 Nevertheless, if we accept even a mild form of realism, the truth of some contradictions entails the existence of inconsistent objects and/or states of affairs: those that make the contradictions true (Berto 2007b). One may claim that it makes no sense to talk of inconsistent objects, situations, or states of affairs. The world is all there, all together: how could some pieces of it contradict some other pieces? Consistency and inconsistency might be taken as properties of sentences, or theories (sets of sentences closed under logical consequence), or propositions (what sentences express), or maybe thoughts, or (sets of) beliefs, etc. Contradiction (Widerspruch, the Latin contradictio) has to do with discourse (diction, sprechen, dicere). The world, with its non-mental and non-linguistic inhabitants—armchairs, trees, people—is not the right kind of thing that can be consistent or inconsistent, and ascribing such properties to (a part of) the world is, to use Gilbert Ryle’s terminology, a category mistake.   These considerations might drive dialetheism towards an anti-realist interpretation of the claim that there are dialetheias, true contradictions; and anti-realist dialetheic theories of truth have, in fact, been proposed (see e.g. Beall’s ‘constructive methodological deflationism’, in Beall 2004). But other options are available to a dialetheist who wants to embrace some form of metaphysically robust realism about truth. For instance, she can stress that consistency and inconsistency can be ascribed to (pieces of) the world in a derived sense: to say that the world is (locally) inconsistent just is to say that some true purely descriptive sentences about the world have true negations. Consequently, and not accidentally, it is quite common in the current literature both for and against dialetheism to straightforwardly speak of inconsistent objects, states of affairs, and entire inconsistent worlds. A dialetheic correspondence theory of truth might be committed, in particular, to negative facts (requiring the simultaneous existence of truth-makers both for \(A\) and for its negation, when \(A\) is a dialetheia); but these may be not too difficult to handle (see e.g. Priest 2006, pp. 51–3).  There are further intermediate positions. One is ‘semantic dialetheism’ which accepts true contradictions without inconsistent objects or states of affairs as their truth-makers. This position has been explored in the literature (Kroon 2004, Mares 2004). Beall’s view, expressed in his transparent truth theory in Beall 2009, may also be seen as a form of semantic dialetheism. Transparency can be naturally paired with a  deflationary view of truth.  For suppose the truth predicate is a merely semantic device, coined, as Quine famously stressed, for expressive, ‘disquotational’ purposes. Then dialetheias such as the Liar(s) may well be semantic side-effects (‘spandrels’, in Beall’s terminology) of the introduction of such device, not involving any metaphysically committing contradiction in a language- and mind- independent world. Woodbridge and Armour-Garb (2013) argue that a deflationary view of truth is best understood in terms of semantic pretense (a hermeneutic fictionalist perspective), and on that basis offered a pretense account of the semantic paradoxes. Wansing (2022) advances a view called dimathematism, where there may be contradictions in information (information being “what is left from knowledge when you subtract, justification, truth, and belief” as Dunn puts it) again distinct from contradictions in truth.   Debates on realism and anti-realism quickly spill over into questions concerning the nature of reality in general. Thus the dialetheic programme looks to metaphysical issues: if reality is dialetheic, how should the ontology of a dialetheic world be spelt out? If metaphysics should be placed (once again) at the very core of philosophy, the debate on the possibility of dialetheias occupies a central place in the core. This was, after all, Aristotle’s view, too: he decided to speak on behalf of the unconditional validity of the LNC, not in his Organon (his writings on the subject of logic), but in the Metaphysics, for this was for him an issue to be addressed ontologically, not (only) via formal logical tools. For work in dialetheic metaphysics see Priest 2014, which grounds the very unity of objects in an inconsistent theory of parthood and boundary, and applies it to classic problems such as the One and the Many, and the instantiation of universals. 7. Conclusion  Since Aristotle, the assumption that consistency is a requirement for truth, validity, meaning, and rationality, has gone largely unchallenged. Modern investigations into dialetheism, in pressing the possibility of inconsistent theories that are nevertheless meaningful, valid, rational, and true, call that assumption into question. If consistency does turn out to be a necessary condition for any of these notions, dialetheism prompts us to articulate why; just by pushing philosophers to find arguments for what previously were undisputed beliefs renders a valuable service (Scharp 2007, p. 544). And if consistency turns out not to be an essential requirement for all theories, then the way is open for the rational exploration of areas in philosophy and the sciences that have traditionally been closed off.  