Description du projet
Une rupture avec la tradition aristotélicienne
Pour Aristote, le principe de non-contradiction est le plus solide de tous les principes. Depuis lors, la plupart des logiciens occidentaux ont considéré la tolérance des contradictions comme inacceptable et désastreuse pour la science. Le XXe siècle a été marqué par le développement de nombreux systèmes de logique non-classique, notamment des logiques tolérantes aux incohérences. Le projet ConLog, financé par le CER, ira au-delà de ce développement et étudiera des systèmes logiques qui se montrent non seulement tolérants aux incohérences, mais qui sont eux-mêmes cohérents et pourtant non triviaux. ConLog appliquera des techniques issues de la logique philosophique, telles que les modèles Chellas-Segerberg, ainsi que des méthodes issues de la théorie de la preuve structurelle et de la philosophie expérimentale. Le but du projet consiste à acquérir une compréhension approfondie de certains systèmes logiques incohérents non triviaux.
Objectif
“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.
Champ scientifique
Programme(s)
Thème(s)
Régime de financement
ERC-ADG - Advanced GrantInstitution d’accueil
44801 Bochum
Allemagne