In logic, paraconsistent logic is the tolerance towards inconsistencies. It is a way to reason about inconsistent information without lapsing into absurdity. In a non-paraconsistent logic, inconsistency explodes in the sense that if a contradiction obtains, then everything (everything!) else obtains, too. Someone reasoning with a paraconsistent logic can begin with inconsistent premises and still reach sensible conclusions, without completely exploding into incoherence.
“Logic will get you from A to B. Imagination will take you everywhere.”
– Albert Einstein
Paraconsistency is a thesis about logical consequence: not every contradiction entails arbitrary absurdities.
The contemporary logical orthodoxy has it that, from contradictory premises, anything can be inferred.
“Contrariwise,’ continued Tweedledee, ‘if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.”
– Lewis Carroll, Through the Looking–Glass and What Alice Found There (1871)
Paraconsistent logic accommodates inconsistency in a sensible manner that treats inconsistent information as informative. The prefix ‘para’ in English has two meanings: ‘quasi’ (or ‘similar to, modelled on’) or ‘beyond’. When the term ‘paraconsistent’ was coined by Miró Quesada at the Third Latin America Conference on Mathematical Logic in 1976, he seems to have had the first meaning in mind. Many paraconsistent logicians, however, have taken it to mean the second, which provided different reasons for the development of paraconsistent logic as we will see below.
Historically speaking, paraconsistency has been a common theme in Indian logic,especially Jain and Buddhist logic. Whereas classical Western logic would see a statement as either true or false, but not both nor neither, Indian logics have traditionally been accepting of statements being both true and false simultaneously, or neither true nor false.
“Logic: The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding.”
– Ambrose Bierce