ERC Advanced Grant · 2020
Contradictory Logics: A Radical Challenge to Logical Orthodoxy
“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…
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