Vladimir Voevodsky - What if Current Foundations of Mathematics are Inconsistent

Talk given at the Institute of Advanced Studies at Princeton in 2010.

It's good that some people were allowed to talk about this. See About Logic Interview with Urs Schreiber and in particular Lawvere's Cohesive Toposes and Cantor's 'iaufcer Einsen'. 


The answer is to use a plurality of formal systems and a plurality of formal translations between those systems. Then the provable sentences are not vulnerable to such accidental coincidences of interpretation which are constructed by diagonalisations such the Gödel sentences. This is just a greatest fixpoint. Unfortunately it depends upon mathematicians and logicians actually speaking to one another. 

See An Excellent Talk about Computability and Hilbert's Entscheidungsproblem. 

Subscribe to Institute of Advanced Studies. 

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