The Philosophical Basis of Connexive Logic

• Applicant: Dr. Andreas Kapsner
• Subject Area: Theoretical Philosophy
• Term: from 2020 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 436508789

• Final Report Year: 2024

Final Report Abstract

The Project ’The Philosophical Basis of Connexive Logic’ was concerned with the philosophical interpretation of so-called connexive logics. Several articles that contain results of this project have been published. A comprehensive book length treatment of the subject has been accepted by the faculty as a habilitation thesis. Connexivity is usually understood to lie in adherence to the following principles: ARISTOTLE ¬( A → ¬ A) and ¬(¬ A → A) are valid. BOETHIUS ( A → B) → ¬( A → ¬ B) and ( A → ¬ B) → ¬( A → B) are valid. As the names indicate, these theses have a long and venerable history. This impressive pedigree notwithstanding, few of the known systems of formal logic are actually connexive. Most prominently, classical logic is not connexive, but the same is true of most non-classical logics as well. Moreover, the family of connexive logics holds a very special status amongst non-classical logics in being super-classical; that is, where other non-classical logics tend to criticize classical logic for proving too much, connexive logic’s challenge is that classical logic proves too little. This creates a very distinctive situation, both formally and philosophically. The main question this project sought to answer is what role connexivity has to play in an analysis of natural language statements. Note their prima facie plausibility, no matter whether → is interpreted as an indicative or a counterfactual conditional. If one can free oneself from classical preconceptions, it is hard not to think of instances such as the following as logically true: “It is not the case that if I go to Brazil next year I do not go to Brazil next year.” “It is not the case that if I were to go to Brazil next year, I would not go to Brazil next year.” Similar instances of BOETHIUS feel equally trivially true. The project sought to answer what we should do about those intuitions in our theorizing about logic and natural language semantics. There are different options here; for example, one chapter of the monograph asks whether there might be ways to pragmatically explain these intuitions without necessarily changing anything in the logic. Though the chapter finds some (limited) promise in that direction, the main focus of the project was on actual logical change as implemented in different systems known in the literature, as well as systems that are newly proposed.

Publications

• Connexivity and the Pragmatics of Conditionals. Erkenntnis, 87(6), 2745-2778.
  Kapsner, Andreas
  
• Cutting Corners: A Critical Note on Priest’s Five-Valued Catuṣkoṭi. Comparative Philosophy: An International Journal of Constructive Engagement of Distinct Approaches toward World Philosophy, 11(2).
  KAPSNER, Andreas
  
• Lord Nicholls on the likelihood of crimes. Synthese, 200(6).
  Kapsner, Andreas
  
• Superconnexivity Reconsidered. Electronic Proceedings in Theoretical Computer Science, 358, 160-173.
  Kapsner, Andreas & Omori, Hitoshi
  
• Ineffability, Emptiness and the Aesthetics of Logic. Comparative Philosophy: An International Journal of Constructive Engagement of Distinct Approaches toward World Philosophy, 14(1).
  KAPSNER, Andreas
  
• The Value of the One Value: Exactly True Logic revisited. Journal of Philosophical Logic, 52(5), 1417-1444.
  Kapsner, Andreas & Rivieccio, Umberto
  
• Angell and McCall Meet Wansing. Studia Logica, 112(1-2), 141-165.
  Omori, Hitoshi & Kapsner, Andreas
  
• Flavors of Connexivity. Trends in Logic, 23-48. Springer Nature Switzerland.
  Kapsner, Andreas