but it is worthy of notice that M. Thomas, of Colmar, has recently manufactured an arithmetical machine so perfect in construction and so moderate in cost, that it is frequently employed with profit in mercantile, engineering, and other calculations.

4. 早在十七世纪，我们就发现机器已被用来进行真正的算术计算。帕斯卡的计算机制造于 1642—1645 年间，是一项无愧于那位伟大天才的发明。至于后来伍斯特侯爵、塞缪尔·莫兰爵士、莱布尼茨、格斯滕、朔伊茨、唐金等人提出或制造的机器各有什么特点，这里不必探究；但值得注意的是，科尔马的托马斯先生最近制造出一种算术机，构造如此完善，价格又如此适中，以至于常被用于商业、工程和其他计算，并且有利可图。

6. It is highly remarkable that when we turn to the kindred science of logic we meet with no real mechanical aids or devices. Logical works abound, it is true, with metaphorical expressions implying a consciousness that our reasoning powers require such assistance, even in the most abstract operations of thought. In or before the 15th century the logical works of the greatest logician came to be commonly known as the Organon or Instrument, and, for several centuries, logic itself was defined as Ars instrumentalis dirigens mentem nostram in cognitionem omnium intelligibilium.

6. 非常值得注意的是，当我们转向与之相近的逻辑学时，却找不到任何真正的机械辅助或装置。诚然，逻辑著作中充满了各种隐喻性的说法，表明人们意识到，我们的推理能力即使在最抽象的思维活动中也需要这样的帮助。在十五世纪或更早，那位最伟大的逻辑学家的逻辑著作，就已被普遍称为“工具论”（Organon），即“工具”；好几个世纪里，逻辑本身被定义为“引导我们的心灵去认识一切可理解之物的工具性技艺”（Ars instrumentalis dirigens mentem nostram in cognitionem omnium intelligibilium）。

7. In all such expressions, however, the word Instrument is used metaphorically to denote an invariable formula or rule of words, or system of procedure. Even when Raymond Lully put forth his futile scheme of a mechanical syllogistic, the mechanical apparatus consisted of nothing but written diagrams. It is rarely indeed that any invention is made without some anticipation being sooner or later discovered; but up to the present time I am totally unaware of even a single previous attempt to devise or construct a machine which should perform the operations of logical inference; and it is only I believe in the satirical writings of Swift that an allusion to an actual reasoning machine is to be found.

7. 不过，在所有这些说法中，“工具”一词都是隐喻性的用法，指的是一种不变的公式、一套言辞规则或者一种程序体系。即使雷蒙·卢尔提出他那徒劳的机械三段论方案时，所谓机械装置也不过是一些画在纸上的图解。任何发明，几乎都迟早会被人发现有先例；但直到现在，我完全不知道以前有谁曾经尝试设计或制造一台能够执行逻辑推理运算的机器；而且我相信，只有在斯威夫特的讽刺作品里，才能找到提及真正推理机器的文字。