昨日のRussellの原文を引用します。その前に三浦さんの文章を掲げます。
＊『プリンキピア』全三巻は事実上ラッセル一人の業績であるかのように扱うのが(数学界はともかく)哲学界の通例だ。それには多くの理由がある。成立経緯と内容からしてラッセル著『数学の諸原理』(一九〇三)の続編であったこと、一九〇八年のラッセル単著論文が『プリンキピア』の粗筋を予め示していること、『プリンキピア』の哲学的側面はラッセルが担当したことをホワイトヘッドも『過程と実在』(一九二九)や『マインド』誌(一九二六)で述べていること、ホワイトヘッドの責任担当パートである第四巻以降が未刊に終わったこと、フランク・ラムジーやウィトゲンシュタインの批判を採り入れて第二版(一九二五−二七)を書いたのはラッセル一人だったこと、等々*1。
続いてRussellの話。
There is in some quarters a tendency to suppose that Whitehead's part in our joint work was less than in fact it was. As no one except myself now knows what were our respective shares, I will try to state the facts as nearly as I can remember them*2.
I knew that my mathematical capacity was not equal to accomplishing this task[=the project of deducing mathematics from logic in Principia Mathematica] unaided*3.
In the early part of the Principia, Whitehead contributed the treatment of apparent variables and the notation (x).φx. Chapter 10, 11, 13 of the Principia are in the main his work. He also invented the notations D‘R, R‘x, R“α −in this last case, the concept as well as the notation*4.
In the later parts, the primary responsibility was Whitehead's as regards cardinal arithmetic and mine as regards relation arithmetic. Whitehead alone was responsible for the section on Convergence and Limits of Functions, and for Part VI, on Quantity. Whitehead also contributed some portions which might have been thought to be more in my province, for instance the “Preparatory Statement of Symbolic Conventions” at the beginning of Vol. II, which is concerned with types and systematic ambiguity. He also wrote the bulk of the first chapter of the Introduction.
Whitehead was to have written a fourth volume, on geometry, which would have been entirely his work. A good deal of this was done, and I hope still exists*5.
When our work was sufficiently advanced, we parcelled out the topics, each produced a first draft of whatever was in his assignment, the other then went over it and probably made considerable changes,and then his revised draft was finally revised by the first author. In most parts of the book, there was, in the end, very little for which either had sole responsibility*6.
Neither of us alone could have written the book; even together, and with the alleviation brought by mutual discussion, the effort was so severe that at the end we both turned aside from mathematical logic with a kind of nausea*7.
というわけで、三浦さんの見解と、Russellの話を矛盾なく統一させることはできるのでしょうか？ 少なくともRussellの話からPrincipiaの役割分担は通説を無批判に採用することに対して、少しは慎重であるべきことを教えているのかもしれません。
