Joseph Melia is a philosopher working in the areas of

philosophy of mathematics Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathem ...

modal logic Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...

and

possible world A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their met ...

s. He has made important contributions to the debate over the

Quine–Putnam indispensability argument The Quine–Putnam indispensability argument is an argument in the philosophy of mathematics for the existence of Abstract and concrete, abstract mathematical objects such as numbers and sets, a position known as mathematical platonism. It was ...

, where he argues for a "weaseling" approach to

mathematical nominalism In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are two main versions of nominalism. One denies the existence of universals—that which can be insta ...

. He has also argued against modalism and the

modal realism Modal realism is the view propounded by the philosopher David Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It states that possible worlds exist, possible worlds are ...

of David Lewis.

References

Philosophers of mathematics 20th-century British philosophers Year of birth missing (living people) Living people 21st-century British philosophers {{UK-philosopher-stub