上記のBaysさんの書評をちらちら見やると次のような註がある。これは一番目の註である。
This is probably the right place for a little bit of bibliographical information. The basic fact that one can derive arithmetic from (HP) plus second order logic goes pretty far back. One can find the idea in (Geach, 1951), (Geach, 1955) and (Parsons, 1965). That being said, the idea that this derivation provides an adequate foundation for arithmetic seems to be original to Wright in his influential book Frege’s Conception of Numbers as Objects, (Wright, 1983). At any rate, this is the book that really got the contemporary neo-logicist project off and running. […]
で、‘(Geach, 1951), (Geach, 1955)’とは
Geach, P. (1951). Frege’s Grundlagen. Philosophical Review, 60:535–544.
Geach, P. (1955). Class and concept. Philosophical Review, 64:561–570.
である。C. Parsonsさんが一番最初かと思っていたがそうではないらしい。私としては初耳である。そうだったのか？ 普通はC. Parsonsさんが一番最初であると、しばしば指摘されているのだが。(Geach, 1951)はこの間入手したので(Geach, 1955)をまた今度手に入れようかな。
上記の
- Stanley Peters and Dag Westerstahl “1.2 Quantifiers in Early Predicate Logic”, in their Quantifiers in Language and Logic, Clarendon Press, 2006
をスターバックスで読む。Peirce, Peano, Russell, Fregeの量化理論の極かいつまんだ説明。あまり詳しくはない。そこに見られるnote 29が個人的に気になったのでここに控えておく。
We should observe, however, that although Frege had the resources to deal with arbitrary quantifiers, the only primitive one in his Begriffsschrift was the universal quantifier ∀. Indeed, with Russell he strongly criticized traditional logic for its adherence to subject-predicate form, rightly pointing out that such adherence had hampered the development of an adequate logical formalism. He did not note that a formalization of natural language sentences which preserves this form is possible via systematic employment of quantifiers. That insight came about 100 years later, with the work of Richard Montague (1974).
100年後といわず、Frege存命中の1920年にLesniewskiがOntologyを作っているが、これは正に‘subject-predicate form’を取りつつ論理学を展開していると思うのだが*1、どうなのだろう？
