id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_scmvs6ywcjbtzdhlivdmh4jkam	Carlo Rovelli	Michelangelo's stone: an argument against platonism in mathematics	2016	7	.pdf	application/pdf	5306	411	65	If there is a 'platonic world' M of mathematical facts, what does M contain precisely? Let us assume that a platonic world of mathematical entities and Say we take a Platonic stance about math: in some appropriate sense, the mathematical world M exists. Certainly M includes all the beautiful mathematical theories that mathematicians have discovered so far. All possible true theorems about Euclidean geometry, including We can list many sets of interesting axioms, and imagine the platonic world M to be the ensemble of theorems these imply, all nicely ordered in families, and find new great mathematics, like the people who discovered non-commutative geometry, or those who defined the "Elements" [10], where Euclidean geometry is beautifully developed, has been the ideal reference for all mathematical texts. Two-dimensional Euclidean geometry describes, in particular, the mathematical structure formed by the land. would likely fail to consider euclidean geometry interesting mathematics.	./cache/work_scmvs6ywcjbtzdhlivdmh4jkam.pdf	./txt/work_scmvs6ywcjbtzdhlivdmh4jkam.txt