 Philosophy of pure mathematics deals with two major groups of questions. One pertains to the ontology of mathematical entities and the other to the epistemology of mathematical concepts and judgments (Avigad 2007). The nature and existence of mathematical objects (e.g., numbers and geometrical shapes), the existence and qualifications of infinities (e.g., infinite magnitudes and infinite collections of numbers or numbered things), and the existence and qualifications of continua are some of the most significant ontological issues with which philosophers of mathematics are concerned. On the other hand, some of the most important and challenging epistemological issues about mathematics are the following: the mechanisms through which we grasp mathematical knowledge, the epistemic status of mathematical axioms and principles, the nature of mathematical proofs (that are writable on paper) and their connection to what goes on in the mind of mathematicians, and the role of mathematical knowledge in attaining a better understanding of the physical world.