[FOM] Consequence of PA inconsistency
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
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
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