以下の文献を、出る頃のになれば買おうと思っていて、来年春頃出るのだろうと何となく勝手に思い込んでいたのだが、Oxford UPのcatalogueを何気なく見ていると既にこの春出ていることがわかり、あわてて注文する。
- J. Ferreiros and J. J. Gray ed. The Architecture of Modern Mathematics: Essays in History and Philosophy, Oxford University Press, 2006
いつもOxford UPやCambridge UPなど、イギリスの主要な学術系出版社のcatalogueは毎回checkしているのだけれど、なぜだかわからないが、すっぽり見落としている。不思議だ。あるいは「怖い」と言った方がいいかもしれない。毎度目を通し、しかもしばしば繰り返し見ているのに抜けいている…。やれやれ。
Contents
Introduction , J. Ferreiros and J. J. Gray
Frege and the role of historical elucidation: Methodology and the foundations of mathematics , M. Beaney
Riemann's Habilitationsvortrag at the crossroads of mathematics, physics and philosophy , J. Ferreiros
The Riemannian background to Frege's philosophy , J. Tappenden
Axiomatics, Empiricism, and Anschauung in Hilbert's conception of geometry: Between arithmetic and general relativity , L. Corry
Methodology and metaphysics in the development of Dedekind's theory of ideals , J. Avigad
Emmy Noether's “set-theoretic”topology: from Dedekind to the rise of functors , C. McLarty
Tarski on models and logical consequence , P. Mancosu
A path to the epistemology of mathematics: Homotopy theory , J. P. Marquis
Felix Hausdorff's 'considered empiricism' , M. Epple
Practice-related symbolic realism in H. Weyl's mature view of mathematical knowledge , E. Scholz
From Kant to Hilbert: French philosophy of concepts in the beginning of the 20th Century. , H. Benis-Sinaceur (Translated by J. Deans)
Relative consistency and accessible domains, (Synthese, vol. 84, 1990) , W. Sieg
Modern mathematics as a cultural phenomenon , J. J. Gray
Beaney, Tappenden論文がやはりFrege絡みなので興味深い。Tappenden論文は当人のHPからDL可能なはず。そこから既に自分も入手してある(まだ読んでいません…)。他にも持っているものやDL可能なものがあるはずである。
Intro.にあるTappenden論文要約を以下に引いておこう。
In his thought-provoking study of ‘The Riemannian background to Frege’s philosophy,’ Tappenden considers not only Riemann and Frege, but what he argues has been a distortion of the debate about the philosophy of mathematics that follows from a failure to appreciate the importance of complex analysis in nineteenth-centurymathematics. The theory of complex functionswas one of the greatest creations of nineteenth-century mathematics, and the central branch of the discipline according to the most influential German mathematicians at the time. By not appreciating this, and Frege’s professional interest in it, philosophers and historians of mathematics have failed to see Frege as an essentially pro-Riemannian, anti-Weierstrassian philosopher. If this failure derives from a stunted appreciation of mathematical practice, its consequences are nonetheless a diminished understanding of what Frege was trying to do. Tappenden pursues the Fregean themes of fruitful concepts and centrality of a foundational concept, concentrating on the concept of function. He argues that Riemann’s work presented these methodological issues (which were there connected to both the role of geometry and intuition and applications) in an especially urgent way, and that Frege’s non-foundational work has live roots in this new style of mathematics.
FregeがRiemannにつながること自体は、前々からよく知られている(はずである)。Fregeの先生はE. AbbeでAbbeの先生はRiemannであり、しかもAbbeはRiemannの授業に熱心に出席していたようで、一生懸命ノートを取っていたというような話をシュプリンガー・フェアラーク東京から和訳の出ていたRiemannの伝記に書いてあったと記憶している。
それで何となく、Fregeには射影幾何の理解があり、そこからFregeはRiemann幾何に興味があって、この点で2人は結びつくと思っていたが、上の要約を読むとそうでもないようだ。私のこの勝手な思い込みは、完全に間違っていたのかな？
