Proofs, arguments and dialogues: history, epistemology and logic of justification practices

Proofs and arguments have been at the core of philosophy since the beginning. From the late 19th century onwards, the understanding of proofs and arguments has been strongly influenced by the development of modern mathematical logic and linguistics, while in recent times results in computer science have provided deep insights into the nature and structure of proofs and, thanks to the advancements in computational linguistics, of arguments in general. This exchange between philosophy, mathematics, linguistics and computer science has also led to a renewed approach to dialogues, in particular to the analysis of their context-depending nature and of their information-yielding structure.

In spite of the advancements in philosophy, mathematics, linguistics and computer science, the notions of proof, argument and dialogue still involve many unsolved issues. These issues refer to some fundamental questions such as: why and how do we get convinced by proofs, arguments and dialogues? What is the reliability of the information they convey? Is this reliability context-independent? What is the semantic import of proofs, arguments or dialogues? Co-operation between different disciplines seems to be inevitable for finding solutions to these questions, and such a cooperation has so far proved to be very fruitful. Many mathematised approaches to the study of proofs, arguments and dialogues are inspired by philosophical claims and strictly interlace with parallel investigations in linguistics and computer science. In turn, results in mathematical logic, linguistics and computer science are a continuous source of inspiration for many philosophical approaches.

Main topics addressed

• Argumentation theory
• Proof-theory and proof-based semantics (BHK semantics, Prawitz's semantics, Martin-Löf intuitionistic type theory, and so on)
• Curry-Howard isomorphism
• Inferentialism
• Theory of meaning
• Epistemic aspects of deduction
• Computational linguistics
• Dialogical logics

Learning outcomes

The proposed training consists of courses and invited talks. It aims at providing students with a wide and, above all, transdisciplinary insight into contemporary investigations about proofs, arguments and dialogues in philosophy, linguistics, logic, mathematics and computer science. Students will get acquainted with current approaches and result in proof theory, argumentation theory and dialogue theory, as well as the historical, epistemological and formal connections between these fields. This will allow them to adopt a strongly transdisciplinary point of view on some of the most important research areas in linguistics, logic, philosophy, mathematics and computer science, as well as on some of the most important trends in these fields.