Mathematical Possibilities and Their Discovery

This Chapter attempts to answer the following questions: What is the ontological status of mathematical entities? What enables our epistemic access to such entities? Do we discover mathematical entities or simply invent them? Mathematical entities do not exist in space, time, or as links in a causal chain. Nor are they abstracted from actual-physical reality. Instead, mathematical entities are individual pure possibilities existing independently of our mind, of possible worlds, and of anything actual. Our intellect (by means of proofs, calculations, and the like) and imagination are reliable enough to give us sufficient epistemic access to such entities. Mathematical entities can be discovered; they cannot be invented. Nevertheless, truthful fictions may help us discover such entities as well as their general relations.