Balaguer, Mark

"To understand mathematics is to glimpse the architecture of reality."

"Mathematical properties are real even if mathematical objects are not."

"Our criteria for existence may be too narrow to encompass abstract entities."

"The patterns we discover in mathematics were not invented by us."

"Mathematical necessity differs fundamentally from physical necessity."

"Rejecting Platonism requires us to explain away our deepest mathematical intuitions."

"The relationship between mathematics and physics remains the greatest unsolved mystery."

"Abstract entities exist in a realm of possibility rather than actuality."

"Mathematics reveals eternal truths that transcend human culture and biology."

"The independence of mathematical truths from human minds is undeniable."

"To do mathematics is to commune with eternal forms."

"Mathematical objects may be more fundamental than physical objects."

"The success of applied mathematics vindicates some form of realism."

"Fiction cannot account for the apparent necessity of mathematical truths."

"Mathematics occupies a unique epistemological status among human endeavors."

"Numbers exist in the realm of thought itself."

"The debate over mathematical ontology will ultimately reshape metaphysics."

"Abstract objects pose no greater metaphysical puzzle than concrete objects do."

"Mathematical knowledge is uniquely certain and irrevisable."

"We must take seriously the testimony of working mathematicians about their field."

"The power of mathematics suggests its truth reaches beyond mere convention."

"Nominalism, while admirable in its parsimony, sacrifices explanatory power."

"Mathematical Platonism is not a flight from reason but an embrace of it."

"The ontology of mathematics cannot be separated from the epistemology of mathematics."

"Mathematical entities may exist necessarily rather than contingently."

"Every serious physics requires a robust philosophy of mathematics."

"The nature of mathematical truth may require new categories of being."

"Mathematics does not describe reality; it reveals reality's deepest structure."

"The independence of mathematical objects from human thought is philosophically crucial."

"To deny the reality of numbers is to saw off the branch on which all science sits."