https://forms.gle/WAecNDbtCaUnsG9H6

February 28th,Saturday, 2026. 10:00-18:00 (JST)
2026年2月28日(土) 10:00-18:00

慶應義塾大学三田キャンパス東館6階G-Lab /
G-Lab, 6th floor, East Building, Mita Campus, Keio University
(7 minutes walk from JR-Tamachi, Subway Mita or Akabanebashi)
キャンパスマップ 13番の建物: https://www.keio.ac.jp/ja/maps/mita.html
Campus Map Building #13: https://www.keio.ac.jp/en/maps/mita.html

Hirohiko Abe (Independent Researcher)(*)
Risako Ando (Keio University)
Yuichiro Hosokawa (Gunma Prefectural Women's University)
Ryo Ito (Waseda University)(**)
Onyu Mikami (Tokyo Metropolitan University)
Koji Mineshima (Keio University) (**)
Mitsuhiro Okada (Keio University)(**)
Kentaro Ozeki (University of Tokyo / Keio University)
(*) Chief coordinator, (**) Co-Chairs

Center for Design of Future Symbiosis of Keio University / 慶應義塾大学未来共生デザインセンター
https://www.carls.keio.ac.jp/symbiosis/

同センター論理班　logic@abelatd.flet.keio.ac.jp

Frege and Hilbert had a short but important correspondance between 1895 and 1903. This exchange of letters is a typical example of a disagreement in logic and reasoning, an important topic in contemporary philosophy. Because many different issues are intertwined in the discussion the two logicians had in these letters, it is not clear what exactly Frege and Hilbert were disagreeing about in their exchange. I will revisit this locus classicus of the philosophy of logic from the viewpoint of the analysis of disagreement. This will help us sorting out several kinds of disagreement: when people talk past each others, giving different meanings to the same words, when they do not have the same goals, when they have different scientific projects, when they follow different scientific practice, or when they have various normative ideas about mathematics, logic, and reasoning.

In this paper, I attempt to undertake two tasks concerning disagreements about rules, which I discussed elsewhere. One is to discuss whether we can understand the rule-following paradox in terms of the notion of a disagreement. There appears to be a disagreement between those who think 68 + 57 = 125 and the "bizarre sceptic" who appears in Kripke's presentation of the rule-following paradox; yet, it seems that to make the sceptical point, it is not necessary that the sceptic should be committed to the claim that 68 + 57 = 5. It is thus well to explore the nature of the apparent disagreement between the two parties, and I do so, citing some existing discussions on possible disagreements. The other task is to discuss the nature of a disagreement about the validity of a logical law. I argue that if it is a disagreement about a rule, we cannot simply ask whether the law is correct or not, and what we could do to resolve the disagreement would be different, depending on whether it is about the choice of a rule or about the expression of a rule.

As Popper (1948) essentially revealed, if we directly add classical negation on the top of Maehara's (1954) multi-succedent sequent calculus for intuitionistic logic, the resulting calculus is not conservative over the original system. To elaborate further, intuitionistic negation behaves in the same way as classical negation. This phenomenon points out the difficulty of providing a calculus that has intuitionistic and classical negations and is conservative over both of the logics. Moreover, employing the notion of uniqueness, proposed by Belnap (1962), Humberstone (2011) argued that this phenomenon provides intuitionists with a ground to deny the intelligibility of classical negation. These difficulties can be regarded as obstacles to codify the disagreement between the proponents of the two logics into a formal system. However, as demonstrated by Humberstone (1979) and Toyooka and Sano (2024), the phenomenon can technically be circumvented by implementing a simple modification to the right rule for intuitionistic implication, and consequently, for intuitionistic negation. Although Humberstone (2011) noticed this technical fact, Humberstone philosophically argued that intuitionists should not accept this solution and should maintain the position of denying the intelligibility of classical negation. This talk briefly explains the technical solution and proceeds to add some remarks on Humberstone's philosophical arguments, although it does not give a complete evaluation of the arguments.

With a few historical exceptions, the philosophical debate on mathematical explanation is recent, having largely developed in the last 25 years. Recent literature has focused on the analysis of case studies from different areas of mathematical practice, and on providing competing accounts (and sometimes models) of how it works. In this talk I will propose an analysis of what these accounts disagree about and I will argue that there is not a single dimension to the disagreement on mathematical explanation. For example, some accounts stress the role of understanding in mathematical explanation, while others do not assign a significant role to it. I will argue that this does not represent a form of genuine disagreement because different meanings are attached to the word “explanation”. I will then argue that an important aspect of mathematical explanation has been neglected in the literature, namely, that mathematical explanation is relative to the goals of enquiry, and therefore that there are no proofs that are explanatory in an absolute sense. By using a case study, I will show that understanding explanation in this way resolves certain cases of disagreement. According to this picture, genuine disagreement only occurs when two parties share the same conception of mathematical explanation and the same explanatory goals, but differ in opinion about which proof best achieves the goals in question.

Hosokawa (2024b) showed that the disagreement between similarity analysis (Lewis, 1973) and causality analysis (e.g., Pearl, 1999) of counterfactuals can be resolved in hybrid tense logic for temporal conditionals (Hosokawa, 2023; 2024a). In this talk, we add to the list of its effects a theoretical contribution to counterfactual fairness and counterfactual explanations with actionable recourse in/for AI decision-making

In his excellent textbook on philosophical logic (2020), MacFarlane presented in the Natural Deduction form Williamson’s proof of the collapse of the classical negation and the intuitionistic negation when merging the two underlying logical languages, in the course of Quine’s argument that the dispute between the two parties is only a verbal dispute. While MacFarlane’s Natural Deduction proof is faithful to Williamson’s original proof, slightly modifying the Natural Deduction proof more faithfully to Gentzen’s leads us to make the classical and intuitionistic contradictions explicit, which also results in making further explicit the usually hidden “conclusive context”. We discuss how the new merged logical language opens new proof formations with new logical constants, and how the dispute would go.

Deep disagreement is often seen as a breakdown of rational argument: parties disagree not only about facts, but about what counts as evidence, reasons, and valid inference. This talk proposes a different perspective. Instead of presupposing a fixed logical or semantic framework, I ask how such frameworks can be elucidated—and sometimes formed—through the very practices in which disagreement occurs.
I develop this idea through a genealogy of meaning-theory. Building on Dummett’s reframing of realism debates as disputes over inferential norms, I argue that deep disagreement foregrounds a methodological task of semantics: making explicit the rules that govern justification and refutation. I then revisit Frege’s notion of Erläuterung (elucidation) and Wittgenstein’s view of philosophy as clarificatory activity to show why clarification is not merely descriptive but norm-shaping. Finally, I sketch an interaction-based model, drawing on Girard’s transcendental syntax and ludics, where meaning is characterized by permissible patterns of challenge and response. The central claim is that deep disagreement should be analyzed not only as a failure of shared rules, but as a site in which appropriate rules can emerge through the stabilization of admissible challenges and defenses.