In ‘Tense and Reality’ (2005), Kit Fine introduced and tentatively defended a metaphysical view that he called ‘fragmentalism’. The central idea behind his view was that reality is somehow constituted by conflicting facts, each of which is real, yet which are not ‘real together’. My talk will have two aims. The first aim is to present and discuss some of the broader motivations for adopting some form of fragmentalism. The second aim is to present and evaluate a new formal approach to the view, based on a non-adjunctive paraconsistent logic.