Structuralism has trouble with subjectivity
Philosopher Alain Badiou argues that mathematics is a purely human construct, analogous to fiction.
Quotes (from memory)
math is "a fiction of intelligible consistency" (I found this in Ashton, 270)
"mathematics is a rigorous aesthetic" (I am having trouble finding this quote, bit I think it is in Briefings on Existence)
Fictionalism
Mathematical realists believe that math is objective, existing outside human knowledge. But the belief that mathematics beyond what humans will or could ever discover is a faith (counter to science).
Ashton, Paul, Adam Bartlett, and Justin Clemens. The Praxis of Alain Badiou. Melbourne: Re.press, 2006. Internet resource.
Badiou, Alain, and Norman Madarasz. Briefings on Existence: A Short Treatise on Transitory Ontology. Albany: State University of New York Press, 2006. Print.
Platomism
https://en.wikipedia.org/wiki/Platonism
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