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Kleene’s variant of the Church-Turing thesis
April 6, 2014 by Artem Kaznatcheev 6 Comments
Mathematicians and logicians begat the Church-Turing thesis, so at its inception it was a hypothesis about the Platonic world of mathematical ideas and not about the natural world. There are those that follow Russell (and to some extent Hilbert) and identify mathematics with tautologies. This view is not typically held among mathematicians, who following in the footsteps of Godel know how important it is to distinguish between the true and the provable. Here I side with Lakatos in viewing logic and formal systems as tools to verify and convince others about our intuitions of the mathematical world. Due to Godel’s incompleteness theorems and decades of subsequent results, we know that no single formal system will be a perfect lens on the world of mathematics, but we do have prefered one like ZFC.
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Filed under Commentary Tagged with Alan Turing, Daniel Dennett, philosophy of math, philosophy of science