| dc.description.abstract | The standard axiomatization of set theory known as ZFC provides maybe the most widely accepted foundation for mathematics. But there are natural mathematical statements, such as Cantor's continuum hypothesis (CH), that can neither be proved nor disproved from ZFC. These statements are said to be independent of ZFC. The independence phenomenon in set theory can be seen as motivating two very different conceptions of mathematical reality. Universism has it that ZFC is about a particular mathematical structure, namely the maximal and unique universe of all sets V. The universist claims that the independence phenomenon shows us that our description of V is incomplete but, claims the universist, the independent statements are either true or false in the unique universe. So, we ought to try to formulate and justify new axioms to strengthen our theory and uniquely decide the independent statements. This way we get a more complete description of V. Multiversism, on the other hand, has it that there are many different universes of sets where statements independent of ZFC, such as CH, hold in some of them and fail in others. Thus, there is no point in trying to decide these statements in a unique manner. Instead, we should be content to explore in more detail the different set theoretic universes, all of which, according to the multiversist, are equally real. In this thesis I further explore multiversism. I assess some of the strengths and weaknesses of the view by focusing primarily on philosophical rather than technical issues. I also investigate in more detail in what way multiversism challenges the standard accounts of justification in set theory that the universists have traditionally hoped to avail themselves of. | eng |