"Consequently , the reliability of our knowledge of mathematics remains forever subsidiary to that of our knowledge of physical reality . Every mathematical proof depends absolutely for its validity on our being right about the rules that govern the behaviour of some physical objects, like computers, or ink and paper, or brains. So, contrary to what Hilbert thought , and contrary to what most mathematicians since antiquity have believed and believe to this day , proof theory can never be made into a branch of mathematics. Proof theory is a science: specifically , it is computer science."
Wednesday, June 26, 2013
Proof theory is a science
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