History and Future of Implicit and Inductionless Induction:
Beware the Old Jade and the Zombie!
by Claus-Peter Wirth. My favorite quote so far:
In practice, however, refutational completeness by itself does not help in refuting
invalid conjectures or in finding finite proofs for inductively valid formulas.
Only theoreticians completely detached from reality can consider nonterminating
proof attempts in refutationally complete inference systems to be
successful proofs.
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