Dialetheism (Stanford Encyclopedia of Philosophy)

Dialetheism:

A dialetheia is a sentence, A, such that both it
and its negation, ¬A, are true (we shall talk of sentences
throughout this entry; but one could run the definition in terms of
propositions, statements, or whatever one takes as one’s favourite
truth-bearer: this would make little difference in the context).
Assuming the fairly uncontroversial view that falsity just is the truth
of negation, it can equally be claimed that a dialetheia is a sentence
which is both true and false.

Dialetheism is the view that there are dialetheias. One can
define a contradiction as a couple of sentences, one of which is the
negation of the other, or as a conjunction of such sentences.
Therefore, dialetheism amounts to the claim that there are true
contradictions. As such, dialetheism opposes the so-called Law of
Non-Contradiction (LNC) (sometimes also called the Law of
Contradiction). The Law can, and has been, expressed in various ways,
but the simplest and most perspicuous for our purposes is probably the
following: for any A, it is impossible for both A and
¬A to be true.