A New Logical Machine
一台新的逻辑机
馆员评分7.2Claude · AI
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细致说明一台改进杰文斯设计的机械逻辑机；有真实的历史意义，尤其因为随后的电路草图，但文字枯燥、范围狭窄。
During the year 1881 I constructed a logical machine somewhat similar to the well-known machine of Prof. Jevons, and printed logical diagrams for problems involving as many as ten terms. This earlier instrument and the logical diagrams formed the basis of the machine illustrated on the accompanying plate. The new machine was constructed in Princeton during the winter of 1881–82, by my friend Prof. C. G. Rockwood, Jr., whose mechanical skill and untiring patience gave me invaluable assistance. The machine was made from the wood of a red-cedar post, which once formed part of the enclosure of Princeton's oldest homestead. It measures 32 cm. high by 21 cm. wide and 15 cm. deep. Like the instrument of Prof. Jevons, and that of Prof. Venn, it is constructed for problems involving only four terms, but more readily than either of those instruments admits of being extended for problems involving a larger number of terms.
1881 年，我制作了一台逻辑机，与杰文斯教授那台著名的机器有些相似，还印制了可处理多达十个项的问题的逻辑图。这台早先的仪器和这些逻辑图，构成了附图所示这台机器的基础。新机器是 1881 至 1882 年冬天在普林斯顿由我的朋友小 C. G. 罗克伍德教授制作的，他的机械技巧和不倦的耐心给了我极其宝贵的帮助。机器用一根红雪松木桩的木料做成，这根木桩曾是普林斯顿最古老的宅院围栏的一部分。机器高 32 厘米，宽 21 厘米，深 15 厘米。和杰文斯教授的仪器以及维恩教授的仪器一样，它是为只涉及四个项的问题而造的，但比那两台仪器更容易扩展，用于涉及更多项的问题。
The face of the machine (Fig. I.) presents to view sixteen small pointers representing the sixteen logical combinations of the symbols A, B, C, and D, with their negatives a, b, c, d. These combinations are so arranged that all the A combinations are found in the two vertical columns to our left, the a combinations in the two vertical columns to the right. The A combinations are subdivided vertically into the B and b combinations, and the a series in like manner. Both are also subdivided horizontally into the C and c combinations, and each of these again into the D and d combinations. Thus the uppermost pointer to the left represents the combination A B C D, the horizontally adjoining one A b C D, the next a B C D, and so on until we reach the lowermost to the right, which is a b c d. Below the pointers may be seen the two operation keys marked 1 and 0, and the four positive and four negative letter keys under their respective symbols.
机器的正面（图一）显示出十六根小指针，代表符号 A、B、C、D 及其否定 a、b、c、d 的十六种逻辑组合。这些组合的排列方式是：所有 A 组合都在我们左边的两竖列里，a 组合在右边的两竖列里。A 组合在竖直方向上又分为 B 组合和 b 组合，a 系列也照此划分。两者在水平方向上又都分为 C 组合和 c 组合，每一种再分为 D 组合和 d 组合。因此，左边最上面的指针代表组合 A B C D，横向相邻的一根代表 A b C D，再下一根代表 a B C D，依此类推，直到右边最下面的一根，即 a b c d。指针下面可以看到两个标着 1 和 0 的操作键，以及在各自符号下的四个肯定字母键和四个否定字母键。
The 1 key may be called the restoration key. It prepares the machine for a new problem, by raising all the pointers to the horizontal position. The 0 key may be called the destruction key, as when pressed down it allows the pointers to fall. The function of a letter key is to sustain in the horizontal position the pointers representing the corresponding negative combinations. Thus, if the A key is pressed, the a pointers are sustained; if the b key is pressed, the B pointers are sustained; and similarly for all the remaining letter keys.
1 键可以称为复原键。它把所有指针抬到水平位置，使机器准备好解一个新问题。0 键可以称为消去键，因为按下它时，指针会落下。字母键的功能，是把代表相应否定组合的指针撑在水平位置。因此，如果按下 A 键，a 指针就被撑住；如果按下 b 键，B 指针就被撑住；其余字母键也是如此。
Turning now to Fig. II., the mechanism by which this is effected will be easily seen. On the inner face of the machine, and corresponding to the pointers, are sixteen drops, some of which are pictured in the horizontal position, and some as fallen. The two operation keys move rectangular frameworks, each consisting of four vertical brass rods fastened together, and carrying pins which reach all of the sixteen drops. The framework of the 0 key moves on the inner, that of the 1 key on the outer side of the drops, both horizontally. If we wish to bring all the pointers to the horizontal position and hold them there, both operation keys are pressed down. The 1 key raises all the drops. Releasing first the 0 key, its framework is drawn back by a fixed spring, and by means of its pins holds the drops in position; on releasing the 1 key, its framework is drawn back so as not to interfere with subsequent operations. Each letter key operates two vertical or two horizontal rods, free to revolve on their axes. In each rod are set four pins, conveniently bent, so that when the rods are partially revolved, by pressure of the letter keys, the pins are made to sustain the drops in the horizontal position without raising those which have fallen. The rods return to their original position, by means of small spiral springs, as soon as the pressure of the letter keys is released. The desired motion is communicated to the rods by means of cat-gut strings, there being two such strings from each letter key. Thus the A key operates the two vertical rods which are to hold the a drops; the b key the rods for holding the B drops; and the other letter keys in like manner. By this device it will be seen that, if we should press the A key (this holds the a combinations), and then the 0 key, only the A pointers will fall; or, if both the A and B keys are depressed (this holds the a and b combinations), and then the 0 key, only the A B pointers will fall; and similarly for the other combinations.
现在看图二，就很容易看出实现这一点的机构。在机器的内壁上，与指针相对应，有十六个落片，图中有些处于水平位置，有些已经落下。两个操作键各推动一个长方形框架，每个框架由四根固定在一起的竖直铜杆组成，上面装着能够到全部十六个落片的销钉。0 键的框架在落片的内侧移动，1 键的框架在外侧移动，两者都是水平移动。如果想把所有指针抬到水平位置并保持住，就同时按下两个操作键。1 键把所有落片抬起。先松开 0 键，它的框架被一根固定的弹簧拉回，并用它的销钉把落片撑在原位；再松开 1 键，它的框架被拉回，以免妨碍后续的操作。每个字母键操纵两根竖直的或两根水平的杆，杆可以绕自身的轴转动。每根杆上装有四根弯成合适形状的销钉，当字母键按下、杆转过一定角度时，这些销钉就把落片撑在水平位置，而不会把已经落下的抬起来。字母键一松开，杆就靠小螺旋弹簧回到原来的位置。所需的运动通过羊肠线传给这些杆，每个字母键有两根这样的线。因此，A 键操纵用来撑住 a 落片的两根竖杆；b 键操纵撑住 B 落片的杆；其余字母键也是如此。由这个装置可以看出，如果我们先按 A 键（它撑住 a 组合），再按 0 键，就只有 A 指针会落下；或者，如果同时按下 A 键和 B 键（它们撑住 a 组合和 b 组合），再按 0 键，就只有 A B 指针会落下；其他组合也是如此。
To utilize the instrument for the solution of logical problems, we first raise all the pointers to the horizontal position. This will indicate the state of a logical universe of four terms before the introduction of premises. Now, since the establishment of any combination means the negation of some other, we may express our premises in negative form. Thus, in general, A −< B (every A is B) may be expressed A b −< 0 (A's which are b do not exist). This we express upon our machine by pressing down the letter keys A and b, and then the destruction key. The falling of the A b pointers indicates exactly the change effected in the logical universe by the introduction of the premise A −< B. We may then continue to impress as many premises as we please, until all the pointers have fallen. The following formulæ will suffice to illustrate the manner in which premises may be reduced from the positive to the negative form.
用这台仪器解逻辑问题时，我们先把所有指针抬到水平位置。这表示引入前提之前一个四项的逻辑宇宙的状态。由于确立任何一种组合都意味着否定另外某种组合，我们可以把前提表示成否定形式。例如，一般地，A −< B（每个 A 都是 B）可以表示为 A b −< 0（是 b 的 A 不存在）。在机器上，我们按下字母键 A 和 b，再按消去键，就表示了这一点。A b 指针的落下，恰好表示引入前提 A −< B 给逻辑宇宙带来的变化。然后我们可以继续输入任意多个前提，直到所有指针都落下。下面的公式足以说明如何把前提从肯定形式化为否定形式。
Positive Form. Negative Form.
(1.) A −< B . . . . . . . . . . A b −< 0.
(2.) A + B −< C . . . . . . . . { A c −< 0.
{ B c −< 0.
(3.) A −< B + C . . . . . . . . A b c −< 0.
(4.) A −< b + C D . . . . . . . { A B c −< 0.
{ A B d −< 0.
(5.) A B −< C . . . . . . . . . A B c −< 0.
(6.) A −< B C . . . . . . . . . { A b −< 0.
{ A c −< 0.
(7.) A (B + C) −< D . . . . . . { A B d −< 0.
{ A C d −< 0.
(8.) A −< B (C + D) . . . . . . { A b −< 0.
{ A c d −< 0. 肯定式 否定式
(1.) A −< B . . . . . . . . . . A b −< 0.
(2.) A + B −< C . . . . . . . . { A c −< 0.
{ B c −< 0.
(3.) A −< B + C . . . . . . . . A b c −< 0.
(4.) A −< b + C D . . . . . . . { A B c −< 0.
{ A B d −< 0.
(5.) A B −< C . . . . . . . . . A B c −< 0.
(6.) A −< B C . . . . . . . . . { A b −< 0.
{ A c −< 0.
(7.) A (B + C) −< D . . . . . . { A B d −< 0.
{ A C d −< 0.
(8.) A −< B (C + D) . . . . . . { A b −< 0.
{ A c d −< 0.Having expressed our premises upon the machine, and their effect being recorded by the pointers, it only remains for us to read off the conclusion. The entire conclusion is represented by the fallen pointers, and might be expressed as their joint sum; or it may be viewed as the logical sum of the combinations represented by the horizontal pointers. Thus, the premises of Barbara, A −< B and B −< C, give as the entire conclusion read negatively,
前提在机器上表示出来、它们的作用由指针记录下来之后，剩下的只是读出结论。全部结论由落下的指针表示，可以表示为它们的联合之和；也可以看作由水平指针所代表的那些组合的逻辑和。例如，Barbara 式的两个前提 A −< B 和 B −< C，按否定形式读出的全部结论是：
A b C }
A b c }
A B c } −< 0.
a B c }Read positively, the conclusion is,
按肯定形式读出，结论是：
A B C + a B C + a b C + a b c = 1;or, more briefly,
或者更简短地写成：
B C + a b = 1.Ordinarily, the conclusion called for is part only of the total conclusion. Thus, syllogism with the above premises asks for a conclusion involving only A and C. An inspection of the dial-plate will show us the conclusion A −< C, and also other conclusions involving relations between other terms than A and C; thus,
通常所要求的结论只是全部结论的一部分。例如，以上述前提作三段论，所求的是只涉及 A 和 C 的结论。查看表盘，就能看出结论 A −< C，以及涉及 A、C 以外其他项之间关系的其他结论，例如：
c (A + B) −< 0; b −< a + c, etc.Nor is it necessary that our conclusions should be limited to relations between terms given in the premises, as may be seen in the solution of the following problems.
我们的结论也不必局限于前提中给出的项之间的关系，这从下面两个问题的解法中可以看出。
Problem I.问题一#
Let us suppose that there are four girls at school, Anna, Bertha, Cora, and Dora, and that some one had observed that
假设学校里有四个女孩：安娜、贝尔塔、科拉和多拉；有人观察到：
(1.) Whenever either Anna or Bertha (or both) remained at home, Cora was at home; and
（1）每当安娜或贝尔塔（或两人都）留在家里时，科拉都在家；并且
(2.) When Bertha was out, Anna was out; and
（2）贝尔塔出门时，安娜也出门；并且
(3.) Whenever Cora was at home, Anna was at home.
（3）每当科拉在家时，安娜都在家。
What information is here conveyed concerning Dora?
这里传达了关于多拉的什么信息？
Indicating by the capital letters the fact of remaining at home, and by the small letters that of going out, our premises are
用大写字母表示留在家里，用小写字母表示出门，我们的前提是：
A + B −< C = A c } −< 0
B c }
b −< a = b A −< 0
C −< A = C a −< 0and, impressing them upon the machine, there will result the state of things indicated by Fig. 1. From this we may read off the conclusion,
把它们输入机器，就会得到图一所示的状态。从中我们可以读出结论：
D −< A B C + a b c.
d −< A B C + a b c.Or, if Dora remain at home, her three sisters will be all at home or all out; and the same will be true if Dora goes out.
也就是说，如果多拉留在家里，她的三个姐妹要么都在家，要么都出门；如果多拉出门，情况也是一样。
Problem II.问题二#
If A = B and B = C, what may be said of D?
如果 A = B，并且 B = C，关于 D 能说些什么？
Impressing upon the machine our premises,
把我们的前提输入机器：
(A = B) = A −< B } = A b −< 0
B −< A } B a −< 0
(B = C) = B −< C } = B c −< 0
C −< B } C b −< 0the same state of the logical universe is produced as by the premises of the preceding problem. Hence,
所产生的逻辑宇宙的状态与上一个问题的前提所产生的相同。因此：
D −< A B C + a b c.馆员注 · Claude（AI），二号馆员
艾伦·马昆德先在普林斯顿教拉丁文和逻辑，后来成为一位重要的艺术史家；他在 1881 至 1882 年请人造了这台机器，作为对杰文斯“逻辑钢琴”的改进。十六根指针代表四个项的十六种组合；输入每个前提时，按下按键，让被这个前提排除的组合落下，仍然立着的就是结论。这台机器至今保存在普林斯顿；几年之后，马昆德又按照皮尔士的建议，构想了一个用电路运作的版本。
版本记
- 权利
1885 年宣读，1886 年刊印；马昆德卒于 1924 年。
已按澳大利亚、欧盟、英国、中国大陆和美国的规则核对（截至 2026 年 10 月 11 日）。
- 来源
Internet Archive (JSTOR Early Journal Content), A New Logical Machine
取于 2026 年 10 月 11 日 - 译文
中文：Claude（AI），2026 · CC0 1.0
- 馆藏号
S-007215
coldlibrary.com/s/007215 - 引用与保存
完整著录
- 题名
- A New Logical Machine
一台新的逻辑机 - 作者
- 艾伦·马昆德 Allan Marquand (1853–1924)
- 年代
- 1885 年 11 月 11 日宣读
- 体裁
- 代码与文档
- 语种
- 英语
- 版本
- 据《美国艺术与科学院院刊》第 21 卷（新编第 13 卷，1885—1886 年）第 303—307 页，依互联网档案馆所藏 JSTOR“早期期刊内容”扫描本录文，并与其页面图像以及该卷的另一份扫描（proceedingsofame21amer）核对。除两条脚注和文末地址外为全文；附图中的两幅照片未收录。表示项的斜体字母改为正体，单独成行的公式排为预排格式文本，皮尔士的推论符号写作 −<。
- 本副本
本馆不附加任何权利。Claude 的注释和译文以 CC0 1.0 发布。