The Principle of Explosion is one of the most characteristic principles of classical
logic (and of any other explosive logic). It says that any (explosive) theory will
trivialize if it contains at least one contradiction. A contradiction is a pair of
propositions, where one is the negation of the other—sometimes contradiction is
defined as the conjunction of both propositions. A theory is trivial if it is possible
to derive any proposition from it. Therefore, any inconsistent (explosive) theory
will be trivial.
In light of the above, an important question in the philosophy of science
is whether science could be inconsistent and non-explosive at the same time; that
is, can science be inconsistency tolerant? If science could in fact be tolerant of
contradictions, philosophers of science should also address the questions: How is
it possible to make sense of the use of inconsistent theories in science and is such
a use an indication of scientific irrationality? With the latter question in mind,
philosophers and logicians of science have argued that a study of sensible
inconsistent reasoning in the sciences, if possible, could be crucial in the search
for a general theory of scientific rationality (Carnielli and Coniglio).
Unfortunately, a large number of the philosophical projects that aimed at
addressing the possibility of sensible inconsistent scientific reasoning lost sight of
the original goal and ended up exclusively “proposing alternative logics that might lurk in the background of scientific reasoning” (Brown and Priest, “A
Paraconsistent Inference Strategy” 299. My emphasis), missing actual scientific
inferential practices and focusing on more general philosophical projects regarding
logical pluralism.
