David Peat

Appendix: Gödel’s Theorem 221tem, it is nevertheless a true statement. In other words he had shownthe truth of the statement, “Mathematics is incomplete.”Second, he took a step that is reminiscent of the coexisting statementsDem(Y, X) and ~Dem(Y, X) that would imply that mathematicsis not consistent.What he showed was that, if Statement (b) were in fact demonstrable,it would also follow that the negation of statement (b) wouldbe also demonstrable. That is, both a statement and its negation wouldsimultaneously be demonstrable. But if statement (b) would be demonstrablethis would mean that mathematics is complete—that is,every statement can be demonstrated. Hence Gödel’s second conclusion,“If mathematics were complete—that is, if statement (b) could bedemonstrated—then it would be inconsistent.”