Kurt GödelKurt Gödel was a person, mathematician, who worked on many foundational issues in formal logic. Some of his most interesting results are:
- Gödelization, as a procedure to bootstrap a representation of a formal system inside the formal system itself.
- The completeness theorem of the predicate calculus, which proves that the theorems of the predicate calculus are all and only the logically valid formulas.
- The incompleteness theorem for first order theories sufficiently powerful to express arithmetics, which states that if a theory of this kind is consistent it is also incomplete, i.e. there are statements which cannot be neither proved nor disproved in it.
- The proof that, given a formal theory that can express arithmetics, if we bootstrap in it a proposition expressing the consistency of the theory itself, this proposition cannot be proved in the theory, unless we adopt a definition of "proposition expressing the consistency of the theory itself" based on stronger hypotheses than those on which the formal theory is based upon.
This page is linked from: Methods of Reflection