Projektbeschreibung
Bruch mit der aristotelischen Tradition
Aristoteles bezeichnete das Prinzip des Nicht-Widerspruchs als das sicherste aller Prinzipien. Seitdem sahen die meisten westlichen Logikerinnen und Logiker eine Toleranz gegenüber Widersprüchen als inakzeptabel und verhängnisvoll für die Wissenschaft an. Im 20. Jahrhundert wurden zahlreiche Systeme der nichtklassischen Logik entwickelt, darunter auch Logiken der Widerspruchstoleranz. Das ERC-finanzierte Projekt ConLog wird darüber hinaus gehen und logische Systeme untersuchen, die nicht nur widerspruchstolerant, sondern auch selbst widersprüchlich und dennoch nicht trivial sind. ConLog wird Techniken aus der philosophischen Logik, wie z. B. Chellas-Segerberg-Modelle, sowie Methoden aus der strukturellen Beweistheorie und der experimentellen Philosophie zur Anwendung bringen. Das Ziel des Projekts besteht darin, ein tiefes Verständnis bestimmter nicht-trivialer inkonsistenter logischer Systeme zu gewinnen.
Ziel
“The acceptance of contradictions must lead ... to the end of criticism, and thus to the collapse of science.”
– Karl Popper, Conjectures and Refutations.
In the 20th century, many systems of non-classical logic have been developed, including inconsistency-tolerant logics, which are typically all subsystems of classical logic. There are, however, logical systems that are radically different from classical logic insofar as they are non-trivial but contradictory. These logics are in glaring conflict with logical orthodoxy since Aristotle, who called the Principle of Non-Contradiction the firmest of all principles. Non-trivial contradictory logics, sometimes called “dialetheic logics,” not only permit inconsistencies in theories, but contain provable contradictions.
Can that be reasonable? The Contradictory Logics project (ConLog) takes on the challenge of this rigorous break with the Aristotelian tradition by systematically investigating and developing non-ad hoc contradictory logics. In particular, ConLog studies non-trivial dialetheic systems of connexive logic that already validate certain contra-classical principles, such as the thesis saying that no proposition implies its own negation, and so-called “logics of logical bilattices.”
ConLog develops a clear comprehension of the contradictoriness of non-trivial dialetheic logics and studies the consequences of this understanding within the philosophy of logic. Thereby, the project will yield a paradigm-shift in our conception of what a respectable logical system and an acceptable scientific theory is. It will show that, contrary to the above quote from Popper, the inconsistency of a logical system does not prevent rational belief and does not lead to the end of criticism and a collapse of science. It will achieve this ambitious goal by applying techniques from philosophical logic, such as the use of Chellas-Segerberg models, as well as methods from structural proof theory and experimental philosophy.
Wissenschaftliches Gebiet
Programm/Programme
Thema/Themen
Finanzierungsplan
ERC-ADG - Advanced GrantGastgebende Einrichtung
44801 Bochum
Deutschland