> > The game of symbol manipulation is there to stay with FOL=, nonetheless. > > It doesn't matter what philosophical motivation you might have had, it's > part of the definition of reasoning with rules of inference in FOL with > identity: either you'd conform to it, or betray it. > > Godel betrayed it, and so have we.
Gödel's incompleteness theorem isn't about FOL=.
-- The world will little note, nor long remember what we say here Lincoln at Gettysburg