3261

Paul Budnik

philosophy of mathematics education

2007

22

As the Platonic philosophy of mathematics is increasingly being questioned, computer technology is able to approach Platonic perfection in limited domains. This paper argues for a mathematical philosophy that is both objective and creative. It is objective in that it limits the domain of mathematics to questions that are logically determined by a recursively enumerable sequence of events. This includes the arithmetical and hyperarithmetical hierarchies but excludes questions like the Continuum Hypothesis. This philosophy is creative in recognizing that Gödel’s Incompleteness Theorem implies one can only fully explore this mathematics by considering an ever increasing number of incompatible possibilities without deciding which is correct. This is how biological evolution created the mathematically capable human mind.