Johns Hopkins University Circulars volume 2, number 19, 1882 November, pages 11–12. At Google Books. At Internet Archive.
Reprinted in Writings volume 4, pages 378–382.
Professor C. S. Peirce began his instruction for the current session by a lecture in Hopkins Hall, on the underlying methods of modern logic. It was attended by instructors as well as students. In compliance with a request for an abstract of his address, which was delivered without notes, the speaker has given the following outline.
Mr. Peirce said that he had requested the instructors to do him the favor to listen to his observations, because he thought that a clear understanding of the purpose of the study of logic might remove some prejudices by leading to a true estimate of its nature.
It might be supposed that logic taught that much was to be accomplished by mere rumination, though every one knows that experiment, observation, comparison, active scrutiny of facts, is what is wanted, and that mere thinking will accomplish nothing even in mathematics. Logic had certainly been defined as the "art of thinking," and as the "science of the normative laws of thought." But those are not true definitions. "Dyalectica," says the logical text-book of the middle ages, "est ars artium et scientia scientiarum, ad omnium aliarum scientiarum methodorum principia viam habens," and although the logic of our day must naturally be utterly different from that of the Plantagenet epoch, yet this general conception that it is the art of devising methods of research, — the method of methods, — is the true and worthy idea of the science. Logic will not undertake to inform you what kind of experiments you ought to make in order best to determine the acceleration of gravity, or the value of the Ohm; but it will tell you how to proceed to form a plan of experimentation.
It is impossible to maintain that the superiority of the science of the moderns over that of the ancients is due to anything but a better logic. No one can think that the Greeks were inferior to any modern people whatever in natural aptitude for science. We may grant that their opportunities for research were less; and it may be said that ancient astronomy could make no progress beyond the Ptolemaic system until sufficient time had elapsed to prove the insufficiency of Ptolemy's tables. The ancients could have no dynamics so long as no important dynamical problem had presented itself; they could have no theory of heat without the steam-engine, etc. Of course, these causes had their influence, and of course they were not the main reason of the defects of the ancient civilisation. Ten years' astronomical observations with instruments such as the ancients could have constructed would have sufficed to overthrow the old astronomy. The great mechanical discoveries of Galileo were made with no apparatus to speak of. If, in any direction whatever, the ancients had once commenced research by right methods, opportunities for new advances would have been brought along in the train of those that went before. But read the logical treatise of Philodemus; see how be strenuously argues that inductive reasoning is not utterly without value, and you see where the fault lay. When such an elementary point as that needed serious argumentation it is clear that the conception of scientific method was almost entirely wanting.
Modern methods have created modern science; and this century, and especially the last twenty-five years, have done more to create new methods than any former equal period. We live in the very age of methods. Even mathematics and astronomy have put on new faces. Chemistry and physics are on completely new tracks. Linguistic, history, mythology, sociology, biology, are all getting studied in new ways. Jurisprudence and law have begun to feel the impulse, and must in the future be more and more rapidly influenced by it.
This is the age of methods; and the university which is to be the exponent of the living condition of the human mind, must be the university of methods.
Now I grant you that to say that this is the age of the development of new methods of research is so far from saying that it is the age of the theory of methods, that it is almost to say the reverse. Unfortunately practice generally precedes theory, and it is the usual fate of mankind to get things done in some boggling way first, and find out afterward how they could have been done much more easily and perfectly. And it must be confessed that we students of the science of modern methods are as yet but a voice crying in the wilderness, and saying prepare ye the way for this lord of the sciences which is to come.
Yet even now we can do a little more than that. The theory of any act in no wise aids the doing of it, so long as what is to be done is of a narrow description, so that it can be governed by the unconscious part of our organism. For such purposes, rules of thumb or no rules at all are the best. You cannot play billiards by analytical mechanics nor keep shop by political economy. But when new paths have to be struck out, a spinal cord is not enough; a brain is needed, and that brain an organ of mind, and that mind perfected by a liberal education. And a liberal education — so far as its relation to the understanding goes — means logic. That is indispensable to it, and no other one thing is.
I do not need to be told that science consists of specialties. I know all that, for I belong to the guild of science, have learned one of its trades and am saturated with its current notions. But in my judgment there are scientific men, all whose training has only served to belittle them, and I do not see that a mere scientific specialist stands intellectually much higher than an artisan. I am quite sure that a young man who spends his time exclusively in the laboratory of physics or chemistry or biology, is in danger of profiting but little more from his work than if he were an apprentice in a machine shop.
The scientific specialists — pendulum swingers and the like — are doing a great and useful work; each one very little, but altogether something vast. But the higher places in science in the coming years are for those who succeed in adapting the methods of one science to the investigation of another. That is what the greatest progress of the passing generation has consisted in. Darwin adapted to biology the methods of Malthus and the economists; Maxwell adapted to the theory of gases the methods of the doctrine of chances, and to electricity the methods of hydrodynamics. Wundt adapts to psychology the methods of physiology; Galton adapts to the same study the methods of the theory of errors; Morgan adapted to history a method from biology; Cournot adapted to political economy the calculus of variations. The philologists have adapted to their science the methods of the decipherers of dispatches. The astronomers have learned the methods of chemistry; radiant heat is investigated with an ear trumpet; the mental temperament is read off on a vernier.
Now although a man needs not the theory of a method in order to apply it as it has been applied already, yet in order to adapt to his own science the method of another with which he is less familiar, and to properly modify it so as to suit it to its new use, an acquaintance with the principles upon which it depends will be of the greatest benefit. For that sort of work a man needs to be more than a mere specialist; he needs such a general training of his mind, and such knowledge as shall show him how to make his powers most effective in a new direction. That knowledge is logic.
In short, if my view is the true one, a young man wants a physical education and an aesthetic education, an education in the ways of the world and a moral education, and with all these logic has nothing in particular to do; but so far as he wants an intellectual education, it is precisely logic that he wants; and whether he be in one lecture-room or another, his ultimate purpose is to improve his logical power and his knowledge of methods. To this great end a young man's attention ought to be directed when he first comes to the university; he ought to keep it steadily in view during the whole period of his studies; and finally, he will do well to review his whole work in the light which an education in logic throws upon it.
I should be the very first to insist that logic can never be learned from logic-books or logic lectures. The material of positive science must form its basis and its vehicle. Only relatively little could bo done by the lecturer on method even were he master of the whole circle of the sciences. Nevertheless, I do think that I can impart to you something of real utility, and that the theory of method will shed much light on all your other studies.
The impression is rife that success in logic requires a mathematical head. But this is not true. The habit of looking at questions in a mathematical way is, I must say, of great advantage, and thus a turn for mathematics is of more or less service in any science, physical or moral. But no brilliant talent for mathematics is at all necessary for the study of logic.
The course which I am to give this year begins with some necessary preliminaries upon the theory of cognition. For it is requisite to form a clear idea at the outset of what knowledge consists of, and to consider a little what are the operations of the mind by which it is produced. But I abridge this part of the course as much as possible, partly because it will be treated by other instructors, and partly because I desire to push on to my main subject, the method of science.
I next take up syllogism, the lowest and most rudimentary of all forms of reasoning, but very fundamental because it is rudimentary. I treat this after the general style of DeMorgan, with references to the old traditional doctrine. Next comes the logical algebra of Boole, a subject in itself extremely easy, but very useful both from a theoretical point of view and also as giving a method of solving certain rather frequently occurring and puzzling problems. From this subject, I am naturally led to the consideration of relative terms. The logic of relatives, so far as it has been investigated, is clear and easy, and at the same time it furnishes the key to many of the difficulties of logic, and has already served as the instrument of some discoveries in mathematics. An easy application of this branch of logic is to the doctrine of breadth and depth or the relations between objects and characters. I next introduce the conception of number, and after showing how to treat certain statistical problems, I take up the doctrine of chances A very simple and elegant mathematical method of treating equations of finite differences puts the student into possession of a powerful instrument for the solution of all problems of probability that do not import difficulties extraneous to the theory of probability itself.
We thus arrive at the study of that kind of probable inference that is really distinctive; that is to say, Induction in its broadest sense — Scientific Reasoning. The general theory of the subject is carefully worked out with the aid of real examples in great variety, and rules for the performance of the operation are given. These rules have not been picked up by hazard, nor are they merely such as experience recommends; they are deduced methodically from the general theory.
Finally, it is desirable to illustrate a long concatenation of scientific inferences. For this purpose we take up Kepler's great work, De Motu Stellae Martis, the greatest piece of inductive reasoning ever produced. Owing to the admirable and exceptional manner in which the work is written, it is possible to follow Kepler's whole course of investigation from beginning to end, and to show the application of all the maxims of induction already laid down.
In order to illustrate the method of reasoning about a subject of a more metaphysical kind, I shall then take up the scientific theories of the constitution of matter.
Last of all, I shall give a few lectures to show what are the lessons that a study of scientific procedure teaches with reference to philosophical questions, such as the conception of causation and the like.
. Note by B.U.: "Dyalectica est ars artium et scientia scientiarum, ad omnium aliarum scientiarum methodorum principia viam habens" can be translated as "Logic is the art of arts and science of sciences, with the way to the principles of the methods of all other sciences." The saying, in more than one form, is attributed to Peter of Spain.