It cannot find its own problems; it cannot feed itself. It cannot direct itself between different possible procedures. For example, the simplest proposition of projective geometry, about the ten straight lines in a plane, is proved by von Staudt from a few premises and by reasoning of extreme simplicity, but so complicated is the mode of compounding these premises and forms of inference, that there are no less than 70 or 80 steps in the demonstration. How could we make a machine which would automatically thread its way through such a labyrinth as that? And even if we did succeed in doing so, it would still remain true that the machine would be utterly devoid of original initiative, and would only do the special kind of thing it had been calculated to do. This, however, is no defect in a machine; we do not want it to do its own business, but ours. The difficulty with the balloon, for instance, is that it has too much initiative, that it is not mechanical enough. We no more want an original machine, than a house-builder would want an original journeyman, or an American board of college trustees would hire an original professor. If, however, we will not surrender to the machine, the whole business of initiative is still thrown upon the mind; and this is the principal labor.
In the second place, the capacity of a machine has absolute limitations; it has been contrived to do a certain thing, and it can do nothing else. For instance, the logical machines that have thus far been devised can deal with but a limited number of different letters. The unaided mind is also limited in this as in other respects; but the mind working with a pencil and plenty of paper has no such limitation. It presses on and on, and whatever limits can be assigned to its capacity today, may be over-stepped tomorrow. This is what makes algebra the best of all instruments of thought; nothing is too complicated for it. And this great power it owes, above all, to one kind of symbol, the importance of which is frequently entirely overlooked—I mean the parenthesis. We can, of course, dispense with parentheses as such. Instead of (a + b)c = d, we can write a + b = t and tc = d. The letter t is here a transmogrified parenthesis. We see that the power of adding proposition to proposition is in some sort equivalent to the use of a parenthesis.
Mr. Marquand’s machines, even with only four letters, facilitate the treatment of problems in more letters, while still leaving considerable for the mind to do unaided. It is very desirable a machine on the same principle should be constructed with six letters. It would be a little more elegant, perhaps, instead of two keys to each letter, to have a handle which should stand up when the letter was not used, and be turned to the right or left, according as the letter was to be used, positively or negatively. An obvious extension of the principle of the machine would also render it possible to perform elimination. Thus, if six letters, A, B, C, D, E, F, were used, there could be an additional face which should simply take no notice of F, a third which should take no notice of F or E, a fourth which should take no notice of F, E or D; and these would suffice. With such a machine to represent AB + CD, we should proceed as follows: Put down handle E to the left. (The left hand would naturally signify the negative.) Leaving it down, put down handle A to the right and then bring it back after pulling the cord. Put down handle B to the right and pull the cord, and then restore handles B and E to the vertical. Next, put down handle F to the left and successively put down the handles C and D to the right, as before. After restoring these to the vertical, put down handles E and F to the right, and pull the cord. Then we should see on the third face
or, what comes to the same thing,
I do not think there would be any great difficulty in constructing a machine which should work the logic of relations with a large number of terms. But owing to the great variety of ways in which the same premises can be combined to produce different conclusions in that branch of logic, the machine, in its first state of development, would be no more mechanical than a hand-loom for weaving in many colors with many shuttles. The study of how to pass from such a machine as that to one corresponding to a Jacquard loom, would be likely to do very much for the improvement of logic.
1. 1. Philosophical Transactions for 1870.
2. It would be equally true to say that the machine is based upon Mrs. Franklins system. The face of the machine always shows every possible combination; putting down the keys and pulling the cord only alters the appearance of some of them. For example, the following figure represents, diagrammatically, the face of such a machine with certain combinations modified:
This face may be interpreted in several different ways. First, as showing in the shaded portions—
which is the same as what is seen on the unshaded portions if we regard the small letters as affirmative and the capitals as negative, and interchange addition and multiplication, that is, as—
Or, looking at the unshaded portion, we may regard it as the negative of the above, or—
or, what is the same thing, as—
There are two other obvious interpretations. We see, then, that the machine always shows two states of the universe, one the negative of the other, and each in two conjugate forms of development. In one interpretation simultaneously impressed terms are multiplied and successively impressed combinations added, and in the other interpretation the reverse is the case.
The Peirce-Gurney Dispute over Phantasms of the Living
Criticism on Phantasms of the Living: An Examination of an Argument of Messrs. Gurney, Myers, and Podmore
| December 1887 | Proceedings of the American Society for Psychical Research |
The most imposing of the arguments of Messrs. Gurney, Myers, and Podmore, in favor of spontaneous telepathy, popularly called ghosts, as presented in their Phantasms of the Living is this. Only one person in three thousand each year has a visual hallucination. Hence it is easy to calculate from the annual death-rate that in a population of fifty millions there would be each only one visual hallucination fortuitously coinciding within twelve hours, before or after, with the death of the person represented. But these gentlemen, having addressed, as they estimate, a public of only 300,000 persons, claim to have found thirty-one indubitable cases of this kind of coincidence within twelve years. From this, they cipher out some very enormous odds in favor of the hypothesis of ghosts. I shall not cite these numbers, which captivate the ignorant, but which repel thinking men, who know well that no human certitude reaches such figures as trillions, or even billions to one.
But every one of their thirty-one coincidences sins against one or more of eighteen different conditions to which such an argument must conform to be valid. This I proceed to show.
1st. Every case should have occurred between January 1st, 1874, and December 31st, 1885, for the calculation of the probabilities depends upon this supposition. Now Case 199 occurred in 1873 and Case 355 occurred in 1854.
2nd. The percipient should in each case have been drawn from their public, which they estimate at 300,000 persons who are supposed to have seen the advertisement. But no person could have seen the advertisement who was dead at the time of its publication;