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 backer, 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 would harp still, as I used to do at the Johns Hopkins, upon
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. This 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 one 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