Balaguer, Mark

"Mathematical objects exist timelessly in the logical space of possibilities."

"The truths of mathematics ground all other truths we know."

"Our intuition that numbers are real deserves more philosophical respect than it receives."

"Nominalism purchases simplicity at the cost of unintelligibility."

"The mathematical realm may be more objective than the physical realm."

"Mathematical knowledge demonstrates human capacity for apprehending abstract reality."

"The necessity of mathematical truths points to a realm beyond mere convention."

"Physics without mathematics is incoherent; mathematics without Platonism is mysterious."

"Abstract entities present no greater challenge to materialism than subjective experience does."

"Numbers are the tools by which we carve nature at its joints."

"Mathematical realism explains our mathematical success better than any alternative."

"The indispensability of mathematics to science supports commitment to mathematical objects."

"Mathematical truth is discovered, not created—this remains the deepest insight into mathematics."

"To understand what exists, we must understand what mathematics tells us exists."

"The objectivity of mathematics reflects the objectivity of the rational realm."

"Our evolved minds can grasp eternal truths through mathematical reasoning."

"Mathematical properties are the blueprint upon which physical reality is constructed."

"Numbers inhabit the space of logical possibility that transcends any single universe."

"Mathematical necessity is the closest thing we have to an absolute foundation."

"Fictionalism about mathematics fails because mathematical truths aren't pragmatic conveniences."

"The being of mathematical objects requires a metaphysical category beyond physical substance."

"Mathematics is the universal language because it reflects universal truths."

"Our grasp of mathematical infinity suggests we transcend our finite nature."

"To reject mathematical Platonism is to embrace a kind of mathematical skepticism."

"Abstract objects exist in the realm of forms that gives meaning to the physical world."

"Numbers and their properties are as real as anything we encounter in experience."

"Mathematical truth cannot be contingent upon the existence of mathematicians."

"The universe is written in the language of mathematics—this is no mere metaphor."

"Mathematical objects may be sui generis—neither concrete nor fictional."

"Our knowledge of abstract objects expands the frontier of what we think we can know."