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Contradictory Logics: A Radical Challenge to Logical Orthodoxy

Descrizione del progetto

Una rottura con la tradizione aristotelica

Aristotele definiva il principio di non contraddizione il più certo di tutti i principi. Da allora, la maggior parte dei logici occidentali ha considerato la tolleranza delle contraddizioni inaccettabile e disastrosa per la scienza. Il XX secolo ha visto lo sviluppo di numerosi sistemi di logica non classica, comprese logiche tolleranti all’incoerenza. Il progetto ConLog, finanziato dall’ERC, andrà oltre questo sviluppo e indagherà sui sistemi logici che non solo sono tolleranti all’incoerenza, ma sono essi stessi incoerenti e tuttavia non banali. ConLog applicherà tecniche della logica filosofica, quali i modelli di Chellas-Segerberg, nonché metodi della teoria della prova strutturale e della filosofia sperimentale. L’obiettivo del progetto è acquisire una profonda comprensione di alcuni sistemi logici incoerenti non banali.

Obiettivo

“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.

Meccanismo di finanziamento

ERC-ADG - Advanced Grant
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Coordinatore

RUHR-UNIVERSITAET BOCHUM
Contribution nette de l'UE
€ 2 059 026,00
Indirizzo
Universitaetsstrasse 150
44801 Bochum
Germania

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Regione
Nordrhein-Westfalen Arnsberg Bochum, Kreisfreie Stadt
Tipo di attività
Higher or Secondary Education Establishments
Collegamenti
Altri finanziamenti
€ 0,00

Beneficiari (1)