[FOM] Consequence of PA inconsistency

Harvey Friedman friedman at math.ohio-state.edu
Sun Apr 25 19:25:51 EDT 2010

This posting fits into the long FOM line on "falsify Platonism".

Suppose an inconsistency in PA is found, in the following "weak"  
sense. Let us say that we have an appropriately displayed finitary  
proof that "PA(100) is inconsistent". This could come about, say, from  
a displayed proof of 1 = 0 within PA(100) involving inductions on  
formulas that are in some sense "incomprehensibly complicated" to an  
"arithmetic Platonist".

By using standard techniques, we can create an appropriately displayed  
proof in PA(101) of 1 = 0. You can look and see that the formulas to  
which induction is applied to are comprehensible to the "arithmetic  

Harvey Friedman

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