Descripción del proyecto
Cisma de la tradición aristotélica
Aristóteles consideró el principio de no contradicción como el principio más firme de todos. Desde entonces, la mayoría de los lógicos occidentales consideran inaceptable y contraproducente para la ciencia la tolerancia de las contradicciones. Durante el siglo XX se enunciaron múltiples sistemas de lógica no clásica como, por ejemplo, las lógicas tolerantes a las contradicciones. En el proyecto ConLog, financiado por el Consejo Europeo de Investigación, se irá un paso más allá y se investigarán sistemas lógicos que no solo son tolerantes a las contradicciones, sino que además son contradictorios y, sin embargo, no triviales. El equipo de ConLog empleará técnicas de la lógica filosófica, como los modelos de Chellas-Segerberg, así como métodos de la teoría de la prueba estructural y la filosofía experimental. Su objetivo es lograr una comprensión detallada de ciertos sistemas lógicos contradictorios no triviales.
Objetivo
“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.
Ámbito científico
Programa(s)
Régimen de financiación
ERC-ADG - Advanced GrantInstitución de acogida
44801 Bochum
Alemania