第7章 「数学原理-その哲学的側面」n.1 - PM(数学原理)は協同の成果
我々が論争しなければならない問題は二種類、即ち、哲学的問題と数学的問題の2つがあった。大雑把に言うと、ホワイトヘッドは哲学的問題を私に任せた。数学的問題については、ホワイトヘッドがその記法(notation 記号法)の大部分を、ペアノ(が考案したもの)から借りたものは別として、考案した。(数学的問題については)私は系列(series)に関する仕事の大部分をやり、ホワイトヘッドはそれ以外の大部分をやった。しかしこれは初稿についてのみあてはまる(applies to そうである/該当する)。各部とも、三度書き直された。我々二人のどちらかが初稿を書きあげる、それを相手に送ると、受け取った方はかなり修正を行う(行った)。それが終ると、初稿を書いた方が、決定版(最終稿)に書き直した。三巻全体にわたって、二人の協同の成果(産物)でないものはほとんど一行も存在していない。 |
Chapter 7: Principia Mathematica: Philosophical Aspects, n.1Throughout the years from 1900 to 1910 both Whitehead and I gave the bulk of our time to what ultimately became Principia Mathematica, Although the third volume of this work was not published until 1913, our part in it (apart from proof-reading) was finished in 1910 when we took the whole manuscript to the Cambridge University Press. The Principles of Mathematics which I finished on May 23, 1902, turned out to be a crude and rather immature draft of the subsequent work, from which, however, it differed in containing controversy with other philosophies of mathematics.The problems with which we had to contend were of two sorts: philosophical and mathematical. Broadly speaking, Whitehead left the philosopliical problems to me. As for the mathematical problems, Whitehead invented most of the notation, except in so far as it was taken over from Peano; I did most of the work concerned with series and Whitehead did most of the rest. But this only applies to first drafts. Every part was done three times over. When one of us had produced a first draft, he would send it to the other, who would usually modify it considerably .After which, the one who had made the first draft would put it into final form. There is hardly a line in all the three volumes which is not a joint product. |