MODREQUAM - Modal Reasoning, Quarc and Metaphysics

• Applicant: Jonas Raab, Ph.D.
• Subject Area: Theoretical Philosophy
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 517008210

Combining modal notions (such as ‘necessary’, ‘possible’, etc.) and quantification in a formal setting is known to be a challenging problem and none of the solutions available so far is entirely satisfactory. In the present project we will address this problem in an innovative way via the Quantified Argument Calculus (Quarc), a recent logical framework, which aims at providing a more faithful formal representation of the syntactical and semantic structure of natural language sentences than the one offered by the language of the Predicate Calculus (PC). The project has two main objectives: Obj1 developing a correspondence theory for modal extensions of Quarc; Obj2 using the outcomes of Obj1 to address foundational problems in quantified modal logic. These two objectives give rise to four research questions (Q1-Q2 related to Obj1, Q3-Q4 related to Obj2): Q1 which fragments of Quarc can be axiomatized? Q2 which interactions between quantification and modalities can be captured in Quarc? Q3 what is the relationship of modal logics and natural language? Q4 what metaphysical impact does the choice of a modal logic have? The methods employed within the project are interdisciplinary, taken from analytic philosophy and logic. From the philosophical point of view, we will use methods such as conceptual analysis, disambiguation of natural language sentences, taxonomies and ontological assessment. From the logical point of view, we will use methods for deductive reasoning, such as axiomatic methods, formal definitions, semantic inference, metalogical theorems and correspondence results. The project will provide a novel and original perspective on quantified modal reasoning, since Quarc is a very recent framework whose technical foundation and philosophical applications still need to be explored to a considerable degree. In many regards, Quarc has the potential to better deal with traditional problems affecting first-order modal logic.

• DFG Programme: Research Grants
• International Connection: Austria
• Cooperation Partner: Matteo Pascucci, Ph.D.