A break with the Aristotelian tradition

Aristotle called the principle of non-contradiction the most certain of all principles. Since then, most Western logicians have viewed tolerance of contradictions as unacceptable and disastrous for science. The 20th century has seen the development of numerous systems of non-classical logic, including inconsistency-tolerant logics. The ERC-funded ConLog project will go beyond that development and will investigate logical systems that are not only inconsistency-tolerant but are inconsistent themselves and nevertheless nontrivial. ConLog will apply techniques from philosophical logic, such as Chellas-Segerberg models, as well as methods from structural proof theory and experimental philosophy. The goal of the project is to gain a deep understanding of certain non-trivial inconsistent logical systems.