Why and how to be a Dialetheist

Dialetheism is the claim that some contradictions are true. For anyone trained in standard logic and raised in the belief that already in antiquity Aristotle settled once and for all that there is the Law of Non-Contradiction dialetheism sounds not just false, but bizarre. On the other hand people contradict each other quite often and a couple of theories have turned out to be inconsistent. Nevertheless the people who held inconsistent beliefs have not (at the time of holding these beliefs) believed just anything, as the standard rule of ex contradictione qoudlibet would have it. Thus paraconsistent logics (logics that invalidate ex contradictione.. and thus can tolerate even provable contradictions) have gained interest and lots of them are investigated and explored nowadays. Dialetheism is strong paraconsistency in the sense that one cannot just tolerate some contradictions, but one should endorse some of them. This certainly needs argument. In this paper the first part gives one of the main arguments why to be a dialetheist. Ever since its arrival dialetheism (the thesis that there are true contradictions) has been met with the proverbial " incredulous stare " , not only because of the inconsistent ontology of Routley's " noneism " (Routley 1979), but also with respect to the dialetheist's claim that one can knowingly believe and assert contradictions. Priest in the paper introducing his " logic of paradox " LP (Priest 1979) admits that the thesis of dialetheism is a dialetheia itself, and seems to be content with this. In his book In Contradiction (Priest 1987) he argues that one can avoid dialetheism being a dialetheia itself if one is prepared to give up contraposition for the conditional in Convention (T). Nevertheless he defends that one can believe and assert contradictions. Up to now (see some of the papers in (Priest/Beall/Armour-Garb 2004) or (Field 200x)) criticism of dialetheism has focused on the problems what the status of dialetheism itself is and how it may be possible to believe knowingly contradictions. In the second part of this paper it is argued that within dialetheism the resources are available to claim that dialetheism is true only (i.e. not false at the same time). Furthermore there may be occasions on which it is rational to believe and/or even assert contradictions, without thereby positioning oneself on a slippery slope towards an attitude of " anything goes " .