Logics: from tolerance to pluralism

• Applicant: Privatdozent Dr. Martin Fischer
• Subject Area: Theoretical Philosophy
• Term: from 2018 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 407312485

• Final Report Year: 2024

Final Report Abstract

The investigations of the project confirmed that logical pluralism is an attractive philosophy of logic. In contrast to logical monism it offers a simple explanation of the fruitful applicability of different logics. Monistic positions are usually tied to a criterion of correctness and assume either a universalist account or a primary area of application. The case study of a Kripkean conception of truth shows that the assumption of a criterion of correctness is not in all cases warranted. Both models of the discourse, in classical as well as in a nonclassical logic, are able to provide important insights with a differing emphasis depending on the interests. One of the findings of the project is that one of the main arguments for a classical monistic position can be answered. The logic of HYPE offers a suitable expansion of the many-valued logic of FDE to bridge the gap of proof-theoretic strength. The results show that classical arguments, such as Gentzen’s proof of transfinite induction can also be carried out in the framework of HYPE. The calculi that have been developed for the logic of HYPE within the project provide the necessary formal background for the philosophical conclusions. The conjecture that the ‘intuitionistic’ conditional of HYPE plays a crucial role for this was confirmed. Surprisingly already in the propositional case the extension of the FDE calculus led to complications for the standard cut-elimination procedure. In contrast to a monistic position Carnap’s position with his principle of tolerance offers more options for the choice of formal tools. In my investigations of internal categoricity I was able to show that in the area of arithmetic there are good arguments for the choice of classical logic even without invoking a realist ontology. Moreover, it could be shown that for the justification of the determinacy of the arithmetical discourse theories of truth can be fruitfully applied. The hereby applied internal categoricity arguments are innovative. The investigations offer therefore a relevant contribution to the question of suitable framework choice for different undertakings. For the question of logical pluralism a confirmation of the conjecture that a domain relativistic pluralism is plausible and provides an interesting form of pluralism was confirmed. Whereas in some areas the choice of classical logic is warranted there are areas such as the Kripkean conception of truth where the choice is not uniquely determined and dependent on interests. A classical modelling convinces through simplicity and its fit within the scientific framework but requires delicate conceptual adjustments. A non-classical version stays true to the conception and is less idealised, but requires a convincing form of recapture. In the project some strategies were investigated in order to show that both forms of modelings are adequate.

Publications

• Another Look at Reflection. Erkenntnis, 88(2), 479-509.
  Fischer, Martin
  
• NONCLASSICAL TRUTH WITH CLASSICAL STRENGTH. A PROOF-THEORETIC ANALYSIS OF COMPOSITIONAL TRUTH OVER HYPE. The Review of Symbolic Logic, 16(2), 425-448.
  FISCHER, MARTIN; NICOLAI, CARLO & DOPICO, PABLO
  
• Sequent Calculi for the Propositional Logic of HYPE. Studia Logica, 110(3), 643-677.
  Fischer, Martin
  
• Is the HYPE about strength warranted?. Synthese, 200(3).
  Fischer, Martin
  
• Internal Categoricity, Truth and Determinacy. Journal of Philosophical Logic, 52(5), 1295-1325.
  Fischer, Martin & Zicchetti, Matteo
  
• Definite totalities and determinate truth in conceptual structuralism. Synthese, 203(1).
  Fischer, Martin & Zicchetti, Matteo