今日はカフェで読書をする。
Chetの伝記を読み、薬袋本で英語の復習をし、
- G.ブール 『論理の数学的分析 −演繹的推論の計算に関する試論−』 末木剛博監修、西脇与作訳
のintroにあたるブールの「緒言」を読み、
- W.V.Quine “MacHale on Boole”
を読む。このQuineの文は
- Desmond MacHale George Boole −His Life and Work
の一般向け書評。次にその興味深い文章を引用する。
The avenue from Boole through Peirce to the present is one of continuous development, and this, if anything, is the justification for dating modern logic from Boole; for there had been no comparable influence on Boole from his more primitive antecedents. But logic became a substantial branch of mathematics only with the emergence of general quantification theory at the hands of Frege and Peirce. I date modern logic from there.
Frege got there first. His initial and succeeding contributions were richer and more refined, moreover, than any other logical work until the present century, when the current from Boole through Peirce and the current from Frege converged. Thus I have long hailed Frege as the founder of modern logic, and viewed Boole, De Morgan, and Jevons as forerunners. John Venn and Lewis Carroll also belong back with them, though coming on the scene only after the great event.
文章中ほどの‘general quantification theory’の‘general’とはmonadicではない、より一般的なquantification theoryということである。現代論理学以前と以後を、一般的な量化理論の成立以前と以後に重ね合わせてQuineは理解しているということがわかる。これによるとBooleは現代論理学以前であり、FregeとPeirceが現代論理学の始まりということになる。
