Opis projektu
Zerwanie z arystotelesowską tradycją
Arystoteles nazwał zasadę niesprzeczności najbardziej pewną ze wszystkich zasad. Od tamtej pory większość zachodnich logików uważa tolerowanie sprzeczności za niedopuszczalne i zgubne dla nauki. W XX wieku powstało wiele systemów logiki nieklasycznej, w tym logiki tolerujące niespójność. Finansowany przez ERBN projekt ConLog ma pójść o krok dalej i zbadać systemy logiczne, które nie tylko są odporne na niespójności, ale same są niespójne, a mimo to nietrywialne. Zespół ConLog zastosuje techniki z zakresu logiki filozoficznej, takie jak modele Chellasa-Segerberga, jak również metody z dziedziny strukturalnej teorii dowodu i filozofii eksperymentalnej. Celem projektu jest dogłębne poznanie pewnych nietrywialnych niespójnych systemów logicznych.
Cel
“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.
Dziedzina nauki
Program(-y)
Temat(-y)
System finansowania
ERC-ADG - Advanced GrantInstytucja przyjmująca
44801 Bochum
Niemcy