入手文献名を明記する。加えて主にFrege関係文献のabstract等を付す。
- Fernando Ferreira “Amending Frege’s Grundgesetze der Arithmetik ”, in: Synthese, vol. 147, no. 1, 2005.
Abstract
Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this extended system.
FregeとHilbert特集の号から。同号の他の論文のabstractやreferenceも一通り入手しておく。必要とあらば、それらの他の論文おのおの全体もそのうち入手する。
- Alan Weir “There Are No True Contradictions”, in: The Law of Non-Contradiction, Oxford University Press, 2004.
- ditto “Neo-Fregeanism: An Embarrassment of Riches”, in: The Notre Dame Journal of Formal Logic, vol. 44, no. 1, 2003.
Abstract
Neo-Fregeans argue that substantial mathematics can be derived from a priori abstraction principles, Hume's Principle connecting numerical identities with one:one correspondences being a prominent example. The embarrassment of riches objection is that there is a plurality of consistent but pairwise inconsistent abstraction principles, thus not all consistent abstractions can be true. This paper considers and criticizes various further criteria on acceptable abstractions proposed by Wright settling on another one—stability—as the best bet for neo-Fregeans. However, an analogue of the embarrassment of riches objection resurfaces in the metatheory and I conclude by arguing that the neo-Fregean program, at least insofar as it includes a platonistic ontology, is fatally wounded by it.
Description
哲学的な議論や論証そのものに焦点を当てる「問題中心型」のスタイルで、現代の言語哲学の主要な論点を紹介する。
言語哲学は20世紀を通して哲学の焦点の一つであったが、1960年代以降、とりわけ大きな進展をみせた。本書は言語哲学の領域を四つに分けて概説したものである。第Ⅰ部はラッセルと最近のクリプキの理論、第Ⅱ部は本書の中核をなす意味の理論、第Ⅲ部は言語行為論と語用論、第Ⅳ部はメタファー論である。
同じ勁草書房から出ている服部裕幸著『言語哲学入門』は充分なぐらいやさしかったので入手しなかったが、この新刊は程よくやさしい。また時間があるときに復習がてらに読んでみることにしよう。
- Timothy Bays “The Mathematics of Skolem’s Paradox”, in: Philosophy of Logic, Dale Jacquette (ed.), forthcoming.
- Michael Glanzberg “Truth”, Entry for The Stanford Encyclopedia of Philosophy, forthcoming.
- Cesare Cozzo “Can a Proof Compel us?”, in Mathematical Reasoning and Heuristics, C. Cellucci and D. Gillies (eds.), King's College Publications, 2005.
- Richard E. Grandy, Richard Warner “Paul Grice”, in: The Stanford Encyclopedia of Philosophy, 2005.
- Ross P Cameron “Lewisian Realism: Methodology, Epistemology, and Circularity”, in: Synthese, forthcoming.
- Phillip Bricker “Concrete possible worlds”, in: Contemporary Debates in Metaphysics, J. Hawthorne, T. Sider, and D. Zimmerman (eds.), Blackwell Publishing 2005, forthcoming.
最後の2本はDavid Lewisものである。
