3 ms·
Kurt Gödel then showed that this was impossible and the number system needs to be inconsistent for it to be complete. IMO this is favoring the wrong en
by al2o3cr 5y ago
Kurt Gödel then showed that this was impossible
and the number system needs to be inconsistent for it to
be complete.
IMO this is favoring the wrong end of Gödel's argument: a "complete" number system sounds like something desirable, but it's equivalent to one where "1 = 0" is a true statement and literally anything can be proved.
The converse part is usually more important: given any consistent system of mathematical logic, it is always possible to produce a theorem in that system that the system cannot prove to be EITHER true or false.