Is p and ¬p a Contradiction?

We discuss how to formulate and understand contradiction. After emphasizing the importance of a correct formulation for a notion as important as the notion of contradiction, we present a variety of formulations of the proposition corresponding to “p and ¬p”, which is often considered as expressing contradiction. We then discuss the standard example of contradiction in classical logic and the way Wittgenstein defines contradiction in the Tractatus, not using negation. After that, we point out the variety of connectives which are nowadays called negations and often denoted by the same symbol, underlying that negations obeying neither the law of non-contradiction, nor the excluded middle are considered part of the family. We then recall how contradiction is defined within the theory of oppositions, drawing attention to the fact that this theory is against considering that the pair p and ¬p forms a contradiction if we take into account the whole family of negations, including paraconsistent negations. At the end of the journey, we set up a list of notions involving negation and contradiction and propose a terminology that may be useful to dispel confusion and promote understanding.