Lecture I to the Adirondack Summer School 1905
I have a difficult task before me to render these four lectures profitable to you. It would be less so if you came without a single idea on the subject. But everybody, every butcher and baker, has ideas of logic and even used the technical terminology of the subject. He says he deals in articles of "prime necessity." Perhaps he would be surprised to learn that the phrase "prime necessity" was inserted by logicians to express a logical conception which has now become in common mouths very vague, it is true; but which still has a little of the original concept in a vague form clinging to it.
If I had a class in logic to conduct for a year, I should harp still, as I used to do at the Johns Hopkins, upon
maieutic character of my office,--which means that I should do all I could to make my hearers think for themselves, by which I earned the gratitude of men who are useful to mankind. I should insist that they must not suppose that my opinions were bound to be correct, but must work out their own ways of thinking. But now that there are but four lectures, and all falling in one week, the case is otherwise. I must beg you to remember that comprehension comes first and criticism later. It will be as much as you can possibly do in this week with diligent endeavors, to understand what I mean by logic and what the general outline of my system is. In order to do as much as that you must endeavor to take up a sympathetic attitude,--to try to catch what it is that I am driving at, and to store up in your minds
an outline of my theory which you will subject to criticism in the months to come.
In order that you may understand me, that you may for this one week put yourselves, as far as you can, in my intellectual shoes,--leaving yourselves to decide only after you have worn them for a while whether they really fit or not,--that I am going to begin by telling you something about my classification of the sciences; because it will aid you in the difficult task of imbibing my notion of the kind of science that I hold logic to be.
I have gained an unfortunate reputation as a writer upon the algebra of logic. It is generally understood that I hold logical algebra to be the main part of logic. But that is quite a mistake. I am in the world but not of the world of formal logic. A calculus, even in mathematics
proper, is like the sword that our warriors by sea and land carry at their sides. Having it there at hand marks the mathematician as the sword marks his officer. Moreover it is like a sword a most handy instrument. There is a traditional use of the calculus just as there is a traditional sword practice. But just as swords
are as far as practical use, goes are more to the purpose in opening tomato cans than men's abdomens, so the calculus is put by real mathematicians to uses its inventor little dreamed of. And if this is true of the differential calculus, it is a hundred times true of any logical calculus.
Professor Dedekind, one of the leading logico-mathematicians,- but like the rest, a
l mathematician in fact, and not a logician,--urges that mathematics is nothing but a particular branch of logic.
He is quite mistaken. Having no inside acquaintance with the logical household, he does not know as I do from having been an inmate of both houses, that the logicians aims and ideals are entirely foreign to the mathematician, and the mathematician's to the logician. The mathematician is intent on finding ways of making intricacies intelligible. He wants to facilitate reasoning. The logician does not care a straw about that. He wants to know what the essential ingredients of reasoning and thought in general are. Far from wishing to abridge reasonings, as the mathematician
[seek??] is perpetually doing where he can, the logician prefers to have them cumbrous so that no element may be overlooked. This difference is striking enough even where the logician is upon