MODREQUAM - Modal Reasoning, Quarc and Metaphysics

In ordinary reasoning we often use sentences combining quantifying expressions (such as all, some, most, etc.) and modal expressions (such as must, can, should, etc.). The analysis of the structure and of the interpretation of these sentences has given rise to an intense debate over the last few decades. Many proposals are nowadays available and yet there is still little consensus on how to answer fundamental questions like the following: - What counts as an appropriate logical representation of sentences including modal expressions and quantifiers? - What are the semantic ingredients required to interpret such sentences? - Does an interpretation of such sentences commit one to claim the existence of any sort of entity (such as possible worlds, possible individuals, etc.)? In the present project we will address these questions and related problems within an innovative formal framework that combines modal logic and the Quantified Argument Calculus. The former component offers technical tools that have been corroborated by a long tradition of studies; the latter component offers a new perspective on the relation between natural languages and formal languages. We will first investigate the possible challenges of combining these two ingredients in a single formal framework and then compare our results with alternative frameworks for the representation of quantified modal reasoning that have been proposed in the literature, so as to assess the distinguishing features, advantages and disadvantages of each proposal. The methodology employed within our project is interdisciplinary since it relies on resources taken from logic, philosophy of language and metaphysics, with the addition of some insights from linguistics. In particular, from the philosophical point of view, we will use methods such as conceptual analysis, disambiguation of natural language sentences, semantic taxonomies and ontological assessment. Moreover, from the logical point of view, we will use methods such as axiomatic systems, formal definitions, models, truth-valuations, metalogical theorems and correspondence theory. The project is expected to provide a novel and original contribution to the debate on quantified modal reasoning, since the Quantified Argument Calculus is a very recent framework whose technical foundation and philosophical applications still need to be explored to a considerable degree. Moreover, in many regards the Quantified Argument Calculus has the potential to better deal with certain problems of natural language representation that affect systems of modal logic built over classical logic. The two researchers that will jointly carry out the project are Dr. Matteo Pascucci and Dr. Jonas Raab. Dr. Pascucci will be hosted by the Department of Philosophy of Central European University (Vienna), whereas Dr. Raab will be hosted by the Munich Center for Mathematical Philosophy at Ludwig-Maximilians-University (Munich).