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

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.

"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/

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

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