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Contradictory Logics: A Radical Challenge to Logical Orthodoxy

Project description

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.


“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.

Host institution

Net EU contribution
€ 2 059 026,00
44801 Bochum

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Nordrhein-Westfalen Arnsberg Bochum, Kreisfreie Stadt
Activity type
Higher or Secondary Education Establishments
Total cost
€ 2 059 026,00

Beneficiaries (1)