直前ですが、次の数学と論理の哲学分野の会合案内をこのメールリストで流させていただきます。ハイブリッド形式、要事前登録、途中入退室自由です。 慶應義塾大学 岡田光弘 ーーーー BrouwerとHusserlの論理の諸問題に関するMark van Atten 教授の２つのレクチャーと討論Two lectures and discussion by Prof. Mark van Atten on various issues in Brouwer and Husserl's logic

Apr 16th, 2024, at Keio University 日時：2024年4月16日（火） 日本時間16:30-19:40 (JST)

最新情報は次のページをご覧ください。４月１２日中に開設予定です。See below for the updated information after April 12th. https://abelard.flet.keio.ac.jp/Two_lectures_and_discussion_by_Prof_Mark_van... ------------------------------ ------------------------------ 事前登録 / Pre-registration*事前登録フォームはこちら (要事前登録):https://forms.gle/vKdraEaFakMZTnLw7 https://forms.gle/vKdraEaFakMZTnLw7**Preregistration is HERE (required) : https://forms.gle/vKdraEaFakMZTnLw7 https://forms.gle/vKdraEaFakMZTnLw7*

ハイブリッド形式会議です。対面参加かオンライン参加可を選択して事前登録してください。 Pre-registration required: Please select “in person” or “online” ------------------------------ ------------------------------

会場 / Venue

慶應義塾大学三田キャンパス南校舎7階471, the South School Building 7th Floor, Room 471 （正門からすぐの校舎です. The first building after the Main Gate of the Campus）

Mita Campus, Keio University (7 minutes walk from JR-Tamachi, Subway Mita or Akabanebashi)

キャンパスマップ 4番の建物: https://www.keio.ac.jp/ja/maps/mita.html Campus Map Building #4: https://www.keio.ac.jp/en/maps/mita.html

プログラム / PROGRAM

Mark van Atten教授(Professor, Husserl Archives (CNRS/ENS))の下記の２つの講義をもとに次のテーマを討論します。 第1部 BROUWERとHeytingのInductive definition について 第２部 HUSSERLと完全性定理 討論：Husserlと論理学完全性/不完全性定理―FTL（「形式論理学と超越論的論的論理学」）解釈に与える影響について

Discussion Coordinator for Part 1: Ryota Akiyoshi (Keio University) Discussion Coordinator for Part 2: Mitsuhiro Okada (Keio University)

ABSTRACTS of the TWO LECTURES Lecture 1: Brouwer and Heyting on intuitionistic inductive definitions

Here is the Abstract: "Neither Brouwer nor Heyting has offered an explicit foundational analysis of inductive definitions. This paper argues that they had an implicit one, and makes it explicit. The clauses must be understood neither as propositions nor as permissions, but as commands. Correspondingly, inductive definitions are governed by the grammar of the imperative. Three consequences of this analysis are noted: (1) The extremal clause is redundant. (2) The logic to be used in the conditions is coherent logic. (3) On account of (2), the intuitionistic analysis in effect meets a desideratum on analyses of inductive definitions formulated by Kreisel. Overall, this reconstructed analysis provides an example of how, in intuitionism, pragmatic aspects of a definition can contribute to its mathematical content."

Lecture 2: Husserl and the incompleteness theorems

Here is the Abstract: "By way of commenting on the prior literature (especially Cavaillès, Tran, Bachelard, Lohmar), it is argued that both the first and the second of Gödel’s Incompleteness Theorems have a bearing on the view on mathematics that Husserl presents in Formale und transzendentale Logik, and that this bearing is not small."

The talk is mostly for philosophers who are not specialists in logic.

[参考]Van Atten 教授のBrouwerとHusserlに関する主な著作の一部

"Why Husserl should have been a strong revisionist in mathematics". Husserl Studies 18 (1), 1–18, 2002.

On Brouwer. Belmont (MA), Wadsworth, 2004.

Brouwer Meets Husserl: On the Phenomenology of Choice Sequences, Dordrecht, Springer, 2007.

"Construction and constitution in mathematics". The New Yearbook for Phenomenology and Phenomenological Philosophy 10, 43–90, 2010.

Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Dordrecht, Springer, 2015.

"The Creating Subject, the Brouwer-Kripke Schema, and infinite proofs". Indagationes Mathematicae 29, 1565-1636, 2018.

"Dummett’s objection to the ontological route to intuitonistic logic : a rejoinder". Inquiry 65(6), 725-742, 2022.

"Intuition, iteration, induction", Philosophia Mathematica 32(1), 34-81, 2024.

"Luitzen Egbertus Jan Brouwer", SEP, https://plato.stanford.edu/entries/brouwer/

"The development of intuitionistic logic", SEP, https://plato.stanford.edu/entries/intuitionistic-logic-development/

オーガナイザ / Organizing Committee

- Ryota Akiyoshi (Keio University) - Koji Mineshima (Keio University) - Mitsuhiro Okada (Keio University) - Kentaro Ozeki (Keio University)

問い合わせ先 / Contact address of the Meeting Office

logic[At]abelard.flet.keio.ac.jp